Charactering baseline shift with 4th polynomial function for portable biomedical near-infrared spectroscopy device

NASA Astrophysics Data System (ADS)

Zhao, Ke; Ji, Yaoyao; Pan, Boan; Li, Ting

2018-02-01

The continuous-wave Near-infrared spectroscopy (NIRS) devices have been highlighted for its clinical and health care applications in noninvasive hemodynamic measurements. The baseline shift of the deviation measurement attracts lots of attentions for its clinical importance. Nonetheless current published methods have low reliability or high variability. In this study, we found a perfect polynomial fitting function for baseline removal, using NIRS. Unlike previous studies on baseline correction for near-infrared spectroscopy evaluation of non-hemodynamic particles, we focused on baseline fitting and corresponding correction method for NIRS and found that the polynomial fitting function at 4th order is greater than the function at 2nd order reported in previous research. Through experimental tests of hemodynamic parameters of the solid phantom, we compared the fitting effect between the 4th order polynomial and the 2nd order polynomial, by recording and analyzing the R values and the SSE (the sum of squares due to error) values. The R values of the 4th order polynomial function fitting are all higher than 0.99, which are significantly higher than the corresponding ones of 2nd order, while the SSE values of the 4th order are significantly smaller than the corresponding ones of the 2nd order. By using the high-reliable and low-variable 4th order polynomial fitting function, we are able to remove the baseline online to obtain more accurate NIRS measurements.

Bicubic uniform B-spline wavefront fitting technology applied in computer-generated holograms

NASA Astrophysics Data System (ADS)

Cao, Hui; Sun, Jun-qiang; Chen, Guo-jie

2006-02-01

This paper presented a bicubic uniform B-spline wavefront fitting technology to figure out the analytical expression for object wavefront used in Computer-Generated Holograms (CGHs). In many cases, to decrease the difficulty of optical processing, off-axis CGHs rather than complex aspherical surface elements are used in modern advanced military optical systems. In order to design and fabricate off-axis CGH, we have to fit out the analytical expression for object wavefront. Zernike Polynomial is competent for fitting wavefront of centrosymmetric optical systems, but not for axisymmetrical optical systems. Although adopting high-degree polynomials fitting method would achieve higher fitting precision in all fitting nodes, the greatest shortcoming of this method is that any departure from the fitting nodes would result in great fitting error, which is so-called pulsation phenomenon. Furthermore, high-degree polynomials fitting method would increase the calculation time in coding computer-generated hologram and solving basic equation. Basing on the basis function of cubic uniform B-spline and the character mesh of bicubic uniform B-spline wavefront, bicubic uniform B-spline wavefront are described as the product of a series of matrices. Employing standard MATLAB routines, four kinds of different analytical expressions for object wavefront are fitted out by bicubic uniform B-spline as well as high-degree polynomials. Calculation results indicate that, compared with high-degree polynomials, bicubic uniform B-spline is a more competitive method to fit out the analytical expression for object wavefront used in off-axis CGH, for its higher fitting precision and C2 continuity.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

PubMed

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl.

PubMed

De Beuckeleer, Liene I; Herrebout, Wouter A

2016-02-05

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before. Copyright © 2015 Elsevier B.V. All rights reserved.

Cylinder surface test with Chebyshev polynomial fitting method

NASA Astrophysics Data System (ADS)

Yu, Kui-bang; Guo, Pei-ji; Chen, Xi

2017-10-01

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.

Student Support for Research in Hierarchical Control and Trajectory Planning

NASA Technical Reports Server (NTRS)

Martin, Clyde F.

1999-01-01

Generally, classical polynomial splines tend to exhibit unwanted undulations. In this work, we discuss a technique, based on control principles, for eliminating these undulations and increasing the smoothness properties of the spline interpolants. We give a generalization of the classical polynomial splines and show that this generalization is, in fact, a family of splines that covers the broad spectrum of polynomial, trigonometric and exponential splines. A particular element in this family is determined by the appropriate control data. It is shown that this technique is easy to implement. Several numerical and curve-fitting examples are given to illustrate the advantages of this technique over the classical approach. Finally, we discuss the convergence properties of the interpolant.

Detection and correction of laser induced breakdown spectroscopy spectral background based on spline interpolation method

NASA Astrophysics Data System (ADS)

