Extended sine-Gordon Equation Method and Its Application to Maccari's System

International Nuclear Information System (INIS)

Song Lina; Zhang Hongqing

2005-01-01

An extended sine-Gordon equation method is proposed to construct exact travelling wave solutions to Maccari's equation based upon a generalized sine-Gordon equation. It is shown that more new travelling wave solutions can be found by this new method, which include bell-shaped soliton solutions, kink-shaped soliton solutions, periodic wave solution, and new travelling waves.

Integro-differential equation approach extended to larger nuclei

International Nuclear Information System (INIS)

Adam, R.M.; Sofianos, S.A.; Fiedeldey, H.; Fabre de la Ripelle, M.

1992-01-01

We extend the integro-differential equation approach (IDEA) from few-nucleon to closed-shell and closed-subshell nuclei and outline the analytical methods required for the calculation of the density functions, which enter into the integro-differential equations. These contain all the physics for a system of fermions associated with the Pauli principle. In order to test the accuracy of the IDEA comparisons are made of the binding energies of 4 He, 12 C and 16 O obtained with effective potentials using the hypercentral approximation (HCA) providing a variational solution without correlations, the IDEA which fully includes the two-body correlations, the S-states integro-differential equation (SIDE) valid for potentials operating only on pairs in the S-state and those calculated by several variational or perturbative methods in the literature. (author)

Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Directory of Open Access Journals (Sweden)

Lieberman Gary M

2007-01-01

Full Text Available We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previous methods. In particular, we have no restrictions on the maximum eigenvalue of the coefficient matrix and we obtain interior gradient estimates for so-called false mean curvature equation.

The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

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 ...

The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV-MKdV, Broer-Kaup-Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs

DYNAMIC ESTIMATION FOR PARAMETERS OF INTERFERENCE SIGNALS BY THE SECOND ORDER EXTENDED KALMAN FILTERING

Directory of Open Access Journals (Sweden)

P. A. Ermolaev

2014-03-01

Full Text Available Data processing in the interferometer systems requires high-resolution and high-speed algorithms. Recurrence algorithms based on parametric representation of signals execute consequent processing of signal samples. In some cases recurrence algorithms make it possible to increase speed and quality of data processing as compared with classic processing methods. Dependence of the measured interferometer signal on parameters of its model and stochastic nature of noise formation in the system is, in general, nonlinear. The usage of nonlinear stochastic filtering algorithms is expedient for such signals processing. Extended Kalman filter with linearization of state and output equations by the first vector parameters derivatives is an example of these algorithms. To decrease approximation error of this method the second order extended Kalman filtering is suggested with additionally usage of the second vector parameters derivatives of model equations. Examples of algorithm implementation with the different sets of estimated parameters are described. The proposed algorithm gives the possibility to increase the quality of data processing in interferometer systems in which signals are forming according to considered models. Obtained standard deviation of estimated amplitude envelope does not exceed 4% of the maximum. It is shown that signal-to-noise ratio of reconstructed signal is increased by 60%.

Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials

International Nuclear Information System (INIS)

Hartwig, J. T.; Stokman, J. V.

2013-01-01

We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schrödinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schrödinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations as functions of the momenta. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with delta-function interactions is indicated.

Soliton-like solutions to the GKdV equation by extended mapping method

International Nuclear Information System (INIS)

Wu Ranchao; Sun Jianhua

2007-01-01

In this note, many new exact solutions of the generalized KdV equation, such as rational solutions, periodic solutions like Jacobian elliptic and triangular functions, soliton-like solutions, are constructed by symbolic computation and the extended mapping method, with the auxiliary ordinary equation replaced by a more general one

Flexible and efficient estimating equations for variogram estimation

KAUST Repository

Sun, Ying; Chang, Xiaohui; Guan, Yongtao

2018-01-01

Variogram estimation plays a vastly important role in spatial modeling. Different methods for variogram estimation can be largely classified into least squares methods and likelihood based methods. A general framework to estimate the variogram through a set of estimating equations is proposed. This approach serves as an alternative approach to likelihood based methods and includes commonly used least squares approaches as its special cases. The proposed method is highly efficient as a low dimensional representation of the weight matrix is employed. The statistical efficiency of various estimators is explored and the lag effect is examined. An application to a hydrology dataset is also presented.

Flexible and efficient estimating equations for variogram estimation

KAUST Repository

Sun, Ying

2018-01-11

Variogram estimation plays a vastly important role in spatial modeling. Different methods for variogram estimation can be largely classified into least squares methods and likelihood based methods. A general framework to estimate the variogram through a set of estimating equations is proposed. This approach serves as an alternative approach to likelihood based methods and includes commonly used least squares approaches as its special cases. The proposed method is highly efficient as a low dimensional representation of the weight matrix is employed. The statistical efficiency of various estimators is explored and the lag effect is examined. An application to a hydrology dataset is also presented.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

Science.gov (United States)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

KAUST Repository

Aldoghaither, Abeer

2015-12-01

In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton\\'s iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

KAUST Repository

Aldoghaither, Abeer; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem

2015-01-01

In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

Parameter estimation in stochastic differential equations

CERN Document Server

Bishwal, Jaya P N

2008-01-01

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.

Analyticity estimates for the Navier-Stokes equations

DEFF Research Database (Denmark)

Herbst, I.; Skibsted, Erik

We study spatial analyticity properties of solutions of the Navier-Stokes equation and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes equation with data in and prove a stability result...

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

Science.gov (United States)

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Quasi-Newton methods for parameter estimation in functional differential equations

Science.gov (United States)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

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

Science.gov (United States)

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

2016-04-01

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

Equations for estimating bankfull channel geometry and discharge for streams in Massachusetts

Science.gov (United States)

Bent, Gardner C.; Waite, Andrew M.

2013-01-01

Regression equations were developed for estimating bankfull geometry—width, mean depth, cross-sectional area—and discharge for streams in Massachusetts. The equations provide water-resource and conservation managers with methods for estimating bankfull characteristics at specific stream sites in Massachusetts. This information can be used for the adminstration of the Commonwealth of Massachusetts Rivers Protection Act of 1996, which establishes a protected riverfront area extending from the mean annual high-water line corresponding to the elevation of bankfull discharge along each side of a perennial stream. Additionally, information on bankfull channel geometry and discharge are important to Federal, State, and local government agencies and private organizations involved in stream assessment and restoration projects. Regression equations are based on data from stream surveys at 33 sites (32 streamgages and 1 crest-stage gage operated by the U.S. Geological Survey) in and near Massachusetts. Drainage areas of the 33 sites ranged from 0.60 to 329 square miles (mi2). At 27 of the 33 sites, field data were collected and analyses were done to determine bankfull channel geometry and discharge as part of the present study. For 6 of the 33 sites, data on bankfull channel geometry and discharge were compiled from other studies done by the U.S. Geological Survey, Natural Resources Conservation Service of the U.S. Department of Agriculture, and the Vermont Department of Environmental Conservation. Similar techniques were used for field data collection and analysis for bankfull channel geometry and discharge at all 33 sites. Recurrence intervals of the bankfull discharge, which represent the frequency with which a stream fills its channel, averaged 1.53 years (median value 1.34 years) at the 33 sites. Simple regression equations were developed for bankfull width, mean depth, cross-sectional area, and discharge using drainage area, which is the most significant explanatory

Developing a generalized allometric equation for aboveground biomass estimation

Science.gov (United States)

Xu, Q.; Balamuta, J. J.; Greenberg, J. A.; Li, B.; Man, A.; Xu, Z.

2015-12-01

A key potential uncertainty in estimating carbon stocks across multiple scales stems from the use of empirically calibrated allometric equations, which estimate aboveground biomass (AGB) from plant characteristics such as diameter at breast height (DBH) and/or height (H). The equations themselves contain significant and, at times, poorly characterized errors. Species-specific equations may be missing. Plant responses to their local biophysical environment may lead to spatially varying allometric relationships. The structural predictor may be difficult or impossible to measure accurately, particularly when derived from remote sensing data. All of these issues may lead to significant and spatially varying uncertainties in the estimation of AGB that are unexplored in the literature. We sought to quantify the errors in predicting AGB at the tree and plot level for vegetation plots in California. To accomplish this, we derived a generalized allometric equation (GAE) which we used to model the AGB on a full set of tree information such as DBH, H, taxonomy, and biophysical environment. The GAE was derived using published allometric equations in the GlobAllomeTree database. The equations were sparse in details about the error since authors provide the coefficient of determination (R2) and the sample size. A more realistic simulation of tree AGB should also contain the noise that was not captured by the allometric equation. We derived an empirically corrected variance estimate for the amount of noise to represent the errors in the real biomass. Also, we accounted for the hierarchical relationship between different species by treating each taxonomic level as a covariate nested within a higher taxonomic level (e.g. species contribution of each different covariate in estimating the AGB of trees. Lastly, we applied the GAE to an existing vegetation plot database - Forest Inventory and Analysis database - to derive per-tree and per-plot AGB estimations, their errors, and how

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

Science.gov (United States)

Ding, A Adam; Wu, Hulin

2014-10-01

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

Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

International Nuclear Information System (INIS)

Wang Yun-Hu; Chen Yong

2013-01-01

We investigate the extended (2+1)-dimensional shallow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Bäcklund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method. (general)

Efficient Estimating Functions for Stochastic Differential Equations

DEFF Research Database (Denmark)

Jakobsen, Nina Munkholt

The overall topic of this thesis is approximate martingale estimating function-based estimationfor solutions of stochastic differential equations, sampled at high frequency. Focuslies on the asymptotic properties of the estimators. The first part of the thesis deals with diffusions observed over...

Gradient estimates on the weighted p-Laplace heat equation

Science.gov (United States)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

Toward Analytic Solution of Nonlinear Differential Difference Equations via Extended Sensitivity Approach

International Nuclear Information System (INIS)

Darmani, G.; Setayeshi, S.; Ramezanpour, H.

2012-01-01

In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)

Sonographic fetal weight estimation using femoral length: Honarvar Equation

International Nuclear Information System (INIS)

Firoozabadi, Raziah Dehghani; Ghasemi, N.; Firoozabadi, Mehdi Dehghani

2007-01-01

Fetal growth is the result of interactions between various factors and can be estimated by ultrasonic measurements. Fetal femur length is a scale for estimating the fetal weight in individual races because fetal growth patterns differ among different races. This was a prospective study involving 500 pregnant women at 36 weeks of gestational age. Real-time sonography was done to measure the femoral length and the weight of the fetus was estimated by the Honarvar 2 equation. The correlation between estimated fetal weight (EFW) and real weight was tested by Pearson correlation coefficient and relationships with the age and BMI of mother, the sex of the neonate and parity were tested by multiple regression. EFW by the Honarvar 2 equation correlated significantly with actual birthweight. Therefore, this equation is valid for fetal weight estimation. It also does not depend on the age and BMI of the mother, sex of the neonate, parity. Ethnicity potentially plays an important role in the fetal weight estimation. The Honarvar formula produced the best estimate of the actual birthweight for Iranian fetuses, and its use is recommended. (author)

Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

Directory of Open Access Journals (Sweden)

Wei Li

2014-01-01

Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

Parameter Estimates in Differential Equation Models for Chemical Kinetics

Science.gov (United States)

Winkel, Brian

2011-01-01

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

Science.gov (United States)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

Science.gov (United States)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations

KAUST Repository

Asiri, Sharefa M.

2017-10-08

Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions\\' parameters. (iii) Propose an effective algorithm for selecting the method\\'s design parameters

Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II

Science.gov (United States)

Kazeykina, Anna; Muñoz, Claudio

2018-04-01

We continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensional Schrödinger operator at a fixed energy parameter. This work is concerned with the more involved case of a positive energy parameter. For the solution of the linearized equation we derive smoothing and Strichartz estimates by combining new estimates for two different frequency regimes, extending our previous results for the negative energy case [18]. The low frequency regime, which our previous result was not able to treat, is studied in detail. At non-low frequencies we also derive improved smoothing estimates with gain of almost one derivative. Then we combine the linear estimates with a Fourier decomposition method and Xs,b spaces to obtain local well-posedness of NV at positive energy in Hs, s > 1/2. Our result implies, in particular, that at least for s > 1/2, NV does not change its behavior from semilinear to quasilinear as energy changes sign, in contrast to the closely related Kadomtsev-Petviashvili equations. As a complement to our LWP results, we also provide some new explicit solutions of NV at zero energy, generalizations of the lumps solutions, which exhibit new and nonstandard long time behavior. In particular, these solutions blow up in infinite time in L2.

Differential equations extended to superspace

International Nuclear Information System (INIS)

Torres, J.; Rosu, H.C.

2003-01-01

We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

Differential equations extended to superspace

Energy Technology Data Exchange (ETDEWEB)

Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)

2003-07-01

We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

International Nuclear Information System (INIS)

Feng Qinghua

2013-01-01

In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)

Stable estimation of two coefficients in a nonlinear Fisher–KPP equation

International Nuclear Information System (INIS)

Cristofol, Michel; Roques, Lionel

2013-01-01

We consider the inverse problem of determining two non-constant coefficients in a nonlinear parabolic equation of the Fisher–Kolmogorov–Petrovsky–Piskunov type. For the equation u t = DΔu + μ(x) u − γ(x)u 2 in (0, T) × Ω, which corresponds to a classical model of population dynamics in a bounded heterogeneous environment, our results give a stability inequality between the couple of coefficients (μ, γ) and some observations of the solution u. These observations consist in measurements of u: in the whole domain Ω at two fixed times, in a subset ω⊂⊂Ω during a finite time interval and on the boundary of Ω at all times t ∈ (0, T). The proof relies on parabolic estimates together with the parabolic maximum principle and Hopf’s lemma which enable us to use a Carleman inequality. This work extends previous studies on the stable determination of non-constant coefficients in parabolic equations, as it deals with two coefficients and with a nonlinear term. A consequence of our results is the uniqueness of the couple of coefficients (μ, γ), given the observation of u. This uniqueness result was obtained in a previous paper but in the one-dimensional case only. (paper)

Novel Equations for Estimating Lean Body Mass in Peritoneal Dialysis Patients.

Science.gov (United States)

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

2015-12-01

♦ To develop and validate equations for estimating lean body mass (LBM) in peritoneal dialysis (PD) patients. ♦ Two equations for estimating LBM, one based on mid-arm muscle circumference (MAMC) and hand grip strength (HGS), i.e., LBM-M-H, and the other based on HGS, i.e., LBM-H, were developed and validated with LBM obtained by dual-energy X-ray absorptiometry (DEXA). The developed equations were compared to LBM estimated from creatinine kinetics (LBM-CK) and anthropometry (LBM-A) in terms of bias, precision, and accuracy. The prognostic values of LBM estimated from the equations in all-cause mortality risk were assessed. ♦ The developed equations incorporated gender, height, weight, and dialysis duration. Compared to LBM-DEXA, the bias of the developed equations was lower than that of LBM-CK and LBM-A. Additionally, LBM-M-H and LBM-H had better accuracy and precision. The prognostic values of LBM in all-cause mortality risk based on LBM-M-H, LBM-H, LBM-CK, and LBM-A were similar. ♦ Lean body mass estimated by the new equations based on MAMC and HGS was correlated with LBM obtained by DEXA and may serve as practical surrogate markers of LBM in PD patients. Copyright © 2015 International Society for Peritoneal Dialysis.

Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets

KAUST Repository

Sun, Ying; Stein, Michael L.

2014-01-01

For Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n3) operations and O(n2) memory. Various approximation methods have been developed to address the computational difficulties. In this paper, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean.

Statistically and Computationally Efficient Estimating Equations for Large Spatial Datasets

KAUST Repository

Sun, Ying

2014-11-07

For Gaussian process models, likelihood based methods are often difficult to use with large irregularly spaced spatial datasets, because exact calculations of the likelihood for n observations require O(n3) operations and O(n2) memory. Various approximation methods have been developed to address the computational difficulties. In this paper, we propose new unbiased estimating equations based on score equation approximations that are both computationally and statistically efficient. We replace the inverse covariance matrix that appears in the score equations by a sparse matrix to approximate the quadratic forms, then set the resulting quadratic forms equal to their expected values to obtain unbiased estimating equations. The sparse matrix is constructed by a sparse inverse Cholesky approach to approximate the inverse covariance matrix. The statistical efficiency of the resulting unbiased estimating equations are evaluated both in theory and by numerical studies. Our methods are applied to nearly 90,000 satellite-based measurements of water vapor levels over a region in the Southeast Pacific Ocean.

Quantitative Compactness Estimates for Hamilton-Jacobi Equations

Science.gov (United States)

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

2016-02-01

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

Spacecraft Angular Rates Estimation with Gyrowheel Based on Extended High Gain Observer

Directory of Open Access Journals (Sweden)

Xiaokun Liu

2016-04-01

Full Text Available A gyrowheel (GW is a kind of electronic electric-mechanical servo system, which can be applied to a spacecraft attitude control system (ACS as both an actuator and a sensor simultaneously. In order to solve the problem of two-dimensional spacecraft angular rate sensing as a GW outputting three-dimensional control torque, this paper proposed a method of an extended high gain observer (EHGO with the derived GW mathematical model to implement the spacecraft angular rate estimation when the GW rotor is working at large angles. For this purpose, the GW dynamic equation is firstly derived with the second kind Lagrange method, and the relationship between the measurable and unmeasurable variables is built. Then, the EHGO is designed to estimate and calculate spacecraft angular rates with the GW, and the stability of the designed EHGO is proven by the Lyapunov function. Moreover, considering the engineering application, the effect of measurement noise in the tilt angle sensors on the estimation accuracy of the EHGO is analyzed. Finally, the numerical simulation is performed to illustrate the validity of the method proposed in this paper.

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

Science.gov (United States)

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

The Extended-Window Channel Estimator for Iterative Channel-and-Symbol Estimation

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Barry John R

2005-01-01

Full Text Available The application of the expectation-maximization (EM algorithm to channel estimation results in a well-known iterative channel-and-symbol estimator (ICSE. The EM-ICSE iterates between a symbol estimator based on the forward-backward recursion (BCJR equalizer and a channel estimator, and may provide approximate maximum-likelihood blind or semiblind channel estimates. Nevertheless, the EM-ICSE has high complexity, and it is prone to misconvergence. In this paper, we propose the extended-window (EW estimator, a novel channel estimator for ICSE that can be used with any soft-output symbol estimator. Therefore, the symbol estimator may be chosen according to performance or complexity specifications. We show that the EW-ICSE, an ICSE that uses the EW estimator and the BCJR equalizer, is less complex and less susceptible to misconvergence than the EM-ICSE. Simulation results reveal that the EW-ICSE may converge faster than the EM-ICSE.

Estimate of body composition by Hume's equation: validation with DXA.

Science.gov (United States)

Carnevale, Vincenzo; Piscitelli, Pamela Angela; Minonne, Rita; Castriotta, Valeria; Cipriani, Cristiana; Guglielmi, Giuseppe; Scillitani, Alfredo; Romagnoli, Elisabetta

2015-05-01

We investigated how the Hume's equation, using the antipyrine space, could perform in estimating fat mass (FM) and lean body mass (LBM). In 100 (40 male ad 60 female) subjects, we estimated FM and LBM by the equation and compared these values with those measured by a last generation DXA device. The correlation coefficients between measured and estimated FM were r = 0.940 (p LBM were r = 0.913 (p LBM, though the equation underestimated FM and overestimated LBM in respect to DXA. The mean difference for FM was 1.40 kg (limits of agreement of -6.54 and 8.37 kg). For LBM, the mean difference in respect to DXA was 1.36 kg (limits of agreement -8.26 and 6.52 kg). The root mean square error was 3.61 kg for FM and 3.56 kg for LBM. Our results show that in clinically stable subjects the Hume's equation could reliably assess body composition, and the estimated FM and LBM approached those measured by a modern DXA device.

Validation of equations for pleural effusion volume estimation by ultrasonography.

Science.gov (United States)

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

2017-12-01

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

Estimation of Sideslip Angle Based on Extended Kalman Filter

Directory of Open Access Journals (Sweden)

Yupeng Huang

2017-01-01

Full Text Available The sideslip angle plays an extremely important role in vehicle stability control, but the sideslip angle in production car cannot be obtained from sensor directly in consideration of the cost of the sensor; it is essential to estimate the sideslip angle indirectly by means of other vehicle motion parameters; therefore, an estimation algorithm with real-time performance and accuracy is critical. Traditional estimation method based on Kalman filter algorithm is correct in vehicle linear control area; however, on low adhesion road, vehicles have obvious nonlinear characteristics. In this paper, extended Kalman filtering algorithm had been put forward in consideration of the nonlinear characteristic of the tire and was verified by the Carsim and Simulink joint simulation, such as the simulation on the wet cement road and the ice and snow road with double lane change. To test and verify the effect of extended Kalman filtering estimation algorithm, the real vehicle test was carried out on the limit test field. The experimental results show that the accuracy of vehicle sideslip angle acquired by extended Kalman filtering algorithm is obviously higher than that acquired by Kalman filtering in the area of the nonlinearity.

Extending Teach and Repeat to Pivoting Wheelchairs

Directory of Open Access Journals (Sweden)

Guillermo Del Castillo

2003-02-01

Full Text Available The paper extends the teach-and-repeat paradigm that has been successful for the control of holonomic robots to nonholonomic wheelchairs which may undergo pivoting action over the course of their taught movement. Due to the nonholonomic nature of the vehicle kinematics, estimation is required -- in the example given herein, based upon video detection of wall-mounted cues -- both in the teaching and the tracking events. In order to accommodate motion that approaches pivoting action as well as motion that approaches straight-line action, the estimation equations of the Extended Kalman Filter and the control equations are formulated using two different definitions of a nontemporal independent variable. The paper motivates the need for pivoting action in real-life settings by reporting extensively on the abilities and limitations of estimation-based teach-and-repeat action where pivoting and near-pivoting action is disallowed. Following formulation of the equations in the near-pivot mode, the paper reports upon experiments where taught trajectories which entail a seamless mix of near-straight and near-pivot action are tracked.

A Priori Regularity of Parabolic Partial Differential Equations

KAUST Repository

Berkemeier, Francisco

2018-05-13

In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

Directory of Open Access Journals (Sweden)

Jishan Fan

2013-04-01

Full Text Available Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.

On the Schauder estimates of solutions to parabolic equations

International Nuclear Information System (INIS)

Han Qing

1998-01-01

This paper gives a priori estimates on asymptotic polynomials of solutions to parabolic differential equations at any points. This leads to a pointwise version of Schauder estimates. The result improves the classical Schauder estimates in a way that the estimates of solutions and their derivatives at one point depend on the coefficient and nonhomogeneous terms at this particular point

A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

Science.gov (United States)

Choi, Sae Il

2009-01-01

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

Science.gov (United States)

Nestler, Steffen

2014-05-01

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

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

Science.gov (United States)

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

2018-05-01

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

Time-course window estimator for ordinary differential equations linear in the parameters

NARCIS (Netherlands)

Vujacic, Ivan; Dattner, Itai; Gonzalez, Javier; Wit, Ernst

In many applications obtaining ordinary differential equation descriptions of dynamic processes is scientifically important. In both, Bayesian and likelihood approaches for estimating parameters of ordinary differential equations, the speed and the convergence of the estimation procedure may

Explicit estimating equations for semiparametric generalized linear latent variable models

KAUST Repository

Ma, Yanyuan; Genton, Marc G.

2010-01-01

which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n

Estimating Soil Hydraulic Parameters using Gradient Based Approach

Science.gov (United States)

Rai, P. K.; Tripathi, S.

2017-12-01

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

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

International Nuclear Information System (INIS)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su

2014-01-01

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core

Rhodium SPND's Error Reduction using Extended Kalman Filter combined with Time Dependent Neutron Diffusion Equation

Energy Technology Data Exchange (ETDEWEB)

Lee, Jeong Hun; Park, Tong Kyu; Jeon, Seong Su [FNC Technology Co., Ltd., Yongin (Korea, Republic of)

2014-05-15

The Rhodium SPND is accurate in steady-state conditions but responds slowly to changes in neutron flux. The slow response time of Rhodium SPND precludes its direct use for control and protection purposes specially when nuclear power plant is used for load following. To shorten the response time of Rhodium SPND, there were some acceleration methods but they could not reflect neutron flux distribution in reactor core. On the other hands, some methods for core power distribution monitoring could not consider the slow response time of Rhodium SPND and noise effect. In this paper, time dependent neutron diffusion equation is directly used to estimate reactor power distribution and extended Kalman filter method is used to correct neutron flux with Rhodium SPND's and to shorten the response time of them. Extended Kalman filter is effective tool to reduce measurement error of Rhodium SPND's and even simple FDM to solve time dependent neutron diffusion equation can be an effective measure. This method reduces random errors of detectors and can follow reactor power level without cross-section change. It means monitoring system may not calculate cross-section at every time steps and computing time will be shorten. To minimize delay of Rhodium SPND's conversion function h should be evaluated in next study. Neutron and Rh-103 reaction has several decay chains and half-lives over 40 seconds causing delay of detection. Time dependent neutron diffusion equation will be combined with decay chains. Power level and distribution change corresponding movement of control rod will be tested with more complicated reference code as well as xenon effect. With these efforts, final result is expected to be used as a powerful monitoring tool of nuclear reactor core.

ALLOMETRIC EQUATIONS FOR ESTIMATING ABOVEGROUND BIOMASS IN PAPUA TROPICAL FOREST

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Sandhi Imam Maulana

2014-10-01

Full Text Available Allometric equations can be used to estimate biomass and carbon stock of  the forest. However, so far the allometric equations for commercial species in Papua tropical forests have not been appropriately developed. In this research, allometric equations are presented based on the genera of  commercial species. Few equations have been developed for the commercial species of  Intsia, Pometia, Palaquium and Vatica genera and an equation of  a mix of  these genera. The number of  trees sampled in this research was 49, with diameters (1.30 m above-ground or above buttresses ranging from 5 to 40 cm. Destructive sampling was used to collect the samples where Diameter at Breast Height (DBH and Wood Density (WD were used as predictors for dry weight of  Total Above-Ground Biomass (TAGB. Model comparison and selection were based on the values of  F-statistics, R-sq, R-sq (adj, and average deviation. Based on these statistical indicators, the most suitable model for Intsia, Pometia, Palaquium and Vatica genera respectively are Log(TAGB = -0.76 + 2.51Log(DBH, Log(TAGB = -0.84 + 2.57Log(DBH, Log(TAGB = -1.52 + 2.96Log(DBH, and Log(TAGB = -0.09 + 2.08Log(DBH. Additional explanatory variables such as Commercial Bole Height (CBH do not really increase the indicators’ goodness of  fit for the equation. An alternative model to incorporate wood density should  be considered for estimating the above-ground biomass for mixed genera. Comparing the presented mixed-genera equation; Log(TAGB = 0.205 + 2.08Log(DBH + 1.75Log(WD, R-sq: 97.0%, R-sq (adj: 96.9%, F statistics 750.67, average deviation: 3.5%; to previously published datashows that this local species specific equation differs substantially from previously published equations and this site-specific equation is  considered to give a better estimation of  biomass.

Distributed Dynamic State Estimation with Extended Kalman Filter

Energy Technology Data Exchange (ETDEWEB)

Du, Pengwei; Huang, Zhenyu; Sun, Yannan; Diao, Ruisheng; Kalsi, Karanjit; Anderson, Kevin K.; Li, Yulan; Lee, Barry

2011-08-04

Increasing complexity associated with large-scale renewable resources and novel smart-grid technologies necessitates real-time monitoring and control. Our previous work applied the extended Kalman filter (EKF) with the use of phasor measurement data (PMU) for dynamic state estimation. However, high computation complexity creates significant challenges for real-time applications. In this paper, the problem of distributed dynamic state estimation is investigated. One domain decomposition method is proposed to utilize decentralized computing resources. The performance of distributed dynamic state estimation is tested on a 16-machine, 68-bus test system.

Classification of kink type solutions to the extended derivative nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Wyller, J.; Fla, T.; Juul Rasmussen, J.

1998-01-01

The Raman Extended Derivative Non Linear Schrodinger (R-EDNLS) equation which models single mode propagation in optical fibers, is shown to possess travelling and stationary kink envelope solutions of monotonic and oscillatory type. These structures have been called optical shocks in analogy...

