DEFF Research Database (Denmark)
Puig Arnavat, Maria; López-Villada, Jesús; Bruno, Joan Carles
2010-01-01
of the characteristic equation method developed by Kühn and Ziegler (2005) is the simplest and that it provides similar or better accuracy than the other approach. This selected approach has been used to fit catalogue and experimental data of single-effect chillers and has been extended to double-effect commercial......Two approaches to the characteristic equation method have been compared in order to find a simple model that best describes the performance of thermal chillers. After comparing the results obtained using experimental data from a single-effect absorption chiller, we concluded that the adaptation...
Regression Equations for Birth Weight Estimation using ...
African Journals Online (AJOL)
In this study, Birth Weight has been estimated from anthropometric measurements of hand and foot. Linear regression equations were formed from each of the measured variables. These simple equations can be used to estimate Birth Weight of new born babies, in order to identify those with low birth weight and referred to ...
Hierarchical regression analysis in structural Equation Modeling
de Jong, P.F.
1999-01-01
In a hierarchical or fixed-order regression analysis, the independent variables are entered into the regression equation in a prespecified order. Such an analysis is often performed when the extra amount of variance accounted for in a dependent variable by a specific independent variable is the main
Unbalanced Regressions and the Predictive Equation
DEFF Research Database (Denmark)
Osterrieder, Daniela; Ventosa-Santaulària, Daniel; Vera-Valdés, J. Eduardo
Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness...... in the theoretical predictive equation by suggesting a data generating process, where returns are generated as linear functions of a lagged latent I(0) risk process. The observed predictor is a function of this latent I(0) process, but it is corrupted by a fractionally integrated noise. Such a process may arise due...... to aggregation or unexpected level shifts. In this setup, the practitioner estimates a misspecified, unbalanced, and endogenous predictive regression. We show that the OLS estimate of this regression is inconsistent, but standard inference is possible. To obtain a consistent slope estimate, we then suggest...
Unbalanced Regressions and the Predictive Equation
DEFF Research Database (Denmark)
Osterrieder, Daniela; Ventosa-Santaulària, Daniel; Vera-Valdés, J. Eduardo
Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness in the theoreti......Predictive return regressions with persistent regressors are typically plagued by (asymptotically) biased/inconsistent estimates of the slope, non-standard or potentially even spurious statistical inference, and regression unbalancedness. We alleviate the problem of unbalancedness...
Optimal Estimating Equation for Logistic Regression with Linked Data
Tsui, Jenkin; Dasylva, Abel; Chu, Kenneth
2017-01-01
We propose an optimal estimating equation for logistic regression with linked data while accounting for false positives. It builds on a previous solution but estimates the regression coefficients with a smaller variance, in large samples.
Regression equations for the estimation of radial length from its ...
African Journals Online (AJOL)
HD) were measured using digital vernier caliper while the circumference of the radial head and the circumference at the radial tuberosity were measured using an anthropometric tape. Pearson correlation and Persian regression were used to derive the liner regression equations for the measured parameters that showed a ...
Development of a preliminary regression equation for estimating the ...
African Journals Online (AJOL)
Abstract. Objective: To develop a regression equation to estimate the weight of black male paraplegic South African subjects. Design: Cross-sectional study. Setting: Outpatient paraplegic clinic of Kalafong Hospital, Tshwane, South Africa. Subjects: Subjects (n = 43) were selected from a population of black paraplegic males ...
Regression equations for circular CFST columns carrying capacity evaluation
Directory of Open Access Journals (Sweden)
Vatulia Glib
2017-01-01
Full Text Available Within the last decades, a considerable amount of experimental studies have been carried out by numerous researchers across the world with the purpose to study the carrying capacity of concrete-filled steel tubular (CFST columns and evaluation of their stressed-strained state. The array of the obtained results have allowed designing a mathematical model to determine the maximum carrying capacity value of such constructions using the methods of mathematical statistics. The authors obtained three types of regression equations for short and long circular CFST columns with different geometrical and physical properties under axial compression. Statistical quality of the obtained models was verified by both regression equation quality in general and statistical significance of the equation parameters. The comparison of the obtained carrying capacity values with the results calculated by Eurocode 4 and AIJ methodologies allows making a conclusion on the sufficient calculation accuracy of the designed mathematical models.
Ballistic Limit Equation for Single Wall Titanium
Ratliff, J. M.; Christiansen, Eric L.; Bryant, C.
2009-01-01
Hypervelocity impact tests and hydrocode simulations were used to determine the ballistic limit equation (BLE) for perforation of a titanium wall, as a function of wall thickness. Two titanium alloys were considered, and separate BLEs were derived for each. Tested wall thicknesses ranged from 0.5mm to 2.0mm. The single-wall damage equation of Cour-Palais [ref. 1] was used to analyze the Ti wall's shielding effectiveness. It was concluded that the Cour-Palais single-wall equation produced a non-conservative prediction of the ballistic limit for the Ti shield. The inaccurate prediction was not a particularly surprising result; the Cour-Palais single-wall BLE contains shield material properties as parameters, but it was formulated only from tests of different aluminum alloys. Single-wall Ti shield tests were run (thicknesses of 2.0 mm, 1.5 mm, 1.0 mm, and 0.5 mm) on Ti 15-3-3-3 material custom cut from rod stock. Hypervelocity impact (HVI) tests were used to establish the failure threshold empirically, using the additional constraint that the damage scales with impact energy, as was indicated by hydrocode simulations. The criterion for shield failure was defined as no detached spall from the shield back surface during HVI. Based on the test results, which confirmed an approximately energy-dependent shield effectiveness, the Cour-Palais equation was modified.
Effects of Employing Ridge Regression in Structural Equation Models.
McQuitty, Shaun
1997-01-01
LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)
Mixture of Regression Models with Single-Index
Xiang, Sijia; Yao, Weixin
2016-01-01
In this article, we propose a class of semiparametric mixture regression models with single-index. We argue that many recently proposed semiparametric/nonparametric mixture regression models can be considered special cases of the proposed model. However, unlike existing semiparametric mixture regression models, the new pro- posed model can easily incorporate multivariate predictors into the nonparametric components. Backfitting estimates and the corresponding algorithms have been proposed for...
Sintering equation: determination of its coefficients by experiments - using multiple regression
International Nuclear Information System (INIS)
Windelberg, D.
1999-01-01
Sintering is a method for volume-compression (or volume-contraction) of powdered or grained material applying high temperature (less than the melting point of the material). Maekipirtti tried to find an equation which describes the process of sintering by its main parameters sintering time, sintering temperature and volume contracting. Such equation is called a sintering equation. It also contains some coefficients which characterise the behaviour of the material during the process of sintering. These coefficients have to be determined by experiments. Here we show that some linear regressions will produce wrong coefficients, but multiple regression results in an useful sintering equation. (orig.)
[Confirmatory study on the regression equation for children dental behavior in Beijing].
Xia, Bin; Wang, Chun-li; Zhang, Sun
2013-12-01
To test and verify the regression equation got before for children's dental behavior management problems(BMP). The study group included 279 children aged 2- pediatric dentists in the Department of Pediatric Dentistry, Peking University School of and Hospital of Stomatology. Interviews were conducted with accompanying guardians and children's dental behavior was rated by a modified Venham's clinical anxiety scale and a cooperative behavior rating scale. The variables were put into the regression equation and the results were compared with their dental behavior scale. The accuracy rate of regression equation reached 84.2% (235/279) , sensitivity was 0.613 (95%CI:0.514-0.712) and specificity was 0.957 (95%CI:0.928-0.986). The regression equation is characterized by its accuracy rate at a good level. Younger age, negative guardian expectations of the child's behavior during treatment, anxiety or shyness around strangers, and presence of toothache were four risk factors for children's dental BMP.
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
A regression approach for Zircaloy-2 in-reactor creep constitutive equations
International Nuclear Information System (INIS)
Yung Liu, Y.; Bement, A.L.
1977-01-01
In this paper the methodology of multiple regressions as applied to Zircaloy-2 in-reactor creep data analysis and construction of constitutive equation are illustrated. While the resulting constitutive equation can be used in creep analysis of in-reactor Zircaloy structural components, the methodology itself is entirely general and can be applied to any creep data analysis. The promising aspects of multiple regression creep data analysis are briefly outlined as follows: (1) When there are more than one variable involved, there is no need to make the assumption that each variable affects the response independently. No separate normalizations are required either and the estimation of parameters is obtained by solving many simultaneous equations. The number of simultaneous equations is equal to the number of data sets. (2) Regression statistics such as R 2 - and F-statistics provide measures of the significance of regression creep equation in correlating the overall data. The relative weights of each variable on the response can also be obtained. (3) Special regression techniques such as step-wise, ridge, and robust regressions and residual plots, etc., provide diagnostic tools for model selections. Multiple regression analysis performed on a set of carefully selected Zircaloy-2 in-reactor creep data leads to a model which provides excellent correlations for the data. (Auth.)
Bonfatti, V; Tiezzi, F; Miglior, F; Carnier, P
2017-09-01
The objective of this study was to compare the prediction accuracy of 92 infrared prediction equations obtained by different statistical approaches. The predicted traits included fatty acid composition (n = 1,040); detailed protein composition (n = 1,137); lactoferrin (n = 558); pH and coagulation properties (n = 1,296); curd yield and composition obtained by a micro-cheese making procedure (n = 1,177); and Ca, P, Mg, and K contents (n = 689). The statistical methods used to develop the prediction equations were partial least squares regression (PLSR), Bayesian ridge regression, Bayes A, Bayes B, Bayes C, and Bayesian least absolute shrinkage and selection operator. Model performances were assessed, for each trait and model, in training and validation sets over 10 replicates. In validation sets, Bayesian regression models performed significantly better than PLSR for the prediction of 33 out of 92 traits, especially fatty acids, whereas they yielded a significantly lower prediction accuracy than PLSR in the prediction of 8 traits: the percentage of C18:1n-7 trans-9 in fat; the content of unglycosylated κ-casein and its percentage in protein; the content of α-lactalbumin; the percentage of α S2 -casein in protein; and the contents of Ca, P, and Mg. Even though Bayesian methods produced a significant enhancement of model accuracy in many traits compared with PLSR, most variations in the coefficient of determination in validation sets were smaller than 1 percentage point. Over traits, the highest predictive ability was obtained by Bayes C even though most of the significant differences in accuracy between Bayesian regression models were negligible. Copyright © 2017 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.
Evaluation of mean-monthly streamflow-regression equations for Colorado, 2014
Kohn, Michael S.; Stevens, Michael R.; Bock, Andrew R.; Char, Stephen J.
2015-01-01
The U.S. Geological Survey, in cooperation with the Colorado Water Conservation Board, evaluated the predictive uncertainty of mean-monthly streamflow-regression equations representative of natural streamflow conditions in Colorado. This study evaluates the predictive uncertainty of mean-monthly streamflow-regression equations developed in a 2009 U.S. Geological Survey study using streamflow data collected over the entire period of record at each streamgage through calendar year 2013. The study area for this report is limited to the Mountain, Northwest, Rio Grande, and Southwest hydrologic regions of Colorado.
Directory of Open Access Journals (Sweden)
Sangkertadi Sangkertadi
2012-05-01
Full Text Available This study is about field experimentation in order to construct regression equations of perception of thermalcomfort for outdoor activities under hot and humid environment. Relationships between thermal-comfort perceptions, micro climate variables (temperatures and humidity and body parameters (activity, clothing, body measure have been observed and analyzed. 180 adults, men, and women participated as samples/respondents. This study is limited for situation where wind velocity is about 1 m/s, which touch the body of the respondents/samples. From questionnaires and field measurements, three regression equations have been developed, each for activity of normal walking, brisk walking, and sitting.
Regional regression equations for estimation of natural streamflow statistics in Colorado
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
Generalized single-hidden layer feedforward networks for regression problems.
Wang, Ning; Er, Meng Joo; Han, Min
2015-06-01
In this paper, traditional single-hidden layer feedforward network (SLFN) is extended to novel generalized SLFN (GSLFN) by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes. The significant contributions of this paper are as follows: 1) a primal GSLFN (P-GSLFN) is implemented using randomly generated hidden nodes and polynomial output weights whereby the regression matrix is augmented by full or partial input variables and only polynomial coefficients are to be estimated; 2) a simplified GSLFN (S-GSLFN) is realized by decomposing the polynomial output weights of the P-GSLFN into randomly generated polynomial nodes and tunable output weights; 3) both P- and S-GSLFN are able to achieve universal approximation if the output weights are tuned by ridge regression estimators; and 4) by virtue of the developed batch and online sequential ridge ELM (BR-ELM and OSR-ELM) learning algorithms, high performance of the proposed GSLFNs in terms of generalization and learning speed is guaranteed. Comprehensive simulation studies and comparisons with standard SLFNs are carried out on real-world regression benchmark data sets. Simulation results demonstrate that the innovative GSLFNs using BR-ELM and OSR-ELM are superior to standard SLFNs in terms of accuracy, training speed, and structure compactness.
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…
Saha equation, single and two particle states
Kraeft, W. D.; Girardeau, M. D.; Strege, B.
1990-01-01
Single- and two-particle properties in a dense plasma are discussed in connection with their role in the mass action law for a partially ionized plasma. The two-particle-bound states are nearly density independent, while the continuum is essentially shifted. The single-particle states are damped, and their energy has a negative shift and a parabolic behavior for small momenta.
Záhumenský, P.; Kohútek, I.; Semeňák, J.
2017-12-01
The austenite-ferrite transformation temperatures evaluated by dilatometry using thermo-mechanical simulator Gleeble 1500D are investigated in this paper. The effect of cooling rates 1, 5, 10 and 15°C/s on the upper and lower critical transformation temperatures was evaluated for 30 specimens of six material groups. Considering the cooling rate from dilatometry tests and chemical composition (C ≤ 0.2%, Mn ≤ 2%, Si ≤ 0.26%) of particular specimens, the regression equations for both transformation temperatures were derived. These relations have to be satisfied to avoid the crack formation during continuous casting, as well as to provide the hot rolling control. The proposed regression equations are compared with 32 similar ones adopted from 1961 to 2017 and exhibit a good conformity and accuracy.
Sangkertadi Sangkertadi; Reny Syafriny
2012-01-01
This study is about field experimentation in order to construct regression equations of perception of thermalcomfort for outdoor activities under hot and humid environment. Relationships between thermal-comfort perceptions, micro climate variables (temperatures and humidity) and body parameters (activity, clothing, body measure) have been observed and analyzed. 180 adults, men, and women participated as samples/respondents. This study is limited for situation where wind velocity is about 1 m/...
Is adult gait less susceptible than paediatric gait to hip joint centre regression equation error?
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.
Sklubalova, Zdenka; Zatloukal, Zdenek
2008-01-01
Commercially, cellulose products are designated with viscosity grade measured at 2% w/v concentration in water at 20 degrees C using an Ubbelohde viscometer. To represent viscosity/concentration curves, linear function of the eighth root of dynamic viscosity and the concentration is generally used. In this work, the influence on viscosity of aqueous solutions of methylcellulose 400 and hypromellose 4000 by temperature and polymer concentration was modelled using an empirically proposed multiple linear regression in which the transformation of viscosity by logarithm, the reciprocal value of the absolute temperature, and the concentration by square root was recommended. Due to this, the viscosity of both cellulose derivatives investigated could be predicted simultaneously with the mean difference between the observed data and the ones estimated equal to 16.2%. Expanding the linear regression with the linear interaction between logarithm of the polymer viscosity grade and square root of the polymer concentration, the precision of the viscosity prediction increased to the acceptable level of 4.1%. Other interactions between the studied variables did not provide significantly better results. The optimized regression equation enabled the prediction of kinematic, dynamic, relative, and specific viscosity of the aqueous solutions of cellulose derivatives. The dimensionless relative viscosity could be recommended because it takes into account the water viscosity at the same experimental temperature. Selecting viscosity grade of the cellulose derivative and temperature of measurement, the partial regression equations were obtained from which the relative viscosity could be determined as the function of the polymer concentration with the precision in range of 1.3-4.7%.
Isothermal equation of state of a lithium fluoride single crystal
Energy Technology Data Exchange (ETDEWEB)
Kim, K.Y.
1975-01-01
An isothermal equation of state of a LiF single crystal was determined from length change measurements of the specimen as a function of hydrostatic pressure up to approximately 7 kbars at 28 to 41/sup 0/C. The length change was measured with an accuracy of approximately 500 A by using a Fabry Perot type He--Ne laser interferometer for a 1-m long specimen at temperatures constant to less than 0.002/sup 0/C. Several two- and three-parameter equations of state were used in analyzing the measured pressure-volume data. The computer fit for each equation of state determines not only the value of its parameters but also the standard deviations associated with them and one dependent variable, either pressure or volume. With the parameters determined, the equations of state are extrapolated to approximately 5 megabars in order to see discrepancies. Using the Born model of ionic solids, two equations of state were derived both from a power law potential and from an exponential form for the repulsive energy of alkali metal halides and used to fit the pressure-volume data of a LiF single crystal. They are also extrapolated to approximately 5 megabars. The Birch's two-parameter equation and the Grover, Getting, and Kennedy equation are indistinguishable from the two equations of state derived from the Born model for pressures approximately equal to or less than 800 kbars within +-20 kbars. The above four equations of state also fit closely the Pagannone and Drickamer static compression data, the Christian shock wave data, and the Kormer et al. shock wave data. The isothermal bulk modulus and its first pressure derivative at atmospheric pressure and 28.83/sup 0/C are 664.5 +- 0.5 kbars and 5.40 +- 0.18, respectively, in close agreement with those values ultrasonically measured by R. A. Miller and C. S. Smith. (auth)
Shield Optimization and Formulation of Regression Equations for Split-Ring Resonator
Directory of Open Access Journals (Sweden)
Tahir Ejaz
2016-01-01
Full Text Available Microwave resonators are widely used for numerous applications including communication, biomedical and chemical applications, material testing, and food grading. Split-ring resonators in both planar and nonplanar forms are a simple structure which has been in use for several decades. This type of resonator is characterized with low cost, ease of fabrication, moderate quality factor, low external noise interference, high stability, and so forth. Due to these attractive features and ease in handling, nonplanar form of structure has been utilized for material characterization in 1–5 GHz range. Resonant frequency and quality factor are two important parameters for determination of material properties utilizing perturbation theory. Shield made of conducting material is utilized to enclose split-ring resonator which enhances quality factor. This work presents a novel technique to develop shield around a predesigned nonplanar split-ring resonator to yield optimized quality factor. Based on this technique and statistical analysis regression equations have also been formulated for resonant frequency and quality factor which is a major outcome of this work. These equations quantify dependence of output parameters on various factors of shield made of different materials. Such analysis is instrumental in development of devices/designs where improved/optimum result is required.
Urrutia, Jackie D.; Tampis, Razzcelle L.; Mercado, Joseph; Baygan, Aaron Vito M.; Baccay, Edcon B.
2016-02-01
The objective of this research is to formulate a mathematical model for the Philippines' Real Gross Domestic Product (Real GDP). The following factors are considered: Consumers' Spending (x1), Government's Spending (x2), Capital Formation (x3) and Imports (x4) as the Independent Variables that can actually influence in the Real GDP in the Philippines (y). The researchers used a Normal Estimation Equation using Matrices to create the model for Real GDP and used α = 0.01.The researchers analyzed quarterly data from 1990 to 2013. The data were acquired from the National Statistical Coordination Board (NSCB) resulting to a total of 96 observations for each variable. The data have undergone a logarithmic transformation particularly the Dependent Variable (y) to satisfy all the assumptions of the Multiple Linear Regression Analysis. The mathematical model for Real GDP was formulated using Matrices through MATLAB. Based on the results, only three of the Independent Variables are significant to the Dependent Variable namely: Consumers' Spending (x1), Capital Formation (x3) and Imports (x4), hence, can actually predict Real GDP (y). The regression analysis displays that 98.7% (coefficient of determination) of the Independent Variables can actually predict the Dependent Variable. With 97.6% of the result in Paired T-Test, the Predicted Values obtained from the model showed no significant difference from the Actual Values of Real GDP. This research will be essential in appraising the forthcoming changes to aid the Government in implementing policies for the development of the economy.
Using a Linear Regression Method to Detect Outliers in IRT Common Item Equating
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…
Semiparametric Mixtures of Regressions with Single-index for Model Based Clustering
Xiang, Sijia; Yao, Weixin
2017-01-01
In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models a...
DEFF Research Database (Denmark)
D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar
2012-01-01
and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent...
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…
Comparison of ν-support vector regression and logistic equation for ...
African Journals Online (AJOL)
Jane
2011-07-04
Jul 4, 2011 ... Due to the complexity and high non-linearity of bioprocess, most simple mathematical models fail to describe the exact behavior of ... Key words: Support vector regression, genetic algorithm, logistic model, prediction of biomass. .... method for solving non-linear regression problem, which depends on the ...
Directory of Open Access Journals (Sweden)
Jichul Ryu
2016-04-01
Full Text Available In this study, 52 asymptotic Curve Number (CN regression equations were developed for combinations of representative land covers and hydrologic soil groups. In addition, to overcome the limitations of the original Long-term Hydrologic Impact Assessment (L-THIA model when it is applied to larger watersheds, a watershed-scale L-THIA Asymptotic CN (ACN regression equation model (watershed-scale L-THIA ACN model was developed by integrating the asymptotic CN regressions and various modules for direct runoff/baseflow/channel routing. The watershed-scale L-THIA ACN model was applied to four watersheds in South Korea to evaluate the accuracy of its streamflow prediction. The coefficient of determination (R2 and Nash–Sutcliffe Efficiency (NSE values for observed versus simulated streamflows over intervals of eight days were greater than 0.6 for all four of the watersheds. The watershed-scale L-THIA ACN model, including the asymptotic CN regression equation method, can simulate long-term streamflow sufficiently well with the ten parameters that have been added for the characterization of streamflow.
Comparison of ν-support vector regression and logistic equation for ...
African Journals Online (AJOL)
Due to the complexity and high non-linearity of bioprocess, most simple mathematical models fail to describe the exact behavior of biochemistry systems. As a novel type of learning method, support vector regression (SVR) owns the powerful capability to characterize problems via small sample, nonlinearity, high dimension ...
DEFF Research Database (Denmark)
D'Souza, Sonia; Rasmussen, John; Schwirtz, Ansgar
2012-01-01
and valuable ergonomic tool. Objective: To investigate age and gender effects on the torque-producing ability in the knee and elbow in older adults. To create strength scaled equations based on age, gender, upper/lower limb lengths and masses using multiple linear regression. To reduce the number of dependent......Background: The next fifty years will see a drastic increase in the older population. Among other effects, ageing causes a decrease in strength. It is necessary to provide safe and comfortable environments for the elderly. To achieve this, digital human modelling has proved to be a useful...... predicted KPT (R2=0.60). Gender, forearm mass and age best predicted EPT (R2=0.75). Good crossvalidation was established for both elbow and knee models. Conclusion: This cross-sectional study of muscle strength created and validated strength scaled equations of EPT and KPT using only gender, segment mass...
Staley, Dennis M.; Negri, Jacquelyn A.; Kean, Jason W.; Laber, Jayme L.; Tillery, Anne C.; Youberg, Ann M.
2016-06-30
Wildfire can significantly alter the hydrologic response of a watershed to the extent that even modest rainstorms can generate dangerous flash floods and debris flows. To reduce public exposure to hazard, the U.S. Geological Survey produces post-fire debris-flow hazard assessments for select fires in the western United States. We use publicly available geospatial data describing basin morphology, burn severity, soil properties, and rainfall characteristics to estimate the statistical likelihood that debris flows will occur in response to a storm of a given rainfall intensity. Using an empirical database and refined geospatial analysis methods, we defined new equations for the prediction of debris-flow likelihood using logistic regression methods. We showed that the new logistic regression model outperformed previous models used to predict debris-flow likelihood.
Directory of Open Access Journals (Sweden)
Nikita A. Moiseev
2017-01-01
Full Text Available The paper is devoted to a new randomization method that yields unbiased adjustments of p-values for linear regression models predictors by incorporating the number of potential explanatory variables, their variance-covariance matrix and its uncertainty, based on the number of observations. This adjustment helps to control type I errors in scientific studies, significantly decreasing the number of publications that report false relations to be authentic ones. Comparative analysis with such existing methods as Bonferroni correction and Shehata and White adjustments explicitly shows their imperfections, especially in case when the number of observations and the number of potential explanatory variables are approximately equal. Also during the comparative analysis it was shown that when the variance-covariance matrix of a set of potential predictors is diagonal, i.e. the data are independent, the proposed simple correction is the best and easiest way to implement the method to obtain unbiased corrections of traditional p-values. However, in the case of the presence of strongly correlated data, a simple correction overestimates the true pvalues, which can lead to type II errors. It was also found that the corrected p-values depend on the number of observations, the number of potential explanatory variables and the sample variance-covariance matrix. For example, if there are only two potential explanatory variables competing for one position in the regression model, then if they are weakly correlated, the corrected p-value will be lower than when the number of observations is smaller and vice versa; if the data are highly correlated, the case with a larger number of observations will show a lower corrected p-value. With increasing correlation, all corrections, regardless of the number of observations, tend to the original p-value. This phenomenon is easy to explain: as correlation coefficient tends to one, two variables almost linearly depend on each
Linear Regression on Sparse Features for Single-Channel Speech Separation
DEFF Research Database (Denmark)
Schmidt, Mikkel N.; Olsson, Rasmus Kongsgaard
2007-01-01
In this work we address the problem of separating multiple speakers from a single microphone recording. We formulate a linear regression model for estimating each speaker based on features derived from the mixture. The employed feature representation is a sparse, non-negative encoding of the speech...... compared to linear regression on spectral features and compared to separation based directly on the non-negative sparse features....... mixture in terms of pre-learned speaker-dependent dictionaries. Previous work has shown that this feature representation by itself provides some degree of separation. We show that the performance is significantly improved when regression analysis is performed on the sparse, non-negative features, both...
Kauhanen, Heikki; Komi, Paavo V; Häkkinen, Keijo
2002-02-01
The problems in comparing the performances of Olympic weightlifters arise from the fact that the relationship between body weight and weightlifting results is not linear. In the present study, this relationship was examined by using a nonparametric curve fitting technique of robust locally weighted regression (LOWESS) on relatively large data sets of the weightlifting results made in top international competitions. Power function formulas were derived from the fitted LOWESS values to represent the relationship between the 2 variables in a way that directly compares the snatch, clean-and-jerk, and total weightlifting results of a given athlete with those of the world-class weightlifters (golden standards). A residual analysis of several other parametric models derived from the initial results showed that they all experience inconsistencies, yielding either underestimation or overestimation of certain body weights. In addition, the existing handicapping formulas commonly used in normalizing the performances of Olympic weightlifters did not yield satisfactory results when applied to the present data. It was concluded that the devised formulas may provide objective means for the evaluation of the performances of male weightlifters, regardless of their body weights, ages, or performance levels.
A general equation to obtain multiple cut-off scores on a test from multinomial logistic regression.
Bersabé, Rosa; Rivas, Teresa
2010-05-01
The authors derive a general equation to compute multiple cut-offs on a total test score in order to classify individuals into more than two ordinal categories. The equation is derived from the multinomial logistic regression (MLR) model, which is an extension of the binary logistic regression (BLR) model to accommodate polytomous outcome variables. From this analytical procedure, cut-off scores are established at the test score (the predictor variable) at which an individual is as likely to be in category j as in category j+1 of an ordinal outcome variable. The application of the complete procedure is illustrated by an example with data from an actual study on eating disorders. In this example, two cut-off scores on the Eating Attitudes Test (EAT-26) scores are obtained in order to classify individuals into three ordinal categories: asymptomatic, symptomatic and eating disorder. Diagnoses were made from the responses to a self-report (Q-EDD) that operationalises DSM-IV criteria for eating disorders. Alternatives to the MLR model to set multiple cut-off scores are discussed.
Bertrand, Julie; Balding, David J
2013-03-01
Studies on the influence of single nucleotide polymorphisms (SNPs) on drug pharmacokinetics (PK) have usually been limited to the analysis of observed drug concentration or area under the concentration versus time curve. Nonlinear mixed effects models enable analysis of the entire curve, even for sparse data, but until recently, there has been no systematic method to examine the effects of multiple SNPs on the model parameters. The aim of this study was to assess different penalized regression methods for including SNPs in PK analyses. A total of 200 data sets were simulated under both the null and an alternative hypothesis. In each data set for each of the 300 participants, a PK profile at six sampling times was simulated and 1227 genotypes were generated through haplotypes. After modelling the PK profiles using an expectation maximization algorithm, genetic association with individual parameters was investigated using the following approaches: (i) a classical stepwise approach, (ii) ridge regression modified to include a test, (iii) Lasso and (iv) a generalization of Lasso, the HyperLasso. Penalized regression approaches are often much faster than the stepwise approach. There are significantly fewer true positives for ridge regression than for the stepwise procedure and HyperLasso. The higher number of true positives in the stepwise procedure was accompanied by a higher count of false positives (not significant). We find that all approaches except ridge regression show similar power, but penalized regression can be much less computationally demanding. We conclude that penalized regression should be preferred over stepwise procedures for PK analyses with a large panel of genetic covariates.
International Nuclear Information System (INIS)
Watanabe, Nami; Sugai Yukio; Komatani, Akio; Yamaguchi, Koichi; Takahashi, Kazuei
1999-01-01
This study was designed to investigate the empirical tubular extraction rate (TER) of the normal renal function in childhood and then propose a new equation to obtain TER theoretically. The empirical TER was calculated using Russell's method for determination of single-sample plasma clearance and 99m Tc-MAG 3 in 40 patients with renal disease younger than 10 years of age who were classified as having normal renal function using diagnostic criteria defined by the Paediatric Task Group of EANM. First, we investigated the relationships of the empirical value of absolute TER to age, body weight, body surface area (BSA) and distribution volume. Next we investigated the relationships of the empirical value of BSA corrected TER to age, body weight, BSA and distribution volume. Linear relationship was indicated between the absolute TER and each body dimensional factors, especially regarding to BSA, its correlation coefficient was 0.90 (p value). The BSA-corrected TER showed a logarithmic relationship with BSA, but linear regression did not show any significant correlation. Therefore, it was thought that the normal value of TER could be calculated theoretically using the body surface area, and here we proposed the following linear regression equation; Theoretical TER (ml/min/1.73 m 2 )=(-39.8+257.2 x BSA)/BSA/1.73. The theoretical TER could be one of the reference values of the renal function in the period of the renal maturation. (author)
Howarth, Samuel J; Giangregorio, Lora M; Callaghan, Jack P
2013-08-01
Equations used to determine vertebral failure tolerances without the need for destructive testing are useful for scaling applied sub-maximal forces during in vitro repetitive loading studies. However, existing equations that use vertebral bone density and morphology for calculating compressive failure tolerance are unsuitable for calculating vertebral shear failure tolerance since the primary site of failure is the pars interarticularis and not the vertebral body. Therefore, this investigation developed new equations for non-destructively determining vertebral shear failure tolerance from morphological and/or bone density measures. Shear failure was induced in 40 porcine cervical vertebral joints (20 C3-C4 and 20 C5-C6) by applying a constant posterior displacement to the caudal vertebra at 0.15 mm/s. Prior to destructive testing, morphology and bone density of the posterior elements were made with digital calipers, X-rays, and peripheral quantitative computed tomography. Iterative linear regression identified mathematical relationships between shear failure tolerance, and morphological and bone density measurements. Along with vertebral level, pars interarticularis length and lamina height from the cranial vertebra, and inferior facet height from the caudal vertebra collectively explained 61.8% of shear failure tolerance variance. Accuracy for this relationship, estimated using the same group of specimens, was 211.9 N or 9.8% of the measured shear failure tolerance. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.
Planck scale physics of the single-particle Schrödinger equation ...