Tan, Bing; Huang, Min; Zhu, Qibing; Guo, Ya; Qin, Jianwei

2017-12-01

Laser-induced breakdown spectroscopy (LIBS) is an analytical technique that has gained increasing attention because of many applications. The production of continuous background in LIBS is inevitable because of factors associated with laser energy, gate width, time delay, and experimental environment. The continuous background significantly influences the analysis of the spectrum. Researchers have proposed several background correction methods, such as polynomial fitting, Lorenz fitting and model-free methods. However, less of them apply these methods in the field of LIBS Technology, particularly in qualitative and quantitative analyses. This study proposes a method based on spline interpolation for detecting and estimating the continuous background spectrum according to its smooth property characteristic. Experiment on the background correction simulation indicated that, the spline interpolation method acquired the largest signal-to-background ratio (SBR) over polynomial fitting, Lorenz fitting and model-free method after background correction. These background correction methods all acquire larger SBR values than that acquired before background correction (The SBR value before background correction is 10.0992, whereas the SBR values after background correction by spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 26.9576, 24.6828, 18.9770, and 25.6273 respectively). After adding random noise with different kinds of signal-to-noise ratio to the spectrum, spline interpolation method acquires large SBR value, whereas polynomial fitting and model-free method obtain low SBR values. All of the background correction methods exhibit improved quantitative results of Cu than those acquired before background correction (The linear correlation coefficient value before background correction is 0.9776. Moreover, the linear correlation coefficient values after background correction using spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 0.9998, 0.9915, 0.9895, and 0.9940 respectively). The proposed spline interpolation method exhibits better linear correlation and smaller error in the results of the quantitative analysis of Cu compared with polynomial fitting, Lorentz fitting and model-free methods, The simulation and quantitative experimental results show that the spline interpolation method can effectively detect and correct the continuous background.

Single-wavelength based Thai jasmine rice identification with polynomial fitting function and neural network analysis

NASA Astrophysics Data System (ADS)

Suwansukho, Kajpanya; Sumriddetchkajorn, Sarun; Buranasiri, Prathan

2013-06-01

We previously showed that a combination of image thresholding, chain coding, elliptic Fourier descriptors, and artificial neural network analysis provided a low false acceptance rate (FAR) and a false rejection rate (FRR) of 11.0% and 19.0%, respectively, in identify Thai jasmine rice from three unwanted rice varieties. In this work, we highlight that only a polynomial function fitting on the determined chain code and the neural network analysis are highly sufficient in obtaining a very low FAR of < 3.0% and a very low 0.3% FRR for the separation of Thai jasmine rice from Chainat 1 (CNT1), Prathumtani 1 (PTT1), and Hom-Pitsanulok (HPSL) rice varieties. With this proposed approach, the analytical time is tremendously suppressed from 4,250 seconds down to 2 seconds, implying extremely high potential in practical deployment.

Polynomial Fitting of DT-MRI Fiber Tracts Allows Accurate Estimation of Muscle Architectural Parameters

PubMed Central

Damon, Bruce M.; Heemskerk, Anneriet M.; Ding, Zhaohua

2012-01-01

Fiber curvature is a functionally significant muscle structural property, but its estimation from diffusion-tensor MRI fiber tracking data may be confounded by noise. The purpose of this study was to investigate the use of polynomial fitting of fiber tracts for improving the accuracy and precision of fiber curvature (κ) measurements. Simulated image datasets were created in order to provide data with known values for κ and pennation angle (θ). Simulations were designed to test the effects of increasing inherent fiber curvature (3.8, 7.9, 11.8, and 15.3 m−1), signal-to-noise ratio (50, 75, 100, and 150), and voxel geometry (13.8 and 27.0 mm3 voxel volume with isotropic resolution; 13.5 mm3 volume with an aspect ratio of 4.0) on κ and θ measurements. In the originally reconstructed tracts, θ was estimated accurately under most curvature and all imaging conditions studied; however, the estimates of κ were imprecise and inaccurate. Fitting the tracts to 2nd order polynomial functions provided accurate and precise estimates of κ for all conditions except very high curvature (κ=15.3 m−1), while preserving the accuracy of the θ estimates. Similarly, polynomial fitting of in vivo fiber tracking data reduced the κ values of fitted tracts from those of unfitted tracts and did not change the θ values. Polynomial fitting of fiber tracts allows accurate estimation of physiologically reasonable values of κ, while preserving the accuracy of θ estimation. PMID:22503094

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

Establishing a direct connection between detrended fluctuation analysis and Fourier analysis

NASA Astrophysics Data System (ADS)

Kiyono, Ken

2015-10-01

To understand methodological features of the detrended fluctuation analysis (DFA) using a higher-order polynomial fitting, we establish the direct connection between DFA and Fourier analysis. Based on an exact calculation of the single-frequency response of the DFA, the following facts are shown analytically: (1) in the analysis of stochastic processes exhibiting a power-law scaling of the power spectral density (PSD), S (f ) ˜f-β , a higher-order detrending in the DFA has no adverse effect in the estimation of the DFA scaling exponent α , which satisfies the scaling relation α =(β +1 )/2 ; (2) the upper limit of the scaling exponents detectable by the DFA depends on the order of polynomial fit used in the DFA, and is bounded by m +1 , where m is the order of the polynomial fit; (3) the relation between the time scale in the DFA and the corresponding frequency in the PSD are distorted depending on both the order of the DFA and the frequency dependence of the PSD. We can improve the scale distortion by introducing the corrected time scale in the DFA corresponding to the inverse of the frequency scale in the PSD. In addition, our analytical approach makes it possible to characterize variants of the DFA using different types of detrending. As an application, properties of the detrending moving average algorithm are discussed.

Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials.