Evaluation of Clear-Sky Incoming Radiation Estimating Equations Typically Used in Remote Sensing Evapotranspiration Algorithms

Directory of Open Access Journals (Sweden)

Ted W. Sammis

2013-09-01

Full Text Available Net radiation is a key component of the energy balance, whose estimation accuracy has an impact on energy flux estimates from satellite data. In typical remote sensing evapotranspiration (ET algorithms, the outgoing shortwave and longwave components of net radiation are obtained from remote sensing data, while the incoming shortwave (RS and longwave (RL components are typically estimated from weather data using empirical equations. This study evaluates the accuracy of empirical equations commonly used in remote sensing ET algorithms for estimating RS and RL radiation. Evaluation is carried out through comparison of estimates and observations at five sites that represent different climatic regions from humid to arid. Results reveal (1 both RS and RL estimates from all evaluated equations well correlate with observations (R2 ≥ 0.92, (2 RS estimating equations tend to overestimate, especially at higher values, (3 RL estimating equations tend to give more biased values in arid and semi-arid regions, (4 a model that parameterizes the diffuse component of radiation using two clearness indices and a simple model that assumes a linear increase of atmospheric transmissivity with elevation give better RS estimates, and (5 mean relative absolute errors in the net radiation (Rn estimates caused by the use of RS and RL estimating equations varies from 10% to 22%. This study suggests that Rn estimates using recommended incoming radiation estimating equations could improve ET estimates.

Spin and energy evolution equations for a wide class of extended bodies

International Nuclear Information System (INIS)

Racine, Etienne

2006-01-01

We give a surface integral derivation of the leading-order evolution equations for the spin and energy of a relativistic body interacting with other bodies in the post-Newtonian expansion scheme. The bodies can be arbitrarily shaped and can be strongly self-gravitating. The effects of all mass and current multipoles are taken into account. As part of the computation one of the 2PN potentials parametrizing the metric is obtained. The formulae obtained here for spin and energy evolution coincide with those obtained by Damour, Soffel and Xu for the case of weakly self-gravitating bodies. By combining an Einstein-Infeld-Hoffman-type surface integral approach with multipolar expansions we extend the domain of validity of these evolution equations to a wide class of strongly self-gravitating bodies. This paper completes in a self-contained way a previous work by Racine and Flanagan on translational equations of motion for compact objects

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

Pautz, S. D.; Franke, B. C.; Prinja, A. K.

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

State and parameter estimation in a nuclear fuel pin using the extended Kalman filter

International Nuclear Information System (INIS)

Feeley, J.J.

1979-03-01

The Kalman filter is a powerful tool for the design and analysis of stochastic systems. The general nature of the method permits such diverse applications as on-line state estimation in optimal control systems, as well as state and parameter estimation applications in data analysis and system identification. However, while there have been a large number of Kalman filter applications in the aerospace industry, there have been relatively few in the nuclear industry. The report describes some initial efforts made at the Idaho National Engineering Laboratory to gain experience with the methods of Kalman filtering and to test their applicability to nuclear engineering problems. Two specific cases were considered: first, a real-time state estimation problem using a hybrid computer where the process was simulated on the analog portion of the computer, and the Kalman filter was programmed on the digital portion; second, a system identification problem where a digital extended Kalman filter program was used to estimate states and parameters in a nuclear fuel pin using data generated both by actual experiments and computer simulations. The report contains a derivation of the Kalman filter equations, a development of the mathematical model of the nuclear fuel pin, a description of the computer programs used in the analysis, and a discussion of the results obtained

Determination of source terms in a degenerate parabolic equation

International Nuclear Information System (INIS)

Cannarsa, P; Tort, J; Yamamoto, M

2010-01-01

In this paper, we prove Lipschitz stability results for inverse source problems relative to parabolic equations. We use the method introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates. What is new here is that we study a class of one-dimensional degenerate parabolic equations. In our model, the diffusion coefficient vanishes at one extreme point of the domain. Instead of the classical Carleman estimates obtained by Fursikov and Imanuvilov for non degenerate equations, we use and extend some recent Carleman estimates for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble. Finally, we obtain Lipschitz stability results in inverse source problems for our class of degenerate parabolic equations both in the case of a boundary observation and in the case of a locally distributed observation

Concurrent hyperthermia estimation schemes based on extended Kalman filtering and reduced-order modelling.

Science.gov (United States)

Potocki, J K; Tharp, H S

1993-01-01

The success of treating cancerous tissue with heat depends on the temperature elevation, the amount of tissue elevated to that temperature, and the length of time that the tissue temperature is elevated. In clinical situations the temperature of most of the treated tissue volume is unknown, because only a small number of temperature sensors can be inserted into the tissue. A state space model based on a finite difference approximation of the bioheat transfer equation (BHTE) is developed for identification purposes. A full-order extended Kalman filter (EKF) is designed to estimate both the unknown blood perfusion parameters and the temperature at unmeasured locations. Two reduced-order estimators are designed as computationally less intensive alternatives to the full-order EKF. Simulation results show that the success of the estimation scheme depends strongly on the number and location of the temperature sensors. Superior results occur when a temperature sensor exists in each unknown blood perfusion zone, and the number of sensors is at least as large as the number of unknown perfusion zones. Unacceptable results occur when there are more unknown perfusion parameters than temperature sensors, or when the sensors are placed in locations that do not sample the unknown perfusion information.

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

Science.gov (United States)

Leander, Jacob; Lundh, Torbjörn; Jirstrand, Mats

2014-05-01

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

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

Science.gov (United States)

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

2018-05-03

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

Equation of motion for estimation fidelity of monitored oscillating qubits

CSIR Research Space (South Africa)

Bassa, H

2017-08-01

Full Text Available We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of discrete, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation fidelity from a...

PERTURBATION ESTIMATES FOR THE MAXIMAL SOLUTION OF A NONLINEAR MATRIX EQUATION

Directory of Open Access Journals (Sweden)

Vejdi I. Hasanov

2017-06-01

Full Text Available In this paper a nonlinear matrix equation is considered. Perturba- tion estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical ex- amples.

Body composition in elderly people: effect of criterion estimates on predictive equations

International Nuclear Information System (INIS)

Baumgartner, R.N.; Heymsfield, S.B.; Lichtman, S.; Wang, J.; Pierson, R.N. Jr.

1991-01-01

The purposes of this study were to determine whether there are significant differences between two- and four-compartment model estimates of body composition, whether these differences are associated with aqueous and mineral fractions of the fat-free mass (FFM); and whether the differences are retained in equations for predicting body composition from anthropometry and bioelectric resistance. Body composition was estimated in 98 men and women aged 65-94 y by using a four-compartment model based on hydrodensitometry, 3 H 2 O dilution, and dual-photon absorptiometry. These estimates were significantly different from those obtained by using Siri's two-compartment model. The differences were associated significantly (P less than 0.0001) with variation in the aqueous fraction of FFM. Equations for predicting body composition from anthropometry and resistance, when calibrated against two-compartment model estimates, retained these systematic errors. Equations predicting body composition in elderly people should be calibrated against estimates from multicompartment models that consider variability in FFM composition

Allometric Equations for Estimating Carbon Stocks in Natural Forest in New Zealand

Directory of Open Access Journals (Sweden)

Andrea Brandon

2012-09-01

Full Text Available Species-specific and mixed-species volume and above ground biomass allometric equations were developed for 15 indigenous tree species and four tree fern species in New Zealand. A mixed-species tree equation based on breast height diameter (DBH and tree height (H provided acceptable estimates of stem plus branch (>10 cm in diameter over bark volume, which was multiplied by live tree density to estimate dry matter. For dead standing spars, DBH, estimated original height, actual spar height and compatible volume/taper functions provided estimates of dead stem volume, which was multiplied by live tree density and a density modifier based on log decay class from field assessments to estimate dry matter. Live tree density was estimated using ratio estimators. Ratio estimators were based on biomass sample trees, and utilized density data from outerwood basic density surveys which were available for 35 tree species sampled throughout New Zealand. Foliage and branch ( < 10 cm in diameter over bark dry matter were estimated directly from tree DBH. Tree fern above ground dry matter was estimated using allometric equations based on DBH and H. Due to insufficient data, below ground carbon for trees was estimated using the default IPCC root/shoot ratio of 25%, but for tree ferns it was estimated using measured root/shoot ratios which averaged 20%.

Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

Science.gov (United States)

Finster, Felix; Smoller, Joel

2010-09-01

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.

Estimates for Solutions of Differential Equations in a Banach Space via Commutators

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Gil’ Michael

2018-02-01

Full Text Available In a Banach space we consider the equation dx(t/dt = (A + B(t×(t (t ≥ 0, where A is a constant bounded operator, and B(t is a bounded variable operator.Norm estimates for the solutions of the considered equation are derived in terms of the commutator AB(t − B(tA. These estimates give us sharp stability conditions. Our results are new even in the finite dimensional case.We also discuss applications of the obtained results to a class of integro-differential equations.

Strichartz Estimates for the Schrödinger Equation

OpenAIRE

CORDERO, ELENA; ZUCCO, DAVIDE

2010-01-01

The objective of this paper is to report on recent progress on Strichartz estimates for the Schrödinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in Wiener amalgam and modulation spaces. We present and compare the different technicalities. Then, we illustrate applications to well-posedness. El objetivo de este trabajo es reportar los progresos recientes sobre estimativas de Strichartz para la ecuación ...

Growth of meromorphic solutions of higher-order linear differential equations

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Wenjuan Chen

2009-01-01

Full Text Available In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider the nonhomogeneous linear differential equations.

Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations

OpenAIRE

Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril

2011-01-01

We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hoelder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the loc...

Estimating glomerular filtration rate using the new CKD-EPI equation and other equations in patients with autosomal dominant polycystic kidney disease

DEFF Research Database (Denmark)

Orskov, Bjarne; Borresen, Malene L; Feldt-Rasmussen, Bo

2010-01-01

(CKD-EPI) equation, the Cockcroft-Gault equation adjusted for body surface area and the MDRD equation with cystatin C. Performance was evaluated by mean bias, precision and accuracy. RESULTS: The MDRD equation with cystatin C had 97% of GFR estimates within 30% of measured GFR (accuracy). Both the CKD-EPI....... The CKD-EPI or the Cockcroft-Gault equations showed better performance compared to the 4-variable MDRD equation....

Estimating varying coefficients for partial differential equation models.

Science.gov (United States)

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

2017-09-01

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

A variational approach to parameter estimation in ordinary differential equations

Directory of Open Access Journals (Sweden)

Kaschek Daniel

2012-08-01

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

A variational approach to parameter estimation in ordinary differential equations.

Science.gov (United States)

Kaschek, Daniel; Timmer, Jens

2012-08-14

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

Novel equations to estimate lean body mass in maintenance hemodialysis patients.

Science.gov (United States)

Noori, Nazanin; Kovesdy, Csaba P; Bross, Rachelle; Lee, Martin; Oreopoulos, Antigone; Benner, Deborah; Mehrotra, Rajnish; Kopple, Joel D; Kalantar-Zadeh, Kamyar

2011-01-01

Lean body mass (LBM) is an important nutritional measure representing muscle mass and somatic protein in hemodialysis patients, for whom we developed and tested equations to estimate LBM. A study of diagnostic test accuracy. The development cohort included 118 hemodialysis patients with LBM measured using dual-energy x-ray absorptiometry (DEXA) and near-infrared (NIR) interactance. The validation cohort included 612 additional hemodialysis patients with LBM measured using a portable NIR interactance technique during hemodialysis. 3-month averaged serum concentrations of creatinine, albumin, and prealbumin; normalized protein nitrogen appearance; midarm muscle circumference (MAMC); handgrip strength; and subjective global assessment of nutrition. LBM measured using DEXA in the development cohort and NIR interactance in validation cohorts. In the development cohort, DEXA and NIR interactance correlated strongly (r = 0.94, P < 0.001). DEXA-measured LBM correlated with serum creatinine level, MAMC, and handgrip strength, but not with other nutritional markers. Three regression equations to estimate DEXA-measured LBM were developed based on each of these 3 surrogates and sex, height, weight, and age (and urea reduction ratio for the serum creatinine regression). In the validation cohort, the validity of the equations was tested against the NIR interactance-measured LBM. The equation estimates correlated well with NIR interactance-measured LBM (R² ≥ 0.88), although in higher LBM ranges, they tended to underestimate it. Median (95% confidence interval) differences and interquartile range for differences between equation estimates and NIR interactance-measured LBM were 3.4 (-3.2 to 12.0) and 3.0 (1.1-5.1) kg for serum creatinine and 4.0 (-2.6 to 13.6) and 3.7 (1.3-6.0) kg for MAMC, respectively. DEXA measurements were obtained on a nondialysis day, whereas NIR interactance was performed during hemodialysis treatment, with the likelihood of confounding by volume status

[Estimating glomerular filtration rate in 2012: which adding value for the CKD-EPI equation?].

Science.gov (United States)

Delanaye, Pierre; Mariat, Christophe; Moranne, Olivier; Cavalier, Etienne; Flamant, Martin

2012-07-01

Measuring or estimating glomerular filtration rate (GFR) is still considered as the best way to apprehend global renal function. In 2009, the new Chronic Kidney Disease Epidemiology (CKD-EPI) equation has been proposed as a better estimator of GFR than the Modification of Diet in Renal Disease (MDRD) study equation. This new equation is supposed to underestimate GFR to a lesser degree in higher GFR levels. In this review, we will present and deeply discuss the performances of this equation. Based on articles published between 2009 and 2012, this review will underline advantages, notably the better knowledge of chronic kidney disease prevalence, but also limitations of this new equation, especially in some specific populations. We eventually insist on the fact that all these equations are estimations and nephrologists should remain cautious in their interpretation. Copyright © 2012 Association Société de néphrologie. Published by Elsevier SAS. All rights reserved.

Robust estimation for ordinary differential equation models.

Science.gov (United States)

Cao, J; Wang, L; Xu, J

2011-12-01

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

Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints

Directory of Open Access Journals (Sweden)

Adom Giffin

2014-09-01

Full Text Available In this paper, we continue our efforts to show how maximum relative entropy (MrE can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF. However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA. Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.

Improving North American forest biomass estimates from literature synthesis and meta-analysis of existing biomass equations

Science.gov (United States)

David C. Chojnacky; Jennifer C. Jenkins; Amanda K. Holland

2009-01-01

Thousands of published equations purport to estimate biomass of individual trees. These equations are often based on very small samples, however, and can provide widely different estimates for trees of the same species. We addressed this issue in a previous study by devising 10 new equations that estimated total aboveground biomass for all species in North America (...

Application of the Extended Grunwald-Winstein Equation to Solvolyses of n-Propyl Chloroformate

OpenAIRE

Kyong, Jin Burm; Won, Hoshik; Kevill, Dennis N.

2005-01-01

Abstract: Application of the extended Grunwald-Winstein equation to solvolyses of n-propyl chloroformate in a variety of pure and binary solvents indicates an addition-elimination pathway in the majority of the solvents but an ionization pathway in the solvents of highest ionizing power and lowest nucleophilicity. For methanolysis, a solvent deuterium isotope effect of 2.17 is compatible with the incorporation of general-base catalysis into the substitution process. Activation parameters are ...

Lidar method to estimate emission rates from extended sources

Science.gov (United States)

Currently, point measurements, often combined with models, are the primary means by which atmospheric emission rates are estimated from extended sources. However, these methods often fall short in their spatial and temporal resolution and accuracy. In recent years, lidar has emerged as a suitable to...

Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests.

Science.gov (United States)

Ishihara, Masae I; Utsugi, Hajime; Tanouchi, Hiroyuki; Aiba, Masahiro; Kurokawa, Hiroko; Onoda, Yusuke; Nagano, Masahiro; Umehara, Toru; Ando, Makoto; Miyata, Rie; Hiura, Tsutom

2015-07-01

Accurate estimation of tree and forest biomass is key to evaluating forest ecosystem functions and the global carbon cycle. Allometric equations that estimate tree biomass from a set of predictors, such as stem diameter and tree height, are commonly used. Most allometric equations are site specific, usually developed from a small number of trees harvested in a small area, and are either species specific or ignore interspecific differences in allometry. Due to lack of site-specific allometries, local equations are often applied to sites for which they were not originally developed (foreign sites), sometimes leading to large errors in biomass estimates. In this study, we developed generic allometric equations for aboveground biomass and component (stem, branch, leaf, and root) biomass using large, compiled data sets of 1203 harvested trees belonging to 102 species (60 deciduous angiosperm, 32 evergreen angiosperm, and 10 evergreen gymnosperm species) from 70 boreal, temperate, and subtropical natural forests in Japan. The best generic equations provided better biomass estimates than did local equations that were applied to foreign sites. The best generic equations included explanatory variables that represent interspecific differences in allometry in addition to stem diameter, reducing error by 4-12% compared to the generic equations that did not include the interspecific difference. Different explanatory variables were selected for different components. For aboveground and stem biomass, the best generic equations had species-specific wood specific gravity as an explanatory variable. For branch, leaf, and root biomass, the best equations had functional types (deciduous angiosperm, evergreen angiosperm, and evergreen gymnosperm) instead of functional traits (wood specific gravity or leaf mass per area), suggesting importance of other traits in addition to these traits, such as canopy and root architecture. Inclusion of tree height in addition to stem diameter improved

Parameter estimation in a simple stochastic differential equation for phytoplankton modelling

DEFF Research Database (Denmark)

Møller, Jan Kloppenborg; Madsen, Henrik; Carstensen, Jacob

2011-01-01

The use of stochastic differential equations (SDEs) for simulation of aquatic ecosystems has attracted increasing attention in recent years. The SDE setting also provides the opportunity for statistical estimation of ecosystem parameters. We present an estimation procedure, based on Kalman...

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

Convex Hypersurfaces and $L^p$ Estimates for Schr\\"odinger Equations

OpenAIRE

Zheng, Quan; Yao, Xiaohua; Fan, Da

2004-01-01

This paper is concerned with Schr\\"odinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the $L^p$ estimate of solutions for the initial data belonging to a dense subset of $L^p$ in the case of integrable potentials.

A relativistic extended Fermi-Thomas-like equation for a self-gravitating system of fermions

International Nuclear Information System (INIS)

Merloni, A.; Ruffini, R.; Torroni, V.

1998-01-01

The authors extend previous results of a Fermi-Thomas model, describing self-gravitating fermions in their ground state, to a relativistic gravitational theory in Minkowski space. In such a theory the source term of the gravitational potential depends both on the pressure and the density of the fluid. It is shown that, in correspondence of this relativistic treatment, still a Fermi-Thomas-like equation can be derived for the self-gravitating system, though the non-linearities are much more complex. No Fermi-Thomas-like equation can be obtained in the General Relativistic treatment. The canonical results for neutron stars and white dwarfs are recovered and also some erroneous statements in the scientific literature are corrected

Estimation of monthly solar exposure on horizontal surface by Angstrom-type regression equation

International Nuclear Information System (INIS)

Ravanshid, S.H.

1981-01-01

To obtain solar flux intensity, solar radiation measuring instruments are the best. In the absence of instrumental data there are other meteorological measurements which are related to solar energy and also it is possible to use empirical relationships to estimate solar flux intensit. One of these empirical relationships to estimate monthly averages of total solar radiation on a horizontal surface is the modified angstrom-type regression equation which has been employed in this report in order to estimate the solar flux intensity on a horizontal surface for Tehran. By comparing the results of this equation with four years measured valued by Tehran's meteorological weather station the values of meteorological constants (a,b) in the equation were obtained for Tehran. (author)

A New Equation to Estimate Muscle Mass from Creatinine and Cystatin C.

Directory of Open Access Journals (Sweden)

Sun-wook Kim

Full Text Available With evaluation for physical performance, measuring muscle mass is an important step in detecting sarcopenia. However, there are no methods to estimate muscle mass from blood sampling.To develop a new equation to estimate total-body muscle mass with serum creatinine and cystatin C level, we designed a cross-sectional study with separate derivation and validation cohorts. Total body muscle mass and fat mass were measured using dual-energy x-ray absorptiometry (DXA in 214 adults aged 25 to 84 years who underwent physical checkups from 2010 to 2013 in a single tertiary hospital. Serum creatinine and cystatin C levels were also examined.Serum creatinine was correlated with muscle mass (P < .001, and serum cystatin C was correlated with body fat mass (P < .001 after adjusting glomerular filtration rate (GFR. After eliminating GFR, an equation to estimate total-body muscle mass was generated and coefficients were calculated in the derivation cohort. There was an agreement between muscle mass calculated by the novel equation and measured by DXA in both the derivation and validation cohort (P < .001, adjusted R2 = 0.829, β = 0.95, P < .001, adjusted R2 = 0.856, β = 1.03, respectively.The new equation based on serum creatinine and cystatin C levels can be used to estimate total-body muscle mass.

Design of TIR collimating lens for ordinary differential equation of extended light source

Science.gov (United States)

Zhan, Qianjing; Liu, Xiaoqin; Hou, Zaihong; Wu, Yi

2017-10-01

The source of LED has been widely used in our daily life. The intensity angle distribution of single LED is lambert distribution, which does not satisfy the requirement of people. Therefore, we need to distribute light and change the LED's intensity angle distribution. The most commonly method to change its intensity angle distribution is the free surface. Generally, using ordinary differential equations to calculate free surface can only be applied in a point source, but it will lead to a big error for the expand light. This paper proposes a LED collimating lens based on the ordinary differential equation, combined with the LED's light distribution curve, and adopt the method of calculating the center gravity of the extended light to get the normal vector. According to the law of Snell, the ordinary differential equations are constructed. Using the runge-kutta method for solution of ordinary differential equation solution, the curve point coordinates are gotten. Meanwhile, the edge point data of lens are imported into the optical simulation software TracePro. Based on 1mm×1mm single lambert body for light conditions, The degrees of collimating light can be close to +/-3. Furthermore, the energy utilization rate is higher than 85%. In this paper, the point light source is used to calculate partial differential equation method and compared with the simulation of the lens, which improve the effect of 1 degree of collimation.

Rhythmic Extended Kalman Filter for Gait Rehabilitation Motion Estimation and Segmentation.

Science.gov (United States)

Joukov, Vladimir; Bonnet, Vincent; Karg, Michelle; Venture, Gentiane; Kulic, Dana

2018-02-01

This paper proposes a method to enable the use of non-intrusive, small, wearable, and wireless sensors to estimate the pose of the lower body during gait and other periodic motions and to extract objective performance measures useful for physiotherapy. The Rhythmic Extended Kalman Filter (Rhythmic-EKF) algorithm is developed to estimate the pose, learn an individualized model of periodic movement over time, and use the learned model to improve pose estimation. The proposed approach learns a canonical dynamical system model of the movement during online observation, which is used to accurately model the acceleration during pose estimation. The canonical dynamical system models the motion as a periodic signal. The estimated phase and frequency of the motion also allow the proposed approach to segment the motion into repetitions and extract useful features, such as gait symmetry, step length, and mean joint movement and variance. The algorithm is shown to outperform the extended Kalman filter in simulation, on healthy participant data, and stroke patient data. For the healthy participant marching dataset, the Rhythmic-EKF improves joint acceleration and velocity estimates over regular EKF by 40% and 37%, respectively, estimates joint angles with 2.4° root mean squared error, and segments the motion into repetitions with 96% accuracy.

Parameter estimation of a three-axis spacecraft simulator using recursive least-squares approach with tracking differentiator and Extended Kalman Filter

Science.gov (United States)

Xu, Zheyao; Qi, Naiming; Chen, Yukun

2015-12-01

Spacecraft simulators are widely used to study the dynamics, guidance, navigation, and control of a spacecraft on the ground. A spacecraft simulator can have three rotational degrees of freedom by using a spherical air-bearing to simulate a frictionless and micro-gravity space environment. The moment of inertia and center of mass are essential for control system design of ground-based three-axis spacecraft simulators. Unfortunately, they cannot be known precisely. This paper presents two approaches, i.e. a recursive least-squares (RLS) approach with tracking differentiator (TD) and Extended Kalman Filter (EKF) method, to estimate inertia parameters. The tracking differentiator (TD) filter the noise coupled with the measured signals and generate derivate of the measured signals. Combination of two TD filters in series obtains the angular accelerations that are required in RLS (TD-TD-RLS). Another method that does not need to estimate the angular accelerations is using the integrated form of dynamics equation. An extended TD (ETD) filter which can also generate the integration of the function of signals is presented for RLS (denoted as ETD-RLS). States and inertia parameters are estimated simultaneously using EKF. The observability is analyzed. All proposed methods are illustrated by simulations and experiments.

Extended Kalman filter-based methods for pose estimation using visual, inertial and magnetic sensors: comparative analysis and performance evaluation.

Science.gov (United States)

Ligorio, Gabriele; Sabatini, Angelo Maria

2013-02-04

In this paper measurements from a monocular vision system are fused with inertial/magnetic measurements from an Inertial Measurement Unit (IMU) rigidly connected to the camera. Two Extended Kalman filters (EKFs) were developed to estimate the pose of the IMU/camera sensor moving relative to a rigid scene (ego-motion), based on a set of fiducials. The two filters were identical as for the state equation and the measurement equations of the inertial/magnetic sensors. The DLT-based EKF exploited visual estimates of the ego-motion using a variant of the Direct Linear Transformation (DLT) method; the error-driven EKF exploited pseudo-measurements based on the projection errors from measured two-dimensional point features to the corresponding three-dimensional fiducials. The two filters were off-line analyzed in different experimental conditions and compared to a purely IMU-based EKF used for estimating the orientation of the IMU/camera sensor. The DLT-based EKF was more accurate than the error-driven EKF, less robust against loss of visual features, and equivalent in terms of computational complexity. Orientation root mean square errors (RMSEs) of 1° (1.5°), and position RMSEs of 3.5 mm (10 mm) were achieved in our experiments by the DLT-based EKF (error-driven EKF); by contrast, orientation RMSEs of 1.6° were achieved by the purely IMU-based EKF.

Estimating structural equation models with non-normal variables by using transformations

NARCIS (Netherlands)

Montfort, van K.; Mooijaart, A.; Meijerink, F.

2009-01-01

We discuss structural equation models for non-normal variables. In this situation the maximum likelihood and the generalized least-squares estimates of the model parameters can give incorrect estimates of the standard errors and the associated goodness-of-fit chi-squared statistics. If the sample

Extended common-image-point gathers for anisotropic wave-equation migration

KAUST Repository

Sava, Paul C.

2010-01-01

In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes anisotropy parameters (Gray et al., 2001). In particular, it is important to construct subsurface velocity models using techniques that are consistent with the methods used for imaging. Generally speaking, there are two possible strategies for velocity estimation from surface seismic data in the context of wavefield-based imaging (Sava et al., 2010). One possibility is to formulate an objective function in the data space, prior to migration, by matching the recorded data with simulated data. Techniques in this category are known by the name of waveform inversion. Another possibility is to formulate an objective function in the image space, after migration, by measuring and correcting image features that indicate model inaccuracies. Techniques in this category are known as wave-equation migration velocity analysis (MVA).

The cluster bootstrap consistency in generalized estimating equations

KAUST Repository

Cheng, Guang

2013-03-01

The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference. © 2012.

Estimation of delays and other parameters in nonlinear functional differential equations

Science.gov (United States)

Banks, H. T.; Lamm, P. K. D.

1983-01-01

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Performance of Chronic Kidney Disease Epidemiology Collaboration Creatinine-Cystatin C Equation for Estimating Kidney Function in Cirrhosis

Science.gov (United States)

Mindikoglu, Ayse L.; Dowling, Thomas C.; Weir, Matthew R.; Seliger, Stephen L.; Christenson, Robert H.; Magder, Laurence S.

2013-01-01

Conventional creatinine-based glomerular filtration rate (GFR) equations are insufficiently accurate for estimating GFR in cirrhosis. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) recently proposed an equation to estimate GFR in subjects without cirrhosis using both serum creatinine and cystatin C levels. Performance of the new CKD-EPI creatinine-cystatin C equation (2012) was superior to previous creatinine- or cystatin C-based GFR equations. To evaluate the performance of the CKD-EPI creatinine-cystatin C equation in subjects with cirrhosis, we compared it to GFR measured by non-radiolabeled iothalamate plasma clearance (mGFR) in 72 subjects with cirrhosis. We compared the “bias”, “precision” and “accuracy” of the new CKD-EPI creatinine-cystatin C equation to that of 24-hour urinary creatinine clearance (CrCl), Cockcroft-Gault (CG) and previously reported creatinine- and/or cystatin C-based GFR-estimating equations. Accuracy of CKD-EPI creatinine-cystatin C equation as quantified by root mean squared error of difference scores [differences between mGFR and estimated GFR (eGFR) or between mGFR and CrCl, or between mGFR and CG equation for each subject] (RMSE=23.56) was significantly better than that of CrCl (37.69, P=0.001), CG (RMSE=36.12, P=0.002) and GFR-estimating equations based on cystatin C only. Its accuracy as quantified by percentage of eGFRs that differed by greater than 30% with respect to mGFR was significantly better compared to CrCl (P=0.024), CG (P=0.0001), 4-variable MDRD (P=0.027) and CKD-EPI creatinine 2009 (P=0.012) equations. However, for 23.61% of the subjects, GFR estimated by CKD-EPI creatinine-cystatin C equation differed from the mGFR by more than 30%. CONCLUSIONS The diagnostic performance of CKD-EPI creatinine-cystatin C equation (2012) in patients with cirrhosis was superior to conventional equations in clinical practice for estimating GFR. However, its diagnostic performance was substantially worse than

Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

KAUST Repository

Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.