Indian Academy of Sciences (India)
August 2002 physics pp. 375–383. Planck scale physics of the single-particle Schrödinger equation with gravitational self-interaction. VIKRAM SONI. National Physical Laboratory, K.S. Krishnan Marg, New Delhi 110 016, India. Abstract. We consider the modification of a single-particle Schrödinger equation by the inclusion.
Wang, Shan-Shan; Zhang, Yu-Qi; Chen, Shu-Bao; Huang, Guo-Ying; Zhang, Hong-Yan; Zhang, Zhi-Fang; Wu, Lan-Ping; Hong, Wen-Jing; Shen, Rong; Liu, Yi-Qing; Zhu, Jun-Xue
2017-06-01
Clinical decision making in children with congenital and acquired heart disease relies on measurements of cardiac structures using two-dimensional echocardiography. We aimed to establish z-score regression equations for right heart structures in healthy Chinese Han children. Two-dimensional and M-mode echocardiography was performed in 515 patients. We measured the dimensions of the pulmonary valve annulus (PVA), main pulmonary artery (MPA), left pulmonary artery (LPA), right pulmonary artery (RPA), right ventricular outflow tract at end-diastole (RVOTd) and at end-systole (RVOTs), tricuspid valve annulus (TVA), right ventricular inflow tract at end-diastole (RVIDd) and at end-systole (RVIDs), and right atrium (RA). Regression analyses were conducted to relate the measurements of right heart structures to 4body surface area (BSA). Right ventricular outflow-tract fractional shortening (RVOTFS) was also calculated. Several models were used, and the best model was chosen to establish a z-score calculator. PVA, MPA, LPA, RPA, RVOTd, RVOTs, TVA, RVIDd, RVIDs, and RA (R 2 = 0.786, 0.705, 0.728, 0.701, 0.706, 0.824, 0.804, 0.663, 0.626, and 0.793, respectively) had a cubic polynomial relationship with BSA; specifically, measurement (M) = β0 + β1 × BSA + β2 × BSA 2 + β3 × BSA. 3 RVOTFS (0.28 ± 0.02) fell within a narrow range (0.12-0.51). Our results provide reference values for z scores and regression equations for right heart structures in Han Chinese children. These data may help interpreting the routine clinical measurement of right heart structures in children with congenital or acquired heart disease. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:293-303, 2017. © 2017 Wiley Periodicals, Inc.
A single model procedure for estimating tank calibration equations
International Nuclear Information System (INIS)
Liebetrau, A.M.
1997-10-01
A fundamental component of any accountability system for nuclear materials is a tank calibration equation that relates the height of liquid in a tank to its volume. Tank volume calibration equations are typically determined from pairs of height and volume measurements taken in a series of calibration runs. After raw calibration data are standardized to a fixed set of reference conditions, the calibration equation is typically fit by dividing the data into several segments--corresponding to regions in the tank--and independently fitting the data for each segment. The estimates obtained for individual segments must then be combined to obtain an estimate of the entire calibration function. This process is tedious and time-consuming. Moreover, uncertainty estimates may be misleading because it is difficult to properly model run-to-run variability and between-segment correlation. In this paper, the authors describe a model whose parameters can be estimated simultaneously for all segments of the calibration data, thereby eliminating the need for segment-by-segment estimation. The essence of the proposed model is to define a suitable polynomial to fit to each segment and then extend its definition to the domain of the entire calibration function, so that it (the entire calibration function) can be expressed as the sum of these extended polynomials. The model provides defensible estimates of between-run variability and yields a proper treatment of between-segment correlations. A portable software package, called TANCS, has been developed to facilitate the acquisition, standardization, and analysis of tank calibration data. The TANCS package was used for the calculations in an example presented to illustrate the unified modeling approach described in this paper. With TANCS, a trial calibration function can be estimated and evaluated in a matter of minutes
Hu, L; Zhang, Z G; Mouraux, A; Iannetti, G D
2015-05-01
Transient sensory, motor or cognitive event elicit not only phase-locked event-related potentials (ERPs) in the ongoing electroencephalogram (EEG), but also induce non-phase-locked modulations of ongoing EEG oscillations. These modulations can be detected when single-trial waveforms are analysed in the time-frequency domain, and consist in stimulus-induced decreases (event-related desynchronization, ERD) or increases (event-related synchronization, ERS) of synchrony in the activity of the underlying neuronal populations. ERD and ERS reflect changes in the parameters that control oscillations in neuronal networks and, depending on the frequency at which they occur, represent neuronal mechanisms involved in cortical activation, inhibition and binding. ERD and ERS are commonly estimated by averaging the time-frequency decomposition of single trials. However, their trial-to-trial variability that can reflect physiologically-important information is lost by across-trial averaging. Here, we aim to (1) develop novel approaches to explore single-trial parameters (including latency, frequency and magnitude) of ERP/ERD/ERS; (2) disclose the relationship between estimated single-trial parameters and other experimental factors (e.g., perceived intensity). We found that (1) stimulus-elicited ERP/ERD/ERS can be correctly separated using principal component analysis (PCA) decomposition with Varimax rotation on the single-trial time-frequency distributions; (2) time-frequency multiple linear regression with dispersion term (TF-MLRd) enhances the signal-to-noise ratio of ERP/ERD/ERS in single trials, and provides an unbiased estimation of their latency, frequency, and magnitude at single-trial level; (3) these estimates can be meaningfully correlated with each other and with other experimental factors at single-trial level (e.g., perceived stimulus intensity and ERP magnitude). The methods described in this article allow exploring fully non-phase-locked stimulus-induced cortical
Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation
International Nuclear Information System (INIS)
Liu Chengshi
2007-01-01
Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.
Directory of Open Access Journals (Sweden)
Yuji Liu
2014-01-01
Full Text Available We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractional-order logistic models.
Single Image Super-Resolution by Non-Linear Sparse Representation and Support Vector Regression
Directory of Open Access Journals (Sweden)
Yungang Zhang
2017-02-01
Full Text Available Sparse representations are widely used tools in image super-resolution (SR tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR. Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained.
Goings, Joshua J; Caricato, Marco; Frisch, Michael J; Li, Xiaosong
2014-10-28
Methods for fast and reliable computation of electronic excitation energies are in short supply, and little is known about their systematic performance. This work reports a comparison of several low-scaling approximations to the equation of motion coupled cluster singles and doubles (EOM-CCSD) and linear-response coupled cluster singles and doubles (LR-CCSD) equations with other single reference methods for computing the vertical electronic transition energies of 11 small organic molecules. The methods, including second order equation-of-motion many-body perturbation theory (EOM-MBPT2) and its partitioned variant, are compared to several valence and Rydberg singlet states. We find that the EOM-MBPT2 method was rarely more than a tenth of an eV from EOM-CCSD calculated energies, yet demonstrates a performance gain of nearly 30%. The partitioned equation-of-motion approach, P-EOM-MBPT2, which is an order of magnitude faster than EOM-CCSD, outperforms the CIS(D) and CC2 in the description of Rydberg states. CC2, on the other hand, excels at describing valence states where P-EOM-MBPT2 does not. The difference between the CC2 and P-EOM-MBPT2 can ultimately be traced back to how each method approximates EOM-CCSD and LR-CCSD. The results suggest that CC2 and P-EOM-MBPT2 are complementary: CC2 is best suited for the description of valence states while P-EOM-MBPT2 proves to be a superior O(N(5)) method for the description of Rydberg states.
Directory of Open Access Journals (Sweden)
Tarquinio Mateus Magalhães
2015-10-01
Full Text Available Background Biomass regression equations are claimed to yield the most accurate biomass estimates than biomass expansion factors (BEFs. Yet, national and regional biomass estimates are generally calculated based on BEFs, especially when using national forest inventory data. Comparison of regression equations based and BEF-based biomass estimates are scarce. Thus, this study was intended to compare these two commonly used methods for estimating tree and forest biomass with regard to errors and biases. Methods The data were collected in 2012 and 2014. In 2012, a two-phase sampling design was used to fit tree component biomass regression models and determine tree BEFs. In 2014, additional trees were felled outside sampling plots to estimate the biases associated with regression equation based and BEF-based biomass estimates; those estimates were then compared in terms of the following sources of error: plot selection and variability, biomass model, model parameter estimates, and residual variability around model prediction. Results The regression equation based below-, aboveground and whole tree biomass stocks were, approximately, 7.7, 8.5 and 8.3 % larger than the BEF-based ones. For the whole tree biomass stock, the percentage of the total error attributed to first phase (random plot selection and variability was 90 and 88 % for regression- and BEF-based estimates, respectively, being the remaining attributed to biomass models (regression and BEF models, respectively. The percent bias of regression equation based and BEF-based biomass estimates for the whole tree biomass stock were −2.7 and 5.4 %, respectively. The errors due to model parameter estimates, those due to residual variability around model prediction, and the percentage of the total error attributed to biomass model were larger for BEF models (than for regression models, except for stem and stem wood components. Conclusions The regression equation based biomass stocks were found to
Single-trial regression elucidates the role of prefrontal theta oscillations in response conflict
Directory of Open Access Journals (Sweden)
Michael X Cohen
2011-02-01
Full Text Available In most cognitive neuroscience experiments there are many behavioral and experimental dynamics, and many indices of brain activity, that vary from trial to trial. For example, in studies of response conflict, conflict is usually treated as a binary variable (i.e., response conflict exists or does not in any given trial, whereas some evidence and intuition suggests that conflict may vary in intensity from trial to trial. Here we demonstrate that single-trial multiple regression of time-frequency electrophysiological activity reveals neural mechanisms of cognitive control that are not apparent in cross-trial averages. We also introduce a novel extension to oscillation phase coherence and synchronization analyses, based on weighted phase modulation, that has advantages over standard coherence measures in terms of linking electrophysiological dynamics to trial-varying behavior and experimental variables. After replicating previous response conflict findings using trial-averaged data, we extend these findings using single trial analytic methods to provide novel evidence for the role of medial frontal-lateral prefrontal theta-band synchronization in conflict-induced response time dynamics, including a role for lateral prefrontal theta-band activity in biasing response times according to perceptual conflict. Given that these methods shed new light on the prefrontal mechanisms of response conflict, they are also likely to be useful for investigating other neurocognitive processes.
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.
Valdés, Felipe
2011-06-01
A new regularized single source equation for analyzing scattering from homogeneous penetrable objects is presented. The proposed equation is a linear combination of a Calderón-preconditioned single source electric field integral equation and a single source magnetic field integral equation. The equation is immune to low-frequency and dense-mesh breakdown, and free from spurious resonances. Unlike dual source formulations, this equation involves operator products that cannot be discretized using standard procedures for discretizing standalone electric, magnetic, and combined field operators. Instead, the single source equation proposed here is discretized using a recently developed technique that achieves a well-conditioned mapping from div- to curl-conforming function spaces, thereby fully respecting the space mapping properties of the operators involved, and guaranteeing accuracy and stability. Numerical results show that the proposed equation and discretization technique give rise to rapidly convergent solutions. They also validate the equation\\'s resonant free character. © 2006 IEEE.
Directory of Open Access Journals (Sweden)
B. Karacaören
2016-07-01
Full Text Available Development of body hair is an important physiological and cellular process that leads to better adaption in tropical environments for dairy cattle. Various studies suggested a major gene and, more recently, associated genes for hairy locus in dairy cattle. Main aim of this study was to i employ a variant of the discordant sib pair model, in which half sibs from the same sires are randomly sampled using their affection statues, ii use various single marker regression approaches, and iii use whole genome regression approaches to dissect genetic architecture of the hairy gene in the cattle. Whole and single genome regression approaches detected strong genomic signals from Chromosome 23. Although there is a major gene effect on hairy phenotype sourced from chromosome 23: whole genome regression approach also suggested polygenic component related with other parts of the genome. Such a result could not be obtained by any of the single marker approaches.
Single-site Green function of the Dirac equation for full-potential electron scattering
Energy Technology Data Exchange (ETDEWEB)
Kordt, Pascal
2012-05-30
I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)
Spontaneous Regression of Lymphangiomas in a Single Center Over 34 Years
Directory of Open Access Journals (Sweden)
Motoi Kato, MD
2017-09-01
Conclusions:. We concluded that elderly patients with macrocystic or mixed type lymphangioma may have to wait for treatment for over 3 months from the initial onset. Conversely, microcystic type could not be expected to show regression in a short period, and prompt initiation of the treatments may be required. The difference of the regression or not may depend on the characteristics of the lymph flow.
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
A Seemingly Unrelated Poisson Regression Model
King, Gary
1989-01-01
This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.
The free-electron laser - Maxwell's equations driven by single-particle currents
Colson, W. B.; Ride, S. K.
1980-01-01
It is shown that if single particle currents are coupled to Maxwell's equations, the resulting set of self-consistent nonlinear equations describes the evolution of the electron beam and the amplitude and phase of the free-electron-laser field. The formulation is based on the slowly varying amplitude and phase approximation, and the distinction between microscopic and macroscopic scales, which distinguishes the microscopic bunching from the macroscopic pulse propagation. The capabilities of this new theoretical approach become apparent when its predictions for the ultrashort pulse free-electron laser are compared to experimental data; the optical pulse evolution, determined simply and accurately, agrees well with observations.
Modified Regression Rate Formula of PMMA Combustion by a Single Plane Impinging Jet
Directory of Open Access Journals (Sweden)
Tsuneyoshi Matsuoka
2017-01-01
Full Text Available A modified regression rate formula for the uppermost stage of CAMUI-type hybrid rocket motor is proposed in this study. Assuming a quasi-steady, one-dimensional, an energy balance against a control volume near the fuel surface is considered. Accordingly, the regression rate formula which can calculate the local regression rate by the quenching distance between the flame and the regression surface is derived. An experimental setup which simulates the combustion phenomenon involved in the uppermost stage of a CAMUI-type hybrid rocket motor was constructed and the burning tests with various flow velocities and impinging distances were performed. A PMMA slab of 20 mm height, 60 mm width, and 20 mm thickness was chosen as a sample specimen and pure oxygen and O2/N2 mixture (50/50 vol.% were employed as the oxidizers. The time-averaged regression rate along the fuel surface was measured by a laser displacement sensor. The quenching distance during the combustion event was also identified from the observation. The comparison between the purely experimental and calculated values showed good agreement, although a large systematic error was expected due to the difficulty in accurately identifying the quenching distance.
Shojai, Mohadese; Kazemnejad, Anoshirvan; Zayeri, Farid; Vahedi, Mohsen
2013-01-01
For the purpose of cost modeling, the semi-parametric single-index two-part model was utilized in the paper. Furthermore, as functional gastrointestinal diseases which are well-known as common causes of illness among the society people in terms of both the number of patients and prevalence in a specific time interval, this research estimated the average cost of functional gastrointestinal diseases. Health care policy-makers seek for real and accurate estimations of society's future medical costs. However, data dealt with in hygienic studies have characteristics which make their analysis complicated; distribution of cost data is highly skewed since many patients pay great costs. In addition, medical costs of many persons are zero in a specific time interval. Indeed, medical costs data are often right skewed, including remarkable number of zeros, and may be distributed non-homogeneously. In modeling these costs by the semi-parametric single-index two-part model, parameters were determined by method of least squares; a result of this method was compared with the results yielded from two-part parametric model. Average costs of functional gastrointestinal diseases and their standard deviation in semi-parametric and parametric methods were yielded as $72.69±108.96 (R(2)=0.38) and $75.93±122.29 (R(2)=0.33) respectively. Based on R(2) index, the semi-parametric model is recognized as the best model. Totally, the two-part parametric regression model is a simple and available model which can be easily interpreted; on the other hand, though the single-index two-part semi-parametric model cannot be easily interpreted, it has considerable flexibility. The study goals can be indeed used as the main factor for choosing one of these two models.
A single-equation study of US petroleum consumption: The role of model specificiation
International Nuclear Information System (INIS)
Jones, C.T.
1993-01-01
The price responsiveness of US petroleum consumption began to attract a great deal of attention following the unexpected and substantial oil price increases of 1973-74. There have been a number of large, multi-equation econometric studies of US energy demand since then which have focused primarily on estimating short run and long run price and income elasticities of individual energy resources (coal, oil, natural gas ampersand electricity) for various consumer sectors (residential, industrial, commercial). Following these early multi-equation studies there have been several single-equation studies of aggregate US petroleum consumption. When choosing an economic model specification for a single-equation study of aggregate US petroleum consumption, an easily estimated model that will provide unbiased price and income elasticity estimates and yield accurate forecasts is needed. Using Hendry's general-to-simple specification search technique and annual data to obtain a restricted, data-acceptable simplification of a general ADL model yielded GNP and short run price elasticities near the consensus estimates, but a long run price elasticity substantially smaller than existing estimates. Comparisons with three other seemingly acceptable simple-to-general models showed that popular model specifications often involve untested, unacceptable parameter restrictions. These models may also demonstrate poorer forecasting performance. Based on results, the general-to-simple approach appears to offer a more accurate methodology for generating superior forecast models of petroleum consumption and other energy use patterns
Huang, Guan-Rong; Saakian, David B.; Hu, Chin-Kun
2018-01-01
Studying gene regulation networks in a single cell is an important, interesting, and hot research topic of molecular biology. Such process can be described by chemical master equations (CMEs). We propose a Hamilton-Jacobi equation method with finite-size corrections to solve such CMEs accurately at the intermediate region of switching, where switching rate is comparable to fast protein production rate. We applied this approach to a model of self-regulating proteins [H. Ge et al., Phys. Rev. Lett. 114, 078101 (2015), 10.1103/PhysRevLett.114.078101] and found that as a parameter related to inducer concentration increases the probability of protein production changes from unimodal to bimodal, then to unimodal, consistent with phenotype switching observed in a single cell.
Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation
Pötz, Walter; Schreilechner, Magdalena
2017-11-01
An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space-time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space-time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac-Lindblad equation, real-space-time Green's function formulations, and higher-order finite-difference schemes are discussed.
Sierra Sanjurjo, Natalia; Montañes, Patricia; Sierra Matamoros, Fabio Alexander; Burin, Debora
2015-01-01
Spanish is the fourth most spoken language in the world, and the majority of Spanish speakers have a Latin American origin. Reading aloud infrequently accentuated words has been established as a National Adult Reading Test-like method to assess premorbid intelligence in Spanish. However, several versions have been proposed and validated with small and selected samples, in particular geographical conditions, and they seldom derive a formula for IQ estimation with the Wechsler Adult Intelligence Scale (WAIS) Full-Scale IQ (FSIQ). The objective of this study was to develop equations to estimate WAIS-Third Edition (WAIS-III) FSIQ from the Word Accentuation Test-Revised (WAT-R), demographic variables, and their combination within diverse Latin American samples. Two hundred and forty participants from Argentina and Colombia, selected according to age and years of education strata, were assessed with the WAT-R, the WAIS-III, and a structured questionnaire about demographic and medical information. A combined approach including place of birth, years of education, and WAT-R provided the best equation, explaining 76% of IQ variance. These equations could be useful for estimating premorbid IQ in patients with Latin American Spanish as their birth language.
On the difficulties of a single three-body Lippmann-Schwinger equation
International Nuclear Information System (INIS)
Sawada, Tatsuro; Miyagawa, Kazuya; Thushima, Kathuhide.
1991-01-01
First, we point out that the often quoted non-uniqueness argument on a single three-body Lippmann-Schwinger equation (the LS equation) is either not valid because the manipulation leading to it is not justifiable, or inconsequential because the non-uniqueness can easily be discerned and eliminated. Next, we discuss the property of the kernel with energy independent absorbing potentials (EIAP) of general forms. We find that the use of EIAP as in the CDCC approach dose not make the kernel compact. It remains non-compact no matter what we use for two-body potentials. Finally, we investigate in what sense the LS equation is solvable in terms of the CDCC approach. When the wave function inside the right-hand side (RHS) of the LS equation is restricted to a small CDCC model space, the difference between the RHS and the ordinary asymptotic form assumed in the approach is found to diverge asymptotically due to contributions from higher partial waves. We conclude that the CDCC solution cannot be claimed to be the solution to the LS equation, not unless it is restricted to a small model space. (author)
GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD
2016-01-01
This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...
Ross, Sarah G; Begeny, John C
2014-08-01
Growing from demands for accountability and research-based practice in the field of education, there is recent focus on developing standards for the implementation and analysis of single-case designs. Effect size methods for single-case designs provide a useful way to discuss treatment magnitude in the context of individual intervention. Although a standard effect size methodology does not yet exist within single-case research, panel experts recently recommended pairing regression and non-parametric approaches when analyzing effect size data. This study compared two single-case effect size methods: the regression-based, Allison-MT method and the newer, non-parametric, Tau-U method. Using previously published research that measured the Words read Correct per Minute (WCPM) variable, these two methods were examined by comparing differences in overall effect size scores and rankings of intervention effect. Results indicated that the regression method produced significantly larger effect sizes than the non-parametric method, but the rankings of the effect size scores had a strong, positive relation. Implications of these findings for research and practice are discussed. Copyright © 2014 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.
Single image super-resolution using locally adaptive multiple linear regression.
Yu, Soohwan; Kang, Wonseok; Ko, Seungyong; Paik, Joonki
2015-12-01
This paper presents a regularized superresolution (SR) reconstruction method using locally adaptive multiple linear regression to overcome the limitation of spatial resolution of digital images. In order to make the SR problem better-posed, the proposed method incorporates the locally adaptive multiple linear regression into the regularization process as a local prior. The local regularization prior assumes that the target high-resolution (HR) pixel is generated by a linear combination of similar pixels in differently scaled patches and optimum weight parameters. In addition, we adapt a modified version of the nonlocal means filter as a smoothness prior to utilize the patch redundancy. Experimental results show that the proposed algorithm better restores HR images than existing state-of-the-art methods in the sense of the most objective measures in the literature.
Valdés, Felipe
2013-03-01
Single-source time-domain electric-and magnetic-field integral equations for analyzing scattering from homogeneous penetrable objects are presented. Their temporal discretization is effected by using shifted piecewise polynomial temporal basis functions and a collocation testing procedure, thus allowing for a marching-on-in-time (MOT) solution scheme. Unlike dual-source formulations, single-source equations involve space-time domain operator products, for which spatial discretization techniques developed for standalone operators do not apply. Here, the spatial discretization of the single-source time-domain integral equations is achieved by using the high-order divergence-conforming basis functions developed by Graglia alongside the high-order divergence-and quasi curl-conforming (DQCC) basis functions of Valdés The combination of these two sets allows for a well-conditioned mapping from div-to curl-conforming function spaces that fully respects the space-mapping properties of the space-time operators involved. Numerical results corroborate the fact that the proposed procedure guarantees accuracy and stability of the MOT scheme. © 2012 IEEE.
Wapenaar, Kees
2017-06-01
A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.
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
Kiss, I.; Cioată, V. G.; Alexa, V.; Raţiu, S. A.
2017-05-01
The braking system is one of the most important and complex subsystems of railway vehicles, especially when it comes for safety. Therefore, installing efficient safe brakes on the modern railway vehicles is essential. Nowadays is devoted attention to solving problems connected with using high performance brake materials and its impact on thermal and mechanical loading of railway wheels. The main factor that influences the selection of a friction material for railway applications is the performance criterion, due to the interaction between the brake block and the wheel produce complex thermos-mechanical phenomena. In this work, the investigated subjects are the cast-iron brake shoes, which are still widely used on freight wagons. Therefore, the cast-iron brake shoes - with lamellar graphite and with a high content of phosphorus (0.8-1.1%) - need a special investigation. In order to establish the optimal condition for the cast-iron brake shoes we proposed a mathematical modelling study by using the statistical analysis and multiple regression equations. Multivariate research is important in areas of cast-iron brake shoes manufacturing, because many variables interact with each other simultaneously. Multivariate visualization comes to the fore when researchers have difficulties in comprehending many dimensions at one time. Technological data (hardness and chemical composition) obtained from cast-iron brake shoes were used for this purpose. In order to settle the multiple correlation between the hardness of the cast-iron brake shoes, and the chemical compositions elements several model of regression equation types has been proposed. Because a three-dimensional surface with variables on three axes is a common way to illustrate multivariate data, in which the maximum and minimum values are easily highlighted, we plotted graphical representation of the regression equations in order to explain interaction of the variables and locate the optimal level of each variable for
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
Lim, S. C.; Teo, L. P.
2009-08-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann-Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion.
Directory of Open Access Journals (Sweden)
Hayduk Leslie A
2012-10-01
Full Text Available Abstract Background Structural equation modeling developed as a statistical melding of path analysis and factor analysis that obscured a fundamental tension between a factor preference for multiple indicators and path modeling’s openness to fewer indicators. Discussion Multiple indicators hamper theory by unnecessarily restricting the number of modeled latents. Using the few best indicators – possibly even the single best indicator of each latent – encourages development of theoretically sophisticated models. Additional latent variables permit stronger statistical control of potential confounders, and encourage detailed investigation of mediating causal mechanisms. Summary We recommend the use of the few best indicators. One or two indicators are often sufficient, but three indicators may occasionally be helpful. More than three indicators are rarely warranted because additional redundant indicators provide less research benefit than single indicators of additional latent variables. Scales created from multiple indicators can introduce additional problems, and are prone to being less desirable than either single or multiple indicators.
Sim, K S; Norhisham, S
2016-11-01
A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first-order interpolation and the combination of both nearest neighbourhood and first-order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.
Single Image Super-Resolution Using Global Regression Based on Multiple Local Linear Mappings.
Choi, Jae-Seok; Kim, Munchurl
2017-03-01
Super-resolution (SR) has become more vital, because of its capability to generate high-quality ultra-high definition (UHD) high-resolution (HR) images from low-resolution (LR) input images. Conventional SR methods entail high computational complexity, which makes them difficult to be implemented for up-scaling of full-high-definition input images into UHD-resolution images. Nevertheless, our previous super-interpolation (SI) method showed a good compromise between Peak-Signal-to-Noise Ratio (PSNR) performances and computational complexity. However, since SI only utilizes simple linear mappings, it may fail to precisely reconstruct HR patches with complex texture. In this paper, we present a novel SR method, which inherits the large-to-small patch conversion scheme from SI but uses global regression based on local linear mappings (GLM). Thus, our new SR method is called GLM-SI. In GLM-SI, each LR input patch is divided into 25 overlapped subpatches. Next, based on the local properties of these subpatches, 25 different local linear mappings are applied to the current LR input patch to generate 25 HR patch candidates, which are then regressed into one final HR patch using a global regressor. The local linear mappings are learned cluster-wise in our off-line training phase. The main contribution of this paper is as follows: Previously, linear-mapping-based conventional SR methods, including SI only used one simple yet coarse linear mapping to each patch to reconstruct its HR version. On the contrary, for each LR input patch, our GLM-SI is the first to apply a combination of multiple local linear mappings, where each local linear mapping is found according to local properties of the current LR patch. Therefore, it can better approximate nonlinear LR-to-HR mappings for HR patches with complex texture. Experiment results show that the proposed GLM-SI method outperforms most of the state-of-the-art methods, and shows comparable PSNR performance with much lower
Sargent, Garrett C.; Ratliff, Bradley M.; Asari, Vijayan K.
2017-08-01
The advantage of division of focal plane imaging polarimeters is their ability to obtain temporally synchronized intensity measurements across a scene; however, they sacrifice spatial resolution in doing so due to their spatially modulated arrangement of the pixel-to-pixel polarizers and often result in aliased imagery. Here, we propose a super-resolution method based upon two previously trained extreme learning machines (ELM) that attempt to recover missing high frequency and low frequency content beyond the spatial resolution of the sensor. This method yields a computationally fast and simple way of recovering lost high and low frequency content from demosaicing raw microgrid polarimetric imagery. The proposed method outperforms other state-of-the-art single-image super-resolution algorithms in terms of structural similarity and peak signal-to-noise ratio.
Reitz, Meredith; Sanford, Ward E.; Senay, Gabriel; Cazenas, J.
2017-01-01
This study presents new data-driven, annual estimates of the division of precipitation into the recharge, quick-flow runoff, and evapotranspiration (ET) water budget components for 2000-2013 for the contiguous United States (CONUS). The algorithms used to produce these maps ensure water budget consistency over this broad spatial scale, with contributions from precipitation influx attributed to each component at 800 m resolution. The quick-flow runoff estimates for the contribution to the rapidly varying portion of the hydrograph are produced using data from 1,434 gaged watersheds, and depend on precipitation, soil saturated hydraulic conductivity, and surficial geology type. Evapotranspiration estimates are produced from a regression using water balance data from 679 gaged watersheds and depend on land cover, temperature, and precipitation. The quick-flow and ET estimates are combined to calculate recharge as the remainder of precipitation. The ET and recharge estimates are checked against independent field data, and the results show good agreement. Comparisons of recharge estimates with groundwater extraction data show that in 15% of the country, groundwater is being extracted at rates higher than the local recharge. These maps of the internally consistent water budget components of recharge, quick-flow runoff, and ET, being derived from and tested against data, are expected to provide reliable first-order estimates of these quantities across the CONUS, even where field measurements are sparse.
Forecasting with Dynamic Regression Models
Pankratz, Alan
2012-01-01
One of the most widely used tools in statistical forecasting, single equation regression models is examined here. A companion to the author's earlier work, Forecasting with Univariate Box-Jenkins Models: Concepts and Cases, the present text pulls together recent time series ideas and gives special attention to possible intertemporal patterns, distributed lag responses of output to input series and the auto correlation patterns of regression disturbance. It also includes six case studies.
Directory of Open Access Journals (Sweden)
M Zarabi
2016-05-01
Full Text Available In order to study the combined and separate effects of phosphorus fertilizer, phosphate-solubilizing bacteria and mycorrhizal fungus on adjusting and reducing the loss of yield resulting from drought stress during the stage of growth of grain corn (SC704 an experiment was performed in Aboureihan Campus of the University of Tehran, Iran, during 2007-2008. The experiment was conducted as split plot based on a randomised completely block design (RCBD with four replications. Experimental factors were drought stress as the main-plot [irrigation after 50 [without drought stress], 100 and 150 mm evaporation from pan class A, and fertilizer compounds as the sub-plot (100% phosphorus (b5, 50% super phosphate triple+ mycorrhizal fungus + Phosphate-solubilizing bacteria (b2, mycorrhizal fungus + Phosphate-solubilizing bacteria (b1, 50% super phosphate triple + Phosphate-solubilizing bacteria (b3, and 50% super phosphate triple + mycorrhizal fungus (b4. Drought stress happened after seedling establishment. Result of variance analysis showed that drought stress significantly affected plant height, stem dry weight, stem diameter, ear height, kernel number per row, 300 kernel weight, ear weight, ear length, ear diameter, cob diameter, kernel depth, cob percentage and total yield traits. Also, there was not significantly difference between fertilizer treatment for number of Leaf per plant, stem diameter and ear height traits. All the assessed traits in b2 inoculated treatment showed of higher values than other treats under water deficit stress condition. Furthermore, the investigated traits of b5 treat under severe water deficit stress were significantly less pronounced than normal irrigation and low stressed conditions. The results showed that all measured traits in seed inoculums with b2 under the low drought stress stood higher than other treats. Using stepwise regression was performed for grain corn in all conditions and in high stress conditions four
Southard, Rodney E.