PubMed

Zhao, Chunyu; Burge, James H

2007-12-24

Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. These functions are generated from gradients of Zernike polynomials, made orthonormal using the Gram- Schmidt technique. This set provides a complete basis for representing vector fields that can be defined as a gradient of some scalar function. It is then efficient to transform from the coefficients of the vector functions to the scalar Zernike polynomials that represent the function whose gradient was fit. These new vector functions have immediate application for fitting data from a Shack-Hartmann wavefront sensor or for fitting mapping distortion for optical testing. A subsequent paper gives an additional set of vector functions consisting only of rotational terms with zero divergence. The two sets together provide a complete basis that can represent all vector distributions in a circular domain.

Edge detection and mathematic fitting for corneal surface with Matlab software.

PubMed

Di, Yue; Li, Mei-Yan; Qiao, Tong; Lu, Na

2017-01-01

To select the optimal edge detection methods to identify the corneal surface, and compare three fitting curve equations with Matlab software. Fifteen subjects were recruited. The corneal images from optical coherence tomography (OCT) were imported into Matlab software. Five edge detection methods (Canny, Log, Prewitt, Roberts, Sobel) were used to identify the corneal surface. Then two manual identifying methods (ginput and getpts) were applied to identify the edge coordinates respectively. The differences among these methods were compared. Binomial curve (y=Ax 2 +Bx+C), Polynomial curve [p(x)=p1x n +p2x n-1 +....+pnx+pn+1] and Conic section (Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0) were used for curve fitting the corneal surface respectively. The relative merits among three fitting curves were analyzed. Finally, the eccentricity (e) obtained by corneal topography and conic section were compared with paired t -test. Five edge detection algorithms all had continuous coordinates which indicated the edge of the corneal surface. The ordinates of manual identifying were close to the inside of the actual edges. Binomial curve was greatly affected by tilt angle. Polynomial curve was lack of geometrical properties and unstable. Conic section could calculate the tilted symmetry axis, eccentricity, circle center, etc . There were no significant differences between 'e' values by corneal topography and conic section ( t =0.9143, P =0.3760 >0.05). It is feasible to simulate the corneal surface with mathematical curve with Matlab software. Edge detection has better repeatability and higher efficiency. The manual identifying approach is an indispensable complement for detection. Polynomial and conic section are both the alternative methods for corneal curve fitting. Conic curve was the optimal choice based on the specific geometrical properties.

A moving hum filter to suppress rotor noise in high-resolution airborne magnetic data

USGS Publications Warehouse

Xia, J.; Doll, W.E.; Miller, R.D.; Gamey, T.J.; Emond, A.M.

2005-01-01

A unique filtering approach is developed to eliminate helicopter rotor noise. It is designed to suppress harmonic noise from a rotor that varies slightly in amplitude, phase, and frequency and that contaminates aero-magnetic data. The filter provides a powerful harmonic noise-suppression tool for data acquired with modern large-dynamic-range recording systems. This three-step approach - polynomial fitting, bandpass filtering, and rotor-noise synthesis - significantly reduces rotor noise without altering the spectra of signals of interest. Two steps before hum filtering - polynomial fitting and bandpass filtering - are critical to accurately model the weak rotor noise. During rotor-noise synthesis, amplitude, phase, and frequency are determined. Data are processed segment by segment so that there is no limit on the length of data. The segment length changes dynamically along a line based on modeling results. Modeling the rotor noise is stable and efficient. Real-world data examples demonstrate that this method can suppress rotor noise by more than 95% when implemented in an aeromagnetic data-processing flow. ?? 2005 Society of Exploration Geophysicists. All rights reserved.

A combined averaging and frequency mixing approach for force identification in weakly nonlinear high-Q oscillators: Atomic force microscope

NASA Astrophysics Data System (ADS)

Sah, Si Mohamed; Forchheimer, Daniel; Borgani, Riccardo; Haviland, David

2018-02-01

We present a polynomial force reconstruction of the tip-sample interaction force in Atomic Force Microscopy. The method uses analytical expressions for the slow-time amplitude and phase evolution, obtained from time-averaging over the rapidly oscillating part of the cantilever dynamics. The slow-time behavior can be easily obtained in either the numerical simulations or the experiment in which a high-Q resonator is perturbed by a weak nonlinearity and a periodic driving force. A direct fit of the theoretical expressions to the simulated and experimental data gives the best-fit parameters for the force model. The method combines and complements previous works (Platz et al., 2013; Forchheimer et al., 2012 [2]) and it allows for computationally more efficient parameter mapping with AFM. Results for the simulated asymmetric piecewise linear force and VdW-DMT force models are compared with the reconstructed polynomial force and show a good agreement. It is also shown that the analytical amplitude and phase modulation equations fit well with the experimental data.

Parametric analysis of ATM solar array.

NASA Technical Reports Server (NTRS)

Singh, B. K.; Adkisson, W. B.