2014-01-01

This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

A quantum extended Kalman filter

International Nuclear Information System (INIS)

Emzir, Muhammad F; Woolley, Matthew J; Petersen, Ian R

2017-01-01

In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements. (paper)

A quantum extended Kalman filter

Science.gov (United States)

Emzir, Muhammad F.; Woolley, Matthew J.; Petersen, Ian R.

2017-06-01

In quantum physics, a stochastic master equation (SME) estimates the state (density operator) of a quantum system in the Schrödinger picture based on a record of measurements made on the system. In the Heisenberg picture, the SME is a quantum filter. For a linear quantum system subject to linear measurements and Gaussian noise, the dynamics may be described by quantum stochastic differential equations (QSDEs), also known as quantum Langevin equations, and the quantum filter reduces to a so-called quantum Kalman filter. In this article, we introduce a quantum extended Kalman filter (quantum EKF), which applies a commutative approximation and a time-varying linearization to systems of nonlinear QSDEs. We will show that there are conditions under which a filter similar to a classical EKF can be implemented for quantum systems. The boundedness of estimation errors and the filtering problem with ‘state-dependent’ covariances for process and measurement noises are also discussed. We demonstrate the effectiveness of the quantum EKF by applying it to systems that involve multiple modes, nonlinear Hamiltonians, and simultaneous jump-diffusive measurements.

Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

Science.gov (United States)

Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-01-01

In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

Rational extended thermodynamics

CERN Document Server

Müller, Ingo

1998-01-01

Ordinary thermodynamics provides reliable results when the thermodynamic fields are smooth, in the sense that there are no steep gradients and no rapid changes. In fluids and gases this is the domain of the equations of Navier-Stokes and Fourier. Extended thermodynamics becomes relevant for rapidly varying and strongly inhomogeneous processes. Thus the propagation of high­ frequency waves, and the shape of shock waves, and the regression of small-scale fluctuation are governed by extended thermodynamics. The field equations of ordinary thermodynamics are parabolic while extended thermodynamics is governed by hyperbolic systems. The main ingredients of extended thermodynamics are • field equations of balance type, • constitutive quantities depending on the present local state and • entropy as a concave function of the state variables. This set of assumptions leads to first order quasi-linear symmetric hyperbolic systems of field equations; it guarantees the well-posedness of initial value problems and f...

Superimposed chirped pulse parameter estimation based on the extended Kalman filter (EKF)

CSIR Research Space (South Africa)

Olivier, JC

2009-05-01

Full Text Available An extended Kalman filter (EKF) is proposed to estimate the frequencies and chirp rate of multiple superimposed chirped pulses. The estimation problem is a difficult one, where maximum likelyhood methods are very complex especially if more than two...

ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations

Directory of Open Access Journals (Sweden)

Espen R. Jakobsen

2002-05-01

Full Text Available Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and Holder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.

Working covariance model selection for generalized estimating equations.

Science.gov (United States)

Carey, Vincent J; Wang, You-Gan

2011-11-20

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

On-line structural response analysis: using the extended Kalman estimator/identifier

International Nuclear Information System (INIS)

Candy, J.V.

1979-01-01

This report disucsses the development of on-line state and parameter estimators used to analyze the structural response of buildings. The estimator/identifier is an extended Kalman filter (EKF), which has been applied with great success in other technological areas. It is shown that the EKF can perform quite well on simulated noisy structural response data

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem

2017-01-01

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a

Parameter Estimates in Differential Equation Models for Population Growth

Science.gov (United States)

Winkel, Brian J.

2011-01-01

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

Generalized Ordinary Differential Equation Models.

Science.gov (United States)

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

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

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

Science.gov (United States)

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

1997-01-01

Design hydrographs computed from design storms, simple models of abstractions (interception, depression storage, and infiltration), and synthetic unit hydrographs provide vital information for stormwater, flood-plain, and water-resources management throughout the United States. Rainfall and runoff data for small watersheds in Lake County collected between 1990 and 1995 were studied to develop equations for estimation of synthetic unit-hydrograph parameters on the basis of watershed and storm characteristics. The synthetic unit-hydrograph parameters of interest were the time of concentration (TC) and watershed-storage coefficient (R) for the Clark unit-hydrograph method, the unit-graph lag (UL) for the Soil Conservation Service (now known as the Natural Resources Conservation Service) dimensionless unit hydrograph, and the hydrograph-time lag (TL) for the linear-reservoir method for unit-hydrograph estimation. Data from 66 storms with effective-precipitation depths greater than 0.4 inches on 9 small watersheds (areas between 0.06 and 37 square miles (mi2)) were utilized to develop the estimation equations, and data from 11 storms on 8 of these watersheds were utilized to verify (test) the estimation equations. The synthetic unit-hydrograph parameters were determined by calibration using the U.S. Army Corps of Engineers Flood Hydrograph Package HEC-1 (TC, R, and UL) or by manual analysis of the rainfall and run-off data (TL). The relation between synthetic unit-hydrograph parameters, and watershed and storm characteristics was determined by multiple linear regression of the logarithms of the parameters and characteristics. Separate sets of equations were developed with watershed area and main channel length as the starting parameters. Percentage of impervious cover, main channel slope, and depth of effective precipitation also were identified as important characteristics for estimation of synthetic unit-hydrograph parameters. The estimation equations utilizing area

Equations to Estimate Creatinine Excretion Rate : The CKD Epidemiology Collaboration

NARCIS (Netherlands)

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.

Background and objectives 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. Design, setting, participants, & measurements Participants

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

Science.gov (United States)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation

Directory of Open Access Journals (Sweden)

Xiaoyan Deng

2009-01-01

into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.

Development of Estimating Equation of Machine Operational Skill by Utilizing Eye Movement Measurement and Analysis of Stress and Fatigue

Directory of Open Access Journals (Sweden)

Satoshi Suzuki

2013-01-01

Full Text Available For an establishment of a skill evaluation method for human support systems, development of an estimating equation of the machine operational skill is presented. Factors of the eye movement such as frequency, velocity, and moving distance of saccade were computed using the developed eye gaze measurement system, and the eye movement features were determined from these factors. The estimating equation was derived through an outlier test (to eliminate nonstandard data and a principal component analysis (to find dominant components. Using a cooperative carrying task (cc-task simulator, the eye movement and operational data of the machine operators were recorded, and effectiveness of the derived estimating equation was investigated. As a result, it was confirmed that the estimating equation was effective strongly against actual simple skill levels (r=0.56–0.84. In addition, effects of internal condition such as fatigue and stress on the estimating equation were analyzed. Using heart rate (HR and coefficient of variation of R-R interval (Cvrri. Correlation analysis between these biosignal indexes and the estimating equation of operational skill found that the equation reflected effects of stress and fatigue, although the equation could estimate the skill level adequately.

Equations for estimating Clark Unit-hydrograph parameters for small rural watersheds in Illinois

Science.gov (United States)

Straub, Timothy D.; Melching, Charles S.; Kocher, Kyle E.

2000-01-01

Equations for estimating the time of concentration (TC) and storage coefficient (R) of the Clark unit-hydrograph method were developed for small rural watersheds [0.02-2.3 square miles (mi2)] in Illinois. The equations will provide State and local engineers and planners with more accurate methods to estimate the TC and R for use in simulating discharge hydrographs on small rural watersheds when designing stormwater-management facilities and other hydraulic structures, determining flood-plain boundaries, and assessing the safety of structures in rivers. The rainfall and runoff data from gaged small rural watersheds (0.02-2.3 mi2) with insignificant amounts of impervious land cover in Illinois were used to develop the equations.

Validation of the Ejike-Ijeh equations for the estimation of body fat ...

African Journals Online (AJOL)

The Ejike-Ijeh equations for the estimation of body fat percentage makes it possible for the body fat content of individuals and populations to be determined without the use of costly equipment. However, because the equations were derived using data from a young-adult (18-29 years old) Nigerian population, it is important ...

Parameter Estimation of Partial Differential Equation Models.

Science.gov (United States)

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

2013-01-01

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

Equi-frequency contour of photonic crystals with the extended Dirichlet-to-Neumann wave vector eigenvalue equation method

International Nuclear Information System (INIS)

Jiang Bin; Zhang Yejing; Wang Yufei; Liu Anjin; Zheng Wanhua

2012-01-01

We present the extended Dirichlet-to-Neumann wave vector eigenvalue equation (DtN-WVEE) method to calculate the equi-frequency contour (EFC) of square lattice photonic crystals (PhCs). With the extended DtN-WVEE method and Snell's law, the effective refractive index of the mode with a circular EFC can be obtained, which is further validated with the refractive index weighted by the electric field or magnetic field. To further verify the EFC calculated by the DtN-WVEE method, the finite-difference time-domain method is also used. Compared with other wave vector eigenvalue equation methods that calculate EFC directly, the size of the eigenmatrix used in the DtN-WVEE method is much smaller, and the computation time is significantly reduced. Since the DtN-WVEE method solves wave vectors for given arbitrary frequencies, it can also find applications in studying the optical properties of a PhC with dispersive, lossy and magnetic materials. (paper)

Explicit estimating equations for semiparametric generalized linear latent variable models

KAUST Repository

Ma, Yanyuan

2010-07-05

We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.

Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation

International Nuclear Information System (INIS)

Ye, Caier; Zhang, Weiguo

2015-01-01

Highlights: • Analyze the dynamical behavior of the planar dynamical system corresponding to the perturbed Klein–Gordon equation. • Present the relations between the properties of traveling wave solutions and the perturbation coefficient. • Obtain all explicit expressions of approximate damped oscillatory solutions. • Investigate error estimates between exact damped oscillatory solutions and the approximate solutions and give some numerical simulations. - Abstract: The influence of perturbation on traveling wave solutions of the perturbed Klein–Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis

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

Energy Technology Data Exchange (ETDEWEB)

Verochana, Karune; Prapayasatok, Sangsom; Janhom, Apirum; Mahasantipiya, Phattaranant May; Korwanich, Narumanas [Faculty of Dentistry, Chiang Mai University, Chiang Mai (Thailand)

2016-03-15

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

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

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Science.gov (United States)

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

2016-03-01

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

Estimation of In Situ Stress and Permeability from an Extended Leak-off Test

Science.gov (United States)

Nghiep Quach, Quoc; Jo, Yeonguk; Chang, Chandong; Song, Insun

2016-04-01

Among many parameters needed to analyze a variety of geomechanical problems related to subsurface CO2 storage projects, two important ones are in situ stress states and permeability of the storage reservoirs and cap rocks. In situ stress is needed for investigating potential risk of fault slip in the reservoir systems and permeability is needed for assessing reservoir flow characteristics and sealing capability of cap rocks. We used an extended leak-off test (XLOT), which is often routinely conducted to assess borehole/casing integrity as well as fracture gradient, to estimate both in situ least principal stress magnitude and in situ permeability in a CO2 storage test site, offshore southeast Korea. The XLOT was conducted at a casing shoe depth (700 m below seafloor) within the cap rock consisting of mudstone, approximately 50 m above the interface between cap rock and storage reservoir. The test depth was cement-grouted and remained for 4 days for curing. Then the hole was further drilled below the casing shoe to create a 4 m open-hole interval at the bottom. Water was injected using hydraulic pump at an approximately constant flowrate into the bottom interval through the casing, during which pressure and flowrate were recorded continuously at the surface. The interval pressure (P) was increased linearly with time (t) as water was injected. At some point, the slope of P-t curve deviated from the linear trend, which indicates leak-off. Pressure reached its peak upon formation breakdown, followed by a gradual pressure decrease. Soon after the formation breakdown, the hole was shut-in by pump shut-off, from which we determined the instantaneous shut-in pressure (ISIP). The ISIP was taken to be the magnitude of the in situ least principal stress (S3), which was determined to be 12.1 MPa. This value is lower than the lithostatic vertical stress, indicating that the S3 is the least horizontal principal stress. The determined S3 magnitude will be used to characterize the

Applicability of the Schwartz Equation and the Chronic Kidney Disease in Children Bedside Equation for Estimating Glomerular Filtration Rate in Overweight Children.

Science.gov (United States)

Lewis, Teresa V; Harrison, Donald L; Gildon, Brooke L; Carter, Sandra M; Turman, Martin A

2016-06-01

To determine if significant correlations exist between glomerular filtration rate (GFR) prediction equation values, derived by using the original Schwartz equation and the Chronic Kidney Disease in Children (CKiD) bedside equation with a 24-hour urine creatinine clearance (Clcr ) value normalized to a body surface area of 1.73 m(2) in overweight and obese children. Prospective analysis (20 patients) and retrospective analysis (43 patients). Pediatric inpatient ward and pediatric nephrology clinic at a comprehensive academic medical center. Sixty-three pediatric patients (aged 5-17 years), of whom 27 were overweight (body mass index [BMI] at the 85th percentile or higher) and 36 were not overweight (BMI lower than the 85th percentile [controls]) between 2007 and 2012. Data from the overweight patients were compared with nonoverweight controls. GFR values were calculated by using the original Schwartz equation and the CKiD bedside equation. Each patient's 24-hour urine Clcr value normalized to a body surface area of 1.73 m(2) served as the index value. A Pearson correlation coefficient model was used to determine association between the 24-hour urine Clcr value (index value) with the Schwartz and CKiD GFR estimations. Significant correlation was found to exist between the Schwartz and CKiD bedside GFR estimations relative to the 24-hour urine Clcr in the control subjects (r = 0.85, poverweight subjects (r = 0.86, poverweight children with a kidney disorder. The CKiD bedside GFR estimations were not significantly different compared with 24-hour urine Clcr values for the overweight group with kidney disorder (p=0.85). The Schwartz and CKiD bedside estimations of GFR correlated with 24-hour urine Clcr values in both overweight and nonoverweight children. Compared with the Schwartz equation, which tended to overestimate renal function, the CKiD bedside equation appeared to approximate 24-hour urine Clcr more closely in overweight children with kidney disorder. © 2016

Estimation of the Dynamic States of Synchronous Machines Using an Extended Particle Filter

Energy Technology Data Exchange (ETDEWEB)

Zhou, Ning; Meng, Da; Lu, Shuai

2013-11-11

In this paper, an extended particle filter (PF) is proposed to estimate the dynamic states of a synchronous machine using phasor measurement unit (PMU) data. A PF propagates the mean and covariance of states via Monte Carlo simulation, is easy to implement, and can be directly applied to a non-linear system with non-Gaussian noise. The extended PF modifies a basic PF to improve robustness. Using Monte Carlo simulations with practical noise and model uncertainty considerations, the extended PF’s performance is evaluated and compared with the basic PF and an extended Kalman filter (EKF). The extended PF results showed high accuracy and robustness against measurement and model noise.

Application of the Extended Grunwald-Winstein Equation to Solvolyses of n-Propyl Chloroformate

Directory of Open Access Journals (Sweden)

Dennis N. Kevill

2005-01-01

Full Text Available Abstract: Application of the extended Grunwald-Winstein equation to solvolyses of n-propyl chloroformate in a variety of pure and binary solvents indicates an addition-elimination pathway in the majority of the solvents but an ionization pathway in the solvents of highest ionizing power and lowest nucleophilicity. For methanolysis, a solvent deuterium isotope effect of 2.17 is compatible with the incorporation of general-base catalysis into the substitution process. Activation parameters are consistent with the duality of mechanism. Very modest positive salt effects are observed on adding chloride or bromide salts to the ethanolysis.

High precision estimation of inertial rotation via the extended Kalman filter

Science.gov (United States)

Liu, Lijun; Qi, Bo; Cheng, Shuming; Xi, Zairong

2015-11-01

Recent developments in technology have enabled atomic gyroscopes to become the most sensitive inertial sensors. Atomic spin gyroscopes essentially output an estimate of the inertial rotation rate to be measured. In this paper, we present a simple yet efficient estimation method, the extended Kalman filter (EKF), for the atomic spin gyroscope. Numerical results show that the EKF method is much more accurate than the steady-state estimation method, which is used in the most sensitive atomic gyroscopes at present. Specifically, the root-mean-squared errors obtained by the EKF method are at least 103 times smaller than those obtained by the steady-state estimation method under the same response time.

Allometric Equations for Estimating Biomass and Carbon Stocks in the Temperate Forests of North-Western Mexico

Directory of Open Access Journals (Sweden)

Benedicto Vargas-Larreta

2017-07-01

Full Text Available This paper presents new equations for estimating above-ground biomass (AGB and biomass components of seventeen forest species in the temperate forests of northwestern Mexico. A data set corresponding to 1336 destructively sampled oak and pine trees was used to fit the models. The generalized method of moments was used to simultaneously fit systems of equations for biomass components and AGB, to ensure additivity. In addition, the carbon content of each tree component was calculated by the dry combustion method, in a TOC analyser. The results of cross-validation indicated that the fitted equations accounted for on average 91%, 82%, 83% and 76% of the observed variance in stem wood and stem bark, branch and foliage biomass, respectively, whereas the total AGB equations explained on average 93% of the total observed variance in AGB. The inclusion of total height (h or diameter at breast height2 × total height (d2h as a predictor in the d-only based equations systems slightly improved estimates for stem wood, stem bark and total above-ground biomass, and greatly improved the estimates produced by the branch and foliage biomass equations. The predictive power of the proposed equations is higher than that of existing models for the study area. The fitted equations were used to estimate stand level AGB stocks from data on growing stock in 429 permanent sampling plots. Three machine-learning techniques were used to model the estimated stand level AGB and carbon contents; the selected models were used to map the AGB and carbon distributions in the study area, for which mean values of respectively 129.84 Mg ha−1 and 63.80 Mg ha−1 were obtained.

Coupling of atom-by-atom calculations of extended defects with B kick-out equations: application to the simulation of boron ted

International Nuclear Information System (INIS)

Lampin, E.; Cristiano, F.; Lamrani, Y.; Colombeau, B.

2004-01-01

We present simulations of B TED based on a complete calculation of the extended defect growth/shrinkage during annealing. The Si self-interstitial supersaturation calculated at the extended defect depth is coupled to the set of equations for the B kick-out diffusion through a generation/recombination term in the diffusion equation of the Si self-interstitials. The simulations are compared to the measurements performed on a Si wafer containing several B marker layers, where the amount of TED varies from one peak to the other. The good agreement obtained on this experiment is very promising for the application of these calculations to the case of ultra-shallow B + implants

Modelling conjugation with stochastic differential equations

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

2010-01-01

Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

Model Selection and Risk Estimation with Applications to Nonlinear Ordinary Differential Equation Systems

DEFF Research Database (Denmark)

Mikkelsen, Frederik Vissing

eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various......Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... package, episode. This package incorporates a collection of sparsity inducing penalties into two types of loss functions: a squared loss function relying on numerically solving the equations and an approximate loss function based on inverse collocation methods. The goal of this framework is to provide...

Development and validation of GFR-estimating equations using diabetes, transplant and weight

DEFF Research Database (Denmark)

Stevens, L.A.; Schmid, C.H.; Zhang, Y.L.

2009-01-01

interactions. Equations were developed in a pooled database of 10 studies [2/3 (N = 5504) for development and 1/3 (N = 2750) for internal validation], and final model selection occurred in 16 additional studies [external validation (N = 3896)]. RESULTS: The mean mGFR was 68, 67 and 68 ml/min/ 1.73 m(2......BACKGROUND: We have reported a new equation (CKD-EPI equation) that reduces bias and improves accuracy for GFR estimation compared to the MDRD study equation while using the same four basic predictor variables: creatinine, age, sex and race. Here, we describe the development and validation...... of this equation as well as other equations that incorporate diabetes, transplant and weight as additional predictor variables. METHODS: Linear regression was used to relate log-measured GFR (mGFR) to sex, race, diabetes, transplant, weight, various transformations of creatinine and age with and without...

Variable separation solutions for the Nizhnik-Novikov-Veselov equation via the extended tanh-function method

International Nuclear Information System (INIS)

Zhang Jiefang; Dai Chaoqing; Zong Fengde

2007-01-01

In this paper, with the variable separation approach and based on the general reduction theory, we successfully generalize this extended tanh-function method to obtain new types of variable separation solutions for the following Nizhnik-Novikov-Veselov (NNV) equation. Among the solutions, two solutions are new types of variable separation solutions, while the last solution is similar to the solution given by Darboux transformation in Hu et al 2003 Chin. Phys. Lett. 20 1413

Estimation of Resting Energy Expenditure: Validation of Previous and New Predictive Equations in Obese Children and Adolescents.

Science.gov (United States)

Acar-Tek, Nilüfer; Ağagündüz, Duygu; Çelik, Bülent; Bozbulut, Rukiye

2017-08-01

Accurate estimation of resting energy expenditure (REE) in childrenand adolescents is important to establish estimated energy requirements. The aim of the present study was to measure REE in obese children and adolescents by indirect calorimetry method, compare these values with REE values estimated by equations, and develop the most appropriate equation for this group. One hundred and three obese children and adolescents (57 males, 46 females) between 7 and 17 years (10.6 ± 2.19 years) were recruited for the study. REE measurements of subjects were made with indirect calorimetry (COSMED, FitMatePro, Rome, Italy) and body compositions were analyzed. In females, the percentage of accurate prediction varied from 32.6 (World Health Organization [WHO]) to 43.5 (Molnar and Lazzer). The bias for equations was -0.2% (Kim), 3.7% (Molnar), and 22.6% (Derumeaux-Burel). Kim's (266 kcal/d), Schmelzle's (267 kcal/d), and Henry's equations (268 kcal/d) had the lowest root mean square error (RMSE; respectively 266, 267, 268 kcal/d). The equation that has the highest RMSE values among female subjects was the Derumeaux-Burel equation (394 kcal/d). In males, when the Institute of Medicine (IOM) had the lowest accurate prediction value (12.3%), the highest values were found using Schmelzle's (42.1%), Henry's (43.9%), and Müller's equations (fat-free mass, FFM; 45.6%). When Kim and Müller had the smallest bias (-0.6%, 9.9%), Schmelzle's equation had the smallest RMSE (331 kcal/d). The new specific equation based on FFM was generated as follows: REE = 451.722 + (23.202 * FFM). According to Bland-Altman plots, it has been found out that the new equations are distributed randomly in both males and females. Previously developed predictive equations mostly provided unaccurate and biased estimates of REE. However, the new predictive equations allow clinicians to estimate REE in an obese children and adolescents with sufficient and acceptable accuracy.

Exact error estimation for solutions of nuclide chain equations

International Nuclear Information System (INIS)

Tachihara, Hidekazu; Sekimoto, Hiroshi

1999-01-01

The exact solution of nuclide chain equations within arbitrary figures is obtained for a linear chain by employing the Bateman method in the multiple-precision arithmetic. The exact error estimation of major calculation methods for a nuclide chain equation is done by using this exact solution as a standard. The Bateman, finite difference, Runge-Kutta and matrix exponential methods are investigated. The present study confirms the following. The original Bateman method has very low accuracy in some cases, because of large-scale cancellations. The revised Bateman method by Siewers reduces the occurrence of cancellations and thereby shows high accuracy. In the time difference method as the finite difference and Runge-Kutta methods, the solutions are mainly affected by the truncation errors in the early decay time, and afterward by the round-off errors. Even though the variable time mesh is employed to suppress the accumulation of round-off errors, it appears to be nonpractical. Judging from these estimations, the matrix exponential method is the best among all the methods except the Bateman method whose calculation process for a linear chain is not identical with that for a general one. (author)

Analytical estimations of limit cycle amplitude for delay-differential equations

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Tamás Molnár

2016-09-01

Full Text Available The amplitude of limit cycles arising from Hopf bifurcation is estimated for nonlinear delay-differential equations by means of analytical formulas. An improved analytical estimation is introduced, which allows more accurate quantitative prediction of periodic solutions than the standard approach that formulates the amplitude as a square-root function of the bifurcation parameter. The improved estimation is based on special global properties of the system: the method can be applied if the limit cycle blows up and disappears at a certain value of the bifurcation parameter. As an illustrative example, the improved analytical formula is applied to the problem of stick balancing.

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

Science.gov (United States)

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

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

Estimation of time- and state-dependent delays and other parameters in functional differential equations

Science.gov (United States)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Parameter Estimation of Partial Differential Equation Models

KAUST Repository

Xun, Xiaolei

2013-09-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.

Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow

KAUST Repository

Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem

2017-01-01

In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations

A Comparison of Regional and SiteSpecific Volume Estimation Equations

Science.gov (United States)

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

1987-01-01

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

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

Science.gov (United States)

Filici, Cristian

2010-06-01

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

Variability of glomerular filtration rate estimation equations in elderly Chinese patients with chronic kidney disease

Directory of Open Access Journals (Sweden)

Liu X

2012-10-01

Full Text Available Xun Liu,1,2,* Mu-hua Cheng,3,* Cheng-gang Shi,1 Cheng Wang,1 Cai-lian Cheng,1 Jin-xia Chen,1 Hua Tang,1 Zhu-jiang Chen,1 Zeng-chun Ye,1 Tan-qi Lou11Division of Nephrology, Department of Internal Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China; 2College of Biology Engineering, South China University of Technology, Guangzhou, China; 3Department of Nuclear Medicine, The Third Affiliated Hospital of Sun Yet-sun University, Guangzhou, China *These authors contributed equally to this paperBackground: Chronic kidney disease (CKD is recognized worldwide as a public health problem, and its prevalence increases as the population ages. However, the applicability of formulas for estimating the glomerular filtration rate (GFR based on serum creatinine (SC levels in elderly Chinese patients with CKD is limited.Materials and methods: Based on values obtained with the technetium-99m diethylenetriaminepentaacetic acid (99mTc-DTPA renal dynamic imaging method, 319 elderly Chinese patients with CKD were enrolled in this study. Serum creatinine was determined by the enzymatic method. The GFR was estimated using the Cockroft–Gault (CG equation, the Modification of Diet in Renal Disease (MDRD equations, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation, the Jelliffe-1973 equation, and the Hull equation.Results: The median of difference ranged from −0.3–4.3 mL/min/1.73 m2. The interquartile range (IQR of differences ranged from 13.9–17.6 mL/min/1.73 m2. Accuracy with a deviation less than 15% ranged from 27.6%–32.9%. Accuracy with a deviation less than 30% ranged from 53.6%–57.7%. Accuracy with a deviation less than 50% ranged from 74.9%–81.5%. None of the equations had accuracy up to the 70% level with a deviation less than 30% from the standard glomerular filtration rate (sGFR. Bland–Altman analysis demonstrated that the mean difference ranged from −3.0–2.4 mL/min/1.73 m2. However, the

Asymptotic estimates and exponential stability for higher-order monotone difference equations

Directory of Open Access Journals (Sweden)

Pituk Mihály

2005-01-01

Full Text Available Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.

Asymptotic estimates and exponential stability for higher-order monotone difference equations

Directory of Open Access Journals (Sweden)

Mihály Pituk

2005-03-01

Full Text Available Asymptotic estimates are established for higher-order scalar difference equations and inequalities the right-hand sides of which generate a monotone system with respect to the discrete exponential ordering. It is shown that in some cases the exponential estimates can be replaced with a more precise limit relation. As corollaries, a generalization of discrete Halanay-type inequalities and explicit sufficient conditions for the global exponential stability of the zero solution are given.

A gradient estimate for solutions to parabolic equations with discontinuous coefficients

OpenAIRE

Fan, Jishan; Kim, Kyoungsun; Nagayasu, Sei; Nakamura, Gen

2011-01-01

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. T...

Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

KAUST Repository

Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem

2016-01-01

In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear

Estimation of three-dimensional radar tracking using modified extended kalman filter

Science.gov (United States)

Aditya, Prima; Apriliani, Erna; Khusnul Arif, Didik; Baihaqi, Komar

2018-03-01

Kalman filter is an estimation method by combining data and mathematical models then developed be extended Kalman filter to handle nonlinear systems. Three-dimensional radar tracking is one of example of nonlinear system. In this paper developed a modification method of extended Kalman filter from the direct decline of the three-dimensional radar tracking case. The development of this filter algorithm can solve the three-dimensional radar measurements in the case proposed in this case the target measured by radar with distance r, azimuth angle θ, and the elevation angle ϕ. Artificial covariance and mean adjusted directly on the three-dimensional radar system. Simulations result show that the proposed formulation is effective in the calculation of nonlinear measurement compared with extended Kalman filter with the value error at 0.77% until 1.15%.

Estimating ice-affected streamflow by extended Kalman filtering

Science.gov (United States)

Holtschlag, D.J.; Grewal, M.S.