2013-01-01
located in Region 1, 120 were located in Region 2, and 10 were located in Region 3. Streamgages located outside of Missouri were selected to extend the range of data used for the independent variables in the regression analyses. Streamgages included in the regression analyses had 10 or more years of record and were considered to be affected minimally by anthropogenic activities or trends. Regional regression analyses identified three characteristics as statistically significant for the development of regional equations. For Region 1, drainage area, longest flow path, and streamflow-variability index were statistically significant. The range in the standard error of estimate for Region 1 is 79.6 to 94.2 percent. For Region 2, drainage area and streamflow variability index were statistically significant, and the range in the standard error of estimate is 48.2 to 72.1 percent. For Region 3, drainage area and streamflow-variability index also were statistically significant with a range in the standard error of estimate of 48.1 to 96.2 percent. Limitations on the use of estimating low-flow frequency statistics at ungaged locations are dependent on the method used. The first method outlined for use in Missouri, power curve equations, were developed to estimate the selected statistics for ungaged locations on 28 selected streams with multiple streamgages located on the same stream. A second method uses a drainage-area ratio to compute statistics at an ungaged location using data from a single streamgage on the same stream with 10 or more years of record. Ungaged locations on these streams may use the ratio of the drainage area at an ungaged location to the drainage area at a streamgage location to scale the selected statistic value from the streamgage location to the ungaged location. This method can be used if the drainage area of the ungaged location is within 40 to 150 percent of the streamgage drainage area. The third method is the use of the regional regression equations
International Nuclear Information System (INIS)
Frank, T.D.
2007-01-01
We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed
DEFF Research Database (Denmark)
Ditlevsen, Susanne; Samson, Adeline
2016-01-01
Dynamics of the membrane potential in a single neuron can be studied by estimating biophysical parameters from intracellular recordings. Diffusion processes, given as continuous solutions to stochastic differential equations, are widely applied as models for the neuronal membrane potential evolut...
Energy Technology Data Exchange (ETDEWEB)
Fox, Zachary [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Neuert, Gregor [Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine, Nashville, Tennessee 37232 (United States); Department of Pharmacology, School of Medicine, Vanderbilt University, Nashville, Tennessee 37232 (United States); Department of Biomedical Engineering, Vanderbilt University School of Engineering, Nashville, Tennessee 37232 (United States); Munsky, Brian [School of Biomedical Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States); Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523 (United States)
2016-08-21
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.
Bry, X; Verron, T; Cazes, P
2009-05-29
In this work, we consider chemical and physical variable groups describing a common set of observations (cigarettes). One of the groups, minor smoke compounds (minSC), is assumed to depend on the others (minSC predictors). PLS regression (PLSR) of m inSC on the set of all predictors appears not to lead to a satisfactory analytic model, because it does not take into account the expert's knowledge. PLS path modeling (PLSPM) does not use the multidimensional structure of predictor groups. Indeed, the expert needs to separate the influence of several pre-designed predictor groups on minSC, in order to see what dimensions this influence involves. To meet these needs, we consider a multi-group component-regression model, and propose a method to extract from each group several strong uncorrelated components that fit the model. Estimation is based on a global multiple covariance criterion, used in combination with an appropriate nesting approach. Compared to PLSR and PLSPM, the structural equation exploratory regression (SEER) we propose fully uses predictor group complementarity, both conceptually and statistically, to predict the dependent group.
Caballero Gaudes, César; Petridou, Natalia; Francis, Susan T; Dryden, Ian L; Gowland, Penny A
2013-03-01
The ability to detect single trial responses in functional magnetic resonance imaging (fMRI) studies is essential, particularly if investigating learning or adaptation processes or unpredictable events. We recently introduced paradigm free mapping (PFM), an analysis method that detects single trial blood oxygenation level dependent (BOLD) responses without specifying prior information on the timing of the events. PFM is based on the deconvolution of the fMRI signal using a linear hemodynamic convolution model. Our previous PFM method (Caballero-Gaudes et al., 2011: Hum Brain Mapp) used the ridge regression estimator for signal deconvolution and required a baseline signal period for statistical inference. In this work, we investigate the application of sparse regression techniques in PFM. In particular, a novel PFM approach is developed using the Dantzig selector estimator, solved via an efficient homotopy procedure, along with statistical model selection criteria. Simulation results demonstrated that, using the Bayesian information criterion to select the regularization parameter, this method obtains high detection rates of the BOLD responses, comparable with a model-based analysis, but requiring no information on the timing of the events and being robust against hemodynamic response function variability. The practical operation of this sparse PFM method was assessed with single-trial fMRI data acquired at 7T, where it automatically detected all task-related events, and was an improvement on our previous PFM method, as it does not require the definition of a baseline state and amplitude thresholding and does not compromise on specificity and sensitivity. Copyright © 2011 Wiley Periodicals, Inc.
Alexandrowicz, Rainer W; Jahn, Rebecca; Friedrich, Fabian; Unger, Anne
2016-06-01
Various studies have shown that caregiving relatives of schizophrenic patients are at risk of suffering from depression. These studies differ with respect to the applied statistical methods, which could influence the findings. Therefore, the present study analyzes to which extent different methods may cause differing results. The present study contrasts by means of one data set the results of three different modelling approaches, Rasch Modelling (RM), Structural Equation Modelling (SEM), and Linear Regression Modelling (LRM). The results of the three models varied considerably, reflecting the different assumptions of the respective models. Latent trait models (i. e., RM and SEM) generally provide more convincing results by correcting for measurement error and the RM specifically proves superior for it treats ordered categorical data most adequately.
Spin-curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes
Zhang, Kai; Zhang, Erhu; Chen, Huawei; Zhang, Shengli
2017-06-01
The spin-curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.
Directory of Open Access Journals (Sweden)
A. Zuber
2015-09-01
Full Text Available AbstractThe correlation of thermodynamic properties of nonaqueous electrolyte solutions is relevant to design and operation of many chemical processes, as in fertilizer production and the pharmaceutical industry. In this work, the Q-electrolattice equation of state (EOS is used to model vapor pressure, mean ionic activity coefficient, osmotic coefficient, and liquid density of sixteen methanol and ten ethanol solutions containing single strong 1:1 and 2:1 salts. The Q-electrolattice comprises the lattice-based Mattedi-Tavares-Castier (MTC EOS, the Born term and the explicit MSA term. The model requires two adjustable parameters per ion, namely the ionic diameter and the solvent-ion interaction energy. Predictions of osmotic coefficient at 298.15 K and liquid density at different temperatures are also presented.
A new definition of a correlation equation for single collector efficiency
Messina, Francesca; Sethi, Rajandrea
2014-05-01
The transport and deposition of colloidal particles in porous media are important phenomena involved in many environmental and engineering problems as, for instance, the use of micro- and nanoscale zerovalent iron, a promising reagent in the field of groundwater remediation [1]. Particle transport and deposition in the proximity of injection or pumping wells and in porous media in general may also be relevant in other fields of chemical and petroleum engineering. Mathematical models able to predict particles transport and deposition in porous media are often needed in order to design field applications. The basic concept of these models is the single collector efficiency η, which predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on a solid grain. Many different approaches and equations exist in the literature, however most of them are valid only under specific conditions (eg. specific range of flow rate, particle size, etc.), and predict, for certain parametric conditions, efficiency values exceeding unity, which is, for an efficiency concept, a contradiction [2][3]. The objectives of this study are to analyze the causes of the failure of the existing models in predicting the deposition rate in certain conditions and to modify the definition of collector efficiency in order to have a more general equation. The definition of collector efficiency, first proposed by Yao at al. [4], is based on the particles deposition onto a spherical grain (the collector) in an infinite domain. It is defined as the ration between the flux of particles that deposit on the grain and the total amount of particles that could reach the collector by advective flux from an area equal to the projection of the spherical grain itself. In the present work Yao's model has been implemented by COMSOL Multiphysics and solved with an Eulerian approach; particles deposition simulations were run. From
Dolecheck, K A; Heersche, G; Bewley, J M
2016-12-01
Assessing the economic implications of investing in automated estrus detection (AED) technologies can be overwhelming for dairy producers. The objectives of this study were to develop new regression equations for estimating the cost per day open (DO) and to apply the results to create a user-friendly, partial budget, decision support tool for investment analysis of AED technologies. In the resulting decision support tool, the end user can adjust herd-specific inputs regarding general management, current reproductive management strategies, and the proposed AED system. Outputs include expected DO, reproductive cull rate, net present value, and payback period for the proposed AED system. Utility of the decision support tool was demonstrated with an example dairy herd created using data from DairyMetrics (Dairy Records Management Systems, Raleigh, NC), Food and Agricultural Policy Research Institute (Columbia, MO), and published literature. Resulting herd size, rolling herd average milk production, milk price, and feed cost were 323 cows, 10,758kg, $0.41/kg, and $0.20/kg of dry matter, respectively. Automated estrus detection technologies with 2 levels of initial system cost (low: $5,000 vs. high: $10,000), tag price (low: $50 vs. high: $100), and estrus detection rate (low: 60% vs. high: 80%) were compared over a 7-yr investment period. Four scenarios were considered in a demonstration of the investment analysis tool: (1) a herd using 100% visual observation for estrus detection before adopting 100% AED, (2) a herd using 100% visual observation before adopting 75% AED and 25% visual observation, (3) a herd using 100% timed artificial insemination (TAI) before adopting 100% AED, and (4) a herd using 100% TAI before adopting 75% AED and 25% TAI. Net present value in scenarios 1 and 2 was always positive, indicating a positive investment situation. Net present value in scenarios 3 and 4 was always positive in combinations using a $50 tag price, and in scenario 4, the $5
Directory of Open Access Journals (Sweden)
Ilhan Özgen
2017-10-01
Full Text Available In urban flood modeling, so-called porosity shallow water equations (PSWEs, which conceptually account for unresolved structures, e.g., buildings, are a promising approach to addressing high CPU times associated with state-of-the-art explicit numerical methods. The PSWE can be formulated with a single porosity term, referred to as the single porosity shallow water model (SP model, which accounts for both the reduced storage in the cell and the reduced conveyance, or with two porosity terms: one accounting for the reduced storage in the cell and another accounting for the reduced conveyance. The latter form is referred to as an integral or anisotropic porosity shallow water model (AP model. The aim of this study was to analyze the differences in wave propagation speeds of the SP model and the AP model and the implications of numerical model results. First, augmented Roe-type solutions were used to assess the influence of the source terms appearing in both models. It is shown that different source terms have different influences on the stability of the models. Second, four computational test cases were presented and the numerical models were compared. It is observed in the eigenvalue-based analysis as well as in the computational test cases that the models converge if the conveyance porosity in the AP model is close to the storage porosity. If the porosity values differ significantly, the AP model yields different wave propagation speeds and numerical fluxes from those of the BP model. In this study, the ratio between the conveyance and storage porosities was determined to be the most significant parameter.
Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential
Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.
2018-03-01
We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p > 0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.
Semiclassical dye-laser equations and the unidirectional single-frequency operation
Fu, Hong; Haken, H.
1987-11-01
A semiclassical description for dye lasers is proposed, where the energy-level diagram of the dye molecule is assumed to consist of a continuous bandlike ground state and an excited singlet state. Unidirectional single-frequency (s.f.) operation is discussed. The linear-stability analysis for this operation reveals a very low threshold instability, which may appear generally in practical lasers. The ratio of the instability threshold to the lasing threshold may be of any value greater than 1, depending mainly on the bandwidth and the distribution of the dipole moments on the band, but it is independent of the cavity loss. This instability may account for that observed in recent experiments by Hillman, Krasinki, Boyd, and Stroud [Phys. Rev. Lett. 52, 1605 (1984)]. A general approach to analyzing the linear stability of the s.f. operation of the Maxwell-Bloch equations is also proposed, which states that only the eigenvalues of a 2×2 matrix are relevant: one concerns the stability of the s.f. operation near the lasing threshold, the other determines the instability threshold of this operation.
Directory of Open Access Journals (Sweden)
Corrado Dimauro
2010-01-01
Full Text Available Two methods of SNPs pre-selection based on single marker regression for the estimation of genomic breeding values (G-EBVs were compared using simulated data provided by the XII QTL-MAS workshop: i Bonferroni correction of the significance threshold and ii Permutation test to obtain the reference distribution of the null hypothesis and identify significant markers at P<0.01 and P<0.001 significance thresholds. From the set of markers significant at P<0.001, random subsets of 50% and 25% markers were extracted, to evaluate the effect of further reducing the number of significant SNPs on G-EBV predictions. The Bonferroni correction method allowed the identification of 595 significant SNPs that gave the best G-EBV accuracies in prediction generations (82.80%. The permutation methods gave slightly lower G-EBV accuracies even if a larger number of SNPs resulted significant (2,053 and 1,352 for 0.01 and 0.001 significance thresholds, respectively. Interestingly, halving or dividing by four the number of SNPs significant at P<0.001 resulted in an only slightly decrease of G-EBV accuracies. The genetic structure of the simulated population with few QTL carrying large effects, might have favoured the Bonferroni method.
Chakraborty, Debdutta; Kar, Susmita; Chattaraj, Pratim Kumar
2015-12-21
The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics.
Directory of Open Access Journals (Sweden)
Md Shamsul Arefin
2012-12-01
Full Text Available This work presents a technique for the chirality (n, m assignment of semiconducting single wall carbon nanotubes by solving a set of empirical equations of the tight binding model parameters. The empirical equations of the nearest neighbor hopping parameters, relating the term (2n, m with the first and second optical transition energies of the semiconducting single wall carbon nanotubes, are also proposed. They provide almost the same level of accuracy for lower and higher diameter nanotubes. An algorithm is presented to determine the chiral index (n, m of any unknown semiconducting tube by solving these empirical equations using values of radial breathing mode frequency and the first or second optical transition energy from resonant Raman spectroscopy. In this paper, the chirality of 55 semiconducting nanotubes is assigned using the first and second optical transition energies. Unlike the existing methods of chirality assignment, this technique does not require graphical comparison or pattern recognition between existing experimental and theoretical Kataura plot.
Planck scale physics of the single-particle Schrödinger equation ...
Indian Academy of Sciences (India)
... t ) is the wave function and is the mass of the particle. This leads to a nonlinear equation, the 'Newton–Schrödinger' equation, which has been found to possess stationary self-bound solutions, whose energy can be determined using an asymptotic method. We ﬁnd that such a particle strongly violates the superposition ...
Pötz, Walter
2017-11-01
A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.
Yu, Wei; Tian, Xiaolin; He, Xiaoliang; Song, Xiaojun; Xue, Liang; Liu, Cheng; Wang, Shouyu
2016-08-01
Microscopy based on transport of intensity equation provides quantitative phase distributions which opens another perspective for cellular observations. However, it requires multi-focal image capturing while mechanical and electrical scanning limits its real time capacity in sample detections. Here, in order to break through this restriction, real time quantitative phase microscopy based on single-shot transport of the intensity equation method is proposed. A programmed phase mask is designed to realize simultaneous multi-focal image recording without any scanning; thus, phase distributions can be quantitatively retrieved in real time. It is believed the proposed method can be potentially applied in various biological and medical applications, especially for live cell imaging.
Dynamics of single-bubble sonoluminescence. An alternative approach to the Rayleigh–Plesset equation
de Barros, Ana L. F.; Nogueira, Álvaro L. M. A.; Paschoal, Ricardo C.; Portes, Dirceu, Jr.; Rodrigues, Hilario
2018-03-01
Sonoluminescence is the phenomenon in which acoustic energy is (partially) transformed into light as a bubble of gas collapses inside a liquid medium. One particular model used to explain the motion of the bubble’s wall forced by acoustic pressure is expressed by the Rayleigh–Plesset equation, which can be obtained from the Navier–Stokes equation. In this article, we describe an alternative approach to derive the Rayleigh–Plesset equation based on Lagrangian mechanics. This work is addressed mainly to undergraduate students and teachers. It requires knowledge of calculus and of many concepts from various fields of physics at the intermediate level.
Mani, Prashant; Tyagi, Chandra Shekhar; Srivastav, Nishant
2016-03-01
In this paper the analytical solution of the 2D Poisson's equation for single gate Fully Depleted SOI (FDSOI) MOSFET's is derived by using a Green's function solution technique. The surface potential is calculated and the threshold voltage of the device is minimized for the low power consumption. Due to minimization of threshold voltage the short channel effect of device is suppressed and after observation we obtain the device is kink free. The structure and characteristics of SingleGate FDSOI MOSFET were matched by using MathCAD and silvaco respectively.
Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger-Boussinesq Equations
Qiao, Li-Jing; Tang, Sheng-Qiang; Zhao, Hai-Xia
2015-06-01
In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schrödinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schrödinger-Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth soliton and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Supported by National Natural Science Foundation of China under Grant Nos. 11361017, 11161013 and Natural Science Foundation of Guangxi under Grant Nos. 2012GXNSFAA053003, 2013GXNSFAA019010, and Program for Innovative Research Team of Guilin University of Electronic Technology
Chhabra, Sunil K
2009-01-01
Information on variations in vital capacity predicted from various regional equations for adult males in India and on their impact on interpretation of spirometric data is not available. In a retrospective study, spirometry data of 1672 male patients, aged 15 years and above were studied. Predicted values of forced vital capacity (FVC), labelled as FVC(North), FVC(East), FVC(West) and FVC(South) were calculated from the available regional prediction equations. A prediction equation for FVC for south Indian adults above 40 years of age is not available. Spirometry data was interpreted using these and the extent of agreement between pairs of equations in detection of pattern of abnormality was analysed. The FVC(North) and FVC(East) were close and greater than FVC(West) and FVC(South), which were in turn, close to each other. Up to the age of 40 years, the FVC(North) exceeded FVC(East), FVC(West) and FVC(South) by 2.4%, 11.8% and 13.3%, respectively, while in the above 40 years age group, it exceeded FVC(East) and FVC(West) by 5.1% and 9.67%, respectively. The differences, however, decreased substantially with increasing FVCs and even reversed at higher values with FVC(East) tending to exceed FVC(North) in both the age groups, and FVC(West) tending to exceed FVC(North) in the above 40 years age group. While northern and eastern, and, western and southern equations gave acceptable differences (less than 5%) in interpretation of abnormality in spirometric data in patients up to 40 years of age, differences between other pairs of equations in this age group, and between all pairs in the above 40 years age group were large and unacceptable. Substantial variations exist in vital capacity predicted from various regional equations in adult males in India. In general, northern and eastern equations, and, western and southern equations yield closer values. While the northern Indian equation gives the highest predicted vital capacity, this is true only for lower values of vital
2000-08-01
Georgetown U. Med. Ctr., 3900 Reservoir Rd., Washington, DC 20007; 2Applied Mathematics Program, Johns Hopkins University, 9601 Medical Center Dr., Rockville...TERMS Nonlinear regresion , Monte-Carlo 15. NUMBER OF PAGES randomization, Scheffe’s test, radioligand binding 16. PRICE CODE 24 17. SECURITY 18...appropriate for this situation. Indeed, here it is necessary to formulate this problem as a multiple linear regression model expressed with the aid of
International Nuclear Information System (INIS)
Ballini, J.-P.; Cazes, P.; Turpin, P.-Y.
1976-01-01
Analysing the histogram of anode pulse amplitudes allows a discussion of the hypothesis that has been proposed to account for the statistical processes of secondary multiplication in a photomultiplier. In an earlier work, good agreement was obtained between experimental and reconstructed spectra, assuming a first dynode distribution including two Poisson distributions of distinct mean values. This first approximation led to a search for a method which could give the weights of several Poisson distributions of distinct mean values. Three methods have been briefly exposed: classical linear regression, constraint regression (d'Esopo's method), and regression on variables subject to error. The use of these methods gives an approach of the frequency function which represents the dispersion of the punctual mean gain around the whole first dynode mean gain value. Comparison between this function and the one employed in Polya distribution allows the statement that the latter is inadequate to describe the statistical process of secondary multiplication. Numerous spectra obtained with two kinds of photomultiplier working under different physical conditions have been analysed. Then two points are discussed: - Does the frequency function represent the dynode structure and the interdynode collection process. - Is the model (the multiplication process of all dynodes but the first one, is Poissonian) valid whatever the photomultiplier and the utilization conditions. (Auth.)
Liu, Yingying; Sowmya, Arcot; Khamis, Heba
2018-01-01
Manually measured anthropometric quantities are used in many applications including human malnutrition assessment. Training is required to collect anthropometric measurements manually, which is not ideal in resource-constrained environments. Photogrammetric methods have been gaining attention in recent years, due to the availability and affordability of digital cameras. The primary goal is to demonstrate that height and mid-upper arm circumference (MUAC)-indicators of malnutrition-can be accurately estimated by applying linear regression to distance measurements from photographs of participants taken from five views, and determine the optimal view combinations. A secondary goal is to observe the effect on estimate error of two approaches which reduce complexity of the setup, computational requirements and the expertise required of the observer. Thirty-one participants (11 female, 20 male; 18-37 years) were photographed from five views. Distances were computed using both camera calibration and reference object techniques from manually annotated photos. To estimate height, linear regression was applied to the distances between the top of the participants head and the floor, as well as the height of a bounding box enclosing the participant's silhouette which eliminates the need to identify the floor. To estimate MUAC, linear regression was applied to the mid-upper arm width. Estimates were computed for all view combinations and performance was compared to other photogrammetric methods from the literature-linear distance method for height, and shape models for MUAC. The mean absolute difference (MAD) between the linear regression estimates and manual measurements were smaller compared to other methods. For the optimal view combinations (smallest MAD), the technical error of measurement and coefficient of reliability also indicate the linear regression methods are more reliable. The optimal view combination was the front and side views. When estimating height by linear
A simple and consistent equation of state for sodium in the single phase and two phase regions
International Nuclear Information System (INIS)
Breton, J.P.
1976-01-01
An equation of state valid over an extended temperature and density range has been derived. Then, the following properties have been deduced : coefficient of thermal expansion, isothermal coefficient of bulk compressibility, thermal pressure coefficient, heat capacity at constant pressure, at constant volume, along the saturation curve for liquid, for vapor, heat of vaporization, speed of sound, and finally the Mollier diagram and the entropy diagram. All the obtained properties are thermodynamically consistent and satisfy the basic relations of thermodynamics for both single phase and two-phase regions. Experimental results were always used when available. (auth.)
Westerhof, E.; Pratt, J.
2014-01-01
In the presence of electron cyclotron current drive (ECCD), the Ohm's law of single fluid magnetohydrodynamics is modified as E + v × B = η(J – J EC). This paper presents a new closure relation for the EC driven current density appearing in this modified Ohm's law. The new relation
Zhou, Jinzhe; Zhou, Yanbing; Cao, Shougen; Li, Shikuan; Wang, Hao; Niu, Zhaojian; Chen, Dong; Wang, Dongsheng; Lv, Liang; Zhang, Jian; Li, Yu; Jiao, Xuelong; Tan, Xiaojie; Zhang, Jianli; Wang, Haibo; Zhang, Bingyuan; Lu, Yun; Sun, Zhenqing
2016-01-01
Reporting of surgical complications is common, but few provide information about the severity and estimate risk factors of complications. If have, but lack of specificity. We retrospectively analyzed data on 2795 gastric cancer patients underwent surgical procedure at the Affiliated Hospital of Qingdao University between June 2007 and June 2012, established multivariate logistic regression model to predictive risk factors related to the postoperative complications according to the Clavien-Dindo classification system. Twenty-four out of 86 variables were identified statistically significant in univariate logistic regression analysis, 11 significant variables entered multivariate analysis were employed to produce the risk model. Liver cirrhosis, diabetes mellitus, Child classification, invasion of neighboring organs, combined resection, introperative transfusion, Billroth II anastomosis of reconstruction, malnutrition, surgical volume of surgeons, operating time and age were independent risk factors for postoperative complications after gastrectomy. Based on logistic regression equation, p=Exp∑BiXi / (1+Exp∑BiXi), multivariate logistic regression predictive model that calculated the risk of postoperative morbidity was developed, p = 1/(1 + e((4.810-1.287X1-0.504X2-0.500X3-0.474X4-0.405X5-0.318X6-0.316X7-0.305X8-0.278X9-0.255X10-0.138X11))). The accuracy, sensitivity and specificity of the model to predict the postoperative complications were 86.7%, 76.2% and 88.6%, respectively. This risk model based on Clavien-Dindo grading severity of complications system and logistic regression analysis can predict severe morbidity specific to an individual patient's risk factors, estimate patients' risks and benefits of gastric surgery as an accurate decision-making tool and may serve as a template for the development of risk models for other surgical groups.
Use of Multiple Regression in Counseling Psychology Research: A Flexible Data-Analytic Strategy.
Wampold, Bruce E.; Freund, Richard D.
1987-01-01
Explains multiple regression, demonstrates its flexibility for analyzing data from various designs, and discusses interpretation of results from multiple regression analysis. Presents regression equations for single independent variable and for two or more independent variables, followed by a discussion of coefficients related to these. Compares…
A Matlab program for stepwise regression
Directory of Open Access Journals (Sweden)
Yanhong Qi
2016-03-01
Full Text Available The stepwise linear regression is a multi-variable regression for identifying statistically significant variables in the linear regression equation. In present study, we presented the Matlab program of stepwise regression.
Recursive Algorithm For Linear Regression
Varanasi, S. V.
1988-01-01
Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.
Wang, Haijun; Gao, Xinbo; Zhang, Kaibing; Li, Jie
2017-05-03
Gaussian process regression (GPR) is an effective statistical learning method for modeling non-linear mapping from an observed space to an expected latent space. When applying it to example learning-based super-resolution (SR), two outstanding issues remain. One is its high computational complexity restricts SR application when a large dataset is available for learning task. The other is that the commonly used Gaussian likelihood in GPR is incompatible with the true observation model for SR reconstruction. To alleviate the above two issues, we propose a GPR-based SR method by using dictionary-based sampling and student-t likelihood, called DSGPR. Considering that dictionary atoms effectively span the original training sample space, we adopt a dictionary-based sampling strategy by combining all the neighborhood samples of each atom into a compact representative training subset so as to reduce the computational complexity. Based on statistical tests, we statistically validate that Studentt likelihood is more suitable to build the observation model for SR problem. Extensive experimental results show that the proposed method outperforms other competitors and produces more pleasing details in texture regions.
Jacob, Benjamin G; Novak, Robert J; Toe, Laurent; Sanfo, Moussa S; Afriyie, Abena N; Ibrahim, Mohammed A; Griffith, Daniel A; Unnasch, Thomas R
2012-01-01
The standard methods for regression analyses of clustered riverine larval habitat data of Simulium damnosum s.l. a major black-fly vector of Onchoceriasis, postulate models relating observational ecological-sampled parameter estimators to prolific habitats without accounting for residual intra-cluster error correlation effects. Generally, this correlation comes from two sources: (1) the design of the random effects and their assumed covariance from the multiple levels within the regression model; and, (2) the correlation structure of the residuals. Unfortunately, inconspicuous errors in residual intra-cluster correlation estimates can overstate precision in forecasted S.damnosum s.l. riverine larval habitat explanatory attributes regardless how they are treated (e.g., independent, autoregressive, Toeplitz, etc). In this research, the geographical locations for multiple riverine-based S. damnosum s.l. larval ecosystem habitats sampled from 2 pre-established epidemiological sites in Togo were identified and recorded from July 2009 to June 2010. Initially the data was aggregated into proc genmod. An agglomerative hierarchical residual cluster-based analysis was then performed. The sampled clustered study site data was then analyzed for statistical correlations using Monthly Biting Rates (MBR). Euclidean distance measurements and terrain-related geomorphological statistics were then generated in ArcGIS. A digital overlay was then performed also in ArcGIS using the georeferenced ground coordinates of high and low density clusters stratified by Annual Biting Rates (ABR). This data was overlain onto multitemporal sub-meter pixel resolution satellite data (i.e., QuickBird 0.61m wavbands ). Orthogonal spatial filter eigenvectors were then generated in SAS/GIS. Univariate and non-linear regression-based models (i.e., Logistic, Poisson and Negative Binomial) were also employed to determine probability distributions and to identify statistically significant parameter
Directory of Open Access Journals (Sweden)
Pål Johan From
2012-04-01
Full Text Available This paper presents the explicit dynamic equations of a mechanical system. The equations are presented so that they can easily be implemented in a simulation software or controller environment and are also well suited for system and controller analysis. The dynamics of a general mechanical system consisting of one or more rigid bodies can be derived from the Lagrangian. We can then use several well known properties of Lie groups to guarantee that these equations are well defined. This will, however, often lead to rather abstract formulation of the dynamic equations that cannot be implemented in a simulation software directly. In this paper we close this gap and show what the explicit dynamic equations look like. These equations can then be implemented directly in a simulation software and no background knowledge on Lie theory and differential geometry on the practitioner's side is required. This is the first of two papers on this topic. In this paper we derive the dynamics for single rigid bodies, while in the second part we study multibody systems. In addition to making the equations more accessible to practitioners, a motivation behind the papers is to correct a few errors commonly found in literature. For the first time, we show the detailed derivations and how to arrive at the correct set of equations. We also show through some simple examples that these correspond with the classical formulations found from Lagrange's equations. The dynamics is derived from the Boltzmann--Hamel equations of motion in terms of local position and velocity variables and the mapping to the corresponding quasi-velocities. Finally we present a new theorem which states that the Boltzmann--Hamel formulation of the dynamics is valid for all transformations with a Lie group topology. This has previously only been indicated through examples, but here we also present the formal proof. The main motivation of these papers is to allow practitioners not familiar with
Poola, Praveen Kumar; John, Renu
2017-10-01
We report the results of characterization of red blood cell (RBC) structure and its dynamics with nanometric sensitivity using transport of intensity equation microscopy (TIEM). Conventional transport of intensity technique requires three intensity images and hence is not suitable for studying real-time dynamics of live biological samples. However, assuming the sample to be homogeneous, phase retrieval using transport of intensity equation has been demonstrated with single defocused measurement with x-rays. We adopt this technique for quantitative phase light microscopy of homogenous cells like RBCs. The main merits of this technique are its simplicity, cost-effectiveness, and ease of implementation on a conventional microscope. The phase information can be easily merged with regular bright-field and fluorescence images to provide multidimensional (three-dimensional spatial and temporal) information without any extra complexity in the setup. The phase measurement from the TIEM has been characterized using polymeric microbeads and the noise stability of the system has been analyzed. We explore the structure and real-time dynamics of RBCs and the subdomain membrane fluctuations using this technique.
Dallas, S. S.; Khan, I.
1976-01-01
The singly-averaged differential equations of motion of a satellite are developed in terms of parameters valid for all eccentricities less than one. The perturbations included in the acceleration model are due to an aspherical central planet (zonal harmonics up to degree 20 and resonant harmonics up to degree and order 20), atmospheric drag for a time-varying atmosphere, third-body gravity (the sun and moon for an earth satellite), solar radiation pressure with shadowing, and impulsive maneuvers. Analytic averaging is used to remove short-period terms due to the aspherical central planet and third-body gravity. Numerical averaging is used to remove short-period terms due to atmospheric drag and solar radiation pressure.
Hu, L; Liang, M; Mouraux, A; Wise, R G; Hu, Y; Iannetti, G D
2011-12-01
Across-trial averaging is a widely used approach to enhance the signal-to-noise ratio (SNR) of event-related potentials (ERPs). However, across-trial variability of ERP latency and amplitude may contain physiologically relevant information that is lost by across-trial averaging. Hence, we aimed to develop a novel method that uses 1) wavelet filtering (WF) to enhance the SNR of ERPs and 2) a multiple linear regression with a dispersion term (MLR(d)) that takes into account shape distortions to estimate the single-trial latency and amplitude of ERP peaks. Using simulated ERP data sets containing different levels of noise, we provide evidence that, compared with other approaches, the proposed WF+MLR(d) method yields the most accurate estimate of single-trial ERP features. When applied to a real laser-evoked potential data set, the WF+MLR(d) approach provides reliable estimation of single-trial latency, amplitude, and morphology of ERPs and thereby allows performing meaningful correlations at single-trial level. We obtained three main findings. First, WF significantly enhances the SNR of single-trial ERPs. Second, MLR(d) effectively captures and measures the variability in the morphology of single-trial ERPs, thus providing an accurate and unbiased estimate of their peak latency and amplitude. Third, intensity of pain perception significantly correlates with the single-trial estimates of N2 and P2 amplitude. These results indicate that WF+MLR(d) can be used to explore the dynamics between different ERP features, behavioral variables, and other neuroimaging measures of brain activity, thus providing new insights into the functional significance of the different brain processes underlying the brain responses to sensory stimuli.