1973-01-01

The paper discusses the methods used for the calculation of ATM solar array performance characteristics and provides the parametric analysis of solar panels used in SKYLAB. To predict the solar array performance under conditions other than test conditions, a mathematical model has been developed. Four computer programs have been used to convert the solar simulator test data to the parametric curves. The first performs module summations, the second determines average solar cell characteristics which will cause a mathematical model to generate a curve matching the test data, the third is a polynomial fit program which determines the polynomial equations for the solar cell characteristics versus temperature, and the fourth program uses the polynomial coefficients generated by the polynomial curve fit program to generate the parametric data.

Fitness Probability Distribution of Bit-Flip Mutation.

PubMed

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

A quadratic regression modelling on paddy production in the area of Perlis

NASA Astrophysics Data System (ADS)

Goh, Aizat Hanis Annas; Ali, Zalila; Nor, Norlida Mohd; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

2017-08-01

Polynomial regression models are useful in situations in which the relationship between a response variable and predictor variables is curvilinear. Polynomial regression fits the nonlinear relationship into a least squares linear regression model by decomposing the predictor variables into a kth order polynomial. The polynomial order determines the number of inflexions on the curvilinear fitted line. A second order polynomial forms a quadratic expression (parabolic curve) with either a single maximum or minimum, a third order polynomial forms a cubic expression with both a relative maximum and a minimum. This study used paddy data in the area of Perlis to model paddy production based on paddy cultivation characteristics and environmental characteristics. The results indicated that a quadratic regression model best fits the data and paddy production is affected by urea fertilizer application and the interaction between amount of average rainfall and percentage of area defected by pest and disease. Urea fertilizer application has a quadratic effect in the model which indicated that if the number of days of urea fertilizer application increased, paddy production is expected to decrease until it achieved a minimum value and paddy production is expected to increase at higher number of days of urea application. The decrease in paddy production with an increased in rainfall is greater, the higher the percentage of area defected by pest and disease.

Statistics of Data Fitting: Flaws and Fixes of Polynomial Analysis of Channeled Spectra

NASA Astrophysics Data System (ADS)

Karstens, William; Smith, David

2013-03-01

Starting from general statistical principles, we have critically examined Baumeister's procedure* for determining the refractive index of thin films from channeled spectra. Briefly, the method assumes that the index and interference fringe order may be approximated by polynomials quadratic and cubic in photon energy, respectively. The coefficients of the polynomials are related by differentiation, which is equivalent to comparing energy differences between fringes. However, we find that when the fringe order is calculated from the published IR index for silicon* and then analyzed with Baumeister's procedure, the results do not reproduce the original index. This problem has been traced to 1. Use of unphysical powers in the polynomials (e.g., time-reversal invariance requires that the index is an even function of photon energy), and 2. Use of insufficient terms of the correct parity. Exclusion of unphysical terms and addition of quartic and quintic terms to the index and order polynomials yields significantly better fits with fewer parameters. This represents a specific example of using statistics to determine if the assumed fitting model adequately captures the physics contained in experimental data. The use of analysis of variance (ANOVA) and the Durbin-Watson statistic to test criteria for the validity of least-squares fitting will be discussed. *D.F. Edwards and E. Ochoa, Appl. Opt. 19, 4130 (1980). Supported in part by the US Department of Energy, Office of Nuclear Physics under contract DE-AC02-06CH11357.

Investigating a continuous shear strain function for depth-dependent properties of native and tissue engineering cartilage using pixel-size data.

PubMed

Motavalli, Mostafa; Whitney, G Adam; Dennis, James E; Mansour, Joseph M

2013-12-01

A previously developed novel imaging technique for determining the depth dependent properties of cartilage in simple shear is implemented. Shear displacement is determined from images of deformed lines photobleached on a sample, and shear strain is obtained from the derivative of the displacement. We investigated the feasibility of an alternative systematic approach to numerical differentiation for computing the shear strain that is based on fitting a continuous function to the shear displacement. Three models for a continuous shear displacement function are evaluated: polynomials, cubic splines, and non-parametric locally weighted scatter plot curves. Four independent approaches are then applied to identify the best-fit model and the accuracy of the first derivative. One approach is based on the Akaiki Information Criteria, and the Bayesian Information Criteria. The second is based on a method developed to smooth and differentiate digitized data from human motion. The third method is based on photobleaching a predefined circular area with a specific radius. Finally, we integrate the shear strain and compare it with the total shear deflection of the sample measured experimentally. Results show that 6th and 7th order polynomials are the best models for the shear displacement and its first derivative. In addition, failure of tissue-engineered cartilage, consistent with previous results, demonstrates the qualitative value of this imaging approach. © 2013 Elsevier Ltd. All rights reserved.

Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard

NASA Astrophysics Data System (ADS)

Roquet, F.; Madec, G.; McDougall, Trevor J.; Barker, Paul M.