1998-01-01

An extended Kalman filter was developed to automate the real-time estimation of ice-affected streamflow on the basis of routine measurements of stream stage and air temperature and on the relation between stage and streamflow during open-water (ice-free) conditions. The filter accommodates three dynamic modes of ice effects: sudden formation/ablation, stable ice conditions, and eventual elimination. The utility of the filter was evaluated by applying it to historical data from two long-term streamflow-gauging stations, St. John River at Dickey, Maine and Platte River at North Bend, Nebr. Results indicate that the filter was stable and that parameters converged for both stations, producing streamflow estimates that are highly correlated with published values. For the Maine station, logarithms of estimated streamflows are within 8% of the logarithms of published values 87.2% of the time during periods of ice effects and within 15% 96.6% of the time. Similarly, for the Nebraska station, logarithms of estimated streamflows are within 8% of the logarithms of published values 90.7% of the time and within 15% 97.7% of the time. In addition, the correlation between temporal updates and published streamflows on days of direct measurements at the Maine station was 0.777 and 0.998 for ice-affected and open-water periods, respectively; for the Nebraska station, corresponding correlations were 0.864 and 0.997.

Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates

NARCIS (Netherlands)

Harutyunyan, D.; Izsak, F.; van der Vegt, Jacobus J.W.; Bochev, Mikhail A.

For the adaptive solution of the Maxwell equations on three-dimensional domains with N´ed´elec edge finite element methods, we consider an implicit a posteriori error estimation technique. On each element of the tessellation an equation for the error is formulated and solved with a properly chosen

Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems

KAUST Repository

Majeed, Muhammad Usman

2017-07-19

Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.

Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates

Energy Technology Data Exchange (ETDEWEB)

Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas

1999-10-01

We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)

Structural Equation Models in a Redundancy Analysis Framework With Covariates.

Science.gov (United States)

Lovaglio, Pietro Giorgio; Vittadini, Giorgio

2014-01-01

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

Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

KAUST Repository

Goswami, Deepjyoti

2013-05-01

In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments combined with a repeated use of an integral operator and without using parabolic type duality technique, optimal L2 L2-error estimates are derived for semidiscrete approximations, when the initial condition is in L2 L2. Due to the presence of the integral term, it is, further, observed that a negative norm estimate plays a crucial role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof techniques used in deriving optimal error estimates for finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, we extend the proposed analysis to the standard mixed method for PIDE with rough initial data and provide an optimal error estimate in L2, L 2, which improves upon the results available in the literature. © 2013 Springer Science+Business Media New York.

Dual extended Kalman filter for combined estimation of vehicle state and road friction

Science.gov (United States)

Zong, Changfu; Hu, Dan; Zheng, Hongyu

2013-03-01

Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute(HSRI) tire model; the dual extended Kalman filter (DEKF) technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions(high-friction, low-friction, and joint-friction). On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.

Stability estimates for solution of IBVP to fractional parabolic differential and difference equations

Science.gov (United States)

Ashyralyev, Allaberen; Cakir, Zafer

2016-08-01

In this work, we investigate initial-boundary value problems for fractional parabolic equations with the Neumann boundary condition. Stability estimates for the solution of this problem are established. Difference schemes for approximate solution of initial-boundary value problem are constructed. Furthermore, we give theorem on coercive stability estimates for the solution of the difference schemes.

Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations

Energy Technology Data Exchange (ETDEWEB)

Singhatanadgid, Pairod; Jommalai, Panupan [Chulalongkorn University, Bangkok (Thailand)

2016-05-15

The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.

Modulating functions method for parameters estimation in the fifth order KdV equation

KAUST Repository

Asiri, Sharefa M.

2017-07-25

In this work, the modulating functions method is proposed for estimating coefficients in higher-order nonlinear partial differential equation which is the fifth order Kortewegde Vries (KdV) equation. The proposed method transforms the problem into a system of linear algebraic equations of the unknowns. The statistical properties of the modulating functions solution are described in this paper. In addition, guidelines for choosing the number of modulating functions, which is an important design parameter, are provided. The effectiveness and robustness of the proposed method are shown through numerical simulations in both noise-free and noisy cases.

An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

KAUST Repository

Asiri, Sharefa M.; Zayane, Chadia; Laleg-Kirati, Taous-Meriem

2015-01-01

Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

KAUST Repository

Asiri, Sharefa M.

2015-08-31

Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

Equations of motion derived from a generalization of Einstein's equation for the gravitational field

International Nuclear Information System (INIS)

Mociutchi, C.

1980-01-01

The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)

Estimating order-picking times for return heuristic - equations and simulations

Directory of Open Access Journals (Sweden)

Grzegorz Tarczyński

2015-09-01

Full Text Available Background: A key element of the evaluation of warehouse operation is the average order-picking time. In warehouses where the order-picking process is carried out according to the "picker-to-part" rule the order-picking time is usually proportional to the distance covered by the picker while picking items. This distance can by estimated by simulations or using mathematical equations. In the paper only the best described in the literature one-block rectangular warehouses are considered. Material and methods: For the one-block rectangular warehouses there are well known five routing heuristics. In the paper the author considers the return heuristic in two variants. The paper presents well known Hall's and De Koster's equations for the average distance traveled by the picker while completing items from one pick list. The author presents own proposals for calculating the expected distance. Results: the results calculated by the use of mathematical equations (the formulas of Hall, De Koster and own propositions were compared with the average values obtained using computer simulations. For the most cases the average error does not exceed 1% (except for Hall's equations. To carry out simulation the computer software Warehouse Real-Time Simulator was used. Conclusions: the order-picking time is a function of many variables and its optimization is not easy. It can be done in two stages: firstly using mathematical equations the set of the potentially best variants is established, next the results are verified using simulations. The results calculated by the use of equations are not precise, but possible to achieve immediately. The simulations are more time-consuming, but allow to analyze the order-picking process more accurately.

Allometric equations for estimating standing biomass of Avicennia marina in Bushehr of Iran

Directory of Open Access Journals (Sweden)

Akbar Ghasemi

2016-07-01

Full Text Available Today, it is important to use of ecological indicators, such as biomass for recognizing the special status of ecosystems, such as mangrove forests and also monitoring and evaluating changes through a specific period. Because using the direct method of evaluating biomass would be destructive, it is common in all similar area to use determine exact Allometric equations by using the statistical relationship between the structural characteristics of trees and their biomass and use these equations to estimate the biomass of trees. The aim of this study is estimate the aboveground biomass of mangroves and determine Allometric models for Nayband area in Bushehr, located in southern Iran. A number of mangrove trees were randomly selected. Collar diameter, crown diameter and tree height of standing trees were measured. After logging and weighing fresh weight, dry weight, trunk and branches were obtained in laboratory and biomass of components was calculated. The relationship between quantities feature of trees and biomass for determination of allometric equation was studied by using linear, power and exponential regression. The equations were compared with each other based on the different modeling parameters. The highest significant correlation was found between crown diameters and dry weight (R > 0.90. The best equations were obtained by means of an exponential and power regression models (R2adj> 0.90. The models were obtained from explained factor, suggests that there might be a relationship between the characteristics of mangrove trees and biomass.

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

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.

[Consensus document: recommendations for the use of equations to estimate glomerular filtration rate in children].

Science.gov (United States)

Montañés Bermúdez, R; Gràcia Garcia, S; Fraga Rodríguez, G M; Escribano Subias, J; Diez de Los Ríos Carrasco, M J; Alonso Melgar, A; García Nieto, V

2014-05-01

The appearance of the K/DOQI guidelines in 2002 on the definition, evaluation and staging of chronic kidney disease (CKD) have led to a major change in how to assess renal function in adults and children. These guidelines, recently updated, recommended that the study of renal function is based, not only on measuring the serum creatinine concentration, but this must be accompanied by the estimation of glomerular filtration rate (GFR) obtained by an equation. However, the implementation of this recommendation in the clinical laboratory reports in the paediatric population has been negligible. Numerous studies have appeared in recent years on the importance of screening and monitoring of patients with CKD, the emergence of new equations for estimating GFR, and advances in clinical laboratories regarding the methods for measuring plasma creatinine and cystatin C, determined by the collaboration between the departments of paediatrics and clinical laboratories to establish recommendations based on the best scientific evidence on the use of equations to estimate GFR in this population. The purpose of this document is to provide recommendations on the evaluation of renal function and the use of equations to estimate GFR in children from birth to 18 years of age. The recipients of these recommendations are paediatricians, nephrologists, clinical biochemistry, clinical analysts, and all health professionals involved in the study and evaluation of renal function in this group of patients. Copyright © 2013 Asociación Española de Pediatría. Published by Elsevier Espana. All rights reserved.

Bi Input-extended Kalman filter based estimation technique for speed-sensorless control of induction motors

International Nuclear Information System (INIS)

Barut, Murat

2010-01-01

This study offers a novel extended Kalman filter (EKF) based estimation technique for the solution of the on-line estimation problem related to uncertainties in the stator and rotor resistances inherent to the speed-sensorless high efficiency control of induction motors (IMs) in the wide speed range as well as extending the limited number of states and parameter estimations possible with a conventional single EKF algorithm. For this aim, the introduced estimation technique in this work utilizes a single EKF algorithm with the consecutive execution of two inputs derived from the two individual extended IM models based on the stator resistance and rotor resistance estimation, differently from the other approaches in past studies, which require two separate EKF algorithms operating in a switching or braided manner; thus, it has superiority over the previous EKF schemes in this regard. The proposed EKF based estimation technique performing the on-line estimations of the stator currents, the rotor flux, the rotor angular velocity, and the load torque involving the viscous friction term together with the rotor and stator resistance is also used in the combination with the speed-sensorless direct vector control of IM and tested with simulations under the challenging 12 scenarios generated instantaneously via step and/or linear variations of the velocity reference, the load torque, the stator resistance, and the rotor resistance in the range of high and zero speed, assuming that the measured stator phase currents and voltages are available. Even under those variations, the performance of the speed-sensorless direct vector control system established on the novel EKF based estimation technique is observed to be quite good.

Bi Input-extended Kalman filter based estimation technique for speed-sensorless control of induction motors

Energy Technology Data Exchange (ETDEWEB)

Barut, Murat, E-mail: muratbarut27@yahoo.co [Nigde University, Department of Electrical and Electronics Engineering, 51245 Nigde (Turkey)

2010-10-15

This study offers a novel extended Kalman filter (EKF) based estimation technique for the solution of the on-line estimation problem related to uncertainties in the stator and rotor resistances inherent to the speed-sensorless high efficiency control of induction motors (IMs) in the wide speed range as well as extending the limited number of states and parameter estimations possible with a conventional single EKF algorithm. For this aim, the introduced estimation technique in this work utilizes a single EKF algorithm with the consecutive execution of two inputs derived from the two individual extended IM models based on the stator resistance and rotor resistance estimation, differently from the other approaches in past studies, which require two separate EKF algorithms operating in a switching or braided manner; thus, it has superiority over the previous EKF schemes in this regard. The proposed EKF based estimation technique performing the on-line estimations of the stator currents, the rotor flux, the rotor angular velocity, and the load torque involving the viscous friction term together with the rotor and stator resistance is also used in the combination with the speed-sensorless direct vector control of IM and tested with simulations under the challenging 12 scenarios generated instantaneously via step and/or linear variations of the velocity reference, the load torque, the stator resistance, and the rotor resistance in the range of high and zero speed, assuming that the measured stator phase currents and voltages are available. Even under those variations, the performance of the speed-sensorless direct vector control system established on the novel EKF based estimation technique is observed to be quite good.

Full information estimations of a system of simultaneous equations with error component structure

OpenAIRE

Balestra, Pietro; Krishnakumar, Jaya

1987-01-01

In this paper we develop full information methods for estimating the parameters of a system of simultaneous equations with error component struc-ture and establish relationships between the various structural estimat

OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

KAUST Repository

GOSWAMI, DEEPJYOTI; PANI, AMIYA K.; YADAV, SANGITA

2014-01-01

AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.

Unit Price and Cost Estimation Equations through Items Percentage of Construction Works in a Desert Area

Directory of Open Access Journals (Sweden)

Kadhim Raheem

2015-02-01

Full Text Available This research will cover different aspects of estimating process of construction work in a desert area. The inherent difficulties which accompany the cost estimating of the construction works in desert environment in a developing country, will stem from the limited information available, resources scarcity, low level of skilled workers, the prevailing severe weather conditions and many others, which definitely don't provide a fair, reliable and accurate estimation. This study tries to present unit price to estimate the cost in preliminary phase of a project. Estimations are supported by developing mathematical equations based on the historical data of maintenance, new construction of managerial and school projects. Meanwhile, the research has determined the percentage of project items, in such a remote environment. Estimation equations suitable for remote areas have been formulated. Moreover, a procedure for unite price calculation is concluded.

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

Science.gov (United States)

Xu, Peiliang

2018-06-01

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

From quantum to semiclassical kinetic equations: Nuclear matter estimates

International Nuclear Information System (INIS)

Galetti, D.; Mizrahi, S.S.; Nemes, M.C.; Toledo Piza, A.F.R. de

1985-01-01

Starting from the exact microscopic time evolution of the quantum one body density associated with a many fermion system semiclassical approximations are derived to it. In the limit where small momentum transfer two body collisions are dominant we get a Fokker-Planck equation and work out friction and diffusion tensors explicitly for nuclear matter. If arbitrary momentum transfers are considered a Boltzmann equation is derived and used to calculate the viscosity coefficient of nuclear matter. A derivation is given of the collision term used by Landau to describe the damping of zero sound waves at low temperature in Plasmas. Memory effects are essential for this. The damping of zero sound waves in nuclear matter is also calculated and the value so obtained associated with the bulk value of the damping of giant resonances in finite nuclei. The bulk value is estimated to be quite small indicating the importance of the nuclear surface for the damping. (Author) [pt

A multivariate family-based association test using generalized estimating equations : FBAT-GEE

NARCIS (Netherlands)

Lange, C; Silverman, SK; Xu, [No Value; Weiss, ST; Laird, NM

In this paper we propose a multivariate extension of family-based association tests based on generalized estimating equations. The test can be applied to multiple phenotypes and to phenotypic data obtained in longitudinal studies without making any distributional assumptions for the phenotypic

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

Science.gov (United States)

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Delan Devakumar

2015-03-01

Full Text Available Background. Body composition is important as a marker of both current and future health. Bioelectrical impedance (BIA is a simple and accurate method for estimating body composition, but requires population-specific calibration equations.Objectives. (1 To generate population specific calibration equations to predict lean mass (LM from BIA in Nepalese children aged 7–9 years. (2 To explore methodological changes that may extend the range and improve accuracy.Methods. BIA measurements were obtained from 102 Nepalese children (52 girls using the Tanita BC-418. Isotope dilution with deuterium oxide was used to measure total body water and to estimate LM. Prediction equations for estimating LM from BIA data were developed using linear regression, and estimates were compared with those obtained from the Tanita system. We assessed the effects of flexing the arms of children to extend the range of coverage towards lower weights. We also estimated potential error if the number of children included in the study was reduced.Findings. Prediction equations were generated, incorporating height, impedance index, weight and sex as predictors (R2 93%. The Tanita system tended to under-estimate LM, with a mean error of 2.2%, but extending up to 25.8%. Flexing the arms to 90° increased the lower weight range, but produced a small error that was not significant when applied to children <16 kg (p 0.42. Reducing the number of children increased the error at the tails of the weight distribution.Conclusions. Population-specific isotope calibration of BIA for Nepalese children has high accuracy. Arm position is important and can be used to extend the range of low weight covered. Smaller samples reduce resource requirements, but leads to large errors at the tails of the weight distribution.

Extended thermodynamics

CERN Document Server

Müller, Ingo

1993-01-01

Physicists firmly believe that the differential equations of nature should be hyperbolic so as to exclude action at a distance; yet the equations of irreversible thermodynamics - those of Navier-Stokes and Fourier - are parabolic. This incompatibility between the expectation of physicists and the classical laws of thermodynamics has prompted the formulation of extended thermodynamics. After describing the motifs and early evolution of this new branch of irreversible thermodynamics, the authors apply the theory to mon-atomic gases, mixtures of gases, relativistic gases, and "gases" of phonons and photons. The discussion brings into perspective the various phenomena called second sound, such as heat propagation, propagation of shear stress and concentration, and the second sound in liquid helium. The formal mathematical structure of extended thermodynamics is exposed and the theory is shown to be fully compatible with the kinetic theory of gases. The study closes with the testing of extended thermodynamics thro...

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

Science.gov (United States)

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

2018-01-01

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

Validation of estimated glomerular filtration rate equations for Japanese children.

Science.gov (United States)

Gotoh, Yoshimitsu; Uemura, Osamu; Ishikura, Kenji; Sakai, Tomoyuki; Hamasaki, Yuko; Araki, Yoshinori; Hamda, Riku; Honda, Masataka

2018-01-25

The gold standard for evaluation of kidney function is renal inulin clearance (Cin). However, the methodology for Cin is complicated and difficult, especially for younger children and/or patients with bladder dysfunction. Therefore, we developed a simple and easier method for obtaining the estimated glomerular filtration rate (eGFR) using equations and values for several biomarkers, i.e., serum creatinine (Cr), serum cystatin C (cystC), serum beta-2 microglobulin (β 2 MG), and creatinine clearance (Ccr). The purpose of the present study was to validate these equations with a new data set. To validate each equation, we used data of 140 patients with CKD with clinical need for Cin, using the measured GFR (mGFR). We compared the results for each eGFR equation with the mGFR using mean error (ME), root mean square error (RMSE), P 30 , and Bland-Altman analysis. The ME of Cr, cystC, β 2 MG, and Ccr based on eGFR was 15.8 ± 13.0, 17.2 ± 16.5, 15.4 ± 14.3, and 10.6 ± 13.0 ml/min/1.73 m 2 , respectively. The RMSE was 29.5, 23.8, 20.9, and 16.7, respectively. The P 30 was 79.4, 71.1, 69.5, and 92.9%, respectively. The Bland-Altman bias analysis showed values of 4.0 ± 18.6, 5.3 ± 16.8, 12.7 ± 17.0, and 2.5 ± 17.2 ml/min/1.73 m 2 , respectively, for these parameters. The bias of each eGFR equation was not large. Therefore, each eGFR equation could be used.

Optimal control problem for the extended Fisher–Kolmogorov equation

Indian Academy of Sciences (India)

by methods of optimal control, such as chemical engineering and vehicle ... ern optimal control theories and applied models are not only represented by .... Obviously, equation (2.5) is an ordinary differential equation and according to ODE.

Optimal control of stochastic difference Volterra equations an introduction

CERN Document Server

Shaikhet, Leonid

2015-01-01

This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equation...

Development and Cross-Validation of Equation for Estimating Percent Body Fat of Korean Adults According to Body Mass Index

Directory of Open Access Journals (Sweden)

Hoyong Sung

2017-06-01

Full Text Available Background : Using BMI as an independent variable is the easiest way to estimate percent body fat. Thus far, few studies have investigated the development and cross-validation of an equation for estimating the percent body fat of Korean adults according to the BMI. The goals of this study were the development and cross-validation of an equation for estimating the percent fat of representative Korean adults using the BMI. Methods : Samples were obtained from the Korea National Health and Nutrition Examination Survey between 2008 and 2011. The samples from 2008-2009 and 2010-2011 were labeled as the validation group (n=10,624 and the cross-validation group (n=8,291, respectively. The percent fat was measured using dual-energy X-ray absorptiometry, and the body mass index, gender, and age were included as independent variables to estimate the measured percent fat. The coefficient of determination (R², standard error of estimation (SEE, and total error (TE were calculated to examine the accuracy of the developed equation. Results : The cross-validated R² was 0.731 for Model 1 and 0.735 for Model 2. The SEE was 3.978 for Model 1 and 3.951 for Model 2. The equations developed in this study are more accurate for estimating percent fat of the cross-validation group than those previously published by other researchers. Conclusion : The newly developed equations are comparatively accurate for the estimation of the percent fat of Korean adults.

Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

KAUST Repository

Asiri, Sharefa M.

2016-10-20

In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.

An estimator for the relative entropy rate of path measures for stochastic differential equations

Energy Technology Data Exchange (ETDEWEB)

Opper, Manfred, E-mail: manfred.opper@tu-berlin.de

2017-02-01

We address the problem of estimating the relative entropy rate (RER) for two stochastic processes described by stochastic differential equations. For the case where the drift of one process is known analytically, but one has only observations from the second process, we use a variational bound on the RER to construct an estimator.

A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces

Energy Technology Data Exchange (ETDEWEB)

Ju, Lili; Tian, Li; Wang, Desheng

2008-10-31

In this paper, we present a residual-based a posteriori error estimate for the finite volume discretization of steady convection– diffusion–reaction equations defined on surfaces in R3, which are often implicitly represented as level sets of smooth functions. Reliability and efficiency of the proposed a posteriori error estimator are rigorously proved. Numerical experiments are also conducted to verify the theoretical results and demonstrate the robustness of the error estimator.

Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

Science.gov (United States)

Krylov, N. V.; Priola, E.

2017-09-01

We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

Adiabatic invariants of the extended KdV equation

Energy Technology Data Exchange (ETDEWEB)

Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)

2017-01-30

When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.

Equations for estimating stand establishment, release, and thinning costs in the Lake States.

Science.gov (United States)

Jeffrey T. Olson; Allen L. Lundgren; Dietmar Rose

1978-01-01

Equations for estimating project costs for certain silvicultural treatments in the Lake States have been developed from project records of public forests. Treatments include machine site preparation, hand planting, aerial spraying, prescribed burning, manual release, and thinning.

Method for estimating critical properties of heavy compounds suitable for cubic equations of state and its application to the prediction of vapor pressures

DEFF Research Database (Denmark)

Kontogeorgis, Georgios; Ioannis, Smirlis; Iakovos, Yakoumis

1997-01-01

S. The proposed scheme employs a recent group-contribution method (Constantinou et al. Fluid Phase Equilib. 1995, 103 (1), 11) for estimating the acentric factor. The two critical properties are estimated via a generalized correlation for the ratio T-c/P-c (with the van der Waals surface area) and the cubic Eo...... pressures for several nonpolar and slightly polar heavy compounds with very satisfactory results, essentially independent of the experimental point used. Furthermore, the method yields critical properties for heavy alkanes (N-c > 20) and other compounds which are in very good agreement with recent available......Cubic equations of state (EoS) are often used for correlating and predicting phase equilibria. Before extending any EoS to mixtures, reliable vapor-pressure prediction is essential. This requires experimental, if possible, critical temperatures T-c, pressures P-c, and acentric factor omega...

A theoretical framework for Ångström equation. Its virtues and liabilities in solar energy estimation

International Nuclear Information System (INIS)

Stefu, Nicoleta; Paulescu, Marius; Blaga, Robert; Calinoiu, Delia; Pop, Nicolina; Boata, Remus; Paulescu, Eugenia

2016-01-01

Highlights: • A self-consistent derivation of the Ångström equation is carried out. • The theoretical assessment on its performance is well supported by the measured data. • The variability in cloud transmittance is a major source of uncertainty for estimates. • The degradation in time and space of the empirical equations calibration is assessed. - Abstract: The relation between solar irradiation and sunshine duration was investigated from the very beginning of solar radiation measurements. Many studies were devoted to this topic aiming to include the complex influence of clouds on solar irradiation into equations. This study is focused on the linear relationship between the clear sky index and the relative sunshine proposed by the pioneering work of Ångström. A full semi-empirical derivation of the equation, highlighting its virtues and liabilities, is presented. Specific Ångström – type equations for beam and diffuse solar irradiation were derived separately. The sum of the two components recovers the traditional form of the Ångström equation. The physical meaning of the Ångström parameter, as the average of the clouds transmittance, emerges naturally. The theoretical results on the Ångström equation performance are well supported by the tests against measured data. Using long-term records of global solar irradiation and sunshine duration from thirteen European radiometric stations, the influence of the Ångström constraint (slope equals one minus intercept) on the accuracy of the estimates is analyzed. Another focus is on the assessment of the degradation of the equation calibration. The temporal variability in cloud transmittance (both long-term trend and fluctuations) is a major source of uncertainty for Ångström equation estimates.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

Science.gov (United States)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

A Performance Comparison Between Extended Kalman Filter and Unscented Kalman Filter in Power System Dynamic State Estimation

DEFF Research Database (Denmark)

Khazraj, Hesam; Silva, Filipe Miguel Faria da; Bak, Claus Leth

2016-01-01

Dynamic State Estimation (DSE) is a critical tool for analysis, monitoring and planning of a power system. The concept of DSE involves designing state estimation with Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) methods, which can be used by wide area monitoring to improve......-linear state estimator is developed in MatLab to solve states by applying the unscented Kalman filter (UKF) and Extended Kalman Filter (EKF) algorithm. Finally, a DSE model is built for a 14 bus power system network to evaluate the proposed algorithm for the networks.This article will focus on comparing...

Spacecraft Trajectory Estimation Using a Sampled-Data Extended Kalman Filter with Range-Only Measurements

National Research Council Canada - National Science Library

Erwin, R. S; Bernstein, Dennis S

2005-01-01

.... In this paper we use a sampled-data extended Kalman Filter to estimate the trajectory or a target satellite when only range measurements are available from a constellation or orbiting spacecraft...

Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

Science.gov (United States)

Wu, Hulin; Xue, Hongqi; Kumar, Arun

2012-06-01

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

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

Science.gov (United States)

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

2018-03-01

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

Estimating the parameters of stochastic differential equations using a criterion function based on the Kolmogorov-Smirnov statistic

OpenAIRE

McDonald, A. David; Sandal, Leif Kristoffer

1998-01-01

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per replication. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic, put forward by Hurn and Lin...

Prediction equation for estimating total daily energy requirements of special operations personnel.

Science.gov (United States)

Barringer, N D; Pasiakos, S M; McClung, H L; Crombie, A P; Margolis, L M

2018-01-01

Special Operations Forces (SOF) engage in a variety of military tasks with many producing high energy expenditures, leading to undesired energy deficits and loss of body mass. Therefore, the ability to accurately estimate daily energy requirements would be useful for accurate logistical planning. Generate a predictive equation estimating energy requirements of SOF. Retrospective analysis of data collected from SOF personnel engaged in 12 different SOF training scenarios. Energy expenditure and total body water were determined using the doubly-labeled water technique. Physical activity level was determined as daily energy expenditure divided by resting metabolic rate. Physical activity level was broken into quartiles (0 = mission prep, 1 = common warrior tasks, 2 = battle drills, 3 = specialized intense activity) to generate a physical activity factor (PAF). Regression analysis was used to construct two predictive equations (Model A; body mass and PAF, Model B; fat-free mass and PAF) estimating daily energy expenditures. Average measured energy expenditure during SOF training was 4468 (range: 3700 to 6300) Kcal·d- 1 . Regression analysis revealed that physical activity level ( r  = 0.91; P  plan appropriate feeding regimens to meet SOF nutritional requirements across their mission profile.

Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow

KAUST Repository

Asiri, Sharefa M.

2017-10-19

In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations of blood mass density. The method is described and its performance is assessed through some numerical simulations. The robustness of the method in presence of noise is also studied.

Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation

Directory of Open Access Journals (Sweden)

Paul E. Brockway

2017-02-01

Full Text Available Capital–labour–energy Constant Elasticity of Substitution (CES production functions and their estimated parameters now form a key part of energy–economy models which inform energy and emissions policy. However, the collation and guidance as to the specification and estimation choices involved with such energy-extended CES functions is disparate. This risks poorly specified and estimated CES functions, with knock-on implications for downstream energy–economic models and climate policy. In response, as a first step, this paper assembles in one place the major considerations involved in the empirical estimation of these CES functions. Discussions of the choices and their implications lead to recommendations for CES empiricists. The extensive bibliography allows those interested to dig deeper into any aspect of the CES parameter estimation process.

Non-destructive equations to estimate the leaf area of Styrax pohlii and Styrax ferrugineus

Directory of Open Access Journals (Sweden)

MC Souza

Full Text Available We developed linear equations to predict the leaf area (LA of the species Styrax pohlii and Styrax ferrugineus using the width (W and length (L leaf dimensions. For both species the linear regression (Y=α+bX using LA as a dependent variable vs. W × L as an independent variable was more efficient than linear regressions using L, W, L2 and W2 as independent variables. Therefore, the LA of S. pohlii can be estimated with the equation LA=0.582+0.683WL, while the LA of S. ferrugineus follows the equation LA=−0.666+0.704WL.

H∞ Channel Estimation for DS-CDMA Systems: A Partial Difference Equation Approach

Directory of Open Access Journals (Sweden)

Wei Wang

2013-01-01

Full Text Available In the communications literature, a number of different algorithms have been proposed for channel estimation problems with the statistics of the channel noise and observation noise exactly known. In practical systems, however, the channel parameters are often estimated using training sequences which lead to the statistics of the channel noise difficult to obtain. Moreover, the received signals are corrupted not only by the ambient noises but also by multiple-access interferences, so the statistics of observation noises is also difficult to obtain. In this paper, we will investigate the H∞ channel estimation problem for direct-sequence code-division multiple-access (DS-CDMA communication systems with time-varying multipath fading channels. The channel estimator is designed by applying a partial difference equation approach together with the innovation analysis theory. This method can give a sufficient and necessary condition for the existence of an H∞ channel estimator.