Baba, Toshimi; Gotoh, Yusaku; Yamaguchi, Satoshi; Nakagawa, Satoshi; Abe, Hayato; Masuda, Yutaka; Kawahara, Takayoshi
2017-08-01
This study aimed to evaluate a validation reliability of single-step genomic best linear unbiased prediction (ssGBLUP) with a multiple-lactation random regression test-day model and investigate an effect of adding genotyped cows on the reliability. Two data sets for test-day records from the first three lactations were used: full data from February 1975 to December 2015 (60 850 534 records from 2 853 810 cows) and reduced data cut off in 2011 (53 091 066 records from 2 502 307 cows). We used marker genotypes of 4480 bulls and 608 cows. Genomic enhanced breeding values (GEBV) of 305-day milk yield in all the lactations were estimated for at least 535 young bulls using two marker data sets: bull genotypes only and both bulls and cows genotypes. The realized reliability (R 2 ) from linear regression analysis was used as an indicator of validation reliability. Using only genotyped bulls, R 2 was ranged from 0.41 to 0.46 and it was always higher than parent averages. The very similar R 2 were observed when genotyped cows were added. An application of ssGBLUP to a multiple-lactation random regression model is feasible and adding a limited number of genotyped cows has no significant effect on reliability of GEBV for genotyped bulls. © 2016 Japanese Society of Animal Science.
Stas, Michiel; Dong, Qinghan; Heremans, Stien; Zhang, Beier; Van Orshoven, Jos
2016-08-01
This paper compares two machine learning techniques to predict regional winter wheat yields. The models, based on Boosted Regression Trees (BRT) and Support Vector Machines (SVM), are constructed of Normalized Difference Vegetation Indices (NDVI) derived from low resolution SPOT VEGETATION satellite imagery. Three types of NDVI-related predictors were used: Single NDVI, Incremental NDVI and Targeted NDVI. BRT and SVM were first used to select features with high relevance for predicting the yield. Although the exact selections differed between the prefectures, certain periods with high influence scores for multiple prefectures could be identified. The same period of high influence stretching from March to June was detected by both machine learning methods. After feature selection, BRT and SVM models were applied to the subset of selected features for actual yield forecasting. Whereas both machine learning methods returned very low prediction errors, BRT seems to slightly but consistently outperform SVM.
Agogo, George O; van der Voet, Hilko; van't Veer, Pieter; Ferrari, Pietro; Leenders, Max; Muller, David C; Sánchez-Cantalejo, Emilio; Bamia, Christina; Braaten, Tonje; Knüppel, Sven; Johansson, Ingegerd; van Eeuwijk, Fred A; Boshuizen, Hendriek
2014-01-01
In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM) and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC) study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model.
Directory of Open Access Journals (Sweden)
George O Agogo
Full Text Available In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model.
Agogo, George O.; van der Voet, Hilko; Veer, Pieter van’t; Ferrari, Pietro; Leenders, Max; Muller, David C.; Sánchez-Cantalejo, Emilio; Bamia, Christina; Braaten, Tonje; Knüppel, Sven; Johansson, Ingegerd; van Eeuwijk, Fred A.; Boshuizen, Hendriek
2014-01-01
In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM) and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC) study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model. PMID:25402487
Wang, Hui; Sui, Weiguo; Xue, Wen; Wu, Junyong; Chen, Jiejing; Dai, Yong
2014-09-01
Immunoglobulin A nephropathy (IgAN) is a complex trait regulated by the interaction among multiple physiologic regulatory systems and probably involving numerous genes, which leads to inconsistent findings in genetic studies. One possibility of failure to replicate some single-locus results is that the underlying genetics of IgAN nephropathy is based on multiple genes with minor effects. To learn the association between 23 single nucleotide polymorphisms (SNPs) in 14 genes predisposing to chronic glomerular diseases and IgAN in Han males, the 23 SNPs genotypes of 21 Han males were detected and analyzed with a BaiO gene chip, and their associations were analyzed with univariate analysis and multiple linear regression analysis. Analysis showed that CTLA4 rs231726 and CR2 rs1048971 revealed a significant association with IgAN. These findings support the multi-gene nature of the etiology of IgAN and propose a potential gene-gene interactive model for future studies.
Grégoire, G.
2014-12-01
The logistic regression originally is intended to explain the relationship between the probability of an event and a set of covariables. The model's coefficients can be interpreted via the odds and odds ratio, which are presented in introduction of the chapter. The observations are possibly got individually, then we speak of binary logistic regression. When they are grouped, the logistic regression is said binomial. In our presentation we mainly focus on the binary case. For statistical inference the main tool is the maximum likelihood methodology: we present the Wald, Rao and likelihoods ratio results and their use to compare nested models. The problems we intend to deal with are essentially the same as in multiple linear regression: testing global effect, individual effect, selection of variables to build a model, measure of the fitness of the model, prediction of new values… . The methods are demonstrated on data sets using R. Finally we briefly consider the binomial case and the situation where we are interested in several events, that is the polytomous (multinomial) logistic regression and the particular case of ordinal logistic regression.
Directory of Open Access Journals (Sweden)
Shih-Sen Chang
1994-01-01
Full Text Available In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.
International Nuclear Information System (INIS)
Grinberg, H.
1983-11-01
The projection operator method of Zwanzig and Feshbach is used to construct the time-dependent field operators in the interaction picture. The formula developed to describe the time dependence involves time-ordered cosine and sine projected evolution (memory) superoperators, from which a master equation for the interaction-picture single-particle Green's function in a Liouville space is derived. (author)
Deriving the Quadratic Regression Equation Using Algebra
Gordon, Sheldon P.; Gordon, Florence S.
2004-01-01
In discussions with leading educators from many different fields, MAA's CRAFTY (Curriculum Renewal Across the First Two Years) committee found that one of the most common mathematical themes in those other disciplines is the idea of fitting a function to a set of data in the least squares sense. The representatives of those partner disciplines…
Rendall, Ricardo; Pereira, Ana Cristina; Reis, Marco S
2017-08-15
In this paper we test and compare advanced predictive approaches for estimating wine age in the context of the production of a high quality fortified wine - Madeira Wine. We consider four different data sets, namely, volatile, polyphenols, organic acids and the UV-vis spectra. Each one of these data sets contain chemical information of a different nature and present diverse data structures, namely a different dimensionality, level of collinearity and degree of sparsity. These different aspects may imply the use of different modelling approaches in order to better explore the data set's information content, namely their predictive potential for wine age. This happens to be so, because different regression methods have different prior assumptions regarding the predictors, response variable(s) and the data generating mechanism, which may or may not find good adherence to the case study under analysis. In order to cover a wide range of modelling domains, we have incorporated in this work methods belonging to four very distinct classes of approaches that cover most applications found in practice: linear regression with variable selection, penalized regression, latent variables regression and tree-based ensemble methods. We have also developed a rigorous comparison framework based on a double Monte Carlo cross-validation scheme, in order to perform the relative assessment of the performance of the various methods. Upon comparison, models built using the polyphenols and volatile composition data sets led to better wine age predictions, showing lower errors under testing conditions. Furthermore, the results obtained for the polyphenols data set suggest a more sparse structure that can be further explored in order to reduce the number of measured variables. In terms of regression methods, tree-based methods, and boosted regression trees in particular, presented the best results for the polyphenols, volatile and the organic acid data sets, suggesting a possible presence of a
Yaguiyan-Colliard, Laurence; Daumas, Caroline; Nguyen, Patrick; Grandjean, Dominique; Cardot, Philippe; Priymenko, Nathalie; Roux, Françoise
2015-08-06
Equations based on single-frequency bioelectrical impedance analysis at 50 kHz for determination of total body water content (TBW) have been previously validated in healthy non-sedated beagle dogs. We investigated whether these equations are predictive of TBW in various canine breeds by comparing the results of these equations with TBW values evaluated directly by deuterium oxide (D2O) dilution. Total body water content of 13 healthy adult pet dogs of various breeds was determined directly using D2O dilution and indirectly using previous equations based on values obtained with a portable bioelectric impedance device. Paired Student's t-tests were used to compare TBW obtained by single-frequency bioelectrical impedance analysis and D2O dilution. A p-value of bioelectrical impedance analysis parameters validated at 50 kHz in healthy adult beagles need to be modified including morphological parameters such as body size and shape in a first approach. As in humans, morphological-specific equations have to be developed and validated.
Olive, David J
2017-01-01
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...
Directory of Open Access Journals (Sweden)
Igor K. Kochanenko
2013-01-01
Full Text Available Procedures of construction of curve regress by criterion of the least fractals, i.e. the greatest probability of the sums of degrees of the least deviations measured intensity from their modelling values are proved. The exponent is defined as fractal dimension of a time number. The difference of results of a well-founded method and a method of the least squares is quantitatively estimated.
Directory of Open Access Journals (Sweden)
Yaoyu Hu
2015-09-01
Full Text Available The solution of the energy equation of thermo-elasto-hydrodynamic analysis for bearings by the finite element method usually leads to convergence difficulties due to the presence of convection terms inherited from the Navier–Stokes equations. In this work, the numerical analysis is performed with finite element method universally by adopting the characteristic-based split method to solve the energy equation. Five case studies of fixed pad thrust bearings have been set up with different geometries, loads, and lubricants. The two-dimensional film pressure is obtained by solving the Reynolds equation with pre-defined axial load on the pad. The energy equation of the lubricant film and the heat transfer equation of the bearing pad are handled by characteristic-based split method and conventional finite element method in three-dimensional space, respectively. Hot oil carry-over effect and variable lubricant viscosity are considered in the simulations. The results of the temperature distributions in the lubricant film and the bearing pad are presented. The possible usability of characteristic-based split method for future thermo-elasto-hydrodynamic analysis is discussed.
Directory of Open Access Journals (Sweden)
Ehri Ryu
2017-05-01
Full Text Available In this article, we evaluated the performance of statistical methods in single-group and multi-group analysis approaches for testing group difference in indirect effects and for testing simple indirect effects in each group. We also investigated whether the performance of the methods in the single-group approach was affected when the assumption of equal variance was not satisfied. The assumption was critical for the performance of the two methods in the single-group analysis: the method using a product term for testing the group difference in a single path coefficient, and the Wald test for testing the group difference in the indirect effect. Bootstrap confidence intervals in the single-group approach and all methods in the multi-group approach were not affected by the violation of the assumption. We compared the performance of the methods and provided recommendations.
Retro-regression--another important multivariate regression improvement.
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.
Gao, Xian; Kobayashi, Tsutomu; Yamaguchi, Masahide; Yokoyama, Jun'ichi
2011-11-18
We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in the most general single-field inflation model with second-order field equations. It is shown that the most general cubic action for the tensor perturbation h(ij) is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each h(ij). The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the presence of the kinetic coupling to the Einstein tensor and predicts an equilateral shape. Thus, only two shapes appear in the graviton bispectrum of the most general single-field inflation model, which could open a new clue to the identification of inflationary gravitational waves in observations of cosmic microwave background anisotropies as well as direct detection experiments.
International Nuclear Information System (INIS)
Liu Chengshi
2008-01-01
Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc, are reduced to an integrable ODE expressed by u + p(u)(u') 2 + q(u) = 0 whose general solution can be given. Furthermore, combining complete discrimination system for polynomial, the classifications of all single travelling wave solutions to these equations are obtained. The equation u + p(u)(u') 2 + q(u) = 0 includes the equation (u') 2 = f(u) as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
Biomass equations for shrub species of Tamualipan thornscrub of North-Eastern Mexico
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...
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Fungible weights in logistic regression.
Jones, Jeff A; Waller, Niels G
2016-06-01
In this article we develop methods for assessing parameter sensitivity in logistic regression models. To set the stage for this work, we first review Waller's (2008) equations for computing fungible weights in linear regression. Next, we describe 2 methods for computing fungible weights in logistic regression. To demonstrate the utility of these methods, we compute fungible logistic regression weights using data from the Centers for Disease Control and Prevention's (2010) Youth Risk Behavior Surveillance Survey, and we illustrate how these alternate weights can be used to evaluate parameter sensitivity. To make our work accessible to the research community, we provide R code (R Core Team, 2015) that will generate both kinds of fungible logistic regression weights. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Principal component regression analysis with SPSS.
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.
Pedrini, D. T.; Pedrini, Bonnie C.
Regression, another mechanism studied by Sigmund Freud, has had much research, e.g., hypnotic regression, frustration regression, schizophrenic regression, and infra-human-animal regression (often directly related to fixation). Many investigators worked with hypnotic age regression, which has a long history, going back to Russian reflexologists.…
Quantile Regression With Measurement Error
Wei, Ying
2009-08-27
Regression quantiles can be substantially biased when the covariates are measured with error. In this paper we propose a new method that produces consistent linear quantile estimation in the presence of covariate measurement error. The method corrects the measurement error induced bias by constructing joint estimating equations that simultaneously hold for all the quantile levels. An iterative EM-type estimation algorithm to obtain the solutions to such joint estimation equations is provided. The finite sample performance of the proposed method is investigated in a simulation study, and compared to the standard regression calibration approach. Finally, we apply our methodology to part of the National Collaborative Perinatal Project growth data, a longitudinal study with an unusual measurement error structure. © 2009 American Statistical Association.
Active set support vector regression.
Musicant, David R; Feinberg, Alexander
2004-03-01
This paper presents active set support vector regression (ASVR), a new active set strategy to solve a straightforward reformulation of the standard support vector regression problem. This new algorithm is based on the successful ASVM algorithm for classification problems, and consists of solving a finite number of linear equations with a typically large dimensionality equal to the number of points to be approximated. However, by making use of the Sherman-Morrison-Woodbury formula, a much smaller matrix of the order of the original input space is inverted at each step. The algorithm requires no specialized quadratic or linear programming code, but merely a linear equation solver which is publicly available. ASVR is extremely fast, produces comparable generalization error to other popular algorithms, and is available on the web for download.
Directory of Open Access Journals (Sweden)
Cengiz AKTAŞ
2005-06-01
Full Text Available In this study, we investigate the importance of tourism for Turkish ecenomy, and define the optimum variables which affect tourism revenues. In this type of econometric study that needs the multiple regression models, one of the problems in estimation of parameters is stationarity in time series. Therefore, usableness of the problem for long run relationship is analyzed. Finally autocorrelation, multicollinearity and heteroscedasticity are investigated.
Regularized Structural Equation Modeling
Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.
2016-01-01
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019
Soliton multidimensional equations and integrable evolutions preserving Laplace's equation
International Nuclear Information System (INIS)
Fokas, A.S.
2008-01-01
The KP equation, which is an integrable nonlinear evolution equation in 2+1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the KP equation, I obtain an integrable nonlinear evolution equation in 4+2. The requirement that real initial conditions remain real under this evolution, implies that the dependent variable satisfies a nonlinear evolution equation in 3+1 coupled with Laplace's equation. A reduction of this system of equations to a single equation in 2+1 contains as particular cases certain singular integro-differential equations which appear in the theory of water waves
Walton, Joseph M.; And Others
1978-01-01
Ridge regression is an approach to the problem of large standard errors of regression estimates of intercorrelated regressors. The effect of ridge regression on the estimated squared multiple correlation coefficient is discussed and illustrated. (JKS)
Directory of Open Access Journals (Sweden)
F.M.O. Borges
2003-12-01
que significou pouca influência da metodologia sobre essa medida. A FDN não mostrou ser melhor preditor de EM do que a FB.One experiment was run with broiler chickens, to obtain prediction equations for metabolizable energy (ME based on feedstuffs chemical analyses, and determined ME of wheat grain and its by-products, using four different methodologies. Seven wheat grain by-products were used in five treatments: wheat grain, wheat germ, white wheat flour, dark wheat flour, wheat bran for human use, wheat bran for animal use and rough wheat bran. Based on chemical analyses of crude fiber (CF, ether extract (EE, crude protein (CP, ash (AS and starch (ST of the feeds and the determined values of apparent energy (MEA, true energy (MEV, apparent corrected energy (MEAn and true energy corrected by nitrogen balance (MEVn in five treatments, prediction equations were obtained using the stepwise procedure. CF showed the best relationship with metabolizable energy values, however, this variable alone was not enough for a good estimate of the energy values (R² below 0.80. When EE and CP were included in the equations, R² increased to 0.90 or higher in most estimates. When the equations were calculated with all treatments, the equation for MEA were less precise and R² decreased. When ME data of the traditional or force-feeding methods were used separately, the precision of the equations increases (R² higher than 0.85. For MEV and MEVn values, the best multiple linear equations included CF, EE and CP (R²>0.90, independently of using all experimental data or separating by methodology. The estimates of MEVn values showed high precision and the linear coefficients (a of the equations were similar for all treatments or methodologies. Therefore, it explains the small influence of the different methodologies on this parameter. NDF was not a better predictor of ME than CF.
Prediction Equations for Spirometry for Children from Northern India.
Chhabra, Sunil K; Kumar, Rajeev; Mittal, Vikas
2016-09-08
To develop prediction equations for spirometry for children from northern India using current international guidelines for standardization. Re-analysis of cross-sectional data from a single school. 670 normal children (age 6-17 y; 365 boys) of northern Indian parentage. After screening for normal health, we carried out spirometry with recommended quality assurance according to current guidelines. We developed linear and nonlinear prediction equations using multiple regression analysis. We selected the final models on the basis of the highest coefficient of multiple determination (R2) and statistical validity. Spirometry parameters: FVC, FEV1, PEFR, FEF50, FEF75 and FEF25-75. The equations for the main parameters were as follows: Boys, Ln FVC = -1.687+0.016*height +0.022*age; Ln FEV1 = -1.748+0.015*height+0.031*age. Girls, Ln FVC = -9.989 +(2.018*Ln(height)) + (0.324*Ln(age)); Ln FEV1 = -10.055 +(1.990*Ln(height))+(0.358*Ln(age)). Nonlinear regression yielded substantially greater R2 values compared to linear models except for FEF50 for girls. Height and age were found to be the significant explanatory variables for all parameters on multiple regression with weight making no significant contribution. We developed prediction equations for spirometry for children from northern India. Nonlinear equations were superior to linear equations.
Standards for Standardized Logistic Regression Coefficients
Menard, Scott
2011-01-01
Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
The reduced rank regression model is a multivariate regression model with a coefficient matrix with reduced rank. The reduced rank regression algorithm is an estimation procedure, which estimates the reduced rank regression model. It is related to canonical correlations and involves calculating...
Logic regression and its extensions.
Schwender, Holger; Ruczinski, Ingo
2010-01-01
Logic regression is an adaptive classification and regression procedure, initially developed to reveal interacting single nucleotide polymorphisms (SNPs) in genetic association studies. In general, this approach can be used in any setting with binary predictors, when the interaction of these covariates is of primary interest. Logic regression searches for Boolean (logic) combinations of binary variables that best explain the variability in the outcome variable, and thus, reveals variables and interactions that are associated with the response and/or have predictive capabilities. The logic expressions are embedded in a generalized linear regression framework, and thus, logic regression can handle a variety of outcome types, such as binary responses in case-control studies, numeric responses, and time-to-event data. In this chapter, we provide an introduction to the logic regression methodology, list some applications in public health and medicine, and summarize some of the direct extensions and modifications of logic regression that have been proposed in the literature. Copyright © 2010 Elsevier Inc. All rights reserved.
African Journals Online (AJOL)
Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
Directory of Open Access Journals (Sweden)
Rachel Jewkes
Full Text Available Interventions to prevent rape perpetration must be designed to address its drivers. This paper seeks to extend understanding of drivers of single and multiple perpetrator rape (referred to here as SPR and MPR respectively and the relationships between socio-economic status, childhood trauma, peer pressure, other masculine behaviours and rape.1370 young men aged 15 to 26 were interviewed as part of the randomised controlled trial evaluation of Stepping Stones in the rural Eastern Cape. We used multinomial to compare the characteristics of men who reported rape perpetration at baseline. We used structural equation modelling (SEM to examine pathways to rape perpetration.76.1% of young men had never raped, 10.0% had perpetrated SPR and 13.9% MPR. The factors associated with both MPR and SPR (compared to never having raped were indicators of socio-economic status (SES, childhood trauma, sexual coercion by a woman, drug and alcohol use, peer pressure susceptibility, having had transactional sex, multiple sexual partners and being physically violent towards a partner. The SEM showed the relationship between SES and rape perpetration to be mediated by gender inequitable masculinity. It was complex as there was a direct path indicating that SES correlated with the masculinity variable directly such that men of higher SES had more gender inequitable masculinities, and indirect path mediated by peer pressure resistance indicated that the former pertained so long as men lacked peer pressure resistance. Having a higher SES conveyed greater resistance for some men. There was also a path mediated through childhood trauma, such that men of lower SES were more likely to have a higher childhood trauma exposure and this correlated with a higher likelihood of having the gender inequitable masculinity (with or without the mediating effect of peer pressure resistance.Both higher and lower socio-economic status were associated with raping. Prevention of rape
Jewkes, Rachel; Nduna, Mzikazi; Jama-Shai, Nwabisa; Chirwa, Esnat; Dunkle, Kristin
2016-01-01
Background Interventions to prevent rape perpetration must be designed to address its drivers. This paper seeks to extend understanding of drivers of single and multiple perpetrator rape (referred to here as SPR and MPR respectively) and the relationships between socio-economic status, childhood trauma, peer pressure, other masculine behaviours and rape. Method 1370 young men aged 15 to 26 were interviewed as part of the randomised controlled trial evaluation of Stepping Stones in the rural Eastern Cape. We used multinomial to compare the characteristics of men who reported rape perpetration at baseline. We used structural equation modelling (SEM) to examine pathways to rape perpetration. Results 76.1% of young men had never raped, 10.0% had perpetrated SPR and 13.9% MPR. The factors associated with both MPR and SPR (compared to never having raped) were indicators of socio-economic status (SES), childhood trauma, sexual coercion by a woman, drug and alcohol use, peer pressure susceptibility, having had transactional sex, multiple sexual partners and being physically violent towards a partner. The SEM showed the relationship between SES and rape perpetration to be mediated by gender inequitable masculinity. It was complex as there was a direct path indicating that SES correlated with the masculinity variable directly such that men of higher SES had more gender inequitable masculinities, and indirect path mediated by peer pressure resistance indicated that the former pertained so long as men lacked peer pressure resistance. Having a higher SES conveyed greater resistance for some men. There was also a path mediated through childhood trauma, such that men of lower SES were more likely to have a higher childhood trauma exposure and this correlated with a higher likelihood of having the gender inequitable masculinity (with or without the mediating effect of peer pressure resistance). Discussion Both higher and lower socio-economic status were associated with raping
Jewkes, Rachel; Nduna, Mzikazi; Jama-Shai, Nwabisa; Chirwa, Esnat; Dunkle, Kristin
2016-01-01
Interventions to prevent rape perpetration must be designed to address its drivers. This paper seeks to extend understanding of drivers of single and multiple perpetrator rape (referred to here as SPR and MPR respectively) and the relationships between socio-economic status, childhood trauma, peer pressure, other masculine behaviours and rape. 1370 young men aged 15 to 26 were interviewed as part of the randomised controlled trial evaluation of Stepping Stones in the rural Eastern Cape. We used multinomial to compare the characteristics of men who reported rape perpetration at baseline. We used structural equation modelling (SEM) to examine pathways to rape perpetration. 76.1% of young men had never raped, 10.0% had perpetrated SPR and 13.9% MPR. The factors associated with both MPR and SPR (compared to never having raped) were indicators of socio-economic status (SES), childhood trauma, sexual coercion by a woman, drug and alcohol use, peer pressure susceptibility, having had transactional sex, multiple sexual partners and being physically violent towards a partner. The SEM showed the relationship between SES and rape perpetration to be mediated by gender inequitable masculinity. It was complex as there was a direct path indicating that SES correlated with the masculinity variable directly such that men of higher SES had more gender inequitable masculinities, and indirect path mediated by peer pressure resistance indicated that the former pertained so long as men lacked peer pressure resistance. Having a higher SES conveyed greater resistance for some men. There was also a path mediated through childhood trauma, such that men of lower SES were more likely to have a higher childhood trauma exposure and this correlated with a higher likelihood of having the gender inequitable masculinity (with or without the mediating effect of peer pressure resistance). Both higher and lower socio-economic status were associated with raping. Prevention of rape perpetration must
Regression analysis by example
Chatterjee, Samprit
2012-01-01
Praise for the Fourth Edition: ""This book is . . . an excellent source of examples for regression analysis. It has been and still is readily readable and understandable."" -Journal of the American Statistical Association 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
Nonparametric modal regression
Chen, Yen-Chi; Genovese, Christopher R.; Tibshirani, Ryan J.; Wasserman, Larry
2016-01-01
Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of $Y$ and $X$. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter...
Flexible survival regression modelling
DEFF Research Database (Denmark)
Cortese, Giuliana; Scheike, Thomas H; Martinussen, Torben
2009-01-01
Regression analysis of survival data, and more generally event history data, is typically based on Cox's regression model. We here review some recent methodology, focusing on the limitations of Cox's regression model. The key limitation is that the model is not well suited to represent time-varyi...
Multinomial logistic regression ensembles.
Lee, Kyewon; Ahn, Hongshik; Moon, Hojin; Kodell, Ralph L; Chen, James J
2013-05-01
This article proposes a method for multiclass classification problems using ensembles of multinomial logistic regression models. A multinomial logit model is used as a base classifier in ensembles from random partitions of predictors. The multinomial logit model can be applied to each mutually exclusive subset of the feature space without variable selection. By combining multiple models the proposed method can handle a huge database without a constraint needed for analyzing high-dimensional data, and the random partition can improve the prediction accuracy by reducing the correlation among base classifiers. The proposed method is implemented using R, and the performance including overall prediction accuracy, sensitivity, and specificity for each category is evaluated on two real data sets and simulation data sets. To investigate the quality of prediction in terms of sensitivity and specificity, the area under the receiver operating characteristic (ROC) curve (AUC) is also examined. The performance of the proposed model is compared to a single multinomial logit model and it shows a substantial improvement in overall prediction accuracy. The proposed method is also compared with other classification methods such as the random forest, support vector machines, and random multinomial logit model.
Who Will Win?: Predicting the Presidential Election Using Linear Regression
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.…
Kilgour, Robert D; Cardiff, Katrina; Rosenthall, Leonard; Lucar, Enriqueta; Trutschnigg, Barbara; Vigano, Antonio
2016-01-01
Measurements of body composition using dual-energy X-ray absorptiometry (DXA) and single abdominal images from computed tomography (CT) in advanced cancer patients (ACP) have important diagnostic and prognostic value. The question arises as to whether CT scans can serve as surrogates for DXA in terms of whole-body fat-free mass (FFM), whole-body fat mass (FM), and appendicular skeletal muscle (ASM) mass. Predictive equations to estimate body composition for ACP from CT images have been proposed (Mourtzakis et al. 2008; Appl. Physiol. Nutr. Metabol. 33(5): 997-1006); however, these equations have yet to be validated in an independent cohort of ACP. Thus, this study evaluated the accuracy of these equations in estimating FFM, FM, and ASM mass using CT images at the level of the third lumbar vertebrae and compared these values with DXA measurements. FFM, FM, and ASM mass were estimated from the prediction equations proposed by Mourtzakis and colleagues (2008) using single abdominal CT images from 43 ACP and were compared with whole-body DXA scans using Spearman correlations and Bland-Altman analyses. Despite a moderate to high correlation between the actual (DXA) and predicted (CT) values for FM (rho = 0.93; p ≤ 0.001), FFM (rho = 0.78; p ≤ 0.001), and ASM mass (rho = 0.70; p ≤ 0.001), Bland-Altman analyses revealed large range-of-agreement differences between the 2 methods (29.39 kg for FFM, 15.47 kg for FM, and 3.99 kg for ASM mass). Based on the magnitude of these differences, we concluded that prediction equations using single abdominal CT images have poor accuracy, cannot be considered as surrogates for DXA, and may have limited clinical utility.
DEFF Research Database (Denmark)
Fitzenberger, Bernd; Wilke, Ralf Andreas
2015-01-01
if the mean regression model does not. We provide a short informal introduction into the principle of quantile regression which includes an illustrative application from empirical labor market research. This is followed by briefly sketching the underlying statistical model for linear quantile regression based......Quantile regression is emerging as a popular statistical approach, which complements the estimation of conditional mean models. While the latter only focuses on one aspect of the conditional distribution of the dependent variable, the mean, quantile regression provides more detailed insights...... by modeling conditional quantiles. Quantile regression can therefore detect whether the partial effect of a regressor on the conditional quantiles is the same for all quantiles or differs across quantiles. Quantile regression can provide evidence for a statistical relationship between two variables even...
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Anthropometric predictive equations for estimating body composition
Salamat, Mohammad Reza; Shanei, Ahmad; Salamat, Amir Hossein; Khoshhali, Mehri; Asgari, Mahdi
2015-01-01
Background: Precise and accurate measurements of body composition are useful in achieving a greater understanding of human energy metabolism in physiology and in different clinical conditions, such as, cardiovascular disease and overall mortality. Dual-energy x-ray absorptiometry (DXA) can be used to measure body composition, but the easiest method to assess body composition is the use of anthropometric indices. This study has been designed to evaluate the accuracy and precision of body composition prediction equations by various anthropometric measures instead of a whole body DXA scan. Materials and Methods: We identified 143 adult patients underwent DXA evaluation of the whole body. The anthropometric indices were also measured. Datasets were split randomly into two parts. Multiple regression analysis with a backward stepwise elimination procedure was used as the derivation set and then the estimates were compared with the actual measurements from the whole-body scans for a validation set. The SPSS version 20 for Windows software was used in multiple regression and data analysis. Results: Using multiple linear regression analyses, the best equation for predicting the whole-body fat mass (R2 = 0.808) included the body mass index (BMI) and gender; the best equation for predicting whole-body lean mass (R2 = 0.780) included BMI, WC, gender, and age; and the best equation for predicting trunk fat mass (R2 = 0.759) included BMI, WC, and gender. Conclusions: Combinations of anthropometric measurements predict whole-body lean mass and trunk fat mass better than any of these single anthropometric indices. Therefore, the findings of the present study may be used to verify the results in patients with various diseases or diets. PMID:25709999
Introduction to regression graphics
Cook, R Dennis
2009-01-01
Covers the use of dynamic and interactive computer graphics in linear regression analysis, focusing on analytical graphics. Features new techniques like plot rotation. The authors have composed their own regression code, using Xlisp-Stat language called R-code, which is a nearly complete system for linear regression analysis and can be utilized as the main computer program in a linear regression course. The accompanying disks, for both Macintosh and Windows computers, contain the R-code and Xlisp-Stat. An Instructor's Manual presenting detailed solutions to all the problems in the book is ava
Alternative Methods of Regression
Birkes, David
2011-01-01
Of related interest. Nonlinear Regression Analysis and its Applications Douglas M. Bates and Donald G. Watts ".an extraordinary presentation of concepts and methods concerning the use and analysis of nonlinear regression models.highly recommend[ed].for anyone needing to use and/or understand issues concerning the analysis of nonlinear regression models." --Technometrics This book provides a balance between theory and practice supported by extensive displays of instructive geometrical constructs. Numerous in-depth case studies illustrate the use of nonlinear regression analysis--with all data s
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
The development of a preliminary regression equation for estimating ...
African Journals Online (AJOL)
of stature, weight, body fat and muscle percentage. However, persons with spinal cord injury (SCI) have a reduced physical capacity which changes their body composition.1 A lesion of the spinal cord leads to denervation of the muscles below that lesion, which leads to disuse atrophy and a loss of lean body mass.
P.M.C. de Boer (Paul); C.M. Hafner (Christian)
2005-01-01
textabstractWe argue in this paper that general ridge (GR) regression implies no major complication compared with simple ridge regression. We introduce a generalization of an explicit GR estimator derived by Hemmerle and by Teekens and de Boer and show that this estimator, which is more
Inferring Mathematical Equations Using Crowdsourcing.