2015-06-01

A new set of approximations to the standard TEOS-10 equation of state are presented. These follow a polynomial form, making it computationally efficient for use in numerical ocean models. Two versions are provided, the first being a fit of density for Boussinesq ocean models, and the second fitting specific volume which is more suitable for compressible models. Both versions are given as the sum of a vertical reference profile (6th-order polynomial) and an anomaly (52-term polynomial, cubic in pressure), with relative errors of ∼0.1% on the thermal expansion coefficients. A 75-term polynomial expression is also presented for computing specific volume, with a better accuracy than the existing TEOS-10 48-term rational approximation, especially regarding the sound speed, and it is suggested that this expression represents a valuable approximation of the TEOS-10 equation of state for hydrographic data analysis. In the last section, practical aspects about the implementation of TEOS-10 in ocean models are discussed.

Sensitivity Analysis of the Static Aeroelastic Response of a Wing

NASA Technical Reports Server (NTRS)

Eldred, Lloyd B.

1993-01-01

A technique to obtain the sensitivity of the static aeroelastic response of a three dimensional wing model is designed and implemented. The formulation is quite general and accepts any aerodynamic and structural analysis capability. A program to combine the discipline level, or local, sensitivities into global sensitivity derivatives is developed. A variety of representations of the wing pressure field are developed and tested to determine the most accurate and efficient scheme for representing the field outside of the aerodynamic code. Chebyshev polynomials are used to globally fit the pressure field. This approach had some difficulties in representing local variations in the field, so a variety of local interpolation polynomial pressure representations are also implemented. These panel based representations use a constant pressure value, a bilinearly interpolated value. or a biquadraticallv interpolated value. The interpolation polynomial approaches do an excellent job of reducing the numerical problems of the global approach for comparable computational effort. Regardless of the pressure representation used. sensitivity and response results with excellent accuracy have been produced for large integrated quantities such as wing tip deflection and trim angle of attack. The sensitivities of such things as individual generalized displacements have been found with fair accuracy. In general, accuracy is found to be proportional to the relative size of the derivatives to the quantity itself.

Ligand Shaping in Induced Fit Docking of MraY Inhibitors. Polynomial Discriminant and Laplacian Operator as Biological Activity Descriptors.

PubMed

Lungu, Claudiu N; Diudea, Mircea V; Putz, Mihai V

2017-06-27

Docking-i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)-represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor-ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in topology and energy, comparative to the receptor. These changes can be described by manifold hypersurfaces, in terms of polynomial discriminant and Laplacian operator. Such topological surfaces were represented for each MraY (phospho-MurNAc-pentapeptide translocase) inhibitor, studied before and after docking with MraY. Binding affinities of all ligands were calculated by this procedure. For each ligand, Laplacian and polynomial discriminant were correlated with the ligand minimum inhibitory concentration (MIC) retrieved from literature. It was observed that MIC is correlated with Laplacian and polynomial discriminant.

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

NASA Technical Reports Server (NTRS)

Chang, T. S.

1974-01-01

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

Determination of the paraxial focal length using Zernike polynomials over different apertures

NASA Astrophysics Data System (ADS)

Binkele, Tobias; Hilbig, David; Henning, Thomas; Fleischmann, Friedrich

2017-02-01

The paraxial focal length is still the most important parameter in the design of a lens. As presented at the SPIE Optics + Photonics 2016, the measured focal length is a function of the aperture. The paraxial focal length can be found when the aperture approaches zero. In this work, we investigate the dependency of the Zernike polynomials on the aperture size with respect to 3D space. By this, conventional wavefront measurement systems that apply Zernike polynomial fitting (e.g. Shack-Hartmann-Sensor) can be used to determine the paraxial focal length, too. Since the Zernike polynomials are orthogonal over a unit circle, the aperture used in the measurement has to be normalized. By shrinking the aperture and keeping up with the normalization, the Zernike coefficients change. The relation between these changes and the paraxial focal length are investigated. The dependency of the focal length on the aperture size is derived analytically and evaluated by simulation and measurement of a strong focusing lens. The measurements are performed using experimental ray tracing and a Shack-Hartmann-Sensor. Using experimental ray tracing for the measurements, the aperture can be chosen easily. Regarding the measurements with the Shack-Hartmann- Sensor, the aperture size is fixed. Thus, the Zernike polynomials have to be adapted to use different aperture sizes by the proposed method. By doing this, the paraxial focal length can be determined from the measurements in both cases.

Tensile stress-strain behavior of graphite/epoxy laminates

NASA Technical Reports Server (NTRS)

Garber, D. P.

1982-01-01

The tensile stress-strain behavior of a variety of graphite/epoxy laminates was examined. Longitudinal and transverse specimens from eleven different layups were monotonically loaded in tension to failure. Ultimate strength, ultimate strain, and strss-strain curves wee obtained from four replicate tests in each case. Polynominal equations were fitted by the method of least squares to the stress-strain data to determine average curves. Values of Young's modulus and Poisson's ratio, derived from polynomial coefficients, were compared with laminate analysis results. While the polynomials appeared to accurately fit the stress-strain data in most cases, the use of polynomial coefficients to calculate elastic moduli appeared to be of questionable value in cases involving sharp changes in the slope of the stress-strain data or extensive scatter.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

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

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrixmore » is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.« less

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

Ligand Shaping in Induced Fit Docking of MraY Inhibitors. Polynomial Discriminant and Laplacian Operator as Biological Activity Descriptors

PubMed Central

Diudea, Mircea V.; Putz, Mihai V.