ESTIMATING BASAL ENERGY EXPENDITURE IN LIVER TRANSPLANT RECIPIENTS: THE VALUE OF THE HARRIS-BENEDICT EQUATION

OpenAIRE

PINTO, Andressa S.; CHEDID, Marcio F.; GUERRA, Léa T.; ÁLVARES-DA-SILVA, Mario R.; ARAÚJO, Alexandre de; GUIMARÃES, Luciano S.; LEIPNITZ, Ian; CHEDID, Aljamir D.; KRUEL, Cleber R. P.; GREZZANA-FILHO, Tomaz J. M.; KRUEL, Cleber D. P.

2016-01-01

ABSTRACT Background: Reliable measurement of basal energy expenditure (BEE) in liver transplant (LT) recipients is necessary for adapting energy requirements, improving nutritional status and preventing weight gain. Indirect calorimetry (IC) is the gold standard for measuring BEE. However, BEE may be estimated through alternative methods, including electrical bioimpedance (BI), Harris-Benedict Equation (HBE), and Mifflin-St. Jeor Equation (MSJ) that carry easier applicability and lower cost....

Direct phase derivative estimation using difference equation modeling in holographic interferometry

International Nuclear Information System (INIS)

Kulkarni, Rishikesh; Rastogi, Pramod

2014-01-01

A new method is proposed for the direct phase derivative estimation from a single spatial frequency modulated carrier fringe pattern in holographic interferometry. The fringe intensity in a given row/column is modeled as a difference equation of intensity with spatially varying coefficients. These coefficients carry the information on the phase derivative. Consequently, the accurate estimation of the coefficients is obtained by approximating the coefficients as a linear combination of the predefined linearly independent basis functions. Unlike Fourier transform based fringe analysis, the method does not call for performing the filtering of the Fourier spectrum of fringe intensity. Moreover, the estimation of the carrier frequency is performed by applying the proposed method to a reference interferogram. The performance of the proposed method is insensitive to the fringe amplitude modulation and is validated with the simulation results. (paper)

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

Science.gov (United States)

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

2017-08-01

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

Generalized equations for estimating DXA percent fat of diverse young women and men: The Tiger Study

Science.gov (United States)

Popular generalized equations for estimating percent body fat (BF%) developed with cross-sectional data are biased when applied to racially/ethnically diverse populations. We developed accurate anthropometric models to estimate dual-energy x-ray absorptiometry BF% (DXA-BF%) that can be generalized t...

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Science.gov (United States)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Technical note: Use of a simplified equation for estimating glomerular filtration rate in beef cattle.

Science.gov (United States)

Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K

2013-11-01

This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, aged<1 yr old, largely fluctuated, presumably due to the rapid ruminal growth and dynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.

Existence Results for Some Nonlinear Functional-Integral Equations in Banach Algebra with Applications

Directory of Open Access Journals (Sweden)

Lakshmi Narayan Mishra

2016-04-01

Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.

Distributed Extended Kalman Filter for Position, Velocity, Time, Estimation in Satellite Navigation Receivers

Directory of Open Access Journals (Sweden)

O. Jakubov

2013-09-01

Full Text Available Common techniques for position-velocity-time estimation in satellite navigation, iterative least squares and the extended Kalman filter, involve matrix operations. The matrix inversion and inclusion of a matrix library pose requirements on a computational power and operating platform of the navigation processor. In this paper, we introduce a novel distributed algorithm suitable for implementation in simple parallel processing units each for a tracked satellite. Such a unit performs only scalar sum, subtraction, multiplication, and division. The algorithm can be efficiently implemented in hardware logic. Given the fast position-velocity-time estimator, frequent estimates can foster dynamic performance of a vector tracking receiver. The algorithm has been designed from a factor graph representing the extended Kalman filter by splitting vector nodes into scalar ones resulting in a cyclic graph with few iterations needed. Monte Carlo simulations have been conducted to investigate convergence and accuracy. Simulation case studies for a vector tracking architecture and experimental measurements with a real-time software receiver developed at CTU in Prague were conducted. The algorithm offers compromises in stability, accuracy, and complexity depending on the number of iterations. In scenarios with a large number of tracked satellites, it can outperform the traditional methods at low complexity.

A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry

OpenAIRE

Wang, Xu-Jia

2006-01-01

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.

Estimates of solutions of certain classes of second-order differential equations in a Hilbert space

International Nuclear Information System (INIS)

Artamonov, N V

2003-01-01

Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained

Calculation of statistic estimates of kinetic parameters from substrate uncompetitive inhibition equation using the median method

Directory of Open Access Journals (Sweden)

Pedro L. Valencia

2017-04-01

Full Text Available We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974. The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis–Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax, Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].

Estimation of the glomerular filtration rate in people older than 85: Comparisons between CKD-EPI, MDRD-IDMS and BIS1 equations

Directory of Open Access Journals (Sweden)

Fernando Bustos-Guadaño

2017-03-01

Conclusions: The GFR estimations obtained with BS1 equation are not interchangeable with MDRD-IDMS or CKD-EPI equations. BIS1 estimates lower GFR values than MDRD-IDMS and CKD-EPI and tends to classify the patients in a more advanced chronic kidney disease stage, especially for estimated GFR higher than 29 mL/min/1.73 m2.

Optimal equation for estimation of glomerular filtration rate in autosomal dominant polycystic kidney disease: influence of tolvaptan.

Science.gov (United States)

Yamaguchi, Tsuyoshi; Higashihara, Eiji; Okegawa, Takatsugu; Miyazaki, Isao; Nutahara, Kikuo

2018-05-22

The reliability of various equations for estimating the GFR in ADPKD patients and the influence of tolvaptan on the resulting estimates have not been examined when GFR is calculated on the basis of inulin clearance. We obtained baseline and on-tolvaptan measured GFRs (mGFRs), calculated on the basis of inulin clearance, in 114 ADPKD, and these mGFRs were compared with eGFRs calculated according to four basic equations: the MDRD, CKD-EPI, and JSN-CKDI equations and the Cockcroft-Gault formula, as well as the influence of tolvaptan and of inclusion of cystatin C on accuracy of the results. Accuracy of each of the seven total equations was evaluated on the basis of the percentage of eGFR values within mGFR ± 30% (P 30 ). mGFRs were distributed throughout CKD stages 1-5. Regardless of the CKD stage, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations did not differ significantly between baseline values and on-tolvaptan values. In CKD 1-2 patients, P 30 of the CKD-EPI equation was 100.0%, whether or not the patient was on-tolvaptan. In CKD 3-5 patients, P 30 s of the MDRD, CKD-EPI, and JSN-CKDI equations were similar. For all four equations, regression coefficients and intercepts did not differ significantly between baseline and on-tolvaptan values, but accuracy of the Cockcroft-Gault formula was inferior to that of the other three equations. Incorporation of serum cystatin C reduced accuracy. The CKD-EPI equation is most reliable, regardless of the severity of CKD. Tolvaptain intake has minimal influence and cystatin C incorporation does not improve accuracy.

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Directory of Open Access Journals (Sweden)

Vitanov Nikolay K.

2018-03-01

Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

A new extended elliptic equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

International Nuclear Information System (INIS)

Wang Baodong; Song Lina; Zhang Hongqing

2007-01-01

In this paper, we present a new elliptic equation rational expansion method to uniformly construct a series of exact solutions for nonlinear partial differential equations. As an application of the method, we choose the (2 + 1)-dimensional Burgers equation to illustrate the method and successfully obtain some new and more general solutions

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

Science.gov (United States)

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

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

Method for calculating the variance and prediction intervals for biomass estimates obtained from allometric equations

CSIR Research Space (South Africa)

Kirton, A

2010-08-01

Full Text Available for calculating the variance and prediction intervals for biomass estimates obtained from allometric equations A KIRTON B SCHOLES S ARCHIBALD CSIR Ecosystem Processes and Dynamics, Natural Resources and the Environment P.O. BOX 395, Pretoria, 0001, South... intervals (confidence intervals for predicted values) for allometric estimates can be obtained using an example of estimating tree biomass from stem diameter. It explains how to deal with relationships which are in the power function form - a common form...

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

Science.gov (United States)

Manning, Robert M.

2004-01-01

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

Science.gov (United States)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians

KAUST Repository

Cagnetti, Filippo; Gomes, Diogo A.; Mitake, Hiroyoshi; Tran, Hung V.

2015-01-01

We investigate large-time asymptotics for viscous Hamilton-Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.

Monitoring hydraulic fractures: state estimation using an extended Kalman filter

International Nuclear Information System (INIS)

Rochinha, Fernando Alves; Peirce, Anthony

2010-01-01

There is considerable interest in using remote elastostatic deformations to identify the evolving geometry of underground fractures that are forced to propagate by the injection of high pressure viscous fluids. These so-called hydraulic fractures are used to increase the permeability in oil and gas reservoirs as well as to pre-fracture ore-bodies for enhanced mineral extraction. The undesirable intrusion of these hydraulic fractures into environmentally sensitive areas or into regions in mines which might pose safety hazards has stimulated the search for techniques to enable the evolving hydraulic fracture geometries to be monitored. Previous approaches to this problem have involved the inversion of the elastostatic data at isolated time steps in the time series provided by tiltmeter measurements of the displacement gradient field at selected points in the elastic medium. At each time step, parameters in simple static models of the fracture (e.g. a single displacement discontinuity) are identified. The approach adopted in this paper is not to regard the sequence of sampled elastostatic data as independent, but rather to treat the data as linked by the coupled elastic-lubrication equations that govern the propagation of the evolving hydraulic fracture. We combine the Extended Kalman Filter (EKF) with features of a recently developed implicit numerical scheme to solve the coupled free boundary problem in order to form a novel algorithm to identify the evolving fracture geometry. Numerical experiments demonstrate that, despite excluding significant physical processes in the forward numerical model, the EKF-numerical algorithm is able to compensate for the un-modeled dynamics by using the information fed back from tiltmeter data. Indeed the proposed algorithm is able to provide reasonably faithful estimates of the fracture geometry, which are shown to converge to the actual hydraulic fracture geometry as the number of tiltmeters is increased. Since the location of

A bias correction for covariance estimators to improve inference with generalized estimating equations that use an unstructured correlation matrix.

Science.gov (United States)

Westgate, Philip M

2013-07-20

Generalized estimating equations (GEEs) are routinely used for the marginal analysis of correlated data. The efficiency of GEE depends on how closely the working covariance structure resembles the true structure, and therefore accurate modeling of the working correlation of the data is important. A popular approach is the use of an unstructured working correlation matrix, as it is not as restrictive as simpler structures such as exchangeable and AR-1 and thus can theoretically improve efficiency. However, because of the potential for having to estimate a large number of correlation parameters, variances of regression parameter estimates can be larger than theoretically expected when utilizing the unstructured working correlation matrix. Therefore, standard error estimates can be negatively biased. To account for this additional finite-sample variability, we derive a bias correction that can be applied to typical estimators of the covariance matrix of parameter estimates. Via simulation and in application to a longitudinal study, we show that our proposed correction improves standard error estimation and statistical inference. Copyright © 2012 John Wiley & Sons, Ltd.

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

Science.gov (United States)

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

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

Extended Kalman Filtering to estimate temperature and irradiation for maximum power point tracking of a photovoltaic module

International Nuclear Information System (INIS)

Docimo, D.J.; Ghanaatpishe, M.; Mamun, A.

2017-01-01

This paper develops an algorithm for estimating photovoltaic (PV) module temperature and effective irradiation level. The power output of a PV system depends directly on both of these states. Estimating the temperature and irradiation allows for improved state-based control methods while eliminating the need of additional sensors. Thermal models and irradiation estimators have been developed in the literature, but none incorporate feedback for estimation. This paper outlines an Extended Kalman Filter for temperature and irradiation estimation. These estimates are, in turn, used within a novel state-based controller that tracks the maximum power point of the PV system. Simulation results indicate this state-based controller provides up to an 8.5% increase in energy produced per day as compared to an impedance matching controller. A sensitivity analysis is provided to examine the impact state estimate errors have on the ability to find the optimal operating point of the PV system. - Highlights: • Developed a temperature and irradiation estimator for photovoltaic systems. • Designed an Extended Kalman Filter to handle model and measurement uncertainty. • Developed a state-based controller for maximum power point tracking (MPPT). • Validated combined estimator/controller algorithm for different weather conditions. • Algorithm increases energy captured up to 8.5% over traditional MPPT algorithms.

Estimating glomerular filtration rate (GFR) in children. The average between a cystatin C- and a creatinine-based equation improves estimation of GFR in both children and adults and enables diagnosing Shrunken Pore Syndrome.

Science.gov (United States)

Leion, Felicia; Hegbrant, Josefine; den Bakker, Emil; Jonsson, Magnus; Abrahamson, Magnus; Nyman, Ulf; Björk, Jonas; Lindström, Veronica; Larsson, Anders; Bökenkamp, Arend; Grubb, Anders

2017-09-01

Estimating glomerular filtration rate (GFR) in adults by using the average of values obtained by a cystatin C- (eGFR cystatin C ) and a creatinine-based (eGFR creatinine ) equation shows at least the same diagnostic performance as GFR estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparison of eGFR cystatin C and eGFR creatinine plays a pivotal role in the diagnosis of Shrunken Pore Syndrome, where low eGFR cystatin C compared to eGFR creatinine has been associated with higher mortality in adults. The present study was undertaken to elucidate if this concept can also be applied in children. Using iohexol and inulin clearance as gold standard in 702 children, we studied the diagnostic performance of 10 creatinine-based, 5 cystatin C-based and 3 combined cystatin C-creatinine eGFR equations and compared them to the result of the average of 9 pairs of a eGFR cystatin C and a eGFR creatinine estimate. While creatinine-based GFR estimations are unsuitable in children unless calibrated in a pediatric or mixed pediatric-adult population, cystatin C-based estimations in general performed well in children. The average of a suitable creatinine-based and a cystatin C-based equation generally displayed a better diagnostic performance than estimates obtained by equations using only one of these analytes or by complex equations using both analytes. Comparing eGFR cystatin and eGFR creatinine may help identify pediatric patients with Shrunken Pore Syndrome.

Development and validation of risk prediction equations to estimate survival in patients with colorectal cancer: cohort study

OpenAIRE

Hippisley-Cox, Julia; Coupland, Carol

2017-01-01

Objective: To develop and externally validate risk prediction equations to estimate absolute and conditional survival in patients with colorectal cancer. \\ud \\ud Design: Cohort study.\\ud \\ud Setting: General practices in England providing data for the QResearch database linked to the national cancer registry.\\ud \\ud Participants: 44 145 patients aged 15-99 with colorectal cancer from 947 practices to derive the equations. The equations were validated in 15 214 patients with colorectal cancer ...

L∞-error estimates of a finite element method for the Hamilton-Jacobi-Bellman equations

International Nuclear Information System (INIS)

Bouldbrachene, M.

1994-11-01

We study the finite element approximation for the solution of the Hamilton-Jacobi-Bellman equations involving a system of quasi-variational inequalities (QVI). We also give the optimal L ∞ -error estimates, using the concepts of subsolutions and discrete regularity. (author). 7 refs

The Euler equation with habits and measurement errors: Estimates on Russian micro data

Directory of Open Access Journals (Sweden)

Khvostova Irina

2016-01-01

Full Text Available This paper presents estimates of the consumption Euler equation for Russia. The estimation is based on micro-level panel data and accounts for the heterogeneity of agents’ preferences and measurement errors. The presence of multiplicative habits is checked using the Lagrange multiplier (LM test in a generalized method of moments (GMM framework. We obtain estimates of the elasticity of intertemporal substitution and of the subjective discount factor, which are consistent with the theoretical model and can be used for the calibration and the Bayesian estimation of dynamic stochastic general equilibrium (DSGE models for the Russian economy. We also show that the effects of habit formation are not significant. The hypotheses of multiplicative habits (external, internal, and both external and internal are not supported by the data.

A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold

Directory of Open Access Journals (Sweden)

Abimbola Abolarinwa

2014-08-01

Full Text Available In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.

On the relation between elementary partial difference equations and partial differential equations

NARCIS (Netherlands)

van den Berg, I.P.

1998-01-01

The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential

An extended set-value observer for position estimation using single range measurements

DEFF Research Database (Denmark)

Marcal, Jose; Jouffroy, Jerome; Fossen, Thor I.

the observability of the system is briefly discussed and an extended set-valued observer is presented, with some discussion about the effect of the measurements noise on the final solution. This observer estimates bounds in the errors assuming that the exogenous signals are bounded, providing a safe region......The ability of estimating the position of an underwater vehicle from single range measurements is important in applications where one transducer marks an important geographical point, when there is a limitation in the size or cost of the vehicle, or when there is a failure in a system...... of transponders. The knowledge of the bearing of the vehicle and the range measurements from a single location can provide a solution which is sensitive to the trajectory that the vehicle is following, since there is no complete constraint on the position estimate with a single beacon. In this paper...

The πHe3H3 coupling constant estimation using the Chew-Low equation

International Nuclear Information System (INIS)

Mach, R.; Nichitiu, F.

1975-01-01

In this paper it is presented an estimation of the πHe 3 H 3 coupling constant using the Chew-Low equation and a semi-phenomenological analysis of the π -+ He 3 elastic differential cross sections at 98, 120, 135 and 156 MeV

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

Science.gov (United States)

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

2016-09-01

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

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

Science.gov (United States)

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

Reconstruction of extended sources for the Helmholtz equation

KAUST Repository

Kress, Rainer; Rundell, William

2013-01-01

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our

Allometric equations for estimating tree biomass in restored mixed-species Atlantic Forest stands

Science.gov (United States)

Lauro Rodrigues Nogueira; Vera Lex Engel; John A. Parrotta; Antonio Carlos Galvão de Melo; Danilo Scorzoni Ré

2014-01-01

Restoration of Atlantic Forests is receiving increasing attention because of its role in both biodiversity conservation and carbon sequestration for global climate change mitigation. This study was carried out in an Atlantic Forest restoration project in the south-central region of São Paulo State – Brazil to develop allometric equations to estimate tree biomass of...

Tourism sector, Travel agencies, and Transport Suppliers: Comparison of Different Estimators in the Structural Equation Modeling

Directory of Open Access Journals (Sweden)

Kovačić Nataša

2015-11-01

Full Text Available The paper addresses the effect of external integration (EI with transport suppliers on the efficiency of travel agencies in the tourism sector supply chains. The main aim is the comparison of different estimation methods used in the structural equation modeling (SEM, applied to discover possible relationships between EIs and efficiencies. The latter are calculated by the means of data envelopment analysis (DEA. While designing the structural equation model, the exploratory and confirmatory factor analyses are also used as preliminary statistical procedures. For the estimation of parameters of SEM model, three different methods are explained, analyzed and compared: maximum likelihood (ML method, Bayesian Markov Chain Monte Carlo (BMCMC method, and unweighted least squares (ULS method. The study reveals that all estimation methods calculate comparable estimated parameters. The results also give an evidence of good model fit performance. Besides, the research confirms that the amplified external integration with transport providers leads to increased efficiency of travel agencies, which might be a very interesting finding for the operational management.

Parameterized equation for the estimation of the hydraulic conductivity function not saturated in ferralsols south of Havana

International Nuclear Information System (INIS)

González Robaina, Felicita; López Seijas, Teresa

2008-01-01

The modeling of the processes involved in the movement of water in soil solutions generally requires the general equation of water flow for the condition of saturation, or Darcy - Buckinghan approach. In this approach the hydraulic - soil moisture (K(0)) conductivity function is a fundamental property of the soil to determine for each field condition. Several methods reported in the literature for determining the hydraulic conductivity are based on simplifications of assuming unit gradient method or a fixed ratio K(0). In recent years related to the search for simple, rapid and inexpensive methods to measure this relationship in the field using a lot of work aftershocks reported. One of these methods is the parameterized equation proposed by Reichardt, using the parameters of the equations describing the process of internal drainage and explain the exponential nature of the relationship K(0). The objective of this work is to estimate the K(0), with the method of the parameterized equation. To do the test results of internal drainage on a Ferralsol area south of Havana will be used. The results show that the parameterized equation provides an estimation of K(0) for those similar to the methods that assume unit gradient conditions

Quantum Potential and Symmetries in Extended Phase Space

Directory of Open Access Journals (Sweden)

Sadollah Nasiri

2006-06-01

Full Text Available The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.

Efficient and robust estimation for longitudinal mixed models for binary data

DEFF Research Database (Denmark)

Holst, René

2009-01-01

This paper proposes a longitudinal mixed model for binary data. The model extends the classical Poisson trick, in which a binomial regression is fitted by switching to a Poisson framework. A recent estimating equations method for generalized linear longitudinal mixed models, called GEEP, is used...... as a vehicle for fitting the conditional Poisson regressions, given a latent process of serial correlated Tweedie variables. The regression parameters are estimated using a quasi-score method, whereas the dispersion and correlation parameters are estimated by use of bias-corrected Pearson-type estimating...... equations, using second moments only. Random effects are predicted by BLUPs. The method provides a computationally efficient and robust approach to the estimation of longitudinal clustered binary data and accommodates linear and non-linear models. A simulation study is used for validation and finally...

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

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.

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

Science.gov (United States)

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

2017-01-01

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

Spectral theories for linear differential equations

International Nuclear Information System (INIS)

Sell, G.R.

1976-01-01

The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

Stochastic Differential Equations and Kondratiev Spaces

Energy Technology Data Exchange (ETDEWEB)

Vaage, G.

1995-05-01

The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.

Neural network versus activity-specific prediction equations for energy expenditure estimation in children.

Science.gov (United States)

Ruch, Nicole; Joss, Franziska; Jimmy, Gerda; Melzer, Katarina; Hänggi, Johanna; Mäder, Urs

2013-11-01

The aim of this study was to compare the energy expenditure (EE) estimations of activity-specific prediction equations (ASPE) and of an artificial neural network (ANNEE) based on accelerometry with measured EE. Forty-three children (age: 9.8 ± 2.4 yr) performed eight different activities. They were equipped with one tri-axial accelerometer that collected data in 1-s epochs and a portable gas analyzer. The ASPE and the ANNEE were trained to estimate the EE by including accelerometry, age, gender, and weight of the participants. To provide the activity-specific information, a decision tree was trained to recognize the type of activity through accelerometer data. The ASPE were applied to the activity-type-specific data recognized by the tree (Tree-ASPE). The Tree-ASPE precisely estimated the EE of all activities except cycling [bias: -1.13 ± 1.33 metabolic equivalent (MET)] and walking (bias: 0.29 ± 0.64 MET; P MET) and walking (bias: 0.61 ± 0.72 MET) and underestimated the EE of cycling (bias: -0.90 ± 1.18 MET; P MET, Tree-ASPE: 0.08 ± 0.21 MET) and walking (ANNEE 0.61 ± 0.72 MET, Tree-ASPE: 0.29 ± 0.64 MET) were significantly smaller in the Tree-ASPE than in the ANNEE (P < 0.05). The Tree-ASPE was more precise in estimating the EE than the ANNEE. The use of activity-type-specific information for subsequent EE prediction equations might be a promising approach for future studies.

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

Science.gov (United States)

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

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

Science.gov (United States)

Mehdizadeh, Saeid; Behmanesh, Javad; Khalili, Keivan

2016-08-01

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

Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations

KAUST Repository

Hofleitner, Aude; Claudel, Christian G.; Bayen, Alexandre M.

2012-01-01

This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. © 2012 IEEE.

Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations

KAUST Repository

Hofleitner, Aude

2012-12-01

This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions. © 2012 IEEE.

Estimated GFR (eGFR by prediction equation in staging of chronic kidney disease compared to gamma camera GFR

Directory of Open Access Journals (Sweden)

Mohammad Masum Alam

2016-07-01

Full Text Available Background: Glomerular filtration rate is an effective tool for diagnosis and staging of chronic kidney disease. The effect ofrenal insufficiency by different method of this tool among patients with CKD is controversial.Objective: The objec­tive of this study was to evaluate the performance of eGFR in staging of CKD compared to gamma camera based GFR.Methods: This cross sectional analytical study was conducted in the Department of Biochemistry Bangabandhu Sheikh Mujib Medical University (BSMMU with the collaboration with National Institute of Nuclear Medicine and Allied Sciences, BSMMU during the period of January 2011 to December 2012. Gama camera based GFR was estimated from DTP A reno gram and eGFR was estimated by three prediction equations. Comparison was done by Bland Altman agree­ment test to see the agreement on the measurement of GFR between three equation based eGFR method and gama camera based GFR method. Staging comparison was done by Kappa analysis to see the agreement between the stages identified by those different methods.Results: Bland-Altman agreement analysis between GFR measured by gamma camera, CG equation ,CG equation corrected by BSA and MDRD equation shows statistically significant. CKD stages determined by CG GFR, CG GFR corrected by BSA , MDRD GFR and gamma camera based GFR was compared by Kappa statistical analysis .The kappa value was 0.66, 0.77 and 0.79 respectively.Conclusions: This study findings suggest that GFR estimation by MDRD equation in CKD patients shows good agreement with gamma camera based GFR and for staging of CKD patients, eGFR by MDRD formula may be used as very effective tool in Bangladeshi population.

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

KAUST Repository

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

2012-01-01

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

A Sequential Multiplicative Extended Kalman Filter for Attitude Estimation Using Vector Observations

Science.gov (United States)

Qin, Fangjun; Jiang, Sai; Zha, Feng

2018-01-01

In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms. PMID:29751538

A Sequential Multiplicative Extended Kalman Filter for Attitude Estimation Using Vector Observations

Directory of Open Access Journals (Sweden)

Fangjun Qin

2018-05-01

Full Text Available In this paper, a sequential multiplicative extended Kalman filter (SMEKF is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms.

Algebraic entropy for differential-delay equations

OpenAIRE

Viallet, Claude M.

2014-01-01

We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

Cellular solutions for the Poisson equation in extended systems

International Nuclear Information System (INIS)

Zhang, X.; Butler, W.H.; MacLaren, J.M.; van Ek, J.

1994-01-01

The Poisson equation for the electrostatic potential in a solid is solved using three different cellular techniques. The relative merits of these different approaches are discussed for two test charge densities for which an analytic solution to the Poisson equation is known. The first approach uses full-cell multiple-scattering theory and results in the famililar structure constant and multipole moment expansion. This solution is shown to be valid everywhere inside the cell, although for points outside the muffin-tin sphere but inside the cell the sums must be performed in the correct order to yield meaningful results. A modification of the multiple-scattering-theory approach yields a second method, a Green-function cellular method, which only requires the solution of a nearest-neighbor linear system of equations. A third approach, a related variational cellular method, is also derived. The variational cellular approach is shown to be the most accurate and reliable, and to have the best convergence in angular momentum of the three methods. Coulomb energies accurate to within 10 -6 hartree are easily achieved with the variational cellular approach, demonstrating the practicality of the approach in electronic structure calculations

Calculation of prevalence estimates through differential equations: application to stroke-related disability.

Science.gov (United States)

Mar, Javier; Sainz-Ezkerra, María; Moler-Cuiral, Jose Antonio

2008-01-01

Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model. (c) 2008 S. Karger AG, Basel.

A Novel Biped Pattern Generator Based on Extended ZMP and Extended Cart-Table Model

Directory of Open Access Journals (Sweden)

Guangbin Sun

2015-07-01

Full Text Available This paper focuses on planning patterns for biped walking on complex terrains. Two problems are solved: ZMP (zero moment point cannot be used on uneven terrain, and the conventional cart-table model does not allow vertical CM (centre of mass motion. For the ZMP definition problem, we propose the extended ZMP (EZMP concept as an extension of ZMP to uneven terrains. It can be used to judge dynamic balance on universal terrains. We achieve a deeper insight into the connection and difference between ZMP and EZMP by adding different constraints. For the model problem, we extend the cart-table model by using a dynamic constraint instead of constant height constraint, which results in a mathematically symmetric set of three equations. In this way, the vertical motion is enabled and the resultant equations are still linear. Based on the extended ZMP concept and extended cart-table model, a biped pattern generator using triple preview controllers is constructed and implemented simultaneously to three dimensions. Using the proposed pattern generator, the Atlas robot is simulated. The simulation results show the robot can walk stably on rather complex terrains by accurately tracking extended ZMP.

Extended reactance domain algorithms for DoA estimation onto an ESPAR antennas

Science.gov (United States)

Harabi, F.; Akkar, S.; Gharsallah, A.

2016-07-01

Based on an extended reactance domain (RD) covariance matrix, this article proposes new alternatives for directions of arrival (DoAs) estimation of narrowband sources through an electronically steerable parasitic array radiator (ESPAR) antennas. Because of the centro symmetry of the classic ESPAR antennas, an unitary transformation is applied to the collected data that allow an important reduction in both computational cost and processing time and, also, an enhancement of the resolution capabilities of the proposed algorithms. Moreover, this article proposes a new approach for eigenvalues estimation through only some linear operations. The developed DoAs estimation algorithms based on this new approach has illustrated a good behaviour with less calculation cost and processing time as compared to other schemes based on the classic eigenvalues approach. The conducted simulations demonstrate that high-precision and high-resolution DoAs estimation can be reached especially in very closely sources situation and low sources power as compared to the RD-MUSIC algorithm and the RD-PM algorithm. The asymptotic behaviours of the proposed DoAs estimators are analysed in various scenarios and compared with the Cramer-Rao bound (CRB). The conducted simulations testify the high-resolution of the developed algorithms and prove the efficiently of the proposed approach.