Directory of Open Access Journals (Sweden)
Szymon Wasik
Full Text Available Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.
Inferring Mathematical Equations Using Crowdsourcing.
Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw
2015-01-01
Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players.
Weisberg, Sanford
2013-01-01
Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus
Hosmer, David W; Sturdivant, Rodney X
2013-01-01
A new edition of the definitive guide to logistic regression modeling for health science and other applications This thoroughly expanded Third Edition provides an easily accessible introduction to the logistic regression (LR) model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables. Applied Logistic Regression, Third Edition emphasizes applications in the health sciences and handpicks topics that best suit the use of modern statistical software. The book provides readers with state-of-
Grégoire, G.
2014-12-01
This chapter deals with the multiple linear regression. That is we investigate the situation where the mean of a variable depends linearly on a set of covariables. The noise is supposed to be gaussian. We develop the least squared method to get the parameter estimators and estimates of their precisions. This leads to design confidence intervals, prediction intervals, global tests, individual tests and more generally tests of submodels defined by linear constraints. Methods for model's choice and variables selection, measures of the quality of the fit, residuals study, diagnostic methods are presented. Finally identification of departures from the model's assumptions and the way to deal with these problems are addressed. A real data set is used to illustrate the methodology with software R. Note that this chapter is intended to serve as a guide for other regression methods, like logistic regression or AFT models and Cox regression.
Glyph: Symbolic Regression Tools
Quade, Markus; Gout, Julien; Abel, Markus
2018-01-01
We present Glyph - a Python package for genetic programming based symbolic regression. Glyph is designed for usage let by numerical simulations let by real world experiments. For experimentalists, glyph-remote provides a separation of tasks: a ZeroMQ interface splits the genetic programming optimization task from the evaluation of an experimental (or numerical) run. Glyph can be accessed at http://github.com/ambrosys/glyph . Domain experts are be able to employ symbolic regression in their ex...
Pansharpening via sparse regression
Tang, Songze; Xiao, Liang; Liu, Pengfei; Huang, Lili; Zhou, Nan; Xu, Yang
2017-09-01
Pansharpening is an effective way to enhance the spatial resolution of a multispectral (MS) image by fusing it with a provided panchromatic image. Instead of restricting the coding coefficients of low-resolution (LR) and high-resolution (HR) images to be equal, we propose a pansharpening approach via sparse regression in which the relationship between sparse coefficients of HR and LR MS images is modeled by ridge regression and elastic-net regression simultaneously learning the corresponding dictionaries. The compact dictionaries are learned based on the sampled patch pairs from the high- and low-resolution images, which can greatly characterize the structural information of the LR MS and HR MS images. Later, taking the complex relationship between the coding coefficients of LR MS and HR MS images into account, the ridge regression is used to characterize the relationship of intrapatches. The elastic-net regression is employed to describe the relationship of interpatches. Thus, the HR MS image can be almost identically reconstructed by multiplying the HR dictionary and the calculated sparse coefficient vector with the learned regression relationship. The simulated and real experimental results illustrate that the proposed method outperforms several well-known methods, both quantitatively and perceptually.
Pulkkinen, Otto; Metzler, Ralf
2015-12-01
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
Directory of Open Access Journals (Sweden)
Mok Tik
2014-06-01
Full Text Available This study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.
DEFF Research Database (Denmark)
Bache, Stefan Holst
A new and alternative quantile regression estimator is developed and it is shown that the estimator is root n-consistent and asymptotically normal. The estimator is based on a minimax ‘deviance function’ and has asymptotically equivalent properties to the usual quantile regression estimator. It is......, however, a different and therefore new estimator. It allows for both linear- and nonlinear model specifications. A simple algorithm for computing the estimates is proposed. It seems to work quite well in practice but whether it has theoretical justification is still an open question....
Practical Session: Logistic Regression
Clausel, M.; Grégoire, G.
2014-12-01
An exercise is proposed to illustrate the logistic regression. One investigates the different risk factors in the apparition of coronary heart disease. It has been proposed in Chapter 5 of the book of D.G. Kleinbaum and M. Klein, "Logistic Regression", Statistics for Biology and Health, Springer Science Business Media, LLC (2010) and also by D. Chessel and A.B. Dufour in Lyon 1 (see Sect. 6 of http://pbil.univ-lyon1.fr/R/pdf/tdr341.pdf). This example is based on data given in the file evans.txt coming from http://www.sph.emory.edu/dkleinb/logreg3.htm#data.
Prediction equations for diffusing capacity (transfer factor) of lung for North Indians.
Chhabra, Sunil Kumar; Kumar, Rajeev; Gupta, Uday A
2016-01-01
Prediction equations for diffusing capacity of lung for carbon monoxide (DLCO), alveolar volume (VA), and DLCO/VA using the current standardization guidelines are not available for Indian population. The present study was carried out to develop equations for these parameters for North Indian adults and examine the ethnic diversity in predictions. DLCO was measured by single-breath technique and VA by single-breath helium dilution using standardized methodology in 357 (258 males, 99 females) normal nonsmoker adult North Indians and DLCO/VA was computed. The subjects were randomized into training and test datasets for development of prediction equations by multiple linear regressions and for validation, respectively. For males, the following equations were developed: DLCO, -7.813 + 0.318 × ht -0.624 × age + 0.00552 × age(2); VA, -8.152 + 0.087 × ht -0.019 × wt; DLCO/VA, 7.315 - 0.037 × age. For females, the equations were: DLCO, -44.15 + 0.449 × ht -0.099 × age; VA, -6.893 + 0.068 × ht. A statistically acceptable prediction equation was not obtained for DLCO/VA in females. It was therefore computed from predicted DLCO and predicted VA. All equations were internally valid. Predictions of DLCO by Indian equations were lower than most Caucasian predictions in both males and females and greater than the Chinese predictions for males. This study has developed validated prediction equations for DLCO, VA, and DLCO/VA in North Indians. Substantial ethnic diversity exists in predictions for DLCO and VA with Caucasian equations generally yielding higher values than the Indian or Chinese equations. However, DLCO/VA predicted by the Indian equations is slightly higher than that by other equations.
Software Regression Verification
2013-12-11
of recursive procedures. Acta Informatica , 45(6):403 – 439, 2008. [GS11] Benny Godlin and Ofer Strichman. Regression verifica- tion. Technical Report...functions. Therefore, we need to rede - fine m-term. – Mutual termination. If either function f or function f ′ (or both) is non- deterministic, then their
Multiple linear regression analysis
Edwards, T. R.
1980-01-01
Program rapidly selects best-suited set of coefficients. User supplies only vectors of independent and dependent data and specifies confidence level required. Program uses stepwise statistical procedure for relating minimal set of variables to set of observations; final regression contains only most statistically significant coefficients. Program is written in FORTRAN IV for batch execution and has been implemented on NOVA 1200.
Mechanisms of neuroblastoma regression
Brodeur, Garrett M.; Bagatell, Rochelle
2014-01-01
Recent genomic and biological studies of neuroblastoma have shed light on the dramatic heterogeneity in the clinical behaviour of this disease, which spans from spontaneous regression or differentiation in some patients, to relentless disease progression in others, despite intensive multimodality therapy. This evidence also suggests several possible mechanisms to explain the phenomena of spontaneous regression in neuroblastomas, including neurotrophin deprivation, humoral or cellular immunity, loss of telomerase activity and alterations in epigenetic regulation. A better understanding of the mechanisms of spontaneous regression might help to identify optimal therapeutic approaches for patients with these tumours. Currently, the most druggable mechanism is the delayed activation of developmentally programmed cell death regulated by the tropomyosin receptor kinase A pathway. Indeed, targeted therapy aimed at inhibiting neurotrophin receptors might be used in lieu of conventional chemotherapy or radiation in infants with biologically favourable tumours that require treatment. Alternative approaches consist of breaking immune tolerance to tumour antigens or activating neurotrophin receptor pathways to induce neuronal differentiation. These approaches are likely to be most effective against biologically favourable tumours, but they might also provide insights into treatment of biologically unfavourable tumours. We describe the different mechanisms of spontaneous neuroblastoma regression and the consequent therapeutic approaches. PMID:25331179
Bounded Gaussian process regression
DEFF Research Database (Denmark)
Jensen, Bjørn Sand; Nielsen, Jens Brehm; Larsen, Jan
2013-01-01
We extend the Gaussian process (GP) framework for bounded regression by introducing two bounded likelihood functions that model the noise on the dependent variable explicitly. This is fundamentally different from the implicit noise assumption in the previously suggested warped GP framework. We...
Bayesian logistic regression analysis
Van Erp, H.R.N.; Van Gelder, P.H.A.J.M.
2012-01-01
In this paper we present a Bayesian logistic regression analysis. It is found that if one wishes to derive the posterior distribution of the probability of some event, then, together with the traditional Bayes Theorem and the integrating out of nuissance parameters, the Jacobian transformation is an
Predictive equations for the estimation of body size in seals and sea lions (Carnivora: Pinnipedia).
Churchill, Morgan; Clementz, Mark T; Kohno, Naoki
2014-08-01
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
Height and Weight Estimation From Anthropometric Measurements Using Machine Learning Regressions.
Rativa, Diego; Fernandes, Bruno J T; Roque, Alexandre
2018-01-01
Height and weight are measurements explored to tracking nutritional diseases, energy expenditure, clinical conditions, drug dosages, and infusion rates. Many patients are not ambulant or may be unable to communicate, and a sequence of these factors may not allow accurate estimation or measurements; in those cases, it can be estimated approximately by anthropometric means. Different groups have proposed different linear or non-linear equations which coefficients are obtained by using single or multiple linear regressions. In this paper, we present a complete study of the application of different learning models to estimate height and weight from anthropometric measurements: support vector regression, Gaussian process, and artificial neural networks. The predicted values are significantly more accurate than that obtained with conventional linear regressions. In all the cases, the predictions are non-sensitive to ethnicity, and to gender, if more than two anthropometric parameters are analyzed. The learning model analysis creates new opportunities for anthropometric applications in industry, textile technology, security, and health care.
equate: An R Package for Observed-Score Linking and Equating
Directory of Open Access Journals (Sweden)
Anthony D. Albano
2016-10-01
Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.
Subset selection in regression
Miller, Alan
2002-01-01
Originally published in 1990, the first edition of Subset Selection in Regression filled a significant gap in the literature, and its critical and popular success has continued for more than a decade. Thoroughly revised to reflect progress in theory, methods, and computing power, the second edition promises to continue that tradition. The author has thoroughly updated each chapter, incorporated new material on recent developments, and included more examples and references. New in the Second Edition:A separate chapter on Bayesian methodsComplete revision of the chapter on estimationA major example from the field of near infrared spectroscopyMore emphasis on cross-validationGreater focus on bootstrappingStochastic algorithms for finding good subsets from large numbers of predictors when an exhaustive search is not feasible Software available on the Internet for implementing many of the algorithms presentedMore examplesSubset Selection in Regression, Second Edition remains dedicated to the techniques for fitting...
Ridge Regression Signal Processing
Kuhl, Mark R.
1990-01-01
The introduction of the Global Positioning System (GPS) into the National Airspace System (NAS) necessitates the development of Receiver Autonomous Integrity Monitoring (RAIM) techniques. In order to guarantee a certain level of integrity, a thorough understanding of modern estimation techniques applied to navigational problems is required. The extended Kalman filter (EKF) is derived and analyzed under poor geometry conditions. It was found that the performance of the EKF is difficult to predict, since the EKF is designed for a Gaussian environment. A novel approach is implemented which incorporates ridge regression to explain the behavior of an EKF in the presence of dynamics under poor geometry conditions. The basic principles of ridge regression theory are presented, followed by the derivation of a linearized recursive ridge estimator. Computer simulations are performed to confirm the underlying theory and to provide a comparative analysis of the EKF and the recursive ridge estimator.
Regression in organizational leadership.
Kernberg, O F
1979-02-01
The choice of good leaders is a major task for all organizations. Inforamtion regarding the prospective administrator's personality should complement questions regarding his previous experience, his general conceptual skills, his technical knowledge, and the specific skills in the area for which he is being selected. The growing psychoanalytic knowledge about the crucial importance of internal, in contrast to external, object relations, and about the mutual relationships of regression in individuals and in groups, constitutes an important practical tool for the selection of leaders.
Classification and regression trees
Breiman, Leo; Olshen, Richard A; Stone, Charles J
1984-01-01
The methodology used to construct tree structured rules is the focus of this monograph. Unlike many other statistical procedures, which moved from pencil and paper to calculators, this text's use of trees was unthinkable before computers. Both the practical and theoretical sides have been developed in the authors' study of tree methods. Classification and Regression Trees reflects these two sides, covering the use of trees as a data analysis method, and in a more mathematical framework, proving some of their fundamental properties.
Better Autologistic Regression
Directory of Open Access Journals (Sweden)
Mark A. Wolters
2017-11-01
Full Text Available Autologistic regression is an important probability model for dichotomous random variables observed along with covariate information. It has been used in various fields for analyzing binary data possessing spatial or network structure. The model can be viewed as an extension of the autologistic model (also known as the Ising model, quadratic exponential binary distribution, or Boltzmann machine to include covariates. It can also be viewed as an extension of logistic regression to handle responses that are not independent. Not all authors use exactly the same form of the autologistic regression model. Variations of the model differ in two respects. First, the variable coding—the two numbers used to represent the two possible states of the variables—might differ. Common coding choices are (zero, one and (minus one, plus one. Second, the model might appear in either of two algebraic forms: a standard form, or a recently proposed centered form. Little attention has been paid to the effect of these differences, and the literature shows ambiguity about their importance. It is shown here that changes to either coding or centering in fact produce distinct, non-nested probability models. Theoretical results, numerical studies, and analysis of an ecological data set all show that the differences among the models can be large and practically significant. Understanding the nature of the differences and making appropriate modeling choices can lead to significantly improved autologistic regression analyses. The results strongly suggest that the standard model with plus/minus coding, which we call the symmetric autologistic model, is the most natural choice among the autologistic variants.
DEFF Research Database (Denmark)
Hansen, Henrik; Tarp, Finn
2001-01-01
. There are, however, decreasing returns to aid, and the estimated effectiveness of aid is highly sensitive to the choice of estimator and the set of control variables. When investment and human capital are controlled for, no positive effect of aid is found. Yet, aid continues to impact on growth via...... investment. We conclude by stressing the need for more theoretical work before this kind of cross-country regressions are used for policy purposes....
Hilbe, Joseph M
2009-01-01
This book really does cover everything you ever wanted to know about logistic regression … with updates available on the author's website. Hilbe, a former national athletics champion, philosopher, and expert in astronomy, is a master at explaining statistical concepts and methods. Readers familiar with his other expository work will know what to expect-great clarity.The book provides considerable detail about all facets of logistic regression. No step of an argument is omitted so that the book will meet the needs of the reader who likes to see everything spelt out, while a person familiar with some of the topics has the option to skip "obvious" sections. The material has been thoroughly road-tested through classroom and web-based teaching. … The focus is on helping the reader to learn and understand logistic regression. The audience is not just students meeting the topic for the first time, but also experienced users. I believe the book really does meet the author's goal … .-Annette J. Dobson, Biometric...
DEFF Research Database (Denmark)
Ozenne, Brice; Sørensen, Anne Lyngholm; Scheike, Thomas
2017-01-01
In the presence of competing risks a prediction of the time-dynamic absolute risk of an event can be based on cause-specific Cox regression models for the event and the competing risks (Benichou and Gail, 1990). We present computationally fast and memory optimized C++ functions with an R interfac...... functionals. The software presented here is implemented in the riskRegression package.......In the presence of competing risks a prediction of the time-dynamic absolute risk of an event can be based on cause-specific Cox regression models for the event and the competing risks (Benichou and Gail, 1990). We present computationally fast and memory optimized C++ functions with an R interface...... for predicting the covariate specific absolute risks, their confidence intervals, and their confidence bands based on right censored time to event data. We provide explicit formulas for our implementation of the estimator of the (stratified) baseline hazard function in the presence of tied event times. As a by...
Using Ridge Regression with Non-Cognitive Variables by Race in Admissions.
Tracey, Terrence J.; Sedlacek, William E.
1984-01-01
A study of the effectiveness of ridge regression over ordinary least squares regression as applied to both cognitive and noncognitive admissions data is reported. Separate race equations and a general equation were used. The analysis used did not improve on existing regression analyses. (MSE)
Bilinear regression model with Kronecker and linear structures for ...
African Journals Online (AJOL)
On the basis of n independent observations from a matrix normal distribution, estimating equations in a flip-flop relation are established and the consistency of estimators is studied. Keywords: Bilinear regression; Estimating equations; Flip- flop algorithm; Kronecker product structure; Linear structured covariance matrix; ...
Ridge Regression: A Regression Procedure for Analyzing correlated Independent Variables
Rakow, Ernest A.
1978-01-01
Ridge regression is a technique used to ameliorate the problem of highly correlated independent variables in multiple regression analysis. This paper explains the fundamentals of ridge regression and illustrates its use. (JKS)
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
DEFF Research Database (Denmark)
Bordacconi, Mats Joe; Larsen, Martin Vinæs
2014-01-01
Humans are fundamentally primed for making causal attributions based on correlations. This implies that researchers must be careful to present their results in a manner that inhibits unwarranted causal attribution. In this paper, we present the results of an experiment that suggests regression...... more likely. Our experiment drew on a sample of 235 university students from three different social science degree programs (political science, sociology and economics), all of whom had received substantial training in statistics. The subjects were asked to compare and evaluate the validity...
Adaptive metric kernel regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
2000-01-01
Kernel smoothing is a widely used non-parametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this contribution, we propose an algorithm that adapts the input metric used in multivariate...... regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms...
Adaptive Metric Kernel Regression
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
1998-01-01
Kernel smoothing is a widely used nonparametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this paper, we propose an algorithm that adapts the input metric used in multivariate regression...... by minimising a cross-validation estimate of the generalisation error. This allows one to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard...
The Variance Normalization Method of Ridge Regression Analysis.
Bulcock, J. W.; And Others
The testing of contemporary sociological theory often calls for the application of structural-equation models to data which are inherently collinear. It is shown that simple ridge regression, which is commonly used for controlling the instability of ordinary least squares regression estimates in ill-conditioned data sets, is not a legitimate…
Lecture notes on ridge regression
van Wieringen, Wessel N.
2015-01-01
The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a penalty (i.e. a function of regression coefficients). The ridge penalty is the sum of squared regression coefficients, giving rise to ridge regression. Here many aspect of ridge regression are reviewed e.g. moments, mean squared error, its equivalence to co...
Tsodikov, O V; Record, M T
1999-03-01
A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Esigma70 RNA polymerase (R)-lambdaPR promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I1, I2), [equation: see text], where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] > [P]) to form long-lived complexes (RPo and I2) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (ka), isomerization (ki), and dissociation (kd) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Esigma70 RNA polymerase (R)-lambdaP(R) promoter (P) open complex formation.
Variable Selection in ROC Regression
Directory of Open Access Journals (Sweden)
Binhuan Wang
2013-01-01
Full Text Available Regression models are introduced into the receiver operating characteristic (ROC analysis to accommodate effects of covariates, such as genes. If many covariates are available, the variable selection issue arises. The traditional induced methodology separately models outcomes of diseased and nondiseased groups; thus, separate application of variable selections to two models will bring barriers in interpretation, due to differences in selected models. Furthermore, in the ROC regression, the accuracy of area under the curve (AUC should be the focus instead of aiming at the consistency of model selection or the good prediction performance. In this paper, we obtain one single objective function with the group SCAD to select grouped variables, which adapts to popular criteria of model selection, and propose a two-stage framework to apply the focused information criterion (FIC. Some asymptotic properties of the proposed methods are derived. Simulation studies show that the grouped variable selection is superior to separate model selections. Furthermore, the FIC improves the accuracy of the estimated AUC compared with other criteria.
KINERJA JACKKNIFE RIDGE REGRESSION DALAM MENGATASI MULTIKOLINEARITAS
Directory of Open Access Journals (Sweden)
HANY DEVITA
2015-02-01
Full Text Available Ordinary least square is a parameter estimations for minimizing residual sum of squares. If the multicollinearity was found in the data, unbias estimator with minimum variance could not be reached. Multicollinearity is a linear correlation between independent variabels in model. Jackknife Ridge Regression(JRR as an extension of Generalized Ridge Regression (GRR for solving multicollinearity. Generalized Ridge Regression is used to overcome the bias of estimators caused of presents multicollinearity by adding different bias parameter for each independent variabel in least square equation after transforming the data into an orthoghonal form. Beside that, JRR can reduce the bias of the ridge estimator. The result showed that JRR model out performs GRR model.
Kuhl, Mark R.
1990-01-01
Current navigation requirements depend on a geometric dilution of precision (GDOP) criterion. As long as the GDOP stays below a specific value, navigation requirements are met. The GDOP will exceed the specified value when the measurement geometry becomes too collinear. A new signal processing technique, called Ridge Regression Processing, can reduce the effects of nearly collinear measurement geometry; thereby reducing the inflation of the measurement errors. It is shown that the Ridge signal processor gives a consistently better mean squared error (MSE) in position than the Ordinary Least Mean Squares (OLS) estimator. The applicability of this technique is currently being investigated to improve the following areas: receiver autonomous integrity monitoring (RAIM), coverage requirements, availability requirements, and precision approaches.
Rigoni, Marta; Torri, Emanuele; Nollo, Giandomenico; Zarantonello, Diana; Laudon, Alessandro; Sottini, Laura; Guarrera, Giovanni Maria; Brunori, Giuliano
2017-06-01
Despite several studies reporting similar outcomes for peritoneal dialysis (PD) and hemodialysis (HD), the former is underused worldwide, with a PD prevalence of 15% in Italy. In 2008, the Unit of Nephrology and Dialysis of the Healthcare Trust of the Autonomous Province of Trento implemented a successful PD program which has increased the proportion of PD incident patients from 7 to 47%. We aimed to assess the effect of this extensive use of PD by comparing HD and PD in terms of survival and time-to-transplantation. A total of 334 HD and 153 PD incident patients were enrolled between January 2008 and December 2014. After screening for exclusion criteria and propensity score matching, 279 HD and 132 PD patients were analyzed. Survival and time-to-transplantation were assessed by competing-risks regression models, using death and transplantation as primary and competing events. Crude and adjusted regression models for survival revealed the absence of significant differences between HD and PD cumulative incidence functions (subhazard ratio: 1.09, p = 0.62 and 1.34, p = 0.10, respectively). Differently, crude and adjusted regression models for transplantation revealed a lower time-to-transplantation for PD versus HD patients (subhazard ratio: 2.34, p < 0.01, and 2.57, p < 0.01, respectively). The waiting time for placement in the transplant waiting list was longer in HD than PD patients (330 vs. 224 days, p < 0.01). The extensive use of PD did not lead to any statistically significant difference in mortality. Furthermore, PD was associated with lower time to transplantation. PD may be a viable option for large-scale dialytic treatment in the advanced chronic kidney disease population.
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-innite time scales. At rst we construct Weyl's theory for the single singular multiparameter dynamic equation with distributional potentials and we prove that the forward jump of at ...
By, Kunthel; Qaqish, Bahjat F; Preisser, John S; Perin, Jamie; Zink, Richard C
2014-02-01
This article describes a new software for modeling correlated binary data based on orthogonalized residuals, a recently developed estimating equations approach that includes, as a special case, alternating logistic regressions. The software is flexible with respect to fitting in that the user can choose estimating equations for association models based on alternating logistic regressions or orthogonalized residuals, the latter choice providing a non-diagonal working covariance matrix for second moment parameters providing potentially greater efficiency. Regression diagnostics based on this method are also implemented in the software. The mathematical background is briefly reviewed and the software is applied to medical data sets. Published by Elsevier Ireland Ltd.
About the solvability of matrix polynomial equations
Netzer, Tim; Thom, Andreas
2016-01-01
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.
Feynman integrals and difference equations
International Nuclear Information System (INIS)
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Calculating a Stepwise Ridge Regression.
Morris, John D.
1986-01-01
Although methods for using ordinary least squares regression computer programs to calculate a ridge regression are available, the calculation of a stepwise ridge regression requires a special purpose algorithm and computer program. The correct stepwise ridge regression procedure is given, and a parallel FORTRAN computer program is described.…
Modeling animal movements using stochastic differential equations
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...
Modified Regression Correlation Coefficient for Poisson Regression Model
Kaengthong, Nattacha; Domthong, Uthumporn
2017-09-01
This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
A Study on Regime Type and Globalization in Simultaneous Equation Framework
Directory of Open Access Journals (Sweden)
SUDHANSHU K. MISHRA
2018-01-01
Full Text Available In this study we build a simultaneous equation model in which the measures of different aspects of globalization (attributable to KOF and different aspects of democracy (attributable to EIU are related in seven structural equations. A bi-directional relationship between democracy and globalization is visualized. The model is estimated by the conventional 2-SLS as well as a modified 2-SLS in which Shapley value regression is used at the second stage of 2-SLS. On the basis of our analysis, we document several findings. First, we find that democracy and globalization promote each other and hence there is a bi-directional causality with positive relationships running both ways between democracy and globalization. At a national level, there may be various intermediary conditions that modify the relationship as well as set in motion a complex of positive and/or negative feedbacks to accelerate or retard the pace of globalization and democratization in a country-specific manner. However, when a large number of countries are studied, a clear relationship emerges out. Second, there is a need to estimate the structural coefficients of the model cautiously since the regression equations may be suffering from collinearity among the predictor variables. The Shapley value regression based 2-SLS has performed better than the conventional regression in estimating the structural parameters of the model. Third, the system methods of estimation of the model gives better results than what are obtained by the single equation methods of estimation of structural parameters of the model.
Luo, Chongliang; Liu, Jin; Dey, Dipak K; Chen, Kun
2016-07-01
In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an [Formula: see text] intercross mice study and an alcohol dependence study. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Polynomial regression analysis and significance test of the regression function
International Nuclear Information System (INIS)
Gao Zhengming; Zhao Juan; He Shengping
2012-01-01
In order to analyze the decay heating power of a certain radioactive isotope per kilogram with polynomial regression method, the paper firstly demonstrated the broad usage of polynomial function and deduced its parameters with ordinary least squares estimate. Then significance test method of polynomial regression function is derived considering the similarity between the polynomial regression model and the multivariable linear regression model. Finally, polynomial regression analysis and significance test of the polynomial function are done to the decay heating power of the iso tope per kilogram in accord with the authors' real work. (authors)
SDE based regression for random PDEs
Bayer, Christian
2016-01-06
A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to an approximation of the global solution of the random PDE. We provide an initial error and complexity analysis of the proposed method along with numerical examples illustrating its behaviour.
AIRLINE ACTIVITY FORECASTING BY REGRESSION MODELS
Directory of Open Access Journals (Sweden)
Н. Білак
2012-04-01
Full Text Available Proposed linear and nonlinear regression models, which take into account the equation of trend and seasonality indices for the analysis and restore the volume of passenger traffic over the past period of time and its prediction for future years, as well as the algorithm of formation of these models based on statistical analysis over the years. The desired model is the first step for the synthesis of more complex models, which will enable forecasting of passenger (income level airline with the highest accuracy and time urgency.
Combining Alphas via Bounded Regression
Directory of Open Access Journals (Sweden)
Zura Kakushadze
2015-11-01
Full Text Available We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications, typically, there is insufficient history to compute a sample covariance matrix (SCM for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples.
Linear regression in astronomy. I
Isobe, Takashi; Feigelson, Eric D.; Akritas, Michael G.; Babu, Gutti Jogesh
1990-01-01
Five methods for obtaining linear regression fits to bivariate data with unknown or insignificant measurement errors are discussed: ordinary least-squares (OLS) regression of Y on X, OLS regression of X on Y, the bisector of the two OLS lines, orthogonal regression, and 'reduced major-axis' regression. These methods have been used by various researchers in observational astronomy, most importantly in cosmic distance scale applications. Formulas for calculating the slope and intercept coefficients and their uncertainties are given for all the methods, including a new general form of the OLS variance estimates. The accuracy of the formulas was confirmed using numerical simulations. The applicability of the procedures is discussed with respect to their mathematical properties, the nature of the astronomical data under consideration, and the scientific purpose of the regression. It is found that, for problems needing symmetrical treatment of the variables, the OLS bisector performs significantly better than orthogonal or reduced major-axis regression.
Equations for formally real meadows
Bergstra, J.A.; Bethke, I.; Ponse, A.
2015-01-01
We consider the signatures Σm = (0,1,−,+,⋅,−1) of meadows and (Σm,s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Directory of Open Access Journals (Sweden)
Jaime Araujo Cobuci
2012-09-01
Full Text Available Milk yield test-day records on the first three lactations of 25,500 Holstein cows were used to estimate genetic parameters and predict breeding values for nine measures of persistency and 305-d milk yield in a random regression animal model using two criteria to define the fixed regression. Legendre polynomials of fourth and fifth orders were used to model the fixed and random regressions of lactation curves. The fixed regressions were adjusted for average milk yield on populations (single or subpopulations (multiple formed by cows that calved at the same age and in the same season. Akaike Information (AIC and Bayesian Information (BIC criteria indicated that models with multiple regression lactation curves had the best fit to test-day milk records of first lactations, while models with a single regression curve had the best fit for the second and third lactations. Heritability and genetic correlation estimates between persistency and milk yield differed significantly depending on the lactation order and the measures of persistency used. These parameters did not differ significantly depending on the criteria used for defining the fixed regressions for lactation curves. In general, the heritability estimates were higher for first (0.07 to 0.43, followed by the second (0.08 to 0.21 and third (0.04 to 0.10 lactation. The rank of sires resulting from the processes of genetic evaluation for milk yield or persistency using random regression models differed according to the criteria used for determining the fixed regression of lactation curve.
Conjoined legs: Sirenomelia or caudal regression syndrome?
Das, Sakti Prasad; Ojha, Niranjan; Ganesh, G Shankar; Mohanty, Ram Narayan
2013-01-01
Presence of single umbilical persistent vitelline artery distinguishes sirenomelia from caudal regression syndrome. We report a case of a12-year-old boy who had bilateral umbilical arteries presented with fusion of both legs in the lower one third of leg. Both feet were rudimentary. The right foot had a valgus rocker-bottom deformity. All toes were present but rudimentary. The left foot showed absence of all toes. Physical examination showed left tibia vara. The chest evaluation in sitting re...
Anthropometric predictive equations for percentage body fat in ...
African Journals Online (AJOL)
Predictive regression equations (with r2 = 0.931 and 0.945 respectively) that worked better for Nigerian women compared to other existing equations such as Durnin and Wormersley, Siri, Vogel el al, (1984) for the estimation of body fat were obtained. These equations·could be validly used for mass screening exercise in ...
Biomass equations for major tree species of the Northeast
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...
Linear regression in astronomy. II
Feigelson, Eric D.; Babu, Gutti J.
1992-01-01
A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.
Time-adaptive quantile regression
DEFF Research Database (Denmark)
Møller, Jan Kloppenborg; Nielsen, Henrik Aalborg; Madsen, Henrik
2008-01-01
An algorithm for time-adaptive quantile regression is presented. The algorithm is based on the simplex algorithm, and the linear optimization formulation of the quantile regression problem is given. The observations have been split to allow a direct use of the simplex algorithm. The simplex method...... and an updating procedure are combined into a new algorithm for time-adaptive quantile regression, which generates new solutions on the basis of the old solution, leading to savings in computation time. The suggested algorithm is tested against a static quantile regression model on a data set with wind power...... production, where the models combine splines and quantile regression. The comparison indicates superior performance for the time-adaptive quantile regression in all the performance parameters considered....