2017-01-01

Docking—i.e., interaction of a small molecule (ligand) with a proteic structure (receptor)—represents the ground of drug action mechanism of the vast majority of bioactive chemicals. Ligand and receptor accommodate their geometry and energy, within this interaction, in the benefit of receptor–ligand complex. In an induced fit docking, the structure of ligand is most susceptible to changes in topology and energy, comparative to the receptor. These changes can be described by manifold hypersurfaces, in terms of polynomial discriminant and Laplacian operator. Such topological surfaces were represented for each MraY (phospho-MurNAc-pentapeptide translocase) inhibitor, studied before and after docking with MraY. Binding affinities of all ligands were calculated by this procedure. For each ligand, Laplacian and polynomial discriminant were correlated with the ligand minimum inhibitory concentration (MIC) retrieved from literature. It was observed that MIC is correlated with Laplacian and polynomial discriminant. PMID:28653980

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle.

PubMed

Pereira, R J; Bignardi, A B; El Faro, L; Verneque, R S; Vercesi Filho, A E; Albuquerque, L G

2013-01-01

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Significantly Reduced Blood Pressure Measurement Variability for Both Normotensive and Hypertensive Subjects: Effect of Polynomial Curve Fitting of Oscillometric Pulses

PubMed Central

Zhu, Mingping; Chen, Aiqing

2017-01-01

This study aimed to compare within-subject blood pressure (BP) variabilities from different measurement techniques. Cuff pressures from three repeated BP measurements were obtained from 30 normotensive and 30 hypertensive subjects. Automatic BPs were determined from the pulses with normalised peak amplitude larger than a threshold (0.5 for SBP, 0.7 for DBP, and 1.0 for MAP). They were also determined from cuff pressures associated with the above thresholds on a fitted curve polynomial curve of the oscillometric pulse peaks. Finally, the standard deviation (SD) of three repeats and its coefficient of variability (CV) were compared between the two automatic techniques. For the normotensive group, polynomial curve fitting significantly reduced SD of repeats from 3.6 to 2.5 mmHg for SBP and from 3.7 to 2.1 mmHg for MAP and reduced CV from 3.0% to 2.2% for SBP and from 4.3% to 2.4% for MAP (all P < 0.01). For the hypertensive group, SD of repeats decreased from 6.5 to 5.5 mmHg for SBP and from 6.7 to 4.2 mmHg for MAP, and CV decreased from 4.2% to 3.6% for SBP and from 5.8% to 3.8% for MAP (all P < 0.05). In conclusion, polynomial curve fitting of oscillometric pulses had the ability to reduce automatic BP measurement variability. PMID:28785580

Investigating and Modelling Effects of Climatically and Hydrologically Indicators on the Urmia Lake Coastline Changes Using Time Series Analysis

NASA Astrophysics Data System (ADS)

Ahmadijamal, M.; Hasanlou, M.

2017-09-01

Study of hydrological parameters of lakes and examine the variation of water level to operate management on water resources are important. The purpose of this study is to investigate and model the Urmia Lake water level changes due to changes in climatically and hydrological indicators that affects in the process of level variation and area of this lake. For this purpose, Landsat satellite images, hydrological data, the daily precipitation, the daily surface evaporation and the daily discharge in total of the lake basin during the period of 2010-2016 have been used. Based on time-series analysis that is conducted on individual data independently with same procedure, to model variation of Urmia Lake level, we used polynomial regression technique and combined polynomial with periodic behavior. In the first scenario, we fit a multivariate linear polynomial to our datasets and determining RMSE, NRSME and R² value. We found that fourth degree polynomial can better fit to our datasets with lowest RMSE value about 9 cm. In the second scenario, we combine polynomial with periodic behavior for modeling. The second scenario has superiority comparing to the first one, by RMSE value about 3 cm.

Creating a non-linear total sediment load formula using polynomial best subset regression model

NASA Astrophysics Data System (ADS)

Okcu, Davut; Pektas, Ali Osman; Uyumaz, Ali

2016-08-01

The aim of this study is to derive a new total sediment load formula which is more accurate and which has less application constraints than the well-known formulae of the literature. 5 most known stream power concept sediment formulae which are approved by ASCE are used for benchmarking on a wide range of datasets that includes both field and flume (lab) observations. The dimensionless parameters of these widely used formulae are used as inputs in a new regression approach. The new approach is called Polynomial Best subset regression (PBSR) analysis. The aim of the PBRS analysis is fitting and testing all possible combinations of the input variables and selecting the best subset. Whole the input variables with their second and third powers are included in the regression to test the possible relation between the explanatory variables and the dependent variable. While selecting the best subset a multistep approach is used that depends on significance values and also the multicollinearity degrees of inputs. The new formula is compared to others in a holdout dataset and detailed performance investigations are conducted for field and lab datasets within this holdout data. Different goodness of fit statistics are used as they represent different perspectives of the model accuracy. After the detailed comparisons are carried out we figured out the most accurate equation that is also applicable on both flume and river data. Especially, on field dataset the prediction performance of the proposed formula outperformed the benchmark formulations.