Improving filtering and prediction of spatially extended turbulent systems with model errors through stochastic parameter estimation

International Nuclear Information System (INIS)

Gershgorin, B.; Harlim, J.; Majda, A.J.

2010-01-01

The filtering and predictive skill for turbulent signals is often limited by the lack of information about the true dynamics of the system and by our inability to resolve the assumed dynamics with sufficiently high resolution using the current computing power. The standard approach is to use a simple yet rich family of constant parameters to account for model errors through parameterization. This approach can have significant skill by fitting the parameters to some statistical feature of the true signal; however in the context of real-time prediction, such a strategy performs poorly when intermittent transitions to instability occur. Alternatively, we need a set of dynamic parameters. One strategy for estimating parameters on the fly is a stochastic parameter estimation through partial observations of the true signal. In this paper, we extend our newly developed stochastic parameter estimation strategy, the Stochastic Parameterization Extended Kalman Filter (SPEKF), to filtering sparsely observed spatially extended turbulent systems which exhibit abrupt stability transition from time to time despite a stable average behavior. For our primary numerical example, we consider a turbulent system of externally forced barotropic Rossby waves with instability introduced through intermittent negative damping. We find high filtering skill of SPEKF applied to this toy model even in the case of very sparse observations (with only 15 out of the 105 grid points observed) and with unspecified external forcing and damping. Additive and multiplicative bias corrections are used to learn the unknown features of the true dynamics from observations. We also present a comprehensive study of predictive skill in the one-mode context including the robustness toward variation of stochastic parameters, imperfect initial conditions and finite ensemble effect. Furthermore, the proposed stochastic parameter estimation scheme applied to the same spatially extended Rossby wave system demonstrates

Equating accelerometer estimates among youth

DEFF Research Database (Denmark)

Brazendale, Keith; Beets, Michael W; Bornstein, Daniel B

2016-01-01

from one set of cutpoints into another. Bland Altman plots illustrate the agreement between actual MVPA and predicted MVPA values. RESULTS: Across the total sample, mean MVPA ranged from 29.7MVPAmind(-1) (Puyau) to 126.1MVPAmind(-1) (Freedson 3 METs). Across conversion equations, median absolute...

On reduction and exact solutions of nonlinear many-dimensional Schroedinger equations

International Nuclear Information System (INIS)

Barannik, A.F.; Marchenko, V.A.; Fushchich, V.I.

1991-01-01

With the help of the canonical decomposition of an arbitrary subalgebra of the orthogonal algebra AO(n) the rank n and n-1 maximal subalgebras of the extended isochronous Galileo algebra, the rank n maximal subalgebras of the generalized extended classical Galileo algebra AG(a,n) the extended special Galileo algebra AG(2,n) and the extended whole Galileo algebra AG(3,n) are described. By using the rank n subalgebras, ansatze reducing the many dimensional Schroedinger equations to ordinary differential equations is found. With the help of the reduced equation solutions exact solutions of the Schroedinger equation are considered

A Generalized Estimating Equations Approach to Model Heterogeneity and Time Dependence in Capture-Recapture Studies

Directory of Open Access Journals (Sweden)

Akanda Md. Abdus Salam

2017-03-01

Full Text Available Individual heterogeneity in capture probabilities and time dependence are fundamentally important for estimating the closed animal population parameters in capture-recapture studies. A generalized estimating equations (GEE approach accounts for linear correlation among capture-recapture occasions, and individual heterogeneity in capture probabilities in a closed population capture-recapture individual heterogeneity and time variation model. The estimated capture probabilities are used to estimate animal population parameters. Two real data sets are used for illustrative purposes. A simulation study is carried out to assess the performance of the GEE estimator. A Quasi-Likelihood Information Criterion (QIC is applied for the selection of the best fitting model. This approach performs well when the estimated population parameters depend on the individual heterogeneity and the nature of linear correlation among capture-recapture occasions.

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Energy Technology Data Exchange (ETDEWEB)

Arima, Takashi, E-mail: tks@stat.nitech.ac.jp [Center for Social Contribution and Collaboration, Nagoya Institute of Technology (Japan); Mentrelli, Andrea, E-mail: andrea.mentrelli@unibo.it [Department of Mathematics and Research Center of Applied Mathematics (CIRAM), University of Bologna (Italy); Ruggeri, Tommaso, E-mail: tommaso.ruggeri@unibo.it [Department of Mathematics and Research Center of Applied Mathematics (CIRAM), University of Bologna (Italy)

2014-06-15

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium characteristic velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N) by Boillat and Ruggeri (1997) (λ{sub (N)}{sup E,max})/(c{sub 0}) ⩾√(6/5 (N−1/2 )),(c{sub 0}=√(5/3 k/m T)) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule. -- Highlights: •Molecular extended thermodynamics of rarefied polyatomic gases is studied. •The relation between two hierarchies of equations for moments is derived. •The equivalence of maximum entropy principle and entropy principle is proven. •The characteristic velocities are compared to those of monatomic gases. •The lower bound of the maximum characteristic velocity is estimated.

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

International Nuclear Information System (INIS)

Arima, Takashi; Mentrelli, Andrea; Ruggeri, Tommaso

2014-01-01

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium characteristic velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N) by Boillat and Ruggeri (1997) (λ (N) E,max )/(c 0 ) ⩾√(6/5 (N−1/2 )),(c 0 =√(5/3 k/m T)) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule. -- Highlights: •Molecular extended thermodynamics of rarefied polyatomic gases is studied. •The relation between two hierarchies of equations for moments is derived. •The equivalence of maximum entropy principle and entropy principle is proven. •The characteristic velocities are compared to those of monatomic gases. •The lower bound of the maximum characteristic velocity is estimated

Allometric equations for estimating aboveground biomass for common shrubs in northeastern California

Science.gov (United States)

Steve Huff; Martin Ritchie; H. Temesgen

2017-01-01

Selected allometric equations and fitting strategies were evaluated for their predictive abilities for estimating above ground biomass for seven species of shrubs common to northeastern California. Size classes for woody biomass were categorized as 1-h fuels (0.1–0.6 cm), 10-h fuels (0.6–2.5 cm), 100-h fuels (2.5–7.6 cm), and 1000-h fuels (greater than 7.7 cm in...

Estimating Renal Function in the Elderly Malaysian Patients Attending Medical Outpatient Clinic: A Comparison between Creatinine Based and Cystatin-C Based Equations.

Science.gov (United States)

Jalalonmuhali, Maisarah; Elagel, Salma Mohamed Abouzriba; Tan, Maw Pin; Lim, Soo Kun; Ng, Kok Peng

2018-01-01

To assess the performance of different GFR estimating equations, test the diagnostic value of serum cystatin-C, and compare the applicability of cystatin-C based equation with serum creatinine based equation for estimating GFR (eGFR) in comparison with measured GFR in the elderly Malaysian patients. A cross-sectional study recruiting volunteered patients 65 years and older attending medical outpatient clinic. 51 chromium EDTA ( 51 Cr-EDTA) was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA), four-variable Modification of Diet in Renal Disease (4-MDRD), and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations using serum creatinine (CKD-EPIcr) as well as serum cystatin-C (CKD-EPIcys) were calculated. A total of 40 patients, 77.5% male, with mean measured GFR 41.2 ± 18.9 ml/min/1.73 m 2 were enrolled. Mean bias was the smallest for 4-MDRD; meanwhile, CKD-EPIcr had the highest precision and accuracy with lower limit of agreement among other equations. CKD-EPIcys equation did not show any improvement in GFR estimation in comparison to CKD-EPIcr and MDRD. The CKD-EPIcr formula appears to be more accurate and correlates better with measured GFR in this cohort of elderly patients.

Calculation of propellant gas pressure by simple extended corresponding state principle

OpenAIRE

Bin Xu; San-jiu Ying; Xin Liao

2016-01-01

The virial equation can well describe gas state at high temperature and pressure, but the difficulties in virial coefficient calculation limit the use of virial equation. Simple extended corresponding state principle (SE-CSP) is introduced in virial equation. Based on a corresponding state equation, including three characteristic parameters, an extended parameter is introduced to describe the second virial coefficient expressions of main products of propellant gas. The modified SE-CSP second ...

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

Science.gov (United States)

Cameron, Stephen; Silvestre, Luis; Snelson, Stanley

2018-05-01

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.

Social security wealth and aggregate consumption : An extended life-cycle model estimated for The Netherlands

NARCIS (Netherlands)

Zant, W.

In this paper a method is developed to calculate a wealth variable accounting for the existence of the basic old-age provisions in The Netherlands (AOW). In line with Feldstein's extended life-cycle model, consumption functions with (gross) social security wealth are estimated for The Netherlands

Singular solitons and other solutions to a couple of nonlinear wave equations

International Nuclear Information System (INIS)

Inc Mustafa; Ulutaş Esma; Biswas Anjan

2013-01-01

This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method

Reliable Quantification of the Potential for Equations Based on Spot Urine Samples to Estimate Population Salt Intake

DEFF Research Database (Denmark)

Huang, Liping; Crino, Michelle; Wu, Jason Hy

2016-01-01

to a standard format. Individual participant records will be compiled and a series of analyses will be completed to: (1) compare existing equations for estimating 24-hour salt intake from spot urine samples with 24-hour urine samples, and assess the degree of bias according to key demographic and clinical......BACKGROUND: Methods based on spot urine samples (a single sample at one time-point) have been identified as a possible alternative approach to 24-hour urine samples for determining mean population salt intake. OBJECTIVE: The aim of this study is to identify a reliable method for estimating mean...... population salt intake from spot urine samples. This will be done by comparing the performance of existing equations against one other and against estimates derived from 24-hour urine samples. The effects of factors such as ethnicity, sex, age, body mass index, antihypertensive drug use, health status...

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

Science.gov (United States)

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

2015-12-01

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

Comparing the measured basal metabolic rates in patients with chronic disorders of consciousness to the estimated basal metabolic rate calculated from common predictive equations.

Science.gov (United States)

Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao

2017-10-01

Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (BMR was estimated for each group using the Harris-Benedict (H-B), Schofield, or Cunningham equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p BMR values estimated using the H-B and Cunningham equations were different significantly from the measured BMR (p BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.

Nonlinear integrodifferential equations as discrete systems

Science.gov (United States)

Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

1999-06-01

We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

Analysis of an a posteriori error estimator for the transport equation with SN and discontinuous Galerkin discretizations

International Nuclear Information System (INIS)

Fournier, D.; Le Tellier, R.; Suteau, C.

2011-01-01

We present an error estimator for the S N neutron transport equation discretized with an arbitrary high-order discontinuous Galerkin method. As a starting point, the estimator is obtained for conforming Cartesian meshes with a uniform polynomial order for the trial space then adapted to deal with non-conforming meshes and a variable polynomial order. Some numerical tests illustrate the properties of the estimator and its limitations. Finally, a simple shielding benchmark is analyzed in order to show the relevance of the estimator in an adaptive process.

Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation

Directory of Open Access Journals (Sweden)

Yuncheng You

2008-12-01

Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.

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

International Nuclear Information System (INIS)

Rupšys, P.

2015-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Rupšys, P. [Aleksandras Stulginskis University, Studenų g. 11, Akademija, Kaunas district, LT – 53361 Lithuania (Lithuania)

2015-10-28

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

Noninvasive estimation of global activation sequence using the extended Kalman filter.

Science.gov (United States)

Liu, Chenguang; He, Bin

2011-03-01

A new algorithm for 3-D imaging of the activation sequence from noninvasive body surface potentials is proposed. After formulating the nonlinear relationship between the 3-D activation sequence and the body surface recordings during activation, the extended Kalman filter (EKF) is utilized to estimate the activation sequence in a recursive way. The state vector containing the activation sequence is optimized during iteration by updating the error variance/covariance matrix. A new regularization scheme is incorporated into the "predict" procedure of EKF to tackle the ill-posedness of the inverse problem. The EKF-based algorithm shows good performance in simulation under single-site pacing. Between the estimated activation sequences and true values, the average correlation coefficient (CC) is 0.95, and the relative error (RE) is 0.13. The average localization error (LE) when localizing the pacing site is 3.0 mm. Good results are also obtained under dual-site pacing (CC = 0.93, RE = 0.16, and LE = 4.3 mm). Furthermore, the algorithm shows robustness to noise. The present promising results demonstrate that the proposed EKF-based inverse approach can noninvasively estimate the 3-D activation sequence with good accuracy and the new algorithm shows good features due to the application of EKF.

Estimating Renal Function in the Elderly Malaysian Patients Attending Medical Outpatient Clinic: A Comparison between Creatinine Based and Cystatin-C Based Equations

Directory of Open Access Journals (Sweden)

Maisarah Jalalonmuhali

2018-01-01

Full Text Available Background. To assess the performance of different GFR estimating equations, test the diagnostic value of serum cystatin-C, and compare the applicability of cystatin-C based equation with serum creatinine based equation for estimating GFR (eGFR in comparison with measured GFR in the elderly Malaysian patients. Methods. A cross-sectional study recruiting volunteered patients 65 years and older attending medical outpatient clinic. 51 chromium EDTA (51Cr-EDTA was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA, four-variable Modification of Diet in Renal Disease (4-MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations using serum creatinine (CKD-EPIcr as well as serum cystatin-C (CKD-EPIcys were calculated. Results. A total of 40 patients, 77.5% male, with mean measured GFR 41.2±18.9 ml/min/1.73 m2 were enrolled. Mean bias was the smallest for 4-MDRD; meanwhile, CKD-EPIcr had the highest precision and accuracy with lower limit of agreement among other equations. CKD-EPIcys equation did not show any improvement in GFR estimation in comparison to CKD-EPIcr and MDRD. Conclusion. The CKD-EPIcr formula appears to be more accurate and correlates better with measured GFR in this cohort of elderly patients.

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

Science.gov (United States)

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

2015-01-01

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

Explorations of the extended ncKP hierarchy

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2004-01-01

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities

Estimation of Physiological Cost Index as an Energy Expenditure Index using MacGregor’s Equation

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Binaya SJB Rana

2015-09-01

Full Text Available Introduction: Physical activity and energy expenditure can be quantified by measuring heart rate, oxygen uptake and respiratory quotient. The Physiological Cost Index (PCI proposed by MacGregor is a simple and straightforward method to estimate the energy expenditure index. Here, we aim to estimate the energy expenditure among young Asian population using MacGregor’s equation. Methods: A total of 50 young randomly selected healthy females performed 50m, 100m and 150m walking test at their self-selected preferred speed. The physiological cost index values for 100 m walk at speeds slower and faster than the preferred speed were also obtained. The physiological cost index during exercise was calculated using MacGregor’s equation considering heart rate and speed of walking over the varying distances. Results: The PCI values on three different distances are consistent during self selected preferred speed. The PCI estimation on second and third tests for all three distances walked consistently reproducible. However for each distance walked, the first test the PCI was significantly higher than the second and third test values. The PCI values increased significantly when subjects walked either slower (p = 0.02 or faster (p = 0.001 than their normal preferred speed. Conclusion: The physiological cost index values were similar for varying distances walks. The PCI was the least at the preferred speed of walking and increased when the subjects either walked slower or faster than the preferred speed. The first estimation was higher than subsequent estimations. Keywords: energy expenditure index; exercise; physiological cost index. | PubMed

Parameter Estimation in Stochastic Grey-Box Models

DEFF Research Database (Denmark)

Kristensen, Niels Rode; Madsen, Henrik; Jørgensen, Sten Bay

2004-01-01

An efficient and flexible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Ito stochastic differential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended...... Kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets, including irregularly sampled data sets and data sets with occasional outliers and missing observations. The software implementation is compared to an existing software tool...... and proves to have better performance both in terms of quality of estimates for nonlinear systems with significant diffusion and in terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the diffusion term....

Behaviour of the extended Toda lattice

Science.gov (United States)

Wattis, Jonathan A. D.; Gordoa, Pilar R.; Pickering, Andrew

2015-11-01

We consider the first member of an extended Toda lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptotic analysis to consider the long wavelength limits of the system. By considering various magnitudes for the parameters involved, we derive reduced equations related to the Korteweg-de Vries and potential Boussinesq equations.

Comparative Performance of Creatinine-Based Estimated Glomerular Filtration Rate Equations in the Malays: A Pilot Study in Tertiary Hospital in Malaysia

Directory of Open Access Journals (Sweden)

Maisarah Jalalonmuhali

2017-01-01

Full Text Available Aim. To validate the accuracy of estimated glomerular filtration rate (eGFR equations in Malay population attending our hospital in comparison with radiolabeled measured GFR. Methods. A cross-sectional study recruiting volunteered patients in the outpatient setting. Chromium EDTA (51Cr-EDTA was used as measured GFR. The predictive capabilities of Cockcroft-Gault equation corrected for body surface area (CGBSA, four-variable Modification of Diet in Renal Disease (4-MDRD, and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equations were calculated. Results. A total of 51 subjects were recruited with mean measured GFR 42.04 (17.70–111.10 ml/min/1.73 m2. Estimated GFR based on CGBSA, 4-MDRD, and CKD-EPI were 40.47 (16.52–115.52, 35.90 (14.00–98.00, and 37.24 (14.00–121.00, respectively. Higher accuracy was noted in 4-MDRD equations throughout all GFR groups except for subgroup of GFR ≥ 60 ml/min/1.73 m2 where CGBSA was better. Conclusions. The 4-MDRD equation seems to perform better in estimating GFR in Malay CKD patients generally and specifically in the subgroup of GFR < 60 ml/min/1.73 m2 and both BMI subgroups.

Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

International Nuclear Information System (INIS)

Aslan İsmail

2014-01-01

The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)

-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

Directory of Open Access Journals (Sweden)

Lee HyunYoung

2010-01-01

Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

Estimation of Resource Productivity and Efficiency: An Extended Evaluation of Sustainability Related to Material Flow

Directory of Open Access Journals (Sweden)

Pin-Chih Wang

2014-09-01

Full Text Available This study is intended to conduct an extended evaluation of sustainability based on the material flow analysis of resource productivity. We first present updated information on the material flow analysis (MFA database in Taiwan. Essential indicators are selected to quantify resource productivity associated with the economy-wide MFA of Taiwan. The study also applies the IPAT (impact-population-affluence-technology master equation to measure trends of material use efficiency in Taiwan and to compare them with those of other Asia-Pacific countries. An extended evaluation of efficiency, in comparison with selected economies by applying data envelopment analysis (DEA, is conducted accordingly. The Malmquist Productivity Index (MPI is thereby adopted to quantify the patterns and the associated changes of efficiency. Observations and summaries can be described as follows. Based on the MFA of the Taiwanese economy, the average growth rates of domestic material input (DMI; 2.83% and domestic material consumption (DMC; 2.13% in the past two decades were both less than that of gross domestic product (GDP; 4.95%. The decoupling of environmental pressures from economic growth can be observed. In terms of the decomposition analysis of the IPAT equation and in comparison with 38 other economies, the material use efficiency of Taiwan did not perform as well as its economic growth. The DEA comparisons of resource productivity show that Denmark, Germany, Luxembourg, Malta, Netherlands, United Kingdom and Japan performed the best in 2008. Since the MPI consists of technological change (frontier-shift or innovation and efficiency change (catch-up, the change in efficiency (catch-up of Taiwan has not been accomplished as expected in spite of the increase in its technological efficiency.

Application of generalized estimating equations to a study in vitro of radiation sensitivity

International Nuclear Information System (INIS)

Cologne, J.B.; Carter, R.L.; Fujita, Shoichiro; Ban, Sadayuki.

1993-08-01

We describes an application of the generalized estimating equation (GEE) method (Liang K-Y, Zeger SL: Longitudinal data analysis using generalized linear models. Biometrika 73:13-22, 1986) for regression analyses of correlated Poisson data. As an alternative to the use of an arbitrarily chosen working correlation matrix, we demonstrate the use of GEE with a reasonable model for the true covariance structure among repeated observations within individuals. We show that, under such a split-plot design with large clusters, the asymptotic relative efficiency of GEE with simple (independence or exchangeable) working correlation matrices is rather low. We also illustrate the use of GEE with an empirically estimated model for overdispersion in a large study of radiation sensitivity where cluster size is small and a simple working correlation structure is sufficient. We conclude by summarizing issues and needs for further work concerning efficiency of the GEE parameter estimates in practice. (author)

External validation of equations to estimate resting energy expenditure in 14952 adults with overweight and obesity and 1948 adults with normal weight from Italy.

Science.gov (United States)

Bedogni, Giorgio; Bertoli, Simona; Leone, Alessandro; De Amicis, Ramona; Lucchetti, Elisa; Agosti, Fiorenza; Marazzi, Nicoletta; Battezzati, Alberto; Sartorio, Alessandro

2017-11-24

We cross-validated 28 equations to estimate resting energy expenditure (REE) in a very large sample of adults with overweight or obesity. 14952 Caucasian men and women with overweight or obesity and 1498 with normal weight were studied. REE was measured using indirect calorimetry and estimated using two meta-regression equations and 26 other equations. The correct classification fraction (CCF) was defined as the fraction of subjects whose estimated REE was within 10% of measured REE. The highest CCF was 79%, 80%, 72%, 64%, and 63% in subjects with normal weight, overweight, class 1 obesity, class 2 obesity, and class 3 obesity, respectively. The Henry weight and height and Mifflin equations performed equally well with CCFs of 77% vs. 77% for subjects with normal weight, 80% vs. 80% for those with overweight, 72% vs. 72% for those with class 1 obesity, 64% vs. 63% for those with class 2 obesity, and 61% vs. 60% for those with class 3 obesity. The Sabounchi meta-regression equations offered an improvement over the above equations only for class 3 obesity (63%). The accuracy of REE equations decreases with increasing values of body mass index. The Henry weight & height and Mifflin equations are similarly accurate and the Sabounchi equations offer an improvement only in subjects with class 3 obesity. Copyright © 2017 Elsevier Ltd and European Society for Clinical Nutrition and Metabolism. All rights reserved.

A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

Hamilton's gradient estimate for the heat kernel on complete manifolds

OpenAIRE

Kotschwar, Brett

2007-01-01

In this paper we extend a gradient estimate of R. Hamilton for positive solutions to the heat equation on closed manifolds to bounded positive solutions on complete, non-compact manifolds with $Rc \\geq -Kg$. We accomplish this extension via a maximum principle of L. Karp and P. Li and a Bernstein-type estimate on the gradient of the solution. An application of our result, together with the bounds of P. Li and S.T. Yau, yields an estimate on the gradient of the heat kernel for complete manifol...

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

Energy Technology Data Exchange (ETDEWEB)

Horn, M.A. [Wichita State Univ., Wichita, KS (United States)

1996-12-31

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

Transformation of nonlinear discrete-time system into the extended observer form

Science.gov (United States)

Kaparin, V.; Kotta, Ü.

2018-04-01

The paper addresses the problem of transforming discrete-time single-input single-output nonlinear state equations into the extended observer form, which, besides the input and output, also depends on a finite number of their past values. Necessary and sufficient conditions for the existence of both the extended coordinate and output transformations, solving the problem, are formulated in terms of differential one-forms, associated with the input-output equation, corresponding to the state equations. An algorithm for transformation of state equations into the extended observer form is proposed and illustrated by an example. Moreover, the considered approach is compared with the method of dynamic observer error linearisation, which likewise is intended to enlarge the class of systems transformable into an observer form.

Tail estimates for stochastic fixed point equations via nonlinear renewal theory

DEFF Research Database (Denmark)

Collamore, Jeffrey F.; Vidyashankar, Anand N.

2013-01-01

estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....

INTERVAL STATE ESTIMATION FOR SINGULAR DIFFERENTIAL EQUATION SYSTEMS WITH DELAYS

Directory of Open Access Journals (Sweden)

T. A. Kharkovskaia

2016-07-01

Full Text Available The paper deals with linear differential equation systems with algebraic restrictions (singular systems and a method of interval observer design for this kind of systems. The systems contain constant time delay, measurement noise and disturbances. Interval observer synthesis is based on monotone and cooperative systems technique, linear matrix inequations, Lyapunov function theory and interval arithmetic. The set of conditions that gives the possibility for interval observer synthesis is proposed. Results of synthesized observer operation are shown on the example of dynamical interindustry balance model. The advantages of proposed method are that it is adapted to observer design for uncertain systems, if the intervals of admissible values for uncertain parameters are given. The designed observer is capable to provide asymptotically definite limits on the estimation accuracy, since the interval of admissible values for the object state is defined at every instant. The obtained result provides an opportunity to develop the interval estimation theory for complex systems that contain parametric uncertainty, varying delay and nonlinear elements. Interval observers increasingly find applications in economics, electrical engineering, mechanical systems with constraints and optimal flow control.

Reliability of CKD-EPI predictive equation in estimating chronic kidney disease prevalence in the Croatian endemic nephropathy area.

Science.gov (United States)

Fuček, Mirjana; Dika, Živka; Karanović, Sandra; Vuković Brinar, Ivana; Premužić, Vedran; Kos, Jelena; Cvitković, Ante; Mišić, Maja; Samardžić, Josip; Rogić, Dunja; Jelaković, Bojan

2018-02-15

Chronic kidney disease (CKD) is a significant public health problem and it is not possible to precisely predict its progression to terminal renal failure. According to current guidelines, CKD stages are classified based on the estimated glomerular filtration rate (eGFR) and albuminuria. Aims of this study were to determine the reliability of predictive equation in estimation of CKD prevalence in Croatian areas with endemic nephropathy (EN), compare the results with non-endemic areas, and to determine if the prevalence of CKD stages 3-5 was increased in subjects with EN. A total of 1573 inhabitants of the Croatian Posavina rural area from 6 endemic and 3 non-endemic villages were enrolled. Participants were classified according to the modified criteria of the World Health Organization for EN. Estimated GFR was calculated using Chronic Kidney Disease Epidemiology Collaboration equation (CKD-EPI). The results showed a very high CKD prevalence in the Croatian rural area (19%). CKD prevalence was significantly higher in EN then in non EN villages with the lowest eGFR value in diseased subgroup. eGFR correlated significantly with the diagnosis of EN. Kidney function assessment using CKD-EPI predictive equation proved to be a good marker in differentiating the study subgroups, remained as one of the diagnostic criteria for EN.

Error estimation for goal-oriented spatial adaptivity for the SN equations on triangular meshes

International Nuclear Information System (INIS)

Lathouwers, D.

2011-01-01

In this paper we investigate different error estimation procedures for use within a goal oriented adaptive algorithm for the S N equations on unstructured meshes. The method is based on a dual-weighted residual approach where an appropriate adjoint problem is formulated and solved in order to obtain the importance of residual errors in the forward problem on the specific goal of interest. The forward residuals and the adjoint function are combined to obtain both economical finite element meshes tailored to the solution of the target functional as well as providing error estimates. Various approximations made to make the calculation of the adjoint angular flux more economically attractive are evaluated by comparing the performance of the resulting adaptive algorithm and the quality of the error estimators when applied to two shielding-type test problems. (author)

Current use of equations for estimating glomerular filtration rate in Spanish laboratories.

Science.gov (United States)

Gràcia-Garcia, Sílvia; Montañés-Bermúdez, Rosario; Morales-García, Luis J; Díez-de Los Ríos, M José; Jiménez-García, Juan Á; Macías-Blanco, Carlos; Martínez-López, Rosalina; Ruiz-Altarejos, Joaquín; Ruiz-Martín, Guadalupe; Sanz-Hernández, Sonia; Ventura-Pedret, Salvador

2012-07-17

In 2006 the Spanish Society of Clinical Biochemistry and Molecular Pathology (SEQC) and the Spanish Society of Nephrology (S.E.N.) developed a consensus document in order to facilitate the diagnosis and monitoring of chronic kidney disease with the incorporation of equations for estimating glomerular filtration rate (eGFR) into laboratory reports. The current national prevalence of eGFR reporting and the degree of adherence to these recommendations among clinical laboratories is unknown. We administered a national survey in 2010-11 to Spanish clinical laboratories. The survey was through e-mail or telephone to laboratories that participated in the SEQC’s Programme for External Quality Assurance, included in the National Hospitals Catalogue 2010, including both primary care and private laboratories. A total of 281 laboratories answered to the survey. Of these, 88.2% reported on the eGFR, with 61.9% reporting on the MDRD equation and 31.6% using the MDRD-IDMS equation. A total of 42.5% of laboratories always reported serum creatinine values, and other variables only when specifically requested. Regarding the way results were presented, 46.2% of laboratories reported the exact numerical value only when the filtration rate was below 60mL/min/1.73m2, while 50.6% reported all values regardless. In 56.3% of the cases reporting eGFR, an interpretive commentary of it was enclosed. Although a high percentage of Spanish laboratories have added eGFR in their reports, this metric is not universally used. Moreover, some aspects, such as the equation used and the correct expression of eGFR results, should be improved.