Bias-corrected quantile regression estimation of censored regression models
Cizek, Pavel; Sadikoglu, Serhan
2018-01-01
In this paper, an extension of the indirect inference methodology to semiparametric estimation is explored in the context of censored regression. Motivated by weak small-sample performance of the censored regression quantile estimator proposed by Powell (J Econom 32:143–155, 1986a), two- and
Quantile regression theory and applications
Davino, Cristina; Vistocco, Domenico
2013-01-01
A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensivedescription of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and
Vaeth, Michael; Skovlund, Eva
2004-06-15
For a given regression problem it is possible to identify a suitably defined equivalent two-sample problem such that the power or sample size obtained for the two-sample problem also applies to the regression problem. For a standard linear regression model the equivalent two-sample problem is easily identified, but for generalized linear models and for Cox regression models the situation is more complicated. An approximately equivalent two-sample problem may, however, also be identified here. In particular, we show that for logistic regression and Cox regression models the equivalent two-sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged. In a simulation study we examine the validity of this approach to power calculations in logistic regression and Cox regression models. Several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives. For the Cox regression model we consider both constant and non-constant hazard rates. The results show that in general the approach is remarkably accurate even in relatively small samples. Some discrepancies are, however, found in small samples with few events and a highly skewed covariate distribution. Comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors. The method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination. Copyright 2004 John Wiley & Sons, Ltd.
Logistic Regression: Concept and Application
Cokluk, Omay
2010-01-01
The main focus of logistic regression analysis is classification of individuals in different groups. The aim of the present study is to explain basic concepts and processes of binary logistic regression analysis intended to determine the combination of independent variables which best explain the membership in certain groups called dichotomous…
Testing discontinuities in nonparametric regression
Dai, Wenlin
2017-01-19
In nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13 H.-G. Müller and U. Stadtmüller, Discontinuous versus smooth regression, Ann. Stat. 27 (1999), pp. 299–337. doi: 10.1214/aos/1018031100
Illuminance Flow Estimation by Regression
Karlsson, S.M.; Pont, S.C.; Koenderink, J.J.; Zisserman, A.
2010-01-01
We investigate the estimation of illuminance flow using Histograms of Oriented Gradient features (HOGs). In a regression setting, we found for both ridge regression and support vector machines, that the optimal solution shows close resemblance to the gradient based structure tensor (also known as
Difference equations by differential equation methods
Hydon, Peter E
2014-01-01
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
Tumor regression patterns in retinoblastoma
International Nuclear Information System (INIS)
Zafar, S.N.; Siddique, S.N.; Zaheer, N.
2016-01-01
To observe the types of tumor regression after treatment, and identify the common pattern of regression in our patients. Study Design: Descriptive study. Place and Duration of Study: Department of Pediatric Ophthalmology and Strabismus, Al-Shifa Trust Eye Hospital, Rawalpindi, Pakistan, from October 2011 to October 2014. Methodology: Children with unilateral and bilateral retinoblastoma were included in the study. Patients were referred to Pakistan Institute of Medical Sciences, Islamabad, for chemotherapy. After every cycle of chemotherapy, dilated funds examination under anesthesia was performed to record response of the treatment. Regression patterns were recorded on RetCam II. Results: Seventy-four tumors were included in the study. Out of 74 tumors, 3 were ICRB group A tumors, 43 were ICRB group B tumors, 14 tumors belonged to ICRB group C, and remaining 14 were ICRB group D tumors. Type IV regression was seen in 39.1% (n=29) tumors, type II in 29.7% (n=22), type III in 25.6% (n=19), and type I in 5.4% (n=4). All group A tumors (100%) showed type IV regression. Seventeen (39.5%) group B tumors showed type IV regression. In group C, 5 tumors (35.7%) showed type II regression and 5 tumors (35.7%) showed type IV regression. In group D, 6 tumors (42.9%) regressed to type II non-calcified remnants. Conclusion: The response and success of the focal and systemic treatment, as judged by the appearance of different patterns of tumor regression, varies with the ICRB grouping of the tumor. (author)
International Nuclear Information System (INIS)
Sarrach, D.; Strohner, P.
1986-01-01
The Gauss-Newton algorithm has been used to evaluate tracer binding parameters of RIA by nonlinear regression analysis. The calculations were carried out on the K1003 desk computer. Equations for simple binding models and its derivatives are presented. The advantages of nonlinear regression analysis over linear regression are demonstrated
Latent Variable Regression: A Technique for Estimating Interaction and Quadratic Coefficients.
Ping, Robert A., Jr.
1996-01-01
A technique is proposed to estimate regression coefficients for interaction and quadratic latent variables that combines regression analysis with the measurement model portion of structural equation analysis. The proposed technique will provide coefficient estimates for regression models involving existing measures or new measures for which a…
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Regression analysis with categorized regression calibrated exposure: some interesting findings
Directory of Open Access Journals (Sweden)
Hjartåker Anette
2006-07-01
Full Text Available Abstract Background Regression calibration as a method for handling measurement error is becoming increasingly well-known and used in epidemiologic research. However, the standard version of the method is not appropriate for exposure analyzed on a categorical (e.g. quintile scale, an approach commonly used in epidemiologic studies. A tempting solution could then be to use the predicted continuous exposure obtained through the regression calibration method and treat it as an approximation to the true exposure, that is, include the categorized calibrated exposure in the main regression analysis. Methods We use semi-analytical calculations and simulations to evaluate the performance of the proposed approach compared to the naive approach of not correcting for measurement error, in situations where analyses are performed on quintile scale and when incorporating the original scale into the categorical variables, respectively. We also present analyses of real data, containing measures of folate intake and depression, from the Norwegian Women and Cancer study (NOWAC. Results In cases where extra information is available through replicated measurements and not validation data, regression calibration does not maintain important qualities of the true exposure distribution, thus estimates of variance and percentiles can be severely biased. We show that the outlined approach maintains much, in some cases all, of the misclassification found in the observed exposure. For that reason, regression analysis with the corrected variable included on a categorical scale is still biased. In some cases the corrected estimates are analytically equal to those obtained by the naive approach. Regression calibration is however vastly superior to the naive method when applying the medians of each category in the analysis. Conclusion Regression calibration in its most well-known form is not appropriate for measurement error correction when the exposure is analyzed on a
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…
Abstract Expression Grammar Symbolic Regression
Korns, Michael F.
This chapter examines the use of Abstract Expression Grammars to perform the entire Symbolic Regression process without the use of Genetic Programming per se. The techniques explored produce a symbolic regression engine which has absolutely no bloat, which allows total user control of the search space and output formulas, which is faster, and more accurate than the engines produced in our previous papers using Genetic Programming. The genome is an all vector structure with four chromosomes plus additional epigenetic and constraint vectors, allowing total user control of the search space and the final output formulas. A combination of specialized compiler techniques, genetic algorithms, particle swarm, aged layered populations, plus discrete and continuous differential evolution are used to produce an improved symbolic regression sytem. Nine base test cases, from the literature, are used to test the improvement in speed and accuracy. The improved results indicate that these techniques move us a big step closer toward future industrial strength symbolic regression systems.
From Rasch scores to regression
DEFF Research Database (Denmark)
Christensen, Karl Bang
2006-01-01
Rasch models provide a framework for measurement and modelling latent variables. Having measured a latent variable in a population a comparison of groups will often be of interest. For this purpose the use of observed raw scores will often be inadequate because these lack interval scale propertie....... This paper compares two approaches to group comparison: linear regression models using estimated person locations as outcome variables and latent regression models based on the distribution of the score....
Testing Heteroscedasticity in Robust Regression
Czech Academy of Sciences Publication Activity Database
Kalina, Jan
2011-01-01
Roč. 1, č. 4 (2011), s. 25-28 ISSN 2045-3345 Grant - others:GA ČR(CZ) GA402/09/0557 Institutional research plan: CEZ:AV0Z10300504 Keywords : robust regression * heteroscedasticity * regression quantiles * diagnostics Subject RIV: BB - Applied Statistics , Operational Research http://www.researchjournals.co.uk/documents/Vol4/06%20Kalina.pdf
Regression methods for medical research
Tai, Bee Choo
2013-01-01
Regression Methods for Medical Research provides medical researchers with the skills they need to critically read and interpret research using more advanced statistical methods. The statistical requirements of interpreting and publishing in medical journals, together with rapid changes in science and technology, increasingly demands an understanding of more complex and sophisticated analytic procedures.The text explains the application of statistical models to a wide variety of practical medical investigative studies and clinical trials. Regression methods are used to appropriately answer the
Directory of Open Access Journals (Sweden)
Taliha KELEŞ
2016-12-01
Full Text Available Regression analysis is a statistical technique for investigating and modeling the relationship between variables. The purpose of this study was the trivial presentation of the equation for orthogonal regression (OR and the comparison of classical linear regression (CLR and OR techniques with respect to the sum of squared perpendicular distances. For that purpose, the analyses were shown by an example. It was found that the sum of squared perpendicular distances of OR is smaller. Thus, it was seen that OR line has appeared to present a much better fit for the data than CLR line. Depending on those results, the OR is thought to be a regression technique to obtain more accurate results than CLR at simple linear regression studies.
Dimension Reduction Regression in R
Directory of Open Access Journals (Sweden)
Sanford Weisberg
2002-01-01
Full Text Available Regression is the study of the dependence of a response variable y on a collection predictors p collected in x. In dimension reduction regression, we seek to find a few linear combinations β1x,...,βdx, such that all the information about the regression is contained in these linear combinations. If d is very small, perhaps one or two, then the regression problem can be summarized using simple graphics; for example, for d=1, the plot of y versus β1x contains all the regression information. When d=2, a 3D plot contains all the information. Several methods for estimating d and relevant functions of β1,..., βdhave been suggested in the literature. In this paper, we describe an R package for three important dimension reduction methods: sliced inverse regression or sir, sliced average variance estimates, or save, and principal Hessian directions, or phd. The package is very general and flexible, and can be easily extended to include other methods of dimension reduction. It includes tests and estimates of the dimension , estimates of the relevant information including β1,..., βd, and some useful graphical summaries as well.
Nelson, Kirk E.; Ginn, Timothy R.
2011-05-01
A new equation for the collector efficiency (η) of the colloid filtration theory (CFT) is developed via nonlinear regression on the numerical data generated by a large number of Lagrangian simulations conducted in Happel's sphere-in-cell porous media model over a wide range of environmentally relevant conditions. The new equation expands the range of CFT's applicability in the natural subsurface primarily by accommodating departures from power law dependence of η on the Peclet and gravity numbers, a necessary but as of yet unavailable feature for applying CFT to large-scale field transport (e.g., of nanoparticles, radionuclides, or genetically modified organisms) under low groundwater velocity conditions. The new equation also departs from prior equations for colloids in the nanoparticle size range at all fluid velocities. These departures are particularly relevant to subsurface colloid and colloid-facilitated transport where low permeabilities and/or hydraulic gradients lead to low groundwater velocities and/or to nanoparticle fate and transport in porous media in general. We also note the importance of consistency in the conceptualization of particle flux through the single collector model on which most η equations are based for the purpose of attaining a mechanistic understanding of the transport and attachment steps of deposition. A lack of sufficient data for small particles and low velocities warrants further experiments to draw more definitive and comprehensive conclusions regarding the most significant discrepancies between the available equations.
Failure analysis of high strength pipeline with single and multiple corrosions
International Nuclear Information System (INIS)
Chen, Yanfei; Zhang, Hong; Zhang, Juan; Li, Xin; Zhou, Jing
2015-01-01
Highlights: • We study failure of high strength pipelines with single corrosion. • We give regression equations for failure pressure prediction. • We propose assessment procedure for pipelines with multiple corrosions. - Abstract: Corrosion will compromise safety operation of oil and gas pipelines, accurate determination of failure pressure finds importance in residual strength assessment and corrosion allowance design of onshore and offshore pipelines. This paper investigates failure pressure of high strength pipeline with single and multiple corrosions using nonlinear finite element analysis. On the basis of developed regression equations for failure pressure prediction of high strength pipeline with single corrosion, the paper proposes an assessment procedure for predicting failure pressure of high strength pipeline with multiple corrosions. Furthermore, failure pressures predicted by proposed solutions are compared with experimental results and various assessment methods available in literature, where accuracy and versatility are demonstrated
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Pseudodifferential equations over non-Archimedean spaces
Zúñiga-Galindo, W A
2016-01-01
Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...
Particle methods for Boltzmann equation
International Nuclear Information System (INIS)
Hermeline, F.
1985-05-01
This work is aimed at showing how to discretize an equation such as Boltzmann equation in its most general form, by particle methods. Then method is applied to some equations of plasma physics which appear as peculiar cases of Boltzmann equation, such as Vlasov equation, Bhatnager-Gross-Krook equation, Fokker-Planck equation and neutron transport equation [fr
Logistic regression for dichotomized counts.
Preisser, John S; Das, Kalyan; Benecha, Habtamu; Stamm, John W
2016-12-01
Sometimes there is interest in a dichotomized outcome indicating whether a count variable is positive or zero. Under this scenario, the application of ordinary logistic regression may result in efficiency loss, which is quantifiable under an assumed model for the counts. In such situations, a shared-parameter hurdle model is investigated for more efficient estimation of regression parameters relating to overall effects of covariates on the dichotomous outcome, while handling count data with many zeroes. One model part provides a logistic regression containing marginal log odds ratio effects of primary interest, while an ancillary model part describes the mean count of a Poisson or negative binomial process in terms of nuisance regression parameters. Asymptotic efficiency of the logistic model parameter estimators of the two-part models is evaluated with respect to ordinary logistic regression. Simulations are used to assess the properties of the models with respect to power and Type I error, the latter investigated under both misspecified and correctly specified models. The methods are applied to data from a randomized clinical trial of three toothpaste formulations to prevent incident dental caries in a large population of Scottish schoolchildren. © The Author(s) 2014.
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Fay, Temple H.
2002-01-01
We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…
Nonparametric Mixture of Regression Models.
Huang, Mian; Li, Runze; Wang, Shaoli
2013-07-01
Motivated by an analysis of US house price index data, we propose nonparametric finite mixture of regression models. We study the identifiability issue of the proposed models, and develop an estimation procedure by employing kernel regression. We further systematically study the sampling properties of the proposed estimators, and establish their asymptotic normality. A modified EM algorithm is proposed to carry out the estimation procedure. We show that our algorithm preserves the ascent property of the EM algorithm in an asymptotic sense. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed estimation procedure. An empirical analysis of the US house price index data is illustrated for the proposed methodology.
Regression filter for signal resolution
International Nuclear Information System (INIS)
Matthes, W.
1975-01-01
The problem considered is that of resolving a measured pulse height spectrum of a material mixture, e.g. gamma ray spectrum, Raman spectrum, into a weighed sum of the spectra of the individual constituents. The model on which the analytical formulation is based is described. The problem reduces to that of a multiple linear regression. A stepwise linear regression procedure was constructed. The efficiency of this method was then tested by transforming the procedure in a computer programme which was used to unfold test spectra obtained by mixing some spectra, from a library of arbitrary chosen spectra, and adding a noise component. (U.K.)
Logistic regression for circular data
Al-Daffaie, Kadhem; Khan, Shahjahan
2017-05-01
This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations.
Bayesian variable selection in regression
Energy Technology Data Exchange (ETDEWEB)
Mitchell, T.J.; Beauchamp, J.J.
1987-01-01
This paper is concerned with the selection of subsets of ''predictor'' variables in a linear regression model for the prediction of a ''dependent'' variable. We take a Bayesian approach and assign a probability distribution to the dependent variable through a specification of prior distributions for the unknown parameters in the regression model. The appropriate posterior probabilities are derived for each submodel and methods are proposed for evaluating the family of prior distributions. Examples are given that show the application of the Bayesian methodology. 23 refs., 3 figs.
A Comparison of IRT Equating and Beta 4 Equating
Kim, Dong-In; Brennan, Robert; Kolen, Michael
2005-01-01
Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equi-percentile equating property. True score…
Constitutive equations for two-phase flows
International Nuclear Information System (INIS)
Boure, J.A.
1974-12-01
The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr
On logistic regression analysis of dichotomized responses.
Lu, Kaifeng
2017-01-01
We study the properties of treatment effect estimate in terms of odds ratio at the study end point from logistic regression model adjusting for the baseline value when the underlying continuous repeated measurements follow a multivariate normal distribution. Compared with the analysis that does not adjust for the baseline value, the adjusted analysis produces a larger treatment effect as well as a larger standard error. However, the increase in standard error is more than offset by the increase in treatment effect so that the adjusted analysis is more powerful than the unadjusted analysis for detecting the treatment effect. On the other hand, the true adjusted odds ratio implied by the normal distribution of the underlying continuous variable is a function of the baseline value and hence is unlikely to be able to be adequately represented by a single value of adjusted odds ratio from the logistic regression model. In contrast, the risk difference function derived from the logistic regression model provides a reasonable approximation to the true risk difference function implied by the normal distribution of the underlying continuous variable over the range of the baseline distribution. We show that different metrics of treatment effect have similar statistical power when evaluated at the baseline mean. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Leukemia prediction using sparse logistic regression.
Directory of Open Access Journals (Sweden)
Tapio Manninen
Full Text Available We describe a supervised prediction method for diagnosis of acute myeloid leukemia (AML from patient samples based on flow cytometry measurements. We use a data driven approach with machine learning methods to train a computational model that takes in flow cytometry measurements from a single patient and gives a confidence score of the patient being AML-positive. Our solution is based on an [Formula: see text] regularized logistic regression model that aggregates AML test statistics calculated from individual test tubes with different cell populations and fluorescent markers. The model construction is entirely data driven and no prior biological knowledge is used. The described solution scored a 100% classification accuracy in the DREAM6/FlowCAP2 Molecular Classification of Acute Myeloid Leukaemia Challenge against a golden standard consisting of 20 AML-positive and 160 healthy patients. Here we perform a more extensive validation of the prediction model performance and further improve and simplify our original method showing that statistically equal results can be obtained by using simple average marker intensities as features in the logistic regression model. In addition to the logistic regression based model, we also present other classification models and compare their performance quantitatively. The key benefit in our prediction method compared to other solutions with similar performance is that our model only uses a small fraction of the flow cytometry measurements making our solution highly economical.
Image superresolution using support vector regression.
Ni, Karl S; Nguyen, Truong Q
2007-06-01
A thorough investigation of the application of support vector regression (SVR) to the superresolution problem is conducted through various frameworks. Prior to the study, the SVR problem is enhanced by finding the optimal kernel. This is done by formulating the kernel learning problem in SVR form as a convex optimization problem, specifically a semi-definite programming (SDP) problem. An additional constraint is added to reduce the SDP to a quadratically constrained quadratic programming (QCQP) problem. After this optimization, investigation of the relevancy of SVR to superresolution proceeds with the possibility of using a single and general support vector regression for all image content, and the results are impressive for small training sets. This idea is improved upon by observing structural properties in the discrete cosine transform (DCT) domain to aid in learning the regression. Further improvement involves a combination of classification and SVR-based techniques, extending works in resolution synthesis. This method, termed kernel resolution synthesis, uses specific regressors for isolated image content to describe the domain through a partitioned look of the vector space, thereby yielding good results.
Survival analysis II: Cox regression
Stel, Vianda S.; Dekker, Friedo W.; Tripepi, Giovanni; Zoccali, Carmine; Jager, Kitty J.
2011-01-01
In contrast to the Kaplan-Meier method, Cox proportional hazards regression can provide an effect estimate by quantifying the difference in survival between patient groups and can adjust for confounding effects of other variables. The purpose of this article is to explain the basic concepts of the
Regression of lumbar disk herniation
Directory of Open Access Journals (Sweden)
G. Yu Evzikov
2015-01-01
Full Text Available Compression of the spinal nerve root, giving rise to pain and sensory and motor disorders in the area of its innervation is the most vivid manifestation of herniated intervertebral disk. Different treatment modalities, including neurosurgery, for evolving these conditions are discussed. There has been recent evidence that spontaneous regression of disk herniation can regress. The paper describes a female patient with large lateralized disc extrusion that has caused compression of the nerve root S1, leading to obvious myotonic and radicular syndrome. Magnetic resonance imaging has shown that the clinical manifestations of discogenic radiculopathy, as well myotonic syndrome and morphological changes completely regressed 8 months later. The likely mechanism is inflammation-induced resorption of a large herniated disk fragment, which agrees with the data available in the literature. A decision to perform neurosurgery for which the patient had indications was made during her first consultation. After regression of discogenic radiculopathy, there was only moderate pain caused by musculoskeletal diseases (facet syndrome, piriformis syndrome that were successfully eliminated by minimally invasive techniques.
Ridge Regression for Interactive Models.
Tate, Richard L.
1988-01-01
An exploratory study of the value of ridge regression for interactive models is reported. Assuming that the linear terms in a simple interactive model are centered to eliminate non-essential multicollinearity, a variety of common models, representing both ordinal and disordinal interactions, are shown to have "orientations" that are…
Regression Models for Repairable Systems
Czech Academy of Sciences Publication Activity Database
Novák, Petr
2015-01-01
Roč. 17, č. 4 (2015), s. 963-972 ISSN 1387-5841 Institutional support: RVO:67985556 Keywords : Reliability analysis * Repair models * Regression Subject RIV: BB - Applied Statistics , Operational Research Impact factor: 0.782, year: 2015 http://library.utia.cas.cz/separaty/2015/SI/novak-0450902.pdf
Cactus: An Introduction to Regression
Hyde, Hartley
2008-01-01
When the author first used "VisiCalc," the author thought it a very useful tool when he had the formulas. But how could he design a spreadsheet if there was no known formula for the quantities he was trying to predict? A few months later, the author relates he learned to use multiple linear regression software and suddenly it all clicked into…
National Research Council Canada - National Science Library
Bielecki, John
2003-01-01
.... Previous research has demonstrated the use of a two-step logistic and multiple regression methodology to predicting cost growth produces desirable results versus traditional single-step regression...
Multiple imputation with multivariate imputation by chained equation (MICE) package.
Zhang, Zhongheng
2016-01-01
Multiple imputation (MI) is an advanced technique for handing missing values. It is superior to single imputation in that it takes into account uncertainty in missing value imputation. However, MI is underutilized in medical literature due to lack of familiarity and computational challenges. The article provides a step-by-step approach to perform MI by using R multivariate imputation by chained equation (MICE) package. The procedure firstly imputed m sets of complete dataset by calling mice() function. Then statistical analysis such as univariate analysis and regression model can be performed within each dataset by calling with() function. This function sets the environment for statistical analysis. Lastly, the results obtained from each analysis are combined by using pool() function.
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Producing The New Regressive Left
DEFF Research Database (Denmark)
Crone, Christine
This thesis is the first comprehensive research work conducted on the Beirut based TV station, an important representative of the post-2011 generation of Arab satellite news media. The launch of al-Mayadeen in June 2012 was closely linked to the political developments across the Arab world...... members, this thesis investigates a growing political trend and ideological discourse in the Arab world that I have called The New Regressive Left. On the premise that a media outlet can function as a forum for ideology production, the thesis argues that an analysis of this material can help to trace...... the contexture of The New Regressive Left. If the first part of the thesis lays out the theoretical approach and draws the contextual framework, through an exploration of the surrounding Arab media-and ideoscapes, the second part is an analytical investigation of the discourse that permeates the programmes aired...
AUTISTIC EPILEPTIFORM REGRESSION (A REVIEW
Directory of Open Access Journals (Sweden)
L. Yu. Glukhova
2012-01-01
Full Text Available The author represents the review of current scientific literature devoted to autistic epileptiform regression — the special form of autistic disorder, characterized by development of severe communicative disorders in children as a result of continuous prolonged epileptiform activity on EEG. This condition has been described by R.F. Tuchman and I. Rapin in 1997. The author describes the aspects of pathogenesis, clinical pictures and diagnostics of this disorder, including the peculiar anomalies on EEG (benign epileptiform patterns of childhood, with a high index of epileptiform activity, especially in the sleep. The especial attention is given to approaches to the treatment of autistic epileptiform regression. Efficacy of valproates, corticosteroid hormones and antiepileptic drugs of other groups is considered.
Polynomial Regressions and Nonsense Inference
Directory of Open Access Journals (Sweden)
Daniel Ventosa-Santaulària
2013-11-01
Full Text Available Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis and psychology, just to mention a few examples. In many cases, the data employed to estimate such specifications are time series that may exhibit stochastic nonstationary behavior. We extend Phillips’ results (Phillips, P. Understanding spurious regressions in econometrics. J. Econom. 1986, 33, 311–340. by proving that an inference drawn from polynomial specifications, under stochastic nonstationarity, is misleading unless the variables cointegrate. We use a generalized polynomial specification as a vehicle to study its asymptotic and finite-sample properties. Our results, therefore, lead to a call to be cautious whenever practitioners estimate polynomial regressions.
Spontaneous regression of colon cancer.
Kihara, Kyoichi; Fujita, Shin; Ohshiro, Taihei; Yamamoto, Seiichiro; Sekine, Shigeki
2015-01-01
A case of spontaneous regression of transverse colon cancer is reported. A 64-year-old man was diagnosed as having cancer of the transverse colon at a local hospital. Initial and second colonoscopy examinations revealed a typical cancer of the transverse colon, which was diagnosed as moderately differentiated adenocarcinoma. The patient underwent right hemicolectomy 6 weeks after the initial colonoscopy. The resected specimen showed only a scar at the tumor site, and no cancerous tissue was proven histologically. The patient is alive with no evidence of recurrence 1 year after surgery. Although an antitumor immune response is the most likely explanation, the exact nature of the phenomenon was unclear. We describe this rare case and review the literature pertaining to spontaneous regression of colorectal cancer. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Directional quantile regression in R
Czech Academy of Sciences Publication Activity Database
Boček, Pavel; Šiman, Miroslav
2017-01-01
Roč. 53, č. 3 (2017), s. 480-492 ISSN 0023-5954 R&D Projects: GA ČR GA14-07234S Institutional support: RVO:67985556 Keywords : multivariate quantile * regression quantile * halfspace depth * depth contour Subject RIV: BD - Theory of Information OBOR OECD: Applied mathematics Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/SI/bocek-0476587.pdf
Gaussian Process Regression Model in Spatial Logistic Regression
Sofro, A.; Oktaviarina, A.
2018-01-01
Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Updated generalized biomass equations for North American tree species
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-...
Regression analysis of censored data using pseudo-observations
DEFF Research Database (Denmark)
Parner, Erik T.; Andersen, Per Kragh
2010-01-01
We draw upon a series of articles in which a method based on pseu- dovalues is proposed for direct regression modeling of the survival function, the restricted mean, and the cumulative incidence function in competing risks with right-censored data. The models, once the pseudovalues have been...... computed, can be fit using standard generalized estimating equation software. Here we present Stata procedures for computing these pseudo-observations. An example from a bone marrow transplantation study is used to illustrate the method....
Application of regression analysis to creep of space shuttle materials
International Nuclear Information System (INIS)
Rummler, D.R.
1975-01-01
Metallic heat shields for Space Shuttle thermal protection systems must operate for many flight cycles at high temperatures in low-pressure air and use thin-gage (less than or equal to 0.65 mm) sheet. Available creep data for thin sheet under those conditions are inadequate. To assess the effects of oxygen partial pressure and sheet thickness on creep behavior and to develop constitutive creep equations for small sets of data, regression techniques are applied and discussed
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
The 'golden' algebraic equations
International Nuclear Information System (INIS)
Stakhov, A.; Rozin, B.
2006-01-01
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Segmented Regression Based on Cut-off Polynomials
Directory of Open Access Journals (Sweden)
Miloš Kaňka
2016-06-01
Full Text Available In Statistika: Statistics and Economy Journal No. 4/2015 (pp. 39–58, author’s paper Segmented Regression Based on B-splines with Solved Examples was published. Use of B-spline basis functions has many advantages, the most important being a special form of matrix of system of normal equations suitable for quick solution of this system. The subject of this paper is to explain how that segmented regression can be mathematically developer in other way, which doesn’t require the knowledge of relatively complicated theory of B-spline basis functions, but is based on simpler apparatus of cut-off polynomials. The author considers a detailed calculation of matrix of system of normal equations elements and elaboration of so called polygonal method, as his contribution to issues of segmented regression. This method can be used to automatically obtain required values of nodal points. Author pays major attention to computing elements of matrix of systém of normal equations, which he also developed as computer program called TRIO.
Language regression in children with Autism Spectrum Disorders.
Kumar, Suman; Karmakar, Probir; Mohanan, Akhil
2014-02-01
Regression in autism applies to the phenomenon of apparently normal early development followed by the loss of previously acquired skills and manifestation of symptoms of autism. Estimates of the frequency of regression in autism range from 10% to 50%. Although there are tools available to evaluate and diagnose Autism Spectrum Disorders, however, there is no published tool available in Indian context to identify the children with ASD at an early age. The study was aimed to describe the differences in language regression between children with ASD and typically developing children and also to determine the age of regression. Regression screening tool, a questionnaire was developed based on Regression Supplement Form (Goldberg et al., 2003). The skills were validated by five Clinical Psychologists. It comprised of 16 skills which included domains like, 'spoken language and non verbal communication', 'social interest and responsiveness' and 'play and imagination'. This retrospective study was conducted on a single group. The participants consisted of parents of 30 children with ASD (22 males and 8 females). The findings revealed a significant regression in children with ASD. The mean regression age is 20.19 months (SD-5.2). The regression profile of the children with ASD revealed regression of language skills occurred at 19.16 months followed by non language skills at 20.5 months. Based on the findings it can be stated that inclusion of regression screening tool will offer clinicians a convenient tool to examine the phenomena of regression in children with ASD and identify them as early as 21 months of age for early intervention. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
On Weighted Support Vector Regression
DEFF Research Database (Denmark)
Han, Xixuan; Clemmensen, Line Katrine Harder
2014-01-01
We propose a new type of weighted support vector regression (SVR), motivated by modeling local dependencies in time and space in prediction of house prices. The classic weights of the weighted SVR are added to the slack variables in the objective function (OF‐weights). This procedure directly...... the differences and similarities of the two types of weights by demonstrating the connection between the Least Absolute Shrinkage and Selection Operator (LASSO) and the SVR. We show that an SVR problem can be transformed to a LASSO problem plus a linear constraint and a box constraint. We demonstrate...
Martin, Roy; Sawrie, Stephen; Gilliam, Frank; Mackey, Melissa; Faught, Edward; Knowlton, Robert; Kuzniekcy, Ruben
2002-12-01
Reliable change indices (RCIs) and standardized regression-based (SRB) change scores norms were established for the recently revised Wechsler Adult Intelligence Scale-III (WAIS-III) and Wechsler Memory Scale-III (WMS-III) in patients with complex partial seizures. Establishment of such standardized change scores can be useful in determining the effects of epilepsy surgery on cognitive functioning independent of test-retest artifacts including practice effects. Forty-two nonoperated-on adult patients with complex partial seizures (primarily of temporal lobe onset) were administered the WMS-III and WAIS-III on two occasions (mean 7-month interval). All patients were receiving stable antiepileptic drug (AED) treatment at both testings. RCI and SRB change scores were calculated. Confidence interval cutoff scores (90% and 80%) and standardized regression equations were calculated for each of the WAIS-III and WMS-III Primary Indices and individual subtests. Age, gender, education, test-retest interval, preoperative test performance, seizure onset, and seizure duration were predictor variables for the SRB equations. Test-retest reliabilities for the WAIS-III and WMS-III Primary Indices were within acceptable ranges, although considerable individual subtest variability was found. Preoperative performance was the single largest contributor to each of the predictive regression equations. Age, gender, education, seizure onset, and seizure duration contributed modest variance to several of the regression equations. We calculated both RCI and SRB change score indices for the recently revised Wechsler instruments. These formulas help control for test-retest methodologic artifacts and provide a standardized method with which to examine both individual and group level cognitive change after epilepsy surgery.
How a dependent's variable non-randomness affects taper equation ...
African Journals Online (AJOL)
In order to apply the least squares method in regression analysis, the values of the dependent variable Y should be random. In an example of regression analysis linear and nonlinear taper equations, which estimate the diameter of the tree dhi at any height of the tree hi, were compared. For each tree the diameter at the ...