Techniques to improve the accuracy of noise power spectrum measurements in digital x-ray imaging based on background trends removal.

PubMed

Zhou, Zhongxing; Gao, Feng; Zhao, Huijuan; Zhang, Lixin

2011-03-01

Noise characterization through estimation of the noise power spectrum (NPS) is a central component of the evaluation of digital x-ray systems. Extensive works have been conducted to achieve accurate and precise measurement of NPS. One approach to improve the accuracy of the NPS measurement is to reduce the statistical variance of the NPS results by involving more data samples. However, this method is based on the assumption that the noise in a radiographic image is arising from stochastic processes. In the practical data, the artifactuals always superimpose on the stochastic noise as low-frequency background trends and prevent us from achieving accurate NPS. The purpose of this study was to investigate an appropriate background detrending technique to improve the accuracy of NPS estimation for digital x-ray systems. In order to achieve the optimal background detrending technique for NPS estimate, four methods for artifactuals removal were quantitatively studied and compared: (1) Subtraction of a low-pass-filtered version of the image, (2) subtraction of a 2-D first-order fit to the image, (3) subtraction of a 2-D second-order polynomial fit to the image, and (4) subtracting two uniform exposure images. In addition, background trend removal was separately applied within original region of interest or its partitioned sub-blocks for all four methods. The performance of background detrending techniques was compared according to the statistical variance of the NPS results and low-frequency systematic rise suppression. Among four methods, subtraction of a 2-D second-order polynomial fit to the image was most effective in low-frequency systematic rise suppression and variances reduction for NPS estimate according to the authors' digital x-ray system. Subtraction of a low-pass-filtered version of the image led to NPS variance increment above low-frequency components because of the side lobe effects of frequency response of the boxcar filtering function. Subtracting two uniform exposure images obtained the worst result on the smoothness of NPS curve, although it was effective in low-frequency systematic rise suppression. Subtraction of a 2-D first-order fit to the image was also identified effective for background detrending, but it was worse than subtraction of a 2-D second-order polynomial fit to the image according to the authors' digital x-ray system. As a result of this study, the authors verified that it is necessary and feasible to get better NPS estimate by appropriate background trend removal. Subtraction of a 2-D second-order polynomial fit to the image was the most appropriate technique for background detrending without consideration of processing time.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression.

PubMed

Schneider, Martin; Iskander, D Robert; Collins, Michael J

2009-02-01

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions

NASA Astrophysics Data System (ADS)

Ziegler, Benjamin; Rauhut, Guntram

2016-03-01

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions.

PubMed

Ziegler, Benjamin; Rauhut, Guntram

2016-03-21

The transformation of multi-dimensional potential energy surfaces (PESs) from a grid-based multimode representation to an analytical one is a standard procedure in quantum chemical programs. Within the framework of linear least squares fitting, a simple and highly efficient algorithm is presented, which relies on a direct product representation of the PES and a repeated use of Kronecker products. It shows the same scalings in computational cost and memory requirements as the potfit approach. In comparison to customary linear least squares fitting algorithms, this corresponds to a speed-up and memory saving by several orders of magnitude. Different fitting bases are tested, namely, polynomials, B-splines, and distributed Gaussians. Benchmark calculations are provided for the PESs of a set of small molecules.

A ROM-Less Direct Digital Frequency Synthesizer Based on Hybrid Polynomial Approximation

PubMed Central

Omran, Qahtan Khalaf; Islam, Mohammad Tariqul; Misran, Norbahiah; Faruque, Mohammad Rashed Iqbal

2014-01-01

In this paper, a novel design approach for a phase to sinusoid amplitude converter (PSAC) has been investigated. Two segments have been used to approximate the first sine quadrant. A first linear segment is used to fit the region near the zero point, while a second fourth-order parabolic segment is used to approximate the rest of the sine curve. The phase sample, where the polynomial changed, was chosen in such a way as to achieve the maximum spurious free dynamic range (SFDR). The invented direct digital frequency synthesizer (DDFS) has been encoded in VHDL and post simulation was carried out. The synthesized architecture exhibits a promising result of 90 dBc SFDR. The targeted structure is expected to show advantages for perceptible reduction of hardware resources and power consumption as well as high clock speeds. PMID:24892092

Fast and accurate fitting and filtering of noisy exponentials in Legendre space.

PubMed

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters.

Optical coherence tomography assessment of vessel wall degradation in aneurysmatic thoracic aortas

NASA Astrophysics Data System (ADS)

Real, Eusebio; Eguizabal, Alma; Pontón, Alejandro; Val-Bernal, J. Fernando; Mayorga, Marta; Revuelta, José M.; López-Higuera, José; Conde, Olga M.