Dispersive estimates for the Schroedinger and Klein-Gordon equations

Energy Technology Data Exchange (ETDEWEB)

Kopylova, Elena A [Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow (Russian Federation)

2010-01-01

This is a survey of results on the long-time asymptotic behaviour of solutions of the Schroedinger and Klein-Gordon equations in weighted energy norms. Results obtained from 1975 to 2001 in the spectral scattering theory of Agmon, Jensen-Kato, Jensen-Nenciu, and Murata are described for the Schroedinger equation, along with the author's recent results obtained jointly with A.I. Komech for the Klein-Gordon equation. The methods used develop the spectral approach as applied to relativistic equations. Bibliography: 40 titles.

Erosivity factor in the Universal Soil Loss Equation estimated from Finnish rainfall data

Directory of Open Access Journals (Sweden)

Maximilian Posch

1993-07-01

Full Text Available Continuous rainfall data recorded for many years at 8 stations in Finland were used to estimate rainfall erosivity, a quantity needed for soil loss predictions with the Universal Soil Loss Equation (USLE. The obtained erosivity values were then used to determine the 2 parameters of a power-law function describing the relationship between daily precipitation and erosivity. This function is of importance in erosion modeling at locations where no breakpoint rainfall data are available. The parameters of the power-law were estimated both by linear regression of the log-transformed data and by non-linear least-square fitting of the original data. Results indicate a considerable seasonal (monthly variation of the erosivity, whereas the spatial variation over Finland is rather small.

Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data

KAUST Repository

Hall, Eric Joseph

2016-12-08

We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.

A review of the effects on IRT item parameter estimates with a focus on misbehaving common items in test equating

Directory of Open Access Journals (Sweden)

Michalis P Michaelides

2010-10-01

Full Text Available Many studies have investigated the topic of change or drift in item parameter estimates in the context of Item Response Theory. Content effects, such as instructional variation and curricular emphasis, as well as context effects, such as the wording, position, or exposure of an item have been found to impact item parameter estimates. The issue becomes more critical when items with estimates exhibiting differential behavior across test administrations are used as common for deriving equating transformations. This paper reviews the types of effects on IRT item parameter estimates and focuses on the impact of misbehaving or aberrant common items on equating transformations. Implications relating to test validity and the judgmental nature of the decision to keep or discard aberrant common items are discussed, with recommendations for future research into more informed and formal ways of dealing with misbehaving common items.

A Review of the Effects on IRT Item Parameter Estimates with a Focus on Misbehaving Common Items in Test Equating.

Science.gov (United States)

Michaelides, Michalis P

2010-01-01

Many studies have investigated the topic of change or drift in item parameter estimates in the context of item response theory (IRT). Content effects, such as instructional variation and curricular emphasis, as well as context effects, such as the wording, position, or exposure of an item have been found to impact item parameter estimates. The issue becomes more critical when items with estimates exhibiting differential behavior across test administrations are used as common for deriving equating transformations. This paper reviews the types of effects on IRT item parameter estimates and focuses on the impact of misbehaving or aberrant common items on equating transformations. Implications relating to test validity and the judgmental nature of the decision to keep or discard aberrant common items are discussed, with recommendations for future research into more informed and formal ways of dealing with misbehaving common items.

Estimation of State of Charge of Lithium-Ion Batteries Used in HEV Using Robust Extended Kalman Filtering

Directory of Open Access Journals (Sweden)

Suleiman M. Sharkh

2012-04-01

Full Text Available A robust extended Kalman filter (EKF is proposed as a method for estimation of the state of charge (SOC of lithium-ion batteries used in hybrid electric vehicles (HEVs. An equivalent circuit model of the battery, including its electromotive force (EMF hysteresis characteristics and polarization characteristics is used. The effect of the robust EKF gain coefficient on SOC estimation is analyzed, and an optimized gain coefficient is determined to restrain battery terminal voltage from fluctuating. Experimental and simulation results are presented. SOC estimates using the standard EKF are compared with the proposed robust EKF algorithm to demonstrate the accuracy and precision of the latter for SOC estimation.

Clarkson-Kruskal Direct Similarity Approach for Differential-Difference Equations

Institute of Scientific and Technical Information of China (English)

SHEN Shou-Feng

2005-01-01

In this letter, the Clarkson-Kruskal direct method is extended to similarity reduce some differentialdifference equations. As examples, the differential-difference KZ equation and KP equation are considered.

Nonlinear von Neumann equations for quantum dissipative systems

International Nuclear Information System (INIS)

Messer, J.; Baumgartner, B.

1978-01-01

For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

Nonlinear von Neumann equations for quantum dissipative systems

International Nuclear Information System (INIS)

Messer, J.; Baumgartner, B.

For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

Parameter estimation and change-point detection from Dynamic Contrast Enhanced MRI data using stochastic differential equations.

Science.gov (United States)

Cuenod, Charles-André; Favetto, Benjamin; Genon-Catalot, Valentine; Rozenholc, Yves; Samson, Adeline

2011-09-01

Dynamic Contrast Enhanced imaging (DCE-imaging) following a contrast agent bolus allows the extraction of information on tissue micro-vascularization. The dynamic signals obtained from DCE-imaging are modeled by pharmacokinetic compartmental models which integrate the Arterial Input Function. These models use ordinary differential equations (ODEs) to describe the exchanges between the arterial and capillary plasma and the extravascular-extracellular space. Their least squares fitting takes into account measurement noises but fails to deal with unpredictable fluctuations due to external/internal sources of variations (patients' anxiety, time-varying parameters, measurement errors in the input function, etc.). Adding Brownian components to the ODEs leads to stochastic differential equations (SDEs). In DCE-imaging, SDEs are discretely observed with an additional measurement noise. We propose to estimate the parameters of these noisy SDEs by maximum likelihood, using the Kalman filter. In DCE-imaging, the contrast agent injected in vein arrives in plasma with an unknown time delay. The delay parameter induces a change-point in the drift of the SDE and ODE models, which is estimated also. Estimations based on the SDE and ODE pharmacokinetic models are compared to real DCE-MRI data. They show that the use of SDE provides robustness in the estimation results. A simulation study confirms these results. Copyright © 2011 Elsevier Inc. All rights reserved.

Qualitative performance comparison of reactivity estimation between the extended Kalman filter technique and the inverse point kinetic method

International Nuclear Information System (INIS)

Shimazu, Y.; Rooijen, W.F.G. van

2014-01-01

Highlights: • Estimation of the reactivity of nuclear reactor based on neutron flux measurements. • Comparison of the traditional method, and the new approach based on Extended Kalman Filtering (EKF). • Estimation accuracy depends on filter parameters, the selection of which is described in this paper. • The EKF algorithm is preferred if the signal to noise ratio is low (low flux situation). • The accuracy of the EKF depends on the ratio of the filter coefficients. - Abstract: The Extended Kalman Filtering (EKF) technique has been applied for estimation of subcriticality with a good noise filtering and accuracy. The Inverse Point Kinetic (IPK) method has also been widely used for reactivity estimation. The important parameters for the EKF estimation are the process noise covariance, and the measurement noise covariance. However the optimal selection is quite difficult. On the other hand, there is only one parameter in the IPK method, namely the time constant for the first order delay filter. Thus, the selection of this parameter is quite easy. Thus, it is required to give certain idea for the selection of which method should be selected and how to select the required parameters. From this point of view, a qualitative performance comparison is carried out

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

Science.gov (United States)

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

A discontinuous Poisson-Boltzmann equation with interfacial jump: homogenisation and residual error estimate.

Science.gov (United States)

Fellner, Klemens; Kovtunenko, Victor A

2016-01-01

A nonlinear Poisson-Boltzmann equation with inhomogeneous Robin type boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue stems from interfacial jumps, which necessitate discontinuous solutions to the problem. Based on variational techniques, we derive the homogenisation of the discontinuous problem and establish a rigorous residual error estimate up to the first-order correction.

Estimating the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm.

Science.gov (United States)

Mehdinejadiani, Behrouz

2017-08-01

This study represents the first attempt to estimate the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm. The numerical studies as well as the experimental studies were performed to certify the integrity of Bees Algorithm. The experimental ones were conducted in a sandbox for homogeneous and heterogeneous soils. A detailed comparative study was carried out between the results obtained from Bees Algorithm and those from Genetic Algorithm and LSQNONLIN routines in FracFit toolbox. The results indicated that, in general, the Bees Algorithm much more accurately appraised the sFADE parameters in comparison with Genetic Algorithm and LSQNONLIN, especially in the heterogeneous soil and for α values near to 1 in the numerical study. Also, the results obtained from Bees Algorithm were more reliable than those from Genetic Algorithm. The Bees Algorithm showed the relative similar performances for all cases, while the Genetic Algorithm and the LSQNONLIN yielded different performances for various cases. The performance of LSQNONLIN strongly depends on the initial guess values so that, compared to the Genetic Algorithm, it can more accurately estimate the sFADE parameters by taking into consideration the suitable initial guess values. To sum up, the Bees Algorithm was found to be very simple, robust and accurate approach to estimate the transport parameters of the spatial fractional advection-dispersion equation. Copyright © 2017 Elsevier B.V. All rights reserved.

On the spectral theory and dispersive estimates for a discrete Schroedinger equation in one dimension

International Nuclear Information System (INIS)

Pelinovsky, D. E.; Stefanov, A.

2008-01-01

Based on the recent work [Komech et al., 'Dispersive estimates for 1D discrete Schroedinger and Klein-Gordon equations', Appl. Anal. 85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schroedinger operator, Hφ=(-Δ+V)φ=-(φ n+1 +φ n-1 -2φ n )+V n φ n . We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates parallel e itH P a.c. (H) parallel l σ 2 →l -σ 2 -3/2 for any fixed σ>(5/2) and any t>0, where P a.c. (H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [''Asymptotic behaviour of small solutions for the discrete nonlinear Schroedinger and Klein-Gordon equations,'' Nonlinearity 18, 1841 (2005)], we find new dispersive estimates parallel e itH P a.c. (H) parallel l 1 →l ∞ -1/3 , which are sharp for the discrete Schroedinger operators even for V=0

Estimating the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm

Science.gov (United States)

Mehdinejadiani, Behrouz

2017-08-01

This study represents the first attempt to estimate the solute transport parameters of the spatial fractional advection-dispersion equation using Bees Algorithm. The numerical studies as well as the experimental studies were performed to certify the integrity of Bees Algorithm. The experimental ones were conducted in a sandbox for homogeneous and heterogeneous soils. A detailed comparative study was carried out between the results obtained from Bees Algorithm and those from Genetic Algorithm and LSQNONLIN routines in FracFit toolbox. The results indicated that, in general, the Bees Algorithm much more accurately appraised the sFADE parameters in comparison with Genetic Algorithm and LSQNONLIN, especially in the heterogeneous soil and for α values near to 1 in the numerical study. Also, the results obtained from Bees Algorithm were more reliable than those from Genetic Algorithm. The Bees Algorithm showed the relative similar performances for all cases, while the Genetic Algorithm and the LSQNONLIN yielded different performances for various cases. The performance of LSQNONLIN strongly depends on the initial guess values so that, compared to the Genetic Algorithm, it can more accurately estimate the sFADE parameters by taking into consideration the suitable initial guess values. To sum up, the Bees Algorithm was found to be very simple, robust and accurate approach to estimate the transport parameters of the spatial fractional advection-dispersion equation.

A note on the extended dispersionless Toda hierarchy

Science.gov (United States)

Lee, Niann-Chern; Tu, Ming-Hsien

2013-04-01

We derive dispersionless Hirota equations for the extended dispersionless Toda hierarchy. We show that the dispersionless Hirota equations are just a direct consequence of the genus-zero topological recurrence relation for the topological ℂP1 model. Using the dispersionless Hirota equations, we compute the twopoint functions and express the result in terms of Catalan numbers

Geometrical-integrability constraints and equations of motion in four plus extended super spaces

International Nuclear Information System (INIS)

Chau, L.L.

1987-01-01

It is pointed out that many equations of motion in physics, including gravitational and Yang-Mills equations, have a common origin: i.e. they are the results of certain geometrical integrability conditions. These integrability conditions lead to linear systems and conservation laws that are important in integrating these equations of motion

A Computationally Efficient and Robust Implementation of the Continuous-Discrete Extended Kalman Filter

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Thomsen, Per Grove; Madsen, Henrik

2007-01-01

for nonlinear stochastic continuous-discrete time systems is more than two orders of magnitude faster than a conventional implementation. This is of significance in nonlinear model predictive control applications, statistical process monitoring as well as grey-box modelling of systems described by stochastic......We present a novel numerically robust and computationally efficient extended Kalman filter for state estimation in nonlinear continuous-discrete stochastic systems. The resulting differential equations for the mean-covariance evolution of the nonlinear stochastic continuous-discrete time systems...

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

Science.gov (United States)

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

Pose and Motion Estimation Using Dual Quaternion-Based Extended Kalman Filtering

Energy Technology Data Exchange (ETDEWEB)

Goddard, J.S.; Abidi, M.A.

1998-06-01

A solution to the remote three-dimensional (3-D) measurement problem is presented for a dynamic system given a sequence of two-dimensional (2-D) intensity images of a moving object. The 3-D transformation is modeled as a nonlinear stochastic system with the state estimate providing the six-degree-of-freedom motion and position values as well as structure. The stochastic model uses the iterated extended Kalman filter (IEKF) as a nonlinear estimator and a screw representation of the 3-D transformation based on dual quaternions. Dual quaternions, whose elements are dual numbers, provide a means to represent both rotation and translation in a unified notation. Linear object features, represented as dual vectors, are transformed using the dual quaternion transformation and are then projected to linear features in the image plane. The method has been implemented and tested with both simulated and actual experimental data. Simulation results are provided, along with comparisons to a point-based IEKF method using rotation and translation, to show the relative advantages of this method. Experimental results from testing using a camera mounted on the end effector of a robot arm are also given.

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

Science.gov (United States)

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

2018-02-01

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

On polynomial solutions of the Heun equation

International Nuclear Information System (INIS)

Gurappa, N; Panigrahi, Prasanta K

2004-01-01

By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)

Tailoring discrete quantum walk dynamics via extended initial conditions

Energy Technology Data Exchange (ETDEWEB)

Valcarcel, German J de; Roldan, Eugenio [Departament d' Optica, Universitat de Valencia, Dr Moliner 50, 46100-Burjassot, Spain, EU (Spain); Romanelli, Alejandro, E-mail: german.valcarcel@uv.es, E-mail: eugenio.roldan@uv.es, E-mail: alejo@fing.edu.uy [Instituto de Fisica, Facultad de IngenierIa, Universidad de la Republica, CC 30, CP 11000, Montevideo (Uruguay)

2010-12-15

We study the evolution of initially extended distributions in the coined quantum walk (QW) on the line. By analysing the dispersion relation of the process, continuous wave equations are derived whose form depends on the initial distribution shape. In particular, for a class of initial conditions, the evolution is dictated by the Schroedinger equation of a free particle. As that equation also governs paraxial optical diffraction, all of the phenomenology of the latter can be implemented in the QW. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.

Tailoring discrete quantum walk dynamics via extended initial conditions

International Nuclear Information System (INIS)

Valcarcel, German J de; Roldan, Eugenio; Romanelli, Alejandro

2010-01-01

We study the evolution of initially extended distributions in the coined quantum walk (QW) on the line. By analysing the dispersion relation of the process, continuous wave equations are derived whose form depends on the initial distribution shape. In particular, for a class of initial conditions, the evolution is dictated by the Schroedinger equation of a free particle. As that equation also governs paraxial optical diffraction, all of the phenomenology of the latter can be implemented in the QW. This allows us, in particular, to devise an initially extended condition leading to a uniform probability distribution whose width increases linearly with time, with increasing homogeneity.

A Sandwich-Type Standard Error Estimator of SEM Models with Multivariate Time Series

Science.gov (United States)

Zhang, Guangjian; Chow, Sy-Miin; Ong, Anthony D.

2011-01-01

Structural equation models are increasingly used as a modeling tool for multivariate time series data in the social and behavioral sciences. Standard error estimators of SEM models, originally developed for independent data, require modifications to accommodate the fact that time series data are inherently dependent. In this article, we extend a…

Unbiased minimum variance estimator of a matrix exponential function. Application to Boltzmann/Bateman coupled equations solving

International Nuclear Information System (INIS)

Dumonteil, E.; Diop, C. M.

2009-01-01

This paper derives an unbiased minimum variance estimator (UMVE) of a matrix exponential function of a normal wean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. The last section will present numerical results on a simple example. (authors)

Estimating the surface area of birds: using the homing pigeon (Columba livia as a model

Directory of Open Access Journals (Sweden)

Cristina R. Perez

2014-05-01

Full Text Available Estimation of the surface area of the avian body is valuable for thermoregulation and metabolism studies as well as for assessing exposure to oil and other surface-active organic pollutants from a spill. The use of frozen carcasses for surface area estimations prevents the ability to modify the posture of the bird. The surface area of six live homing pigeons in the fully extended flight position was estimated using a noninvasive method. An equation was derived to estimate the total surface area of a pigeon based on its body weight. A pigeon's surface area in the fully extended flight position is approximately 4 times larger than the surface area of a pigeon in the perching position. The surface area of a bird is dependent on its physical position, and, therefore, the fully extended flight position exhibits the maximum area of a bird and should be considered the true surface area of a bird.

Estimating the surface area of birds: using the homing pigeon (Columba livia) as a model.

Science.gov (United States)

Perez, Cristina R; Moye, John K; Pritsos, Chris A

2014-05-08

Estimation of the surface area of the avian body is valuable for thermoregulation and metabolism studies as well as for assessing exposure to oil and other surface-active organic pollutants from a spill. The use of frozen carcasses for surface area estimations prevents the ability to modify the posture of the bird. The surface area of six live homing pigeons in the fully extended flight position was estimated using a noninvasive method. An equation was derived to estimate the total surface area of a pigeon based on its body weight. A pigeon's surface area in the fully extended flight position is approximately 4 times larger than the surface area of a pigeon in the perching position. The surface area of a bird is dependent on its physical position, and, therefore, the fully extended flight position exhibits the maximum area of a bird and should be considered the true surface area of a bird. © 2014. Published by The Company of Biologists Ltd | Biology Open.

The forced nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Kaup, D.J.; Hansen, P.J.

1985-01-01

The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

Development of bioelectrical impedance analysis-based equations for estimation of body composition in postpartum rural Bangladeshi women.

Science.gov (United States)

Shaikh, Saijuddin; Schulze, Kerry J; Kurpad, Anura; Ali, Hasmot; Shamim, Abu Ahmed; Mehra, Sucheta; Wu, Lee S-F; Rashid, Mahbubar; Labrique, Alain B; Christian, Parul; West, Keith P

2013-02-28

Equations for predicting body composition from bioelectrical impedance analysis (BIA) parameters are age-, sex- and population-specific. Currently there are no equations applicable to women of reproductive age in rural South Asia. Hence, we developed equations for estimating total body water (TBW), fat-free mass (FFM) and fat mass in rural Bangladeshi women using BIA, with ²H₂O dilution as the criterion method. Women of reproductive age, participating in a community-based placebo-controlled trial of vitamin A or β-carotene supplementation, were enrolled at 19·7 (SD 9·3) weeks postpartum in a study to measure body composition by ²H₂O dilution and impedance at 50 kHz using multi-frequency BIA (n 147), and resistance at 50 kHz using single-frequency BIA (n 82). TBW (kg) by ²H2O dilution was used to derive prediction equations for body composition from BIA measures. The prediction equation was applied to resistance measures obtained at 13 weeks postpartum in a larger population of postpartum women (n 1020). TBW, FFM and fat were 22·6 (SD 2·7), 30·9 (SD 3·7) and 10·2 (SD 3·8) kg by ²H₂O dilution. Height²/impedance or height²/resistance and weight provided the best estimate of TBW, with adjusted R² 0·78 and 0·76, and with paired absolute differences in TBW of 0·02 (SD 1·33) and 0·00 (SD 1·28) kg, respectively, between BIA and ²H₂O. In the larger sample, values for TBW, FFM and fat were 23·8, 32·5 and 10·3 kg, respectively. BIA can be an important tool for assessing body composition in women of reproductive age in rural South Asia where poor maternal nutrition is common.

True amplitude wave equation migration arising from true amplitude one-way wave equations

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

Effectiveness of prediction equations in estimating energy expenditure sample of Brazilian and Spanish women with excess body weight

OpenAIRE

Lopes Rosado, Eliane; Santiago de Brito, Roberta; Bressan, Josefina; Martínez Hernández, José Alfredo

2014-01-01

Objective: To assess the adequacy of predictive equations for estimation of energy expenditure (EE), compared with the EE using indirect calorimetry in a sample of Brazilian and Spanish women with excess body weight Methods: It is a cross-sectional study with 92 obese adult women [26 Brazilian -G1- and 66 Spanish - G2- (aged 20-50)]. Weight and height were evaluated during fasting for the calculation of body mass index and predictive equations. EE was evaluated using the open-circuit indirect...

Correlation of the Rates of Solvolyses of 4-Methylthiophene-2-carbonyl Chloride Using the Extended Grunwald-Winstein Equation

International Nuclear Information System (INIS)

Choi, Ho June; Koo, In Sun

2012-01-01

The specific rates of sovolysis of 4-methylthiophene-2-carbonyl chloride (1) have been determined in 26 pure and binary solvents at 25.0 .deg. C. Product selectivities are reported for solvolyses of 1 in aqueous ethanol and methanol binary mixtures. Comparison of the specific rates of solvolyses of 1 with those for p-methoxybenzoyl chloride (2) in terms of linear free energy relationships (LFER) are helpful in mechanistic considerations, as is also treatment in terms of the extended Grunwald-Winstein equation. It is proposed that the solvolyses of 1 in binary aqueous solvent mixtures proceed through an S N 1 and/or ionization (I) pathway rather than through an associative S N 2 and/or addition-elimination (A-E) pathway

Differential equation analysis in biomedical science and engineering partial differential equation applications with R

CERN Document Server

Schiesser, William E

2014-01-01

Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the com

Nonlinear electrostatic wave equations for magnetized plasmas - II

DEFF Research Database (Denmark)

Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.

1985-01-01

For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....

Estimating calibration equations for predicting Ra-226 soil concentrations using RTRAK in-situ detectors at the Ambrosia Lake, New Mexico, Umtra site

International Nuclear Information System (INIS)

Gilbert, R. O.; Meyer, H. R.; Miller, M. L.; Begley, C.

1988-06-01

This report describes a field study conducted at the Ambrosia Lake, New Mexico, UMTRA site to obtain data for calibrating the RTRAK Sodium Iodide (NaI) detectors for estimating concentrations of Ra-226 in surface soil. The statistical analyses indicate that the data are useful for estimating the calibration equations. Several statistical models are used to evaluate which model is best as a basis for the calibration equations. A procedure is provided for using the estimated calibration equations and extensive RTRAK measurements to estimate the average Ra-226 concentration on 100-m 2 land areas to determine whether additional remedial action is needed. The UMTRA Project office proposes to use the RTRAK for cleanup verification of surface Ra-226 contamination. The system enables 100% coverage of areas having undergone remedial action. The sensitivity of the system enables verification at less than 5 pCi/g averaged over 100 m 2 , as specified by the Environmental Protection Agency (EPA) standards (40 CFR Part 192). This analysis demonstrates RTRAK's ability to meet reasonable standards of statistical accuracy, using commonly accepted procedures. 5 refs., 8 figs., 1 tab

Extended common-image-point gathers for anisotropic wave-equation migration

KAUST Repository

Sava, Paul C.; Alkhalifah, Tariq Ali

2010-01-01

In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes

Soliton solutions and chaotic motion of the extended Zakharov-Kuznetsov equations in a magnetized two-ion-temperature dusty plasma

Energy Technology Data Exchange (ETDEWEB)

Zhen, Hui-Ling; Tian, Bo, E-mail: tian-bupt@163.com; Wang, Yu-Feng; Sun, Wen-Rong; Liu, Li-Cai [State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876 (China)

2014-07-15

The extended Zakharov-Kuznetsov (eZK) equation for the magnetized two-ion-temperature dusty plasma is studied in this paper. With the help of Hirota method, bilinear forms and N-soliton solutions are given, and soliton propagation is graphically analyzed. We find that the soliton amplitude is positively related to the nonlinear coefficient A, while inversely related to the dispersion coefficients B and C. We obtain that the soliton amplitude will increase with the mass of the jth dust grain and the average charge number residing on the dust grain decreased, but the soliton amplitude will increase with the equilibrium number density of the jth dust grain increased. Upon the introduction of the periodic external forcing term, both the weak and developed chaotic motions can occur. Difference between the two chaotic motions roots in the inequality between the nonlinear coefficient l{sub 2} and perturbed term h{sub 1}. The developed chaos can be weakened with B or C decreased and A increased. Periodic motion of the perturbed eZK equation can be observed when there is a balance between l{sub 2} and h{sub 1}.

A new estimate of the Khirzhnits corrections to the zero temperature Thomas-Fermi equation-of-state

International Nuclear Information System (INIS)

Szichman, H.; Krumbein, A.D.; Eliezer, S.

1984-09-01

A method is proposed for estimating the zero temperature limit of the Khirzhnits corrections to the Thomas-Fermi equation-of-state by extrapolation of the finite-temperature results. The cold curves so obtained for Ti, Fe, Cu and Ta are compared with experimental results as well as with those calculated using other variations of the Thomas-Fermi model

Predictive performance for population models using stochastic differential equations applied on data from an oral glucose tolerance test

DEFF Research Database (Denmark)

Møller, Jonas Bech; Overgaard, R.V.; Madsen, Henrik

2010-01-01

Several articles have investigated stochastic differential equations (SDEs) in PK/PD models, but few have quantitatively investigated the benefits to predictive performance of models based on real data. Estimation of first phase insulin secretion which reflects beta-cell function using models of ...... obtained from the glucose tolerance tests. Since, the estimation time of extended models was not heavily increased compared to basic models, the applied method is concluded to have high relevance not only in theory but also in practice....

Solution of differential equations by application of transformation groups

Science.gov (United States)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Reconstruction of extended sources for the Helmholtz equation

International Nuclear Information System (INIS)

Kress, Rainer; Rundell, William

2013-01-01

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our inclusions are interior forces with compact support and our data consist of a single measurement of near-field Cauchy data on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler ‘equivalent point source’ problem, and which uses a Newton scheme to improve the corresponding initial approximation. (paper)

Reconstruction of extended sources for the Helmholtz equation

KAUST Repository

Kress, Rainer

2013-02-26

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Our underlying model is that of inverse acoustic scattering based on the Helmholtz equation. Our inclusions are interior forces with compact support and our data consist of a single measurement of near-field Cauchy data on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler \\'equivalent point source\\' problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2013 IOP Publishing Ltd.

On reductions of the discrete Kadomtsev-Petviashvili-type equations

Science.gov (United States)

Fu, Wei; Nijhoff, Frank W.

2017-12-01

The reduction by restricting the spectral parameters k and k\\prime on a generic algebraic curve of degree N is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable systems possessing a more general solution structure arise from the reduction, and in each case a unified formula for the generic positive integer N≥slant 2 is given to express the corresponding reduced integrable lattice equations. The obtained extended two-dimensional lattice models give rise to many important integrable partial difference equations as special degenerations. Some new integrable lattice models such as the discrete Sawada-Kotera, Kaup-Kupershmidt and Hirota-Satsuma equations in extended form are given as examples within the framework.

Spectrophotometric estimation of ethamsylate and mefenamic acid from a binary mixture by dual wavelength and simultaneous equation methods

OpenAIRE

Goyal Anju; Singhvi I

2008-01-01

Two simple, accurate, economical and reproducible spectrophotometric methods for simultaneous estimation of two-component drug mixture of ethamsylate and mefenamic acid in combined tablet dosage form have been developed. The first developed method involves formation and solving of simultaneous equation using 287.6 nm and 313.2 nm as two wavelengths. Second developed method is based on two wavelength calculation. Two wavelengths selected for estimation of ethamsylate were 274.4 nm and 301.2 nm...

Application of Consider Covariance to the Extended Kalman Filter

Science.gov (United States)

Lundberg, John B.

1996-01-01

The extended Kalman filter (EKF) is the basis for many applications of filtering theory to real-time problems where estimates of the state of a dynamical system are to be computed based upon some set of observations. The form of the EKF may vary somewhat from one application to another, but the fundamental principles are typically unchanged among these various applications. As is the case in many filtering applications, models of the dynamical system (differential equations describing the state variables) and models of the relationship between the observations and the state variables are created. These models typically employ a set of constants whose values are established my means of theory or experimental procedure. Since the estimates of the state are formed assuming that the models are perfect, any modeling errors will affect the accuracy of the computed estimates. Note that the modeling errors may be errors of commission (errors in terms included in the model) or omission (errors in terms excluded from the model). Consequently, it becomes imperative when evaluating the performance of real-time filters to evaluate the effect of modeling errors on the estimates of the state.