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.
fractional differential equations
Indian Academy of Sciences (India)
We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Indian Academy of Sciences (India)
role in converting the Fokas equation into Hirota's bilinear form. Keywords. Bilinearization; multisoliton solution; Fokas equation; Hirota's bilinear method. PACS Nos 05.45.Yv; 04.20.Jb; 02.30.Jr. 1. Introduction. As pointed out by Drazin and Johnson [1], it is not easy to give a comprehensive and precise definition of a soliton.
M. Hazewinkel (Michiel)
1995-01-01
textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an
Elliptic Quadratic Operator Equations
Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor
2017-01-01
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...
Partial differential equations
Indian Academy of Sciences (India)
been a regular stream of high quality work done in these areas. Talking of elliptic partial differen- tial equations, important contributions have been made in the ...... [6] Evans L C 1992 Periodic homogenisation of certain fully nonlinear partial differential equations; Proc. Roy. Soc. Edinburgh Sect. A 120 No. 3–4, 245–265.
Energy Technology Data Exchange (ETDEWEB)
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
International Nuclear Information System (INIS)
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Conjoined legs: Sirenomelia or caudal regression syndrome?
Directory of Open Access Journals (Sweden)
Sakti Prasad Das
2013-01-01
Full Text Available Presence of single umbilical persistent vitelline artery distinguishes sirenomelia from caudal regression syndrome. We report a case of a12-year-old boy who had bilateral umbilical arteries presented with fusion of both legs in the lower one third of leg. Both feet were rudimentary. The right foot had a valgus rocker-bottom deformity. All toes were present but rudimentary. The left foot showed absence of all toes. Physical examination showed left tibia vara. The chest evaluation in sitting revealed pigeon chest and elevated right shoulder. Posterior examination of the trunk showed thoracic scoliosis with convexity to right. The patient was operated and at 1 year followup the boy had two separate legs with a good aesthetic and functional results.
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Robust mislabel logistic regression without modeling mislabel probabilities.
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.
Establishment of regression dependences. Linear and nonlinear dependences
International Nuclear Information System (INIS)
Onishchenko, A.M.
1994-01-01
The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab
Regression calibration with more surrogates than mismeasured variables
Kipnis, Victor
2012-06-29
In a recent paper (Weller EA, Milton DK, Eisen EA, Spiegelman D. Regression calibration for logistic regression with multiple surrogates for one exposure. Journal of Statistical Planning and Inference 2007; 137: 449-461), the authors discussed fitting logistic regression models when a scalar main explanatory variable is measured with error by several surrogates, that is, a situation with more surrogates than variables measured with error. They compared two methods of adjusting for measurement error using a regression calibration approximate model as if it were exact. One is the standard regression calibration approach consisting of substituting an estimated conditional expectation of the true covariate given observed data in the logistic regression. The other is a novel two-stage approach when the logistic regression is fitted to multiple surrogates, and then a linear combination of estimated slopes is formed as the estimate of interest. Applying estimated asymptotic variances for both methods in a single data set with some sensitivity analysis, the authors asserted superiority of their two-stage approach. We investigate this claim in some detail. A troubling aspect of the proposed two-stage method is that, unlike standard regression calibration and a natural form of maximum likelihood, the resulting estimates are not invariant to reparameterization of nuisance parameters in the model. We show, however, that, under the regression calibration approximation, the two-stage method is asymptotically equivalent to a maximum likelihood formulation, and is therefore in theory superior to standard regression calibration. However, our extensive finite-sample simulations in the practically important parameter space where the regression calibration model provides a good approximation failed to uncover such superiority of the two-stage method. We also discuss extensions to different data structures.
Isotonic Regression under Lipschitz Constraint
Wilbur, W.J.
2018-01-01
The pool adjacent violators (PAV) algorithm is an efficient technique for the class of isotonic regression problems with complete ordering. The algorithm yields a stepwise isotonic estimate which approximates the function and assigns maximum likelihood to the data. However, if one has reasons to believe that the data were generated by a continuous function, a smoother estimate may provide a better approximation to that function. In this paper, we consider the formulation which assumes that the data were generated by a continuous monotonic function obeying the Lipschitz condition. We propose a new algorithm, the Lipschitz pool adjacent violators (LPAV) algorithm, which approximates that function; we prove the convergence of the algorithm and examine its complexity. PMID:29456266
Prediction, Regression and Critical Realism
DEFF Research Database (Denmark)
Næss, Petter
2004-01-01
This paper considers the possibility of prediction in land use planning, and the use of statistical research methods in analyses of relationships between urban form and travel behaviour. Influential writers within the tradition of critical realism reject the possibility of predicting social...... phenomena. This position is fundamentally problematic to public planning. Without at least some ability to predict the likely consequences of different proposals, the justification for public sector intervention into market mechanisms will be frail. Statistical methods like regression analyses are commonly...... seen as necessary in order to identify aggregate level effects of policy measures, but are questioned by many advocates of critical realist ontology. Using research into the relationship between urban structure and travel as an example, the paper discusses relevant research methods and the kinds...
Lumbar herniated disc: spontaneous regression.
Altun, Idiris; Yüksel, Kasım Zafer
2017-01-01
Low back pain is a frequent condition that results in substantial disability and causes admission of patients to neurosurgery clinics. To evaluate and present the therapeutic outcomes in lumbar disc hernia (LDH) patients treated by means of a conservative approach, consisting of bed rest and medical therapy. This retrospective cohort was carried out in the neurosurgery departments of hospitals in Kahramanmaraş city and 23 patients diagnosed with LDH at the levels of L3-L4, L4-L5 or L5-S1 were enrolled. The average age was 38.4 ± 8.0 and the chief complaint was low back pain and sciatica radiating to one or both lower extremities. Conservative treatment was administered. Neurological examination findings, durations of treatment and intervals until symptomatic recovery were recorded. Laségue tests and neurosensory examination revealed that mild neurological deficits existed in 16 of our patients. Previously, 5 patients had received physiotherapy and 7 patients had been on medical treatment. The number of patients with LDH at the level of L3-L4, L4-L5, and L5-S1 were 1, 13, and 9, respectively. All patients reported that they had benefit from medical treatment and bed rest, and radiologic improvement was observed simultaneously on MRI scans. The average duration until symptomatic recovery and/or regression of LDH symptoms was 13.6 ± 5.4 months (range: 5-22). It should be kept in mind that lumbar disc hernias could regress with medical treatment and rest without surgery, and there should be an awareness that these patients could recover radiologically. This condition must be taken into account during decision making for surgical intervention in LDH patients devoid of indications for emergent surgery.
Inferring gene regression networks with model trees
Directory of Open Access Journals (Sweden)
Aguilar-Ruiz Jesus S
2010-10-01
Full Text Available Abstract Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear
Ordinary differential equations
Ince, Edward Lindsay
1956-01-01
The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a diffe
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Bayesian logistic regression in detection of gene–steroid interaction ...
Indian Academy of Sciences (India)
cancer. Bayesian logistic regression in PROC GENMOD in SAS statistical software, ver. 9.4 was used to detect gene– steroid interactions influencing cancer. Single marker analysis using PLINK identified 12 SNPs associated with cancer. (P < 0.05); especially, SNP rs6532496 revealed the strongest association with cancer ...
Feature Selection for Ridge Regression with Provable Guarantees.
Paul, Saurabh; Drineas, Petros
2016-04-01
We introduce single-set spectral sparsification as a deterministic sampling-based feature selection technique for regularized least-squares classification, which is the classification analog to ridge regression. The method is unsupervised and gives worst-case guarantees of the generalization power of the classification function after feature selection with respect to the classification function obtained using all features. We also introduce leverage-score sampling as an unsupervised randomized feature selection method for ridge regression. We provide risk bounds for both single-set spectral sparsification and leverage-score sampling on ridge regression in the fixed design setting and show that the risk in the sampled space is comparable to the risk in the full-feature space. We perform experiments on synthetic and real-world data sets; a subset of TechTC-300 data sets, to support our theory. Experimental results indicate that the proposed methods perform better than the existing feature selection methods.
Partial differential equations mathematical techniques for engineers
Epstein, Marcelo
2017-01-01
This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate s...
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
–. (4)) by applying the exp-function method. The computer symbolic systems such as. Maple and Mathematica allow us to perform complicated and tedious calculations. 2. Solutions of (N + 1)-dimensional generalized Boussinesq equation.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Delay-differential equations and the Painlevé transcendents
Grammaticos, B.; Ramani, A.; Moreira, I. C.
1993-07-01
We apply the recently proposed integrability criterion for differential-difference systems (that blends the classical Painlevé analysis with singularity confinement for discrete systems) to a class of first-order differential-delay equations. Our analysis singles out the family of bi-Riccati equations, as integrability candidates. Among these equations that pass the test some are integrable in a straightforward way (usually by reduction to a standard Riccati equation for some transformed variable) while the remaining ones define new hysterodifferential forms of the Painlevé transcendental equations.
Complex nonlinear Lagrangian for the Hasegawa-Mima equation
International Nuclear Information System (INIS)
Dewar, R.L.; Abdullatif, R.F.; Sangeetha, G.G.
2005-01-01
The Hasegawa-Mima equation is the simplest nonlinear single-field model equation that captures the essence of drift wave dynamics. Like the Schroedinger equation it is first order in time. However its coefficients are real, so if the potential φ is initially real it remains real. However, by embedding φ in the space of complex functions a simple Lagrangian is found from which the Hasegawa-Mima equation may be derived from Hamilton's Principle. This Lagrangian is used to derive an action conservation equation which agrees with that of Biskamp and Horton. (author)
General solution of the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Dolan, Louise [Department of Physics, University of North Carolina,Chapel Hill, NC 27599 (United States); Goddard, Peter [School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States)
2016-10-26
The scattering equations, originally introduced by Fairlie and Roberts in 1972 and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension, have been reformulated in polynomial form. The scattering equations for N particles are equivalent to N−3 polynomial equations h{sub m}=0, 1≤m≤N−3, in N−3 variables, where h{sub m} has degree m and is linear in the individual variables. Facilitated by this linearity, elimination theory is used to construct a single variable polynomial equation, Δ{sub N}=0, of degree (N−3)! determining the solutions. Δ{sub N} is the sparse resultant of the system of polynomial scattering equations and it can be identified as the hyperdeterminant of a multidimensional matrix of border format within the terminology of Gel’fand, Kapranov and Zelevinsky. Macaulay’s Unmixedness Theorem is used to show that the polynomials of the scattering equations constitute a regular sequence, enabling the Hilbert series of the variety determined by the scattering equations to be calculated, independently showing that they have (N−3)! solutions.
Ordinary differential equations.
Lebl, Jiří
2013-01-01
In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.
Indian Academy of Sciences (India)
continuous medium is μgrav ≡ μ + 3p/c2. Particular versions of this equation had been obtained earlier, at centers of symmetry by Tolman and Synge (see Raychaud- .... (8) by l ˙l and integrate to find. 3( ˙l)2 − κμl2 − Λl2 = const. (10). This is just the Friedmann equation which governs the time evolution of FLRW universe ...
Insulin resistance: regression and clustering.
Yoon, Sangho; Assimes, Themistocles L; Quertermous, Thomas; Hsiao, Chin-Fu; Chuang, Lee-Ming; Hwu, Chii-Min; Rajaratnam, Bala; Olshen, Richard A
2014-01-01
In this paper we try to define insulin resistance (IR) precisely for a group of Chinese women. Our definition deliberately does not depend upon body mass index (BMI) or age, although in other studies, with particular random effects models quite different from models used here, BMI accounts for a large part of the variability in IR. We accomplish our goal through application of Gauss mixture vector quantization (GMVQ), a technique for clustering that was developed for application to lossy data compression. Defining data come from measurements that play major roles in medical practice. A precise statement of what the data are is in Section 1. Their family structures are described in detail. They concern levels of lipids and the results of an oral glucose tolerance test (OGTT). We apply GMVQ to residuals obtained from regressions of outcomes of an OGTT and lipids on functions of age and BMI that are inferred from the data. A bootstrap procedure developed for our family data supplemented by insights from other approaches leads us to believe that two clusters are appropriate for defining IR precisely. One cluster consists of women who are IR, and the other of women who seem not to be. Genes and other features are used to predict cluster membership. We argue that prediction with "main effects" is not satisfactory, but prediction that includes interactions may be.
Insulin resistance: regression and clustering.
Directory of Open Access Journals (Sweden)
Sangho Yoon
Full Text Available In this paper we try to define insulin resistance (IR precisely for a group of Chinese women. Our definition deliberately does not depend upon body mass index (BMI or age, although in other studies, with particular random effects models quite different from models used here, BMI accounts for a large part of the variability in IR. We accomplish our goal through application of Gauss mixture vector quantization (GMVQ, a technique for clustering that was developed for application to lossy data compression. Defining data come from measurements that play major roles in medical practice. A precise statement of what the data are is in Section 1. Their family structures are described in detail. They concern levels of lipids and the results of an oral glucose tolerance test (OGTT. We apply GMVQ to residuals obtained from regressions of outcomes of an OGTT and lipids on functions of age and BMI that are inferred from the data. A bootstrap procedure developed for our family data supplemented by insights from other approaches leads us to believe that two clusters are appropriate for defining IR precisely. One cluster consists of women who are IR, and the other of women who seem not to be. Genes and other features are used to predict cluster membership. We argue that prediction with "main effects" is not satisfactory, but prediction that includes interactions may be.
Regularized Label Relaxation Linear Regression.
Fang, Xiaozhao; Xu, Yong; Li, Xuelong; Lai, Zhihui; Wong, Wai Keung; Fang, Bingwu
2018-04-01
Linear regression (LR) and some of its variants have been widely used for classification problems. Most of these methods assume that during the learning phase, the training samples can be exactly transformed into a strict binary label matrix, which has too little freedom to fit the labels adequately. To address this problem, in this paper, we propose a novel regularized label relaxation LR method, which has the following notable characteristics. First, the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into LR, which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible. Second, the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting. The class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed. Two different algorithms, which are, respectively, based on -norm and -norm loss functions are devised. These two algorithms have compact closed-form solutions in each iteration so that they are easily implemented. Extensive experiments show that these two algorithms outperform the state-of-the-art algorithms in terms of the classification accuracy and running time.
Equations of radiation hydrodynamics
International Nuclear Information System (INIS)
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
Analysis of Sting Balance Calibration Data Using Optimized Regression Models
Ulbrich, N.; Bader, Jon B.
2010-01-01
Calibration data of a wind tunnel sting balance was processed using a candidate math model search algorithm that recommends an optimized regression model for the data analysis. During the calibration the normal force and the moment at the balance moment center were selected as independent calibration variables. The sting balance itself had two moment gages. Therefore, after analyzing the connection between calibration loads and gage outputs, it was decided to choose the difference and the sum of the gage outputs as the two responses that best describe the behavior of the balance. The math model search algorithm was applied to these two responses. An optimized regression model was obtained for each response. Classical strain gage balance load transformations and the equations of the deflection of a cantilever beam under load are used to show that the search algorithm s two optimized regression models are supported by a theoretical analysis of the relationship between the applied calibration loads and the measured gage outputs. The analysis of the sting balance calibration data set is a rare example of a situation when terms of a regression model of a balance can directly be derived from first principles of physics. In addition, it is interesting to note that the search algorithm recommended the correct regression model term combinations using only a set of statistical quality metrics that were applied to the experimental data during the algorithm s term selection process.
Use of probabilistic weights to enhance linear regression myoelectric control.
Smith, Lauren H; Kuiken, Todd A; Hargrove, Levi J
2015-12-01
Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts' law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p linear regression control. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.
Biostatistics Series Module 6: Correlation and Linear Regression.
Hazra, Avijit; Gogtay, Nithya
2016-01-01
Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this as a correlation coefficient. If both variables x and y are normally distributed, we calculate Pearson's correlation coefficient ( r ). If normality assumption is not met for one or both variables in a correlation analysis, a rank correlation coefficient, such as Spearman's rho (ρ) may be calculated. A hypothesis test of correlation tests whether the linear relationship between the two variables holds in the underlying population, in which case it returns a P linear relation with the independent variable x and is called the coefficient of determination. Linear regression is a technique that attempts to link two correlated variables x and y in the form of a mathematical equation ( y = a + bx ), such that given the value of one variable the other may be predicted. In general, the method of least squares is applied to obtain the equation of the regression line. Correlation and linear regression analysis are based on certain assumptions pertaining to the data sets. If these assumptions are not met, misleading conclusions may be drawn. The first assumption is that of linear relationship between the two variables. A scatter plot is essential before embarking on any correlation-regression analysis to show that this is indeed the case. Outliers or clustering within data sets can distort the correlation coefficient value. Finally, it is vital to remember that though strong correlation can be a pointer toward causation, the two are not synonymous.
Enders, Craig K; Mistler, Stephen A; Keller, Brian T
2016-06-01
Although missing data methods have advanced in recent years, methodologists have devoted less attention to multilevel data structures where observations at level-1 are nested within higher-order organizational units at level-2 (e.g., individuals within neighborhoods; repeated measures nested within individuals; students nested within classrooms). Joint modeling and chained equations imputation are the principal imputation frameworks for single-level data, and both have multilevel counterparts. These approaches differ algorithmically and in their functionality; both are appropriate for simple random intercept analyses with normally distributed data, but they differ beyond that. The purpose of this paper is to describe multilevel imputation strategies and evaluate their performance in a variety of common analysis models. Using multiple imputation theory and computer simulations, we derive 4 major conclusions: (a) joint modeling and chained equations imputation are appropriate for random intercept analyses; (b) the joint model is superior for analyses that posit different within- and between-cluster associations (e.g., a multilevel regression model that includes a level-1 predictor and its cluster means, a multilevel structural equation model with different path values at level-1 and level-2); (c) chained equations imputation provides a dramatic improvement over joint modeling in random slope analyses; and (d) a latent variable formulation for categorical variables is quite effective. We use a real data analysis to demonstrate multilevel imputation, and we suggest a number of avenues for future research. (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Prediction equations for spirometry in four- to six-year-old children.
França, Danielle Corrêa; Camargos, Paulo Augusto Moreira; Jones, Marcus Herbert; Martins, Jocimar Avelar; Vieira, Bruna da Silva Pinto Pinheiro; Colosimo, Enrico Antônio; de Mendonça, Karla Morganna Pereira Pinto; Borja, Raíssa de Oliveira; Britto, Raquel Rodrigues; Parreira, Verônica Franco
2016-01-01
To generate prediction equations for spirometry in 4- to 6-year-old children. Forced vital capacity, forced expiratory volume in 0.5s, forced expiratory volume in one second, peak expiratory flow, and forced expiratory flow at 25-75% of the forced vital capacity were assessed in 195 healthy children residing in the town of Sete Lagoas, state of Minas Gerais, Southeastern Brazil. The least mean squares method was used to derive the prediction equations. The level of significance was established as p<0.05. Overall, 85% of the children succeeded in performing the spirometric maneuvers. In the prediction equation, height was the single predictor of the spirometric variables as follows: forced vital capacity=exponential [(-2.255)+(0.022×height)], forced expiratory volume in 0.5s=exponential [(-2.288)+(0.019×height)], forced expiratory volume in one second=exponential [(-2.767)+(0.026×height)], peak expiratory flow=exponential [(-2.908)+(0.019×height)], and forced expiratory flow at 25-75% of the forced vital capacity=exponential [(-1.404)+(0.016×height)]. Neither age nor weight influenced the regression equations. No significant differences in the predicted values for boys and girls were observed. The predicted values obtained in the present study are comparable to those reported for preschoolers from both Brazil and other countries. Copyright © 2016 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.
DRREP: deep ridge regressed epitope predictor.
Sher, Gene; Zhi, Degui; Zhang, Shaojie
2017-10-03
The ability to predict epitopes plays an enormous role in vaccine development in terms of our ability to zero in on where to do a more thorough in-vivo analysis of the protein in question. Though for the past decade there have been numerous advancements and improvements in epitope prediction, on average the best benchmark prediction accuracies are still only around 60%. New machine learning algorithms have arisen within the domain of deep learning, text mining, and convolutional networks. This paper presents a novel analytically trained and string kernel using deep neural network, which is tailored for continuous epitope prediction, called: Deep Ridge Regressed Epitope Predictor (DRREP). DRREP was tested on long protein sequences from the following datasets: SARS, Pellequer, HIV, AntiJen, and SEQ194. DRREP was compared to numerous state of the art epitope predictors, including the most recently published predictors called LBtope and DMNLBE. Using area under ROC curve (AUC), DRREP achieved a performance improvement over the best performing predictors on SARS (13.7%), HIV (8.9%), Pellequer (1.5%), and SEQ194 (3.1%), with its performance being matched only on the AntiJen dataset, by the LBtope predictor, where both DRREP and LBtope achieved an AUC of 0.702. DRREP is an analytically trained deep neural network, thus capable of learning in a single step through regression. By combining the features of deep learning, string kernels, and convolutional networks, the system is able to perform residue-by-residue prediction of continues epitopes with higher accuracy than the current state of the art predictors.
The Bernoulli-Poiseuille Equation.
Badeer, Henry S.; Synolakis, Costas E.
1989-01-01
Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Jacobi equations as Lagrange equations of the deformed Lagrangian
International Nuclear Information System (INIS)
Casciaro, B.
1995-03-01
We study higher-order variational derivatives of a generic Lagrangian L 0 = L 0 (t,q,q). We introduce two new Lagrangians, L 1 and L 2 , associated to the first and second-order deformations of the original Lagrangian L 0 . In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L 1 . We can furthermore introduce an associated Hamiltonian H 1 = H 1 (t,q,q radical,η,η radical) with η equivalent to δq. If L 0 is independent of time then H 1 is a conserved quantity. (author). 15 refs
Boussinesq evolution equations
DEFF Research Database (Denmark)
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Gaussian process regression analysis for functional data
Shi, Jian Qing
2011-01-01
Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime
Semiparametric regression during 2003–2007
Ruppert, David
2009-01-01
Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.
New ridge parameters for ridge regression
Dorugade, A.V.
2014-01-01
Hoerl and Kennard (1970a) introduced the ridge regression estimator as an alternative to the ordinary least squares (OLS) estimator in the presence of multicollinearity. In ridge regression, ridge parameter plays an important role in parameter estimation. In this article, a new method for estimating ridge parameters in both situations of ordinary ridge regression (ORR) and generalized ridge regression (GRR) is proposed. The simulation study evaluates the performance of the proposed estimator ...
Semiparametric regression for restricted mean residual life under right censoring
DEFF Research Database (Denmark)
Mansourvar, Zahra; Martinussen, Torben; Scheike, Thomas H.
2015-01-01
A mean residual life function (MRLF) is the remaining life expectancy of a subject who has survived to a certain time point. In the presence of covariates, regression models are needed to study the association between the MRLFs and covariates. If the survival time tends to be too long or the tail...... is not observed, the restricted mean residual life must be considered. In this paper, we propose the proportional restricted mean residual life model for fitting survival data under right censoring. For inference on the model parameters, martingale estimating equations are developed, and the asymptotic properties...
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Conservation laws for equations related to soil water equations
C. M. Khalique; F. M. Mahomed
2005-01-01
We obtain all nontrivial conservation laws for a class of ( 2+1 ) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Conservation laws for equations related to soil water equations
Directory of Open Access Journals (Sweden)
Khalique C. M.
2005-01-01
Full Text Available We obtain all nontrivial conservation laws for a class of ( 2+1 nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Abstract. In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian ...
An Interactive Approach to Ridge Regression
Marquette, J. F.; Dufala, M. M.
1978-01-01
Ridge regression is an approach to ameliorating the problem of large standard errors of regression estimates when predictor variables are highly intercorrelated. An interactive computer program is presented which allows for investigation of the effects of using various ridge regression adjustment values. (JKS)
First-order partial differential equations in classical dynamics
Smith, B. R.
2009-12-01
Carathèodory's classic work on the calculus of variations explores in depth the connection between ordinary differential equations and first-order partial differential equations. The n second-order ordinary differential equations of a classical dynamical system reduce to a single first-order differential equation in 2n independent variables. The general solution of first-order partial differential equations touches on many concepts central to graduate-level courses in analytical dynamics including the Hamiltonian, Lagrange and Poisson brackets, and the Hamilton-Jacobi equation. For all but the simplest dynamical systems the solution requires one or more of these techniques. Three elementary dynamical problems (uniform acceleration, harmonic motion, and cyclotron motion) can be solved directly from the appropriate first-order partial differential equation without the use of advanced methods. The process offers an unusual perspective on classical dynamics, which is readily accessible to intermediate students who are not yet fully conversant with advanced approaches.
The Maxwell equations in a uniformly accelerated frame
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Perez S, C.I.
2007-01-01
The solution of the source-free Maxwell equations in a uniformly accelerated frame of reference is expressed in terms of a single complex scalar potential that obeys a second-order equation. The field of a static electric charge is obtained as an example of a stationary axisymmetric field. (Author)
Energy Technology Data Exchange (ETDEWEB)
Smith, H.L. (Arizona State Univ., Tempe (United States))
1993-01-01
It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.
A simultaneous equations model of fiscal policy interactions
Allers, Maarten A.; Elhorst, J. Paul
Existing studies of fiscal policy interactions are based on single equation (SE) models of either taxation or expenditures, without specifying the underlying social welfare function, without taking account of budget constraints and without allowing for cost differences between jurisdictions. Taking
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Indian Academy of Sciences (India)
Design of Four-Link Mechanisms. Ashitava Ghosal. Ashitava Ghosal is a. Professor in the Depart- ment of Mechanical. Engineering and Centre for Product Design, IISc,. Bangalore. His research interests are in the areas of analysis and design of mechanisms and ... Freudenstein's thesis and the equation named af- ter him.
Indian Academy of Sciences (India)
Amalkumar Raychaudhuri's remarkable paper [1] for the first time gave a general derivation of the fundamental equation of gravitational attraction for pressure- free matter, showing the repulsive nature of a positive cosmological constant, and underlying the basic singularity theorem (see below). He used special coordinates.
Solving Equations Applet Project
Thatcher, Kimberly
2011-01-01
The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
Department of Civil Engineering. University of Nigeria Nsukka. ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 8. The Freudenstein Equation - Design of Four-Link Mechanisms. Ashitava Ghosal. General Article Volume 15 Issue 8 August 2010 pp 699-710. Fulltext. Click here to view fulltext PDF. Permanent link:
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Regression with Sparse Approximations of Data
DEFF Research Database (Denmark)
Noorzad, Pardis; Sturm, Bob L.
2012-01-01
We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...
New Predictive Equations for Serum Ionized Calcium in Hospitalized Patients.
Mateu-de Antonio, Javier
2016-01-01
To study a new and easy way to calculate equations to predict ionized calcium (Ca2+) for adult hospitalized patients with the usual laboratory and clinical parameters. This retrospective observational study was conducted in a third-level university hospital. An initial learning cohort (cohort L: 269 patients) was selected to derive the new equations. These equations were tested in a validation of another cohort (cohort V: 146 patients). Patients selected were hospitalized adults who had simultaneous determinations of Ca2+ and serum total calcium (CaTot). They were classified using their estimated glomerular filtration rate (GFRe) into normal function, moderate and severe kidney dysfunction. Demographic and biochemical parameters, in addition to comorbidities, were collected from hospital databases. Nine published equations to predict Ca2+ and 2 widely used equations to predict corrected CaTot were also selected to be compared to newer equations for accuracy in detecting serum calcium alterations. New equations were derived by a multiple linear-regression analysis from patients in cohort L. Three equations were derived containing the CaTot square root as the main independent variable. Equation 1: Ca2+ = 0.815 × CaTot(0.5). Equation 2: Ca2+ = 0.826 × CaTot(0.5) - 0.023 × renal function. Equation 3: Ca2+ = 0.813 × CaTot(0.5) - 0.006 × albumin(0.75) + 0.079. These equations performed better than published equations to predict Ca2+ when their error measures were analyzed in cohort V, even in special populations such as critically ill and very old patients. Three new equations predicting Ca2+ were derived requiring easily available clinical and laboratory parameters. They could be valuable in predicting hypocalcemia but are of limited use in hypercalcemia. © 2015 S. Karger AG, Basel.
Assumptions of Multiple Regression: Correcting Two Misconceptions
Directory of Open Access Journals (Sweden)
Matt N. Williams
2013-09-01
Full Text Available In 2002, an article entitled - Four assumptions of multiple regression that researchers should always test- by.Osborne and Waters was published in PARE. This article has gone on to be viewed more than 275,000 times.(as of August 2013, and it is one of the first results displayed in a Google search for - regression.assumptions- . While Osborne and Waters' efforts in raising awareness of the need to check assumptions.when using regression are laudable, we note that the original article contained at least two fairly important.misconceptions about the assumptions of multiple regression: Firstly, that multiple regression requires the.assumption of normally distributed variables; and secondly, that measurement errors necessarily cause.underestimation of simple regression coefficients. In this article, we clarify that multiple regression models.estimated using ordinary least squares require the assumption of normally distributed errors in order for.trustworthy inferences, at least in small samples, but not the assumption of normally distributed response or.predictor variables. Secondly, we point out that regression coefficients in simple regression models will be.biased (toward zero estimates of the relationships between variables of interest when measurement error is.uncorrelated across those variables, but that when correlated measurement error is present, regression.coefficients may be either upwardly or downwardly biased. We conclude with a brief corrected summary of.the assumptions of multiple regression when using ordinary least squares.
International Nuclear Information System (INIS)
Tian Chou.
1991-05-01
It is important but difficult to find the invariant groups for the differential equations. We found a new invariant group for the MKdV equation. In this paper, we present a new invariance for the CDF equation. By using this invariance, we obtain some new solutions of CDF equation. (author). 5 refs
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Quantum equations from Brownian motions
International Nuclear Information System (INIS)
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Anticipated backward stochastic differential equations
Peng, Shige; Yang, Zhe
2007-01-01
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
Knight, Rodney R.; Gain, W. Scott; Wolfe, William J.
2011-01-01
Predictive equations were developed using stepbackward regression for 19 ecologically relevant streamflow characteristics grouped in five major classes (magnitude, ratio, frequency, variability, and date) for use in the Tennessee and Cumberland River watersheds. Basin characteristics explain 50 percent or more of the variation for 10 of the 19 equations. Independent variables identified through stepbackward regression were statistically significant in 81 of 304 coefficients tested across 19 models (⬚ Ridge streams, similar hydrologic behavior for watersheds with widely varying degrees of forest cover, and distinct hydrologic profiles for streams in different geographic regions.
Determining Balıkesir’s Energy Potential Using a Regression Analysis Computer Program
Directory of Open Access Journals (Sweden)
Bedri Yüksel
2014-01-01
Full Text Available Solar power and wind energy are used concurrently during specific periods, while at other times only the more efficient is used, and hybrid systems make this possible. When establishing a hybrid system, the extent to which these two energy sources support each other needs to be taken into account. This paper is a study of the effects of wind speed, insolation levels, and the meteorological parameters of temperature and humidity on the energy potential in Balıkesir, in the Marmara region of Turkey. The relationship between the parameters was studied using a multiple linear regression method. Using a designed-for-purpose computer program, two different regression equations were derived, with wind speed being the dependent variable in the first and insolation levels in the second. The regression equations yielded accurate results. The computer program allowed for the rapid calculation of different acceptance rates. The results of the statistical analysis proved the reliability of the equations. An estimate of identified meteorological parameters and unknown parameters could be produced with a specified precision by using the regression analysis method. The regression equations also worked for the evaluation of energy potential.
Elimination of variables in simple laser equations
Energy Technology Data Exchange (ETDEWEB)
Ning, C.Z.; Haken, H. (Stuttgart Univ. (Germany). Inst. fuer Theoretische Physik)
1992-08-01
The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorentz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 ({gamma}{sub perpendicular} {sub to}>> {gamma}{sub parallel}, {kappa}) and case 2 ({gamma}{sub perpendicular} {sub to}, {gamma}{sub parallel}>>{kappa}), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 ({gamma}{sub perpendicular} {sub to}, {kappa}>>{gamma}{sub parallel}) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant ({kappa}). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities. (orig.).