Estimate of electrostatic solvation free energy of electron in various polar solvents by using modified born equation

International Nuclear Information System (INIS)

Yamashita, Kazuo; Kitamura, Mitsutaka; Imai, Hideo

1976-01-01

The modified Born equation was tentatively applied to estimate the electrostatic free energies of solvation of the electron in various polar solvents. The related data of halide ions and a datum of the hydration free energy of the electron obtained by radiation chemical studies were used for the numerical calculations. (auth.)

Construction and accuracy of partial differential equation approximations to the chemical master equation.

Science.gov (United States)

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Transmission-less attenuation estimation from time-of-flight PET histo-images using consistency equations

Science.gov (United States)

Li, Yusheng; Defrise, Michel; Metzler, Scott D.; Matej, Samuel

2015-08-01

In positron emission tomography (PET) imaging, attenuation correction with accurate attenuation estimation is crucial for quantitative patient studies. Recent research showed that the attenuation sinogram can be determined up to a scaling constant utilizing the time-of-flight information. The TOF-PET data can be naturally and efficiently stored in a histo-image without information loss, and the radioactive tracer distribution can be efficiently reconstructed using the DIRECT approaches. In this paper, we explore transmission-less attenuation estimation from TOF-PET histo-images. We first present the TOF-PET histo-image formation and the consistency equations in the histo-image parameterization, then we derive a least-squares solution for estimating the directional derivatives of the attenuation factors from the measured emission histo-images. Finally, we present a fast solver to estimate the attenuation factors from their directional derivatives using the discrete sine transform and fast Fourier transform while considering the boundary conditions. We find that the attenuation histo-images can be uniquely determined from the TOF-PET histo-images by considering boundary conditions. Since the estimate of the attenuation directional derivatives can be inaccurate for LORs tangent to the patient boundary, external sources, e.g. a ring or annulus source, might be needed to give an accurate estimate of the attenuation gradient for such LORs. The attenuation estimation from TOF-PET emission histo-images is demonstrated using simulated 2D TOF-PET data.

Mixed-species allometric equations and estimation of aboveground biomass and carbon stocks in restoring degraded landscape in northern Ethiopia

Science.gov (United States)

Mokria, Mulugeta; Mekuria, Wolde; Gebrekirstos, Aster; Aynekulu, Ermias; Belay, Beyene; Gashaw, Tadesse; Bräuning, Achim

2018-02-01

Accurate biomass estimation is critical to quantify the changes in biomass and carbon stocks following the restoration of degraded landscapes. However, there is lack of site-specific allometric equations for the estimation of aboveground biomass (AGB), which consequently limits our understanding of the contributions of restoration efforts in mitigating climate change. This study was conducted in northwestern Ethiopia to develop a multi-species allometric equation and investigate the spatial and temporal variation of C-stocks following the restoration of degraded landscapes. We harvested and weighed 84 trees from eleven dominant species from six grazing exclosures and adjacent communal grazing land. We observed that AGB correlates significantly with diameter at stump height D 30 (R 2 = 0.78 P < 0.01), and tree height H (R 2 = 0.41, P < 0.05). Our best model, which includes D 30 and H as predictors explained 82% of the variations in AGB. This model produced the lowest bias with narrow ranges of errors across different diameter classes. Estimated C-stock showed a significant positive correlation with stem density (R 2 = 0.80, P < 0.01) and basal area (R 2 = 0.84, P < 0.01). At the watershed level, the mean C-stock was 3.8 (±0.5) Mg C ha-1. Plot-level C-stocks varied between 0.1 and 13.7 Mg C ha-1. Estimated C-stocks in three- and seven-year-old exclosures exceeded estimated C-stock in the communal grazing land by 50%. The species that contribute most to C-stocks were Leucaena sp. (28%), Calpurnia aurea (21%), Euclea racemosa (20.9%), and Dodonaea angustifolia (15.8%). The equations developed in this study allow monitoring changes in C-stocks and C-sequestration following the implementation of restoration practices in northern Ethiopia over space and time. The estimated C-stocks can be used as a reference against which future changes in C-stocks can be compared.

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

Science.gov (United States)

Tornøe, Christoffer W; Overgaard, Rune V; Agersø, Henrik; Nielsen, Henrik A; Madsen, Henrik; Jonsson, E Niclas

2005-08-01

The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models. Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix. The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

The Application of Extended Cox Proportional Hazard Method for Estimating Survival Time of Breast Cancer

Science.gov (United States)

Husain, Hartina; Astuti Thamrin, Sri; Tahir, Sulaiha; Mukhlisin, Ahmad; Mirna Apriani, M.

2018-03-01

Breast cancer is one type of cancer that is the leading cause of death worldwide. This study aims to model the factors that affect the survival time and rate of cure of breast cancer patients. The extended cox model, which is a modification of the proportional hazard cox model in which the proportional hazard assumptions are not met, is used in this study. The maximum likelihood estimation approach is used to estimate the parameters of the model. This method is then applied to medical record data of breast cancer patient in 2011-2016, which is taken from Hasanuddin University Education Hospital. The results obtained indicate that the factors that affect the survival time of breast cancer patients are malignancy and leukocyte levels.

Transport parameter estimation from lymph measurements and the Patlak equation.

Science.gov (United States)

Watson, P D; Wolf, M B

1992-01-01

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

An integral transform of the Salpeter equation

International Nuclear Information System (INIS)

Krolikowski, W.

1980-03-01

We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)

An extended role for thermoluminescent phosphors in personnel, environmental and accident dosimetry using sensitisation, re-estimation and fast fading

International Nuclear Information System (INIS)

Charles, M.W.

1983-01-01

This paper summarises some techniques for extending the usefulness of conventional phosphors in personnel, environmental and accident dosimetry. An optimised procedure for utilising radiation sensitisation and UV re-estimation in thermoluminescent LiF is presented. In particular it is shown that optimum performance is achieved by using a UV wavelength of 250 +- 10 nm for both the UV/thermal anneal following sensitisation, and for the UV re-estimation procedure. In the case of Harshaw Lif Chips (3x3x0.9 mm 3 ) the sensitivity is increased by a factor of 4-5 to achieve a minimum detectable dose of approx.=10 μGy (2sigma) and a minimum re-estimable dose of 50-100 mGy (2sigma), dependent on batch. Sensitized LiF also exhibits improved tissue equivalence, extended linearity and improved precision at low doses. The information from fast-fading glow peaks, which is normally rejected, is shown to have a useful application to the evaluation of short-term increases in environmental dose rates such as may occur following accidental releases of radioactivity. (orig.)

Slave equations for spin models

International Nuclear Information System (INIS)

Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

1992-01-01

We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

Isomorphism of Intransitive Linear Lie Equations

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Jose Miguel Martins Veloso

2009-11-01

Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.

Compatible above-ground biomass equations and carbon stock estimation for small diameter Turkish pine (Pinus brutia Ten.).

Science.gov (United States)

Sakici, Oytun Emre; Kucuk, Omer; Ashraf, Muhammad Irfan

2018-04-15

Small trees and saplings are important for forest management, carbon stock estimation, ecological modeling, and fire management planning. Turkish pine (Pinus brutia Ten.) is a common coniferous species and comprises 25.1% of total forest area of Turkey. Turkish pine is also important due to its flammable fuel characteristics. In this study, compatible above-ground biomass equations were developed to predict needle, branch, stem wood, and above-ground total biomass, and carbon stock assessment was also described for Turkish pine which is smaller than 8 cm diameter at breast height or shorter than breast height. Compatible biomass equations are useful for biomass prediction of small diameter individuals of Turkish pine. These equations will also be helpful in determining fire behavior characteristics and calculating their carbon stock. Overall, present study will be useful for developing ecological models, forest management plans, silvicultural plans, and fire management plans.

Estimating unknown input parameters when implementing the NGA ground-motion prediction equations in engineering practice

Science.gov (United States)

Kaklamanos, James; Baise, Laurie G.; Boore, David M.

2011-01-01

The ground-motion prediction equations (GMPEs) developed as part of the Next Generation Attenuation of Ground Motions (NGA-West) project in 2008 are becoming widely used in seismic hazard analyses. However, these new models are considerably more complicated than previous GMPEs, and they require several more input parameters. When employing the NGA models, users routinely face situations in which some of the required input parameters are unknown. In this paper, we present a framework for estimating the unknown source, path, and site parameters when implementing the NGA models in engineering practice, and we derive geometrically-based equations relating the three distance measures found in the NGA models. Our intent is for the content of this paper not only to make the NGA models more accessible, but also to help with the implementation of other present or future GMPEs.

Analysis of a HP-refinement method for solving the neutron transport equation using two error estimators

International Nuclear Information System (INIS)

Fournier, D.; Le Tellier, R.; Suteau, C.; Herbin, R.

2011-01-01

The solution of the time-independent neutron transport equation in a deterministic way invariably consists in the successive discretization of the three variables: energy, angle and space. In the SNATCH solver used in this study, the energy and the angle are respectively discretized with a multigroup approach and the discrete ordinate method. A set of spatial coupled transport equations is obtained and solved using the Discontinuous Galerkin Finite Element Method (DGFEM). Within this method, the spatial domain is decomposed into elements and the solution is approximated by a hierarchical polynomial basis in each one. This approach is time and memory consuming when the mesh becomes fine or the basis order high. To improve the computational time and the memory footprint, adaptive algorithms are proposed. These algorithms are based on an error estimation in each cell. If the error is important in a given region, the mesh has to be refined (h−refinement) or the polynomial basis order increased (p−refinement). This paper is related to the choice between the two types of refinement. Two ways to estimate the error are compared on different benchmarks. Analyzing the differences, a hp−refinement method is proposed and tested. (author)

Comparison of reactivity estimation performance between two extended Kalman filtering schemes

International Nuclear Information System (INIS)

Peng, Xingjie; Cai, Yun; Li, Qing; Wang, Kan

2016-01-01

Highlights: • The performances of two EKF schemes using different Jacobian matrices are compared. • Numerical simulations are used for the validation and comparison of these two EKF schemes. • The simulation results show that the EKF scheme adopted by this paper performs better than the one adopted by previous literatures. - Abstract: The extended Kalman filtering (EKF) technique has been utilized in the estimation of reactivity which is a significantly important parameter to indicate the status of the nuclear reactor. In this paper, the performances of two EKF schemes using different Jacobian matrices are compared. Numerical simulations are used for the validation and comparison of these two EKF schemes, and the results show that the Jacobian matrix obtained directly from the discrete-time state model performs better than the one which is the discretization form of the Jacobian matrix obtained from the continuous-time state model.

On implicit abstract neutral nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br [Universidade de São Paulo, Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto (Brazil); O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie [National University of Ireland, School of Mathematics, Statistics and Applied Mathematics (Ireland)

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

Finite element method for time-space-fractional Schrodinger equation

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Xiaogang Zhu

2017-07-01

Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.

An Introduction to Generalized Estimating Equations and an Application to Assess Selectivity Effects in a Longitudinal Study on Very Old Individuals

Science.gov (United States)

Ghisletta, Paolo; Spini, Dario

2004-01-01

Correlated data are very common in the social sciences. Most common applications include longitudinal and hierarchically organized (or clustered) data. Generalized estimating equations (GEE) are a convenient and general approach to the analysis of several kinds of correlated data. The main advantage of GEE resides in the unbiased estimation of…

A covariance correction that accounts for correlation estimation to improve finite-sample inference with generalized estimating equations: A study on its applicability with structured correlation matrices.

Science.gov (United States)

Westgate, Philip M

2016-01-01

When generalized estimating equations (GEE) incorporate an unstructured working correlation matrix, the variances of regression parameter estimates can inflate due to the estimation of the correlation parameters. In previous work, an approximation for this inflation that results in a corrected version of the sandwich formula for the covariance matrix of regression parameter estimates was derived. Use of this correction for correlation structure selection also reduces the over-selection of the unstructured working correlation matrix. In this manuscript, we conduct a simulation study to demonstrate that an increase in variances of regression parameter estimates can occur when GEE incorporates structured working correlation matrices as well. Correspondingly, we show the ability of the corrected version of the sandwich formula to improve the validity of inference and correlation structure selection. We also study the relative influences of two popular corrections to a different source of bias in the empirical sandwich covariance estimator.

Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

KAUST Repository

Jin, Bangti

2013-01-01

We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.

Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions

International Nuclear Information System (INIS)

Di Cristo, M; Lin, C-L; Morassi, A; Rosset, E; Vessella, S; Wang, J-N

2013-01-01

We prove the upper and lower estimates of the area of an unknown elastic inclusion in a thin plate by one boundary measurement. The plate is made of non-homogeneous linearly elastic material belonging to a general class of anisotropy and the domain of the inclusion is a measurable subset of the plate. The size estimates are expressed in terms of the work exerted by a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate. The main new mathematical tool is a doubling inequality for solutions to fourth-order elliptic equations whose principal part P(x, D) is the product of two second-order elliptic operators P 1 (x, D), P 2 (x, D) such that P 1 (0, D) = P 2 (0, D). The proof of the doubling inequality is based on the Carleman method, a sharp three-spheres inequality and a bootstrapping argument. (paper)

Scour depth estimation using an equation based on wind tunnel experiments

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Tsutsui Takayuki

2016-01-01

Full Text Available Scour is the result of degradation and aggradation by wind or moving fluid in the front and back of a pole standing in sand, respectively, and is often observed at the bottom of bridge piers in rivers. In this study, we propose a method of estimating the scour depth around a cylindrical structure standing in sand. The relationships among the depth of the scour, the aspect ratio of the structure (= height/diameter, the fluid velocity, and the sand properties (particle size and density were determined experimentally using a wind tunnel. The experiments were carried out under clear-water scour conditions. In the experiments, the aspect ratio of the cylindrical structure, the fluid velocity, and the sand particle size were varied systematically. The diameters of the structure were 20, 40, and 60 mm, and the aspect ratio was varied from 0.25 to 3.0. Sand particles of four sizes (200, 275, 475, and 600 μm were used in the experiment, and the velocity was varied from 4 to 11 m/s. The depth and radius of the scour were measured. As a result, we have developed an equation for estimating the scour depth that uses the aspect ratio, fluid velocity, and sand particle size as parameters.

L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

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Hyun Young Lee

2010-01-01

Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2 error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

Multi-component WKI equations and their conservation laws

Energy Technology Data Exchange (ETDEWEB)

Qu Changzheng [Department of Mathematics, Northwest University, Xi' an 710069 (China) and Center for Nonlinear Studies, Northwest University, Xi' an 710069 (China)]. E-mail: qu_changzheng@hotmail.com; Yao Ruoxia [Department of Computer Sciences, East China Normal University, Shanghai 200062 (China); Department of Computer Sciences, Weinan Teacher' s College, Weinan 715500 (China); Liu Ruochen [Department of Mathematics, Northwest University, Xi' an 710069 (China)

2004-10-25

In this Letter, a two-component WKI equation is obtained by using the fact that when curvature and torsion of a space curve satisfy the vector modified KdV equation, a graph of the curve satisfies the two-component WKI equation, which is a natural generalization to the WKI equation. It is shown that the two-component WKI equation can be solved in terms of the extended WKI scheme, and it admits an infinite number of conservation laws. In the same vein, a n-component generalization to the WKI equation is proposed.

Estimation of the thermophysical and mechanical properties and the equation of state of Li2O

International Nuclear Information System (INIS)

Krikorian, O.H.

1985-01-01

Correlation methods based on Knoop microhardness and melting points are developed for estimating tensile strength. Young modulus, and Poisson ratio for Li 2 O as a function of grain size, porosity, and temperature. Generalized expressions for extrapolating the existing data on thermal conductivity and thermal expansivity are given. These derived thermophysical data are combined to predict thermal stress factors for Li 2 O. Based on the available vapor pressure data on Li 2 O and empirical correlations for the equation of state in the liquid and vapor phases, estimates of the properties of Li 2 O are made: an approximate critical temperature of 6800+-800 K is obtained. (author)

OpenMx: An Open Source Extended Structural Equation Modeling Framework

Science.gov (United States)

Boker, Steven; Neale, Michael; Maes, Hermine; Wilde, Michael; Spiegel, Michael; Brick, Timothy; Spies, Jeffrey; Estabrook, Ryne; Kenny, Sarah; Bates, Timothy; Mehta, Paras; Fox, John

2011-01-01

OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…

Integral equation for Coulomb problem

International Nuclear Information System (INIS)

Sasakawa, T.

1986-01-01

For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems

Extension of Gibbs-Duhem equation including influences of external fields

Science.gov (United States)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

State of Charge and State of Health Estimation of AGM VRLA Batteries by Employing a Dual Extended Kalman Filter and an ARX Model for Online Parameter Estimation

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Ngoc-Tham Tran

2017-01-01

Full Text Available State of charge (SOC and state of health (SOH are key issues for the application of batteries, especially the absorbent glass mat valve regulated lead-acid (AGM VRLA type batteries used in the idle stop start systems (ISSs that are popularly integrated into conventional engine-based vehicles. This is due to the fact that SOC and SOH estimation accuracy is crucial for optimizing battery energy utilization, ensuring safety and extending battery life cycles. The dual extended Kalman filter (DEKF, which provides an elegant and powerful solution, is widely applied in SOC and SOH estimation based on a battery parameter model. However, the battery parameters are strongly dependent on operation conditions such as the SOC, current rate and temperature. In addition, battery parameters change significantly over the life cycle of a battery. As a result, many experimental pretests investigating the effects of the internal and external conditions of a battery on its parameters are required, since the accuracy of state estimation depends on the quality of the information regarding battery parameter changes. In this paper, a novel method for SOC and SOH estimation that combines a DEKF algorithm, which considers hysteresis and diffusion effects, and an auto regressive exogenous (ARX model for online parameters estimation is proposed. The DEKF provides precise information concerning the battery open circuit voltage (OCV to the ARX model. Meanwhile, the ARX model continues monitoring parameter variations and supplies information on them to the DEKF. In this way, the estimation accuracy can be maintained despite the changing parameters of a battery. Moreover, online parameter estimation from the ARX model can save the time and effort used for parameter pretests. The validation of the proposed algorithm is given by simulation and experimental results.

A multiscale framework with extended Kalman filter for lithium-ion battery SOC and capacity estimation

International Nuclear Information System (INIS)

Hu, Chao; Youn, Byeng D.; Chung, Jaesik

2012-01-01

Highlights: ► We develop a mutiscale framework with EKF to estimate SOC and capacity. ► The framework is a hybrid of coulomb counting and adaptive filtering techniques. ► It decouples SOC and capacity estimation in terms of measurement and time-scale. ► Results verify the framework achieves higher accuracy and efficiency than dual EKF. -- Abstract: State-of-charge (SOC) and capacity estimation plays an essential role in many battery-powered applications, such as electric vehicle (EV) and hybrid electric vehicle (HEV). However, commonly used joint/dual extended Kalman filter (EKF) suffers from the lack of accuracy in the capacity estimation since (i) the cell voltage is the only measurable data for the SOC and capacity estimation and updates and (ii) the capacity is very weakly linked to the cell voltage. The lack of accuracy in the capacity estimation may further reduce the accuracy in the SOC estimation due to the strong dependency of the SOC on the capacity. Furthermore, although the capacity is a slowly time-varying quantity that indicates cell state-of-health (SOH), the capacity estimation is generally performed on the same time-scale as the quickly time-varying SOC, resulting in high computational complexity. To resolve these difficulties, this paper proposes a multiscale framework with EKF for SOC and capacity estimation. The proposed framework comprises two ideas: (i) a multiscale framework to estimate SOC and capacity that exhibit time-scale separation and (ii) a state projection scheme for accurate and stable capacity estimation. Simulation results with synthetic data based on a valid cell dynamic model suggest that the proposed framework, as a hybrid of coulomb counting and adaptive filtering techniques, achieves higher accuracy and efficiency than joint/dual EKF. Results of the cycle test on Lithium-ion prismatic cells further verify the effectiveness of our framework.

Extended Kalman Filter Channel Estimation for Line-of-Sight Detection in WCDMA Mobile Positioning

Directory of Open Access Journals (Sweden)

Abdelmonaem Lakhzouri

2003-12-01

Full Text Available In mobile positioning, it is very important to estimate correctly the delay between the transmitter and the receiver. When the receiver is in line-of-sight (LOS condition with the transmitter, the computation of the mobile position in two dimensions becomes straightforward. In this paper, the problem of LOS detection in WCDMA for mobile positioning is considered, together with joint estimation of the delays and channel coefficients. These are very challenging topics in multipath fading channels because LOS component is not always present, and when it is present, it might be severely affected by interfering paths spaced at less than one chip distance (closely spaced paths. The extended Kalman filter (EKF is used to estimate jointly the delays and complex channel coefficients. The decision whether the LOS component is present or not is based on statistical tests to determine the distribution of the channel coefficient corresponding to the first path. The statistical test-based techniques are practical, simple, and of low computation complexity, which is suitable for WCDMA receivers. These techniques can provide an accurate decision whether LOS component is present or not.

Properties of meromorphic solutions to certain differential-difference equations

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Xiaoguang Qi

2013-06-01

Full Text Available We consider the properties of meromorphic solutions to certain type of non-linear difference equations. Also we show the existence of meromorphic solutions with finite order for differential-difference equations related to the Fermat type functional equation. This article extends earlier results by Liu et al [12].

Stochastic goal-oriented error estimation with memory

Science.gov (United States)

Ackmann, Jan; Marotzke, Jochem; Korn, Peter

2017-11-01

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

A diagnostic model to estimate winds and small-scale drag from Mars Observer PMIRR data

Science.gov (United States)

Barnes, J. R.

1993-01-01

Theoretical and modeling studies indicate that small-scale drag due to breaking gravity waves is likely to be of considerable importance for the circulation in the middle atmospheric region (approximately 40-100 km altitude) on Mars. Recent earth-based spectroscopic observations have provided evidence for the existence of circulation features, in particular, a warm winter polar region, associated with gravity wave drag. Since the Mars Observer PMIRR experiment will obtain temperature profiles extending from the surface up to about 80 km altitude, it will be extensively sampling middle atmospheric regions in which gravity wave drag may play a dominant role. Estimating the drag then becomes crucial to the estimation of the atmospheric winds from the PMIRR-observed temperatures. An interative diagnostic model based upon one previously developed and tested with earth satellite temperature data will be applied to the PMIRR measurements to produce estimates of the small-scale zonal drag and three-dimensional wind fields in the Mars middle atmosphere. This model is based on the primitive equations, and can allow for time dependence (the time tendencies used may be based upon those computed in a Fast Fourier Mapping procedure). The small-scale zonal drag is estimated as the residual in the zonal momentum equation; the horizontal winds having first been estimated from the meridional momentum equation and the continuity equation. The scheme estimates the vertical motions from the thermodynamic equation, and thus needs estimates of the diabatic heating based upon the observed temperatures. The latter will be generated using a radiative model. It is hoped that the diagnostic scheme will be able to produce good estimates of the zonal gravity wave drag in the Mars middle atmosphere, estimates that can then be used in other diagnostic or assimilation efforts, as well as more theoretical studies.

Quantum Gross-Pitaevskii Equation

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Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

2017-07-01

Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

Error estimates in projective solutions of the radon equation

International Nuclear Information System (INIS)

Lubuma, M.S.

1991-04-01

The model Radon equation is the integral equation of the second kind defined by the interior limits of the electrostatic double layer potential relative to a curve with one angular point and characterized by the non compactness of the operator with respect to the maximum norm. It is shown that the solution to this equation is decomposable into a regular part and a finite linear combination of intrinsic singular functions. The maximal regularity of the solution and explicit formulae for the coefficients of the singular functions are given. The regularity permits to specify how slow the convergence of the classical projection method is, while the above mentioned formulae lead to modified projection methods of the Dual Singular Function Method type, with better approximations for the solution and for the coefficients of singularities. (author). 23 refs

Creatinine-Based and Cystatin C-Based GFR Estimating Equations and Their Non-GFR Determinants in Kidney Transplant Recipients.

Science.gov (United States)

Keddis, Mira T; Amer, Hatem; Voskoboev, Nikolay; Kremers, Walter K; Rule, Andrew D; Lieske, John C

2016-09-07

eGFR equations have been evaluated in kidney transplant recipients with variable performance. We assessed the performance of the Modification of Diet in Renal Disease equation and the Chronic Kidney Disease Epidemiology Collaboration equations on the basis of creatinine, cystatin C, and both (eGFR creatinine-cystatin C) compared with measured GFR by iothalamate clearance and evaluated their non-GFR determinants and associations across 15 cardiovascular risk factors. A cross-sectional cohort of 1139 kidney transplant recipients >1 year after transplant was analyzed. eGFR bias, precision, and accuracy (percentage of estimates within 30% of measured GFR) were assessed. Interaction of each cardiovascular risk factor with eGFR relative to measured GFR was determined. Median measured GFR was 55.0 ml/min per 1.73 m(2). eGFR creatinine overestimated measured GFR by 3.1% (percentage of estimates within 30% of measured GFR of 80.4%), and eGFR Modification of Diet in Renal Disease underestimated measured GFR by 2.2% (percentage of estimates within 30% of measured GFR of 80.4%). eGFR cystatin C underestimated measured GFR by -13.7% (percentage of estimates within 30% of measured GFR of 77.1%), and eGFR creatinine-cystatin C underestimated measured GFR by -8.1% (percentage of estimates within 30% of measured GFR of 86.5%). Lower measured GFR associated with older age, women, obesity, longer time after transplant, lower HDL, lower hemoglobin, lower albumin, higher triglycerides, higher proteinuria, and an elevated cardiac troponin T level but did not associate with diabetes, smoking, cardiovascular events, pretransplant dialysis, or hemoglobin A1c. These risk factor associations differed for five risk factors with eGFR creatinine, six risk factors for eGFR Modification of Diet in Renal Disease, ten risk factors for eGFR cystatin C, and four risk factors for eGFR creatinine-cystatin C. Thus, eGFR creatinine and eGFR creatinine-cystatin C are preferred over eGFR cystatin C in

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

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M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

An observer-theoretic approach to estimating neutron flux distribution

International Nuclear Information System (INIS)

Park, Young Ho; Cho, Nam Zin

1989-01-01

State feedback control provides many advantages such as stabilization and improved transient response. However, when the state feedback control is considered for spatial control of a nuclear reactor, it requires complete knowledge of the distributions of the system state variables. This paper describes a method for estimating the flux spatial distribution using only limited flux measurements. It is based on the Luenberger observer in control theory, extended to the distributed parameter systems such as the space-time reactor dynamics equation. The results of the application of the method to simple reactor models showed that the flux distribution is estimated by the observer very efficiently using information from only a few sensors

Validating the absolute reliability of a fat free mass estimate equation in hemodialysis patients using near-infrared spectroscopy.

Science.gov (United States)

Kono, Kenichi; Nishida, Yusuke; Moriyama, Yoshihumi; Taoka, Masahiro; Sato, Takashi

2015-06-01

The assessment of nutritional states using fat free mass (FFM) measured with near-infrared spectroscopy (NIRS) is clinically useful. This measurement should incorporate the patient's post-dialysis weight ("dry weight"), in order to exclude the effects of any change in water mass. We therefore used NIRS to investigate the regression, independent variables, and absolute reliability of FFM in dry weight. The study included 47 outpatients from the hemodialysis unit. Body weight was measured before dialysis, and FFM was measured using NIRS before and after dialysis treatment. Multiple regression analysis was used to estimate the FFM in dry weight as the dependent variable. The measured FFM before dialysis treatment (Mw-FFM), and the difference between measured and dry weight (Mw-Dw) were independent variables. We performed Bland-Altman analysis to detect errors between the statistically estimated FFM and the measured FFM after dialysis treatment. The multiple regression equation to estimate the FFM in dry weight was: Dw-FFM = 0.038 + (0.984 × Mw-FFM) + (-0.571 × [Mw-Dw]); R(2)  = 0.99). There was no systematic bias between the estimated and the measured values of FFM in dry weight. Using NIRS, FFM in dry weight can be calculated by an equation including FFM in measured weight and the difference between the measured weight and the dry weight. © 2015 The Authors. Therapeutic Apheresis and Dialysis © 2015 International Society for Apheresis.

On the exact solutions of high order wave equations of KdV type (I)

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Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Density-based Monte Carlo filter and its applications in nonlinear stochastic differential equation models.

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Huang, Guanghui; Wan, Jianping; Chen, Hui

2013-02-01

Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.

An extended continuous estimation of distribution algorithm for solving the permutation flow-shop scheduling problem

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Shao, Zhongshi; Pi, Dechang; Shao, Weishi