Crank-Nicolson - Differential quadrature algorithms for the Kawahara equation
Energy Technology Data Exchange (ETDEWEB)
Korkmaz, Alper [Anadolu Guzel Sanatlar Lisesi, Eskisehir Osmangazi University, Kuetahya (Turkey)], E-mail: alperkorkmaz7@gmail.com; Dag, Idris [Computer Engineering Department, Eskisehir Osmangazi University, Eskisehir (Turkey)], E-mail: idag@ogu.edu.tr
2009-10-15
The Kawahara equation is solved numerically using both Lagrange interpolation polynomials based differential quadrature method and cosine expansion based differential quadrature method. The travelling single solitary wave simulation is pictured. Maximum and discrete mean square error norms, lowest three conserved quantities are computed. Height, peak position and velocity of single solitary wave at various times are also computed for both methods. Breakup of an arbitrary single solitary wave into solitons and oscillatory shock wave generation from single solitary wave are studied.
Crank-Nicolson - Differential quadrature algorithms for the Kawahara equation
International Nuclear Information System (INIS)
Korkmaz, Alper; Dag, Idris
2009-01-01
The Kawahara equation is solved numerically using both Lagrange interpolation polynomials based differential quadrature method and cosine expansion based differential quadrature method. The travelling single solitary wave simulation is pictured. Maximum and discrete mean square error norms, lowest three conserved quantities are computed. Height, peak position and velocity of single solitary wave at various times are also computed for both methods. Breakup of an arbitrary single solitary wave into solitons and oscillatory shock wave generation from single solitary wave are studied.
Learning from data with localized regression and differential evolution
Buckner, Mark A.
2003-07-01
Learning from data is fast becoming the rule rather than the exception for many science and engineering research problems, particularly those encountered in nuclear engineering. Problems associated with learning from data fall under the more general category of inverse problems . A data-drive inverse problem involves constructing a predictive model of a target system from a collection of input/output observations. One of the difficulties associated with constructing a model that approximates such unknown causes based solely on observations of their effects is that collinearities in the input data result in the problem being ill-posed. Ill-posed problems cause models obtained by conventional techniques, such as linear regression, neural networks and kernel techniques, to become unstable, producing unreliable results. Methods of regularization using ordinary ridge regression (ORR) and kernel regression (KR) have been proposed as viable solutions to ill-posed problems. Successful application of ORR and KR require the selection of optimal parameter values---ridge parameters for ORR and bandwidth parameters for KR. The common practice for both methods is to select a single parameter based on minimizing an objective function which is an estimate of empirical risk. The single parameter value is then applied to all predictor variables indiscriminately, in a sort of one-size-fits-all fashion. Versions of ORR and KR have been proposed that make use of individual localized ridge and a matrix of localized bandwidth parameters that are optimally selected based on the relevance of their associated predictor variables to reducing empirical risk. While the practical and theoretical value of both localized regression techniques is recognized they have obtained limited use because of the difficulties associated with selecting multiple optimal ridge parameters for localized ridge regression (LRR)---defined as the localized ridge regression problem---and multiple optimal bandwidth
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Derivation of stable Burnett equations for rarefied gas flows.
Singh, Narendra; Jadhav, Ravi Sudam; Agrawal, Amit
2017-07-01
A set of constitutive relations for the stress tensor and heat flux vector for the hydrodynamic description of rarefied gas flows is derived in this work. A phase density function consistent with Onsager's reciprocity principle and H theorem is utilized to capture nonequilibrium thermodynamics effects. The phase density function satisfies the linearized Boltzmann equation and the collision invariance property. Our formulation provides the correct value of the Prandtl number as it involves two different relaxation times for momentum and energy transport by diffusion. Generalized three-dimensional constitutive equations for different kinds of molecules are derived using the phase density function. The derived constitutive equations involve cross single derivatives of field variables such as temperature and velocity, with no higher-order derivative in higher-order terms. This is remarkable feature of the equations as the number of boundary conditions required is the same as needed for conventional Navier-Stokes equations. Linear stability analysis of the equations is performed, which shows that the derived equations are unconditionally stable. A comparison of the derived equations with existing Burnett-type equations is presented and salient features of our equations are outlined. The classic internal flow problem, force-driven compressible plane Poiseuille flow, is chosen to verify the stable Burnett equations and the results for equilibrium variables are presented.
Multiscale functions, scale dynamics, and applications to partial differential equations
Cresson, Jacky; Pierret, Frédéric
2016-05-01
Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.
Faul, Franz; Erdfelder, Edgar; Buchner, Axel; Lang, Albert-Georg
2009-11-01
G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Spontaneous Regression of Lumbar Herniated Disc
Directory of Open Access Journals (Sweden)
Chun-Wei Chang
2009-12-01
Full Text Available Intervertebral disc herniation of the lumbar spine is a common disease presenting with low back pain and involving nerve root radiculopathy. Some neurological symptoms in the majority of patients frequently improve after a period of conservative treatment. This has been regarded as the result of a decrease of pressure exerted from the herniated disc on neighboring neurostructures and a gradual regression of inflammation. Recently, with advances in magnetic resonance imaging, many reports have demonstrated that the herniated disc has the potential for spontaneous regression. Regression coincided with the improvement of associated symptoms. However, the exact regression mechanism remains unclear. Here, we present 2 cases of lumbar intervertebral disc herniation with spontaneous regression. We review the literature and discuss the possible mechanisms, the precipitating factors of spontaneous disc regression and the proper timing of surgical intervention.
Applied regression analysis a research tool
Pantula, Sastry; Dickey, David
1998-01-01
Least squares estimation, when used appropriately, is a powerful research tool. A deeper understanding of the regression concepts is essential for achieving optimal benefits from a least squares analysis. This book builds on the fundamentals of statistical methods and provides appropriate concepts that will allow a scientist to use least squares as an effective research tool. Applied Regression Analysis is aimed at the scientist who wishes to gain a working knowledge of regression analysis. The basic purpose of this book is to develop an understanding of least squares and related statistical methods without becoming excessively mathematical. It is the outgrowth of more than 30 years of consulting experience with scientists and many years of teaching an applied regression course to graduate students. Applied Regression Analysis serves as an excellent text for a service course on regression for non-statisticians and as a reference for researchers. It also provides a bridge between a two-semester introduction to...
Simple and multiple linear regression: sample size considerations.
Hanley, James A
2016-11-01
The suggested "two subjects per variable" (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression. This article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing "exposure" (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or "profiles." It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates. By drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres. Copyright Â© 2016 Elsevier Inc. All rights reserved.
Bulcock, J. W.
The problem of model estimation when the data are collinear was examined. Though the ridge regression (RR) outperforms ordinary least squares (OLS) regression in the presence of acute multicollinearity, it is not a problem free technique for reducing the variance of the estimates. It is a stochastic procedure when it should be nonstochastic and it…
Directory of Open Access Journals (Sweden)
Alizé Lacoste Jeanson
2017-05-01
Full Text Available Background Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. Methods We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT and lean tissue (LT in such material. An intra-class correlation coefficient (ICC was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS linear regressions and support vector machine regression (SVMR. Results and Discussion The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5 and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77 than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08 for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results.
[From clinical judgment to linear regression model.
Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O
2013-01-01
When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R 2 ) indicates the importance of independent variables in the outcome.
Sufficient dimension reduction and prediction in regression.
Adragni, Kofi P; Cook, R Dennis
2009-11-13
Dimension reduction for regression is a prominent issue today because technological advances now allow scientists to routinely formulate regressions in which the number of predictors is considerably larger than in the past. While several methods have been proposed to deal with such regressions, principal components (PCs) still seem to be the most widely used across the applied sciences. We give a broad overview of ideas underlying a particular class of methods for dimension reduction that includes PCs, along with an introduction to the corresponding methodology. New methods are proposed for prediction in regressions with many predictors.
Spontaneous regression of an invasive thymoma.
Yutaka, Yojiro; Omasa, Mitsugu; Shikuma, Kei; Okuda, Masato; Taki, Toshihiko
2009-05-01
Although there are many reports of spontaneous regression of noninvasive thymoma, there are no reports of spontaneous regression of an invasive thymoma. Moreover, the mechanism of the spontaneous regression is still unknown. The present case concerns a 47-year-old man who presented with chest pain. Computed tomography (CT) showed a large anterior mediastinal mass with left pleural effusion that occluded the innominate vein. The tissue obtained by video-assisted thoracic surgery suggested a diagnosis of invasive thymic carcinoma. One month later CT showed prominent regression of the tumor, and the tumor was completely resected. On pathology, the diagnosis was thymoma type B3.
Use of probabilistic weights to enhance linear regression myoelectric control
Smith, Lauren H.; Kuiken, Todd A.; Hargrove, Levi J.
2015-12-01
Objective. Clinically available prostheses for transradial amputees do not allow simultaneous myoelectric control of degrees of freedom (DOFs). Linear regression methods can provide simultaneous myoelectric control, but frequently also result in difficulty with isolating individual DOFs when desired. This study evaluated the potential of using probabilistic estimates of categories of gross prosthesis movement, which are commonly used in classification-based myoelectric control, to enhance linear regression myoelectric control. Approach. Gaussian models were fit to electromyogram (EMG) feature distributions for three movement classes at each DOF (no movement, or movement in either direction) and used to weight the output of linear regression models by the probability that the user intended the movement. Eight able-bodied and two transradial amputee subjects worked in a virtual Fitts’ law task to evaluate differences in controllability between linear regression and probability-weighted regression for an intramuscular EMG-based three-DOF wrist and hand system. Main results. Real-time and offline analyses in able-bodied subjects demonstrated that probability weighting improved performance during single-DOF tasks (p < 0.05) by preventing extraneous movement at additional DOFs. Similar results were seen in experiments with two transradial amputees. Though goodness-of-fit evaluations suggested that the EMG feature distributions showed some deviations from the Gaussian, equal-covariance assumptions used in this experiment, the assumptions were sufficiently met to provide improved performance compared to linear regression control. Significance. Use of probability weights can improve the ability to isolate individual during linear regression myoelectric control, while maintaining the ability to simultaneously control multiple DOFs.
Evaluation of peak power prediction equations in male basketball players.
Duncan, Michael J; Lyons, Mark; Nevill, Alan M
2008-07-01
This study compared peak power estimated using 4 commonly used regression equations with actual peak power derived from force platform data in a group of adolescent basketball players. Twenty-five elite junior male basketball players (age, 16.5 +/- 0.5 years; mass, 74.2 +/- 11.8 kg; height, 181.8 +/- 8.1 cm) volunteered to participate in the study. Actual peak power was determined using a countermovement vertical jump on a force platform. Estimated peak power was determined using countermovement jump height and body mass. All 4 prediction equations were significantly related to actual peak power (all p jump prediction equations, 12% for the Canavan and Vescovi equation, and 6% for the Sayers countermovement jump equation. In all cases peak power was underestimated.
Action principles for the Vlasov equation
International Nuclear Information System (INIS)
Ye, H.; Morrison, P.J.
1992-01-01
Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables
DEFF Research Database (Denmark)
Jacobsen, Torben; Broers, G. H. J.
1977-01-01
The heat evolution at a single irreversibly working electrode is treated onthe basis of the Brønsted heat principle. The resulting equation is analogous to the expression for the total heat evolution in a galvanic cellwith the exception that –DeltaS is substituted by the Peltier entropy, Delta......SP, of theelectrode reaction. eta is the overvoltage at the electrode. This equation is appliedto a high temperature carbonate fuel cell. It is shown that the Peltier entropyterm by far exceeds the heat production due to the irreversible losses, and thatthe main part of heat evolved at the cathode is reabsorbed...
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
Equations to estimate creatinine excretion rate: the CKD epidemiology collaboration.
Ix, Joachim H; Wassel, Christina L; Stevens, Lesley A; Beck, Gerald J; Froissart, Marc; Navis, Gerjan; Rodby, Roger; Torres, Vicente E; Zhang, Yaping Lucy; Greene, Tom; Levey, Andrew S
2011-01-01
Creatinine excretion rate (CER) indicates timed urine collection accuracy. Although equations to estimate CER exist, their bias and precision are untested and none simultaneously include age, sex, race, and weight. Participants (n = 2466) from three kidney disease trials were randomly allocated into equation development (2/3) and internal validation (1/3) data sets. CER served as the dependent variable in linear regression to develop new equations. Their stability was assessed within the internal validation data set. Among 987 individuals from three additional studies the equations were externally validated and compared with existing equations. Mean age was 46 years, 42% were women, and 9% were black. Age, sex, race, weight, and serum phosphorus improved model fit. Two equations were developed, with or without serum phosphorus. In external validation, the new equations showed little bias (mean difference [measured - estimated CER] -0.7% [95% confidence interval -2.5% to 1.0%] and 0.3% [95% confidence interval -2.6% to 3.1%], respectively) and moderate precision (estimated CER within 30% of measured CER among 79% [76% to 81%] and 81% [77% to 85%], respectively). Corresponding numbers within 15% were 51% [48% to 54%] and 54% [50% to 59%]). Compared with existing equations, the new equations had similar accuracy but showed less bias in individuals with high measured CER. CER can be estimated with commonly available variables with little bias and moderate precision, which may facilitate assessment of accuracy of timed urine collections.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Yoshida, Daisuke; Shimada, Hiroyuki; Park, Hyuntae; Anan, Yuya; Ito, Tadashi; Harada, Atsushi; Suzuki, Takao
2014-10-01
Bioelectrical impedance analysis has been reported to have high reliability and accuracy in assessing body composition. However, equations for estimating appendicular skeletal muscle mass are population-specific, and few have been developed for older Japanese adults. Thus, the purpose of the present study was to develop and validate an estimate equation for appendicular skeletal muscle mass using bioelectrical impedance analysis. A total of 250 older adults aged 65 years and older participated in this study. Appendicular skeletal muscle mass was measured using dual-energy X-ray absorptiometry, and bioelectrical resistance was measured using a multifrequency bioelectrical impedance analyzer. Multiple regression analysis was applied to derive sex-specific estimation formulae using bioelectrical impedance analysis, and a Bland-Altman analysis was used to test agreement. The cross-validation results showed that the slopes and intercepts of the regression lines were approximately one and zero, respectively, and the coefficients of determination and standard errors of the estimate of the newly developed equations were similar between the two groups. Thus, the single sex-specific equations were developed using all participants as follows. Men: appendicular skeletal muscle mass=0.197 × (impedance index) +0.179 × (weight) -0.019 (R(2) =0.87, standard error of the estimate=0.98 kg). Women: appendicular skeletal muscle mass=0.221 × (impedance index) +0.117 × (weight) +0.881 (R(2) =0.89, standard error of the estimate=0.81 kg). These new equations offer a valid option for assessing appendicular skeletal muscle mass in older Japanese adults. © 2014 Japan Geriatrics Society.
Regression modeling methods, theory, and computation with SAS
Panik, Michael
2009-01-01
Regression Modeling: Methods, Theory, and Computation with SAS provides an introduction to a diverse assortment of regression techniques using SAS to solve a wide variety of regression problems. The author fully documents the SAS programs and thoroughly explains the output produced by the programs.The text presents the popular ordinary least squares (OLS) approach before introducing many alternative regression methods. It covers nonparametric regression, logistic regression (including Poisson regression), Bayesian regression, robust regression, fuzzy regression, random coefficients regression,
Non-oscillation domains of differential equations with two parameters
Mingarelli, Angelo B
1988-01-01
This research monograph is an introduction to single linear differential equations (systems) with two parameters and extensions to difference equations and Stieltjes integral equations. The scope is a study of the values of the parameters for which the equation has one solution(s) having one (finitely many) zeros. The prototype is Hill's equation or Mathieu's equation. For the most part no periodicity assumptions are used and when such are made, more general notions such as almost periodic functions are introduced, extending many classical and introducing many new results. Many of the proofs in the first part are variational thus allowing for natural extensions to more general settings later. The book should be accessible to graduate students and researchers alike and the proofs are, for the most part, self-contained.
Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo
2009-10-01
In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.
Graphical Tools for Linear Structural Equation Modeling
2014-06-01
regression coefficient βS A.CQ1 van- ishes, which can be used to test whether the specification of Model 2 is compatible with the data. Most...because they are all compatible with the graph in Figure 19a, which displays the skeleton and v-structures. Note that we cannot reverse the edge from...im- plications of linear structual equation models. R-428, <http://ftp.cs.ucla.edu/pub/stat_ser/r428.pdf>, CA. To ap- pear in Proceedings of AAAI-2014
Multispectral colormapping using penalized least square regression
DEFF Research Database (Denmark)
Dissing, Bjørn Skovlund; Carstensen, Jens Michael; Larsen, Rasmus
2010-01-01
-XYZ color matching functions. The target of the regression is a well known color chart, and the models are validated using leave one out cross validation in order to maintain best possible generalization ability. The authors compare the method with a direct linear regression and see...
Gibrat’s law and quantile regressions
DEFF Research Database (Denmark)
Distante, Roberta; Petrella, Ivan; Santoro, Emiliano
2017-01-01
The nexus between firm growth, size and age in U.S. manufacturing is examined through the lens of quantile regression models. This methodology allows us to overcome serious shortcomings entailed by linear regression models employed by much of the existing literature, unveiling a number of important...
ON REGRESSION REPRESENTATIONS OF STOCHASTIC-PROCESSES
RUSCHENDORF, L; DEVALK, [No Value
We construct a.s. nonlinear regression representations of general stochastic processes (X(n))n is-an-element-of N. As a consequence we obtain in particular special regression representations of Markov chains and of certain m-dependent sequences. For m-dependent sequences we obtain a constructive
Variable importance in latent variable regression models
Kvalheim, O.M.; Arneberg, R.; Bleie, O.; Rajalahti, T.; Smilde, A.K.; Westerhuis, J.A.
2014-01-01
The quality and practical usefulness of a regression model are a function of both interpretability and prediction performance. This work presents some new graphical tools for improved interpretation of latent variable regression models that can also assist in improved algorithms for variable
An Identity for Kernel Ridge Regression
Zhdanov, Fedor; Kalnishkan, Yuri
2011-01-01
This paper derives an identity connecting the square loss of ridge regression in on-line mode with the loss of the retrospectively best regressor. Some corollaries about the properties of the cumulative loss of on-line ridge regression are also obtained.
Ridge regression and its degrees of freedom
Dijkstra, Theo K.
2014-01-01
For ridge regression the degrees of freedom are commonly calculated by the trace of the matrix that transforms the vector of observations on the dependent variable into the ridge regression estimate of its expected value. For a fixed ridge parameter this is unobjectionable. When the ridge parameter
Small sample GEE estimation of regression parameters for longitudinal data.
Paul, Sudhir; Zhang, Xuemao
2014-09-28
Longitudinal (clustered) response data arise in many bio-statistical applications which, in general, cannot be assumed to be independent. Generalized estimating equation (GEE) is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified, although their small sample properties are not known. In this paper, two bias adjusted GEE estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small. One is based on a bias correction, and the other is based on a bias reduction. Simulations show that the performances of both the bias-corrected methods are similar in terms of bias, efficiency, coverage probability, average coverage length, impact of misspecification of correlation structure, and impact of cluster size on bias correction. Both these methods show superior properties over the GEE estimates for small samples. Further, analysis of data involving a small number of subjects also shows improvement in bias, MSE, standard error, and length of the confidence interval of the estimates by the two bias adjusted methods over the GEE estimates. For small to moderate sample sizes (N ≤50), either of the bias-corrected methods GEEBc and GEEBr can be used. However, the method GEEBc should be preferred over GEEBr, as the former is computationally easier. For large sample sizes, the GEE method can be used. Copyright © 2014 John Wiley & Sons, Ltd.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Nonelliptic Partial Differential Equations
Tartakoff, David S
2011-01-01
This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this tec
Pathological assessment of liver fibrosis regression
Directory of Open Access Journals (Sweden)
WANG Bingqiong
2017-03-01
Full Text Available Hepatic fibrosis is the common pathological outcome of chronic hepatic diseases. An accurate assessment of fibrosis degree provides an important reference for a definite diagnosis of diseases, treatment decision-making, treatment outcome monitoring, and prognostic evaluation. At present, many clinical studies have proven that regression of hepatic fibrosis and early-stage liver cirrhosis can be achieved by effective treatment, and a correct evaluation of fibrosis regression has become a hot topic in clinical research. Liver biopsy has long been regarded as the gold standard for the assessment of hepatic fibrosis, and thus it plays an important role in the evaluation of fibrosis regression. This article reviews the clinical application of current pathological staging systems in the evaluation of fibrosis regression from the perspectives of semi-quantitative scoring system, quantitative approach, and qualitative approach, in order to propose a better pathological evaluation system for the assessment of fibrosis regression.
Atherosclerotic plaque regression: fact or fiction?
Shanmugam, Nesan; Román-Rego, Ana; Ong, Peter; Kaski, Juan Carlos
2010-08-01
Coronary artery disease is the major cause of death in the western world. The formation and rapid progression of atheromatous plaques can lead to serious cardiovascular events in patients with atherosclerosis. The better understanding, in recent years, of the mechanisms leading to atheromatous plaque growth and disruption and the availability of powerful HMG CoA-reductase inhibitors (statins) has permitted the consideration of plaque regression as a realistic therapeutic goal. This article reviews the existing evidence underpinning current therapeutic strategies aimed at achieving atherosclerotic plaque regression. In this review we also discuss imaging modalities for the assessment of plaque regression, predictors of regression and whether plaque regression is associated with a survival benefit.
Should metacognition be measured by logistic regression?
Rausch, Manuel; Zehetleitner, Michael
2017-03-01
Are logistic regression slopes suitable to quantify metacognitive sensitivity, i.e. the efficiency with which subjective reports differentiate between correct and incorrect task responses? We analytically show that logistic regression slopes are independent from rating criteria in one specific model of metacognition, which assumes (i) that rating decisions are based on sensory evidence generated independently of the sensory evidence used for primary task responses and (ii) that the distributions of evidence are logistic. Given a hierarchical model of metacognition, logistic regression slopes depend on rating criteria. According to all considered models, regression slopes depend on the primary task criterion. A reanalysis of previous data revealed that massive numbers of trials are required to distinguish between hierarchical and independent models with tolerable accuracy. It is argued that researchers who wish to use logistic regression as measure of metacognitive sensitivity need to control the primary task criterion and rating criteria. Copyright © 2017 Elsevier Inc. All rights reserved.
Kuznetsov equation with variable coefficients
Indian Academy of Sciences (India)
like solutions of the PDE in (2+1) dimension with variable coefficients. ... Shivamoggi [12] gives only four polynomial conservation laws of the ZK equation ..... [3] P J Olver, Application of Lie group to differential equation (Springer, New York,.
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Functional equations for Feynman integrals
International Nuclear Information System (INIS)
Tarasov, O.V.
2011-01-01
New types of equations for Feynman integrals are found. It is shown that Feynman integrals satisfy functional equations connecting integrals with different kinematics. A regular method is proposed for obtaining such relations. The derivation of functional equations for one-loop two-, three- and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains
Classical solutions of quasielliptic equations
International Nuclear Information System (INIS)
Belonosov, V S
1999-01-01
Fundamental solutions of quasielliptic equations are constructed; this allows the author to develop a relevant theory of volume potentials, establish estimates for the Holder norms of solutions of equations with constant coefficients, and extend them after that to equations with variable coefficients. As a result, sharp Schauder-type interior estimates are obtained, of which the well-known classical results for elliptic and parabolic equations are special cases
Weighted linear regression using D2H and D2 as the independent variables
Hans T. Schreuder; Michael S. Williams
1998-01-01
Several error structures for weighted regression equations used for predicting volume were examined for 2 large data sets of felled and standing loblolly pine trees (Pinus taeda L.). The generally accepted model with variance of error proportional to the value of the covariate squared ( D2H = diameter squared times height or D...
Cason, Gerald J.; Schoultz, Ture W.
A counseling program for senior medical school students is described. Each student who wishes to participate is provided with a prediction of his or her Federal Licensing Examination (FLEX) score, as well as the probability of passing the FLEX in Arkansas. Predictions were computed by performing regression analyses to obtain equations relating…
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity; loop quantum cosmology. PACS Nos 04.20.Jb; 04.2 ...
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...
Completely integrable operator evolutionary equations
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)
On the Saha Ionization Equation
Indian Academy of Sciences (India)
Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...
An allometric equation for estimating stem biomass of Acacia ...
African Journals Online (AJOL)
Twelve different forms of linear, power and exponential equations were compared in this study to select the best model. Two models (VI and XI) were selected based on R 2, adjusted R 2, the Akaike information criterion, F-statistics and the five assumptions of linear regression. Model VI was discarded based on the ...
Sensitivity Analysis in Structural Equation Models: Cases and Their Influence
Pek, Jolynn; MacCallum, Robert C.
2011-01-01
The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model…
A Success Prediction Equation for the Intern Training Center.
A multiple regression equation predicting Intern Training Center grade point average was developed using a sample of sixty-two trainees from the ... Intern Training Center at Red River Army Depot. Possible predictor variables were taken as age, number of dependents, undergraduate college grades
Correlation and prediction equations for eight-week bodyweight in ...
African Journals Online (AJOL)
The 10 regression models used were: Linear; Logarithmic; Inverse; Quadratic; Cubic; Compound; Power; Sigmoidal; Growth; and Exponential equation. The results showed that Orpington breed had higher body weight than Sussex chicken for most weeks. Male chicks were generally higher in weekly body weight from 4 to 8 ...
Allegrini, Franco; Braga, Jez W B; Moreira, Alessandro C O; Olivieri, Alejandro C
2018-06-29
A new multivariate regression model, named Error Covariance Penalized Regression (ECPR) is presented. Following a penalized regression strategy, the proposed model incorporates information about the measurement error structure of the system, using the error covariance matrix (ECM) as a penalization term. Results are reported from both simulations and experimental data based on replicate mid and near infrared (MIR and NIR) spectral measurements. The results for ECPR are better under non-iid conditions when compared with traditional first-order multivariate methods such as ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLS). Copyright © 2018 Elsevier B.V. All rights reserved.
Regression modeling of ground-water flow
Cooley, R.L.; Naff, R.L.
1985-01-01
Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)
Directory of Open Access Journals (Sweden)
Hailun Wang
2017-01-01
Full Text Available Support vector regression algorithm is widely used in fault diagnosis of rolling bearing. A new model parameter selection method for support vector regression based on adaptive fusion of the mixed kernel function is proposed in this paper. We choose the mixed kernel function as the kernel function of support vector regression. The mixed kernel function of the fusion coefficients, kernel function parameters, and regression parameters are combined together as the parameters of the state vector. Thus, the model selection problem is transformed into a nonlinear system state estimation problem. We use a 5th-degree cubature Kalman filter to estimate the parameters. In this way, we realize the adaptive selection of mixed kernel function weighted coefficients and the kernel parameters, the regression parameters. Compared with a single kernel function, unscented Kalman filter (UKF support vector regression algorithms, and genetic algorithms, the decision regression function obtained by the proposed method has better generalization ability and higher prediction accuracy.
Discordance in Spirometric Interpretations Based on Korean and Non-Korean Reference Equations
2013-01-01
Objectives Korean regression models for spirometric reference values are different from those of other ethnic groups. The purpose of this study was to evaluate discordance in spirometric interpretations based on using Korean reference equations versus non-Korean reference equations. Methods Spirometry was performed on 825 Korean male workers from April 2009 to November 2011. The spirometric patterns and disease severity were evaluated using two Korean equations (Choi's and Lee's) and three equations for Caucasians (NHANES III, Morris's, and Knudson's), and the results of Choi's equation were compared with the non-Korean equations. The spirometric patterns were defined as normal, restrictive, and mild and moderate obstructive. Results The mean differences in the FEV1% and FVC% between the two Korean equations were 2.0 ± 1.3% and 3.5 ± 2.2%, respectively. Morris's equation had the greatest difference in the FEV1% from Choi's equation: 32.9 ± 8.5%. Knudson's equation had the greatest difference in the FVC% from Choi's equation: 10.5 ± 6.5%. Conclusions The two Korean equations shared similar characteristics of spirometric interpretation. The spirometric interpretations of Choi's equation were significantly different from those of Morris's equation and Knudson's equation. PMID:24472140
Applied Regression Modeling A Business Approach
Pardoe, Iain
2012-01-01
An applied and concise treatment of statistical regression techniques for business students and professionals who have little or no background in calculusRegression analysis is an invaluable statistical methodology in business settings and is vital to model the relationship between a response variable and one or more predictor variables, as well as the prediction of a response value given values of the predictors. In view of the inherent uncertainty of business processes, such as the volatility of consumer spending and the presence of market uncertainty, business professionals use regression a
Variable and subset selection in PLS regression
DEFF Research Database (Denmark)
Høskuldsson, Agnar
2001-01-01
The purpose of this paper is to present some useful methods for introductory analysis of variables and subsets in relation to PLS regression. We present here methods that are efficient in finding the appropriate variables or subset to use in the PLS regression. The general conclusion...... is that variable selection is important for successful analysis of chemometric data. An important aspect of the results presented is that lack of variable selection can spoil the PLS regression, and that cross-validation measures using a test set can show larger variation, when we use different subsets of X, than...
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Two Approaches for Using Multiple Anchors in NEAT Equating: A Description and Demonstration
Moses, Tim; Deng, Weiling; Zhang, Yu-Li
2011-01-01
Nonequivalent groups with anchor test (NEAT) equating functions that use a single anchor can have accuracy problems when the groups are extremely different and/or when the anchor weakly correlates with the tests being equated. Proposals have been made to address these issues by incorporating more than one anchor into NEAT equating functions. These…
Directory of Open Access Journals (Sweden)
Taouil Hajer
2012-08-01
Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.
p-Euler equations and p-Navier-Stokes equations
Li, Lei; Liu, Jian-Guo
2018-04-01
We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.
Generalized quantal equation of motion
International Nuclear Information System (INIS)
Morsy, M.W.; Embaby, M.
1986-07-01
In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)
DEFF Research Database (Denmark)
Kiani, Alishir; Chwalibog, André; Nielsen, Mette O
2007-01-01
study metabolizable energy (ME) intake ranges for twin-bearing ewes were 220-440, 350- 700, 350-900 kJ per metabolic body weight (W0.75) at week seven, five, two pre-partum respectively. Indirect calorimetry and a linear regression approach were used to quantify EE(gest) and then partition to EE......(conceptus) and EE(homeorhetic). Energy expenditure of basal metabolism of the non-gravid tissues (EE(bmng)), derived from the intercept of the linear regression equation of retained energy [kJ/W0.75] and ME intake [kJ/W(0.75)], was 298 [kJ/ W0.75]. Values of the intercepts of the regression equations at week seven...
Directory of Open Access Journals (Sweden)
Paul Robert Martin Werfette
2010-06-01
Full Text Available Analysis of quantitative structure - activity relationship (QSAR for a series of antimalarial compound artemisinin derivatives has been done using principal component regression. The descriptors for QSAR study were representation of electronic structure i.e. atomic net charges of the artemisinin skeleton calculated by AM1 semi-empirical method. The antimalarial activity of the compound was expressed in log 1/IC50 which is an experimental data. The main purpose of the principal component analysis approach is to transform a large data set of atomic net charges to simplify into a data set which known as latent variables. The best QSAR equation to analyze of log 1/IC50 can be obtained from the regression method as a linear function of several latent variables i.e. x1, x2, x3, x4 and x5. The best QSAR model is expressed in the following equation, (;; Keywords: QSAR, antimalarial, artemisinin, principal component regression
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2015-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789
Energy Technology Data Exchange (ETDEWEB)
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
Energy Technology Data Exchange (ETDEWEB)
Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-17
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Differential equations with involutions
Cabada, Alberto
2015-01-01
This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.