2013-06-01

Optical coherence tomographic images of ascending thoracic human aortas from aneurysms exhibit disorders on the smooth muscle cell structure of the media layer of the aortic vessel as well as elastin degradation. Ex-vivo measurements of human samples provide results that correlate with pathologist diagnosis in aneurysmatic and control aortas. The observed disorders are studied as possible hallmarks for aneurysm diagnosis. To this end, the backscattering profile along the vessel thickness has been evaluated by fitting its decay against two different models, a third order polynomial fitting and an exponential fitting. The discontinuities present on the vessel wall on aneurysmatic aortas are slightly better identified with the exponential approach. Aneurysmatic aortic walls present uneven reflectivity decay when compared with healthy vessels. The fitting error has revealed as the most favorable indicator for aneurysm diagnosis as it provides a measure of how uniform is the decay along the vessel thickness.

Employing general fit-bases for construction of potential energy surfaces with an adaptive density-guided approach

NASA Astrophysics Data System (ADS)

Klinting, Emil Lund; Thomsen, Bo; Godtliebsen, Ian Heide; Christiansen, Ove

2018-02-01

We present an approach to treat sets of general fit-basis functions in a single uniform framework, where the functional form is supplied on input, i.e., the use of different functions does not require new code to be written. The fit-basis functions can be used to carry out linear fits to the grid of single points, which are generated with an adaptive density-guided approach (ADGA). A non-linear conjugate gradient method is used to optimize non-linear parameters if such are present in the fit-basis functions. This means that a set of fit-basis functions with the same inherent shape as the potential cuts can be requested and no other choices with regards to the fit-basis functions need to be taken. The general fit-basis framework is explored in relation to anharmonic potentials for model systems, diatomic molecules, water, and imidazole. The behaviour and performance of Morse and double-well fit-basis functions are compared to that of polynomial fit-basis functions for unsymmetrical single-minimum and symmetrical double-well potentials. Furthermore, calculations for water and imidazole were carried out using both normal coordinates and hybrid optimized and localized coordinates (HOLCs). Our results suggest that choosing a suitable set of fit-basis functions can improve the stability of the fitting routine and the overall efficiency of potential construction by lowering the number of single point calculations required for the ADGA. It is possible to reduce the number of terms in the potential by choosing the Morse and double-well fit-basis functions. These effects are substantial for normal coordinates but become even more pronounced if HOLCs are used.

Automated image segmentation-assisted flattening of atomic force microscopy images.

PubMed

Wang, Yuliang; Lu, Tongda; Li, Xiaolai; Wang, Huimin

2018-01-01

Atomic force microscopy (AFM) images normally exhibit various artifacts. As a result, image flattening is required prior to image analysis. To obtain optimized flattening results, foreground features are generally manually excluded using rectangular masks in image flattening, which is time consuming and inaccurate. In this study, a two-step scheme was proposed to achieve optimized image flattening in an automated manner. In the first step, the convex and concave features in the foreground were automatically segmented with accurate boundary detection. The extracted foreground features were taken as exclusion masks. In the second step, data points in the background were fitted as polynomial curves/surfaces, which were then subtracted from raw images to get the flattened images. Moreover, sliding-window-based polynomial fitting was proposed to process images with complex background trends. The working principle of the two-step image flattening scheme were presented, followed by the investigation of the influence of a sliding-window size and polynomial fitting direction on the flattened images. Additionally, the role of image flattening on the morphological characterization and segmentation of AFM images were verified with the proposed method.

Comparison of three methods for wind turbine capacity factor estimation.

PubMed

Ditkovich, Y; Kuperman, A

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first "quasiexact" approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second "analytic" approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third "approximate" approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

Genetic parameters of legendre polynomials for first parity lactation curves.

PubMed

Pool, M H; Janss, L L; Meuwissen, T H

2000-11-01

Variance components of the covariance function coefficients in a random regression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. Two Legendre polynomials of equal order were used to model the random part of the lactation curve, one for the genetic component and one for permanent environment. Test-day records from cows registered between 1990 to 1996 and collected by regular milk recording were available. For the data set, 23,700 complete lactations were selected from 475 herds sired by 262 sires. Because the application of a random regression model is limited by computing capacity, we investigated the minimum order needed to fit the variance structure in the data sufficiently. Predictions of genetic and permanent environmental variance structures were compared with bivariate estimates on 30-d intervals. A third-order or higher polynomial modeled the shape of variance curves over DIM with sufficient accuracy for the genetic and permanent environment part. Also, the genetic correlation structure was fitted with sufficient accuracy by a third-order polynomial, but, for the permanent environmental component, a fourth order was needed. Because equal orders are suggested in the literature, a fourth-order Legendre polynomial is recommended in this study. However, a rank of three for the genetic covariance matrix and of four for permanent environment allows a simpler covariance function with a reduced number of parameters based on the eigenvalues and eigenvectors.

Real-Time Curvature Defect Detection on Outer Surfaces Using Best-Fit Polynomial Interpolation

PubMed Central

Golkar, Ehsan; Prabuwono, Anton Satria; Patel, Ahmed

2012-01-01

This paper presents a novel, real-time defect detection system, based on a best-fit polynomial interpolation, that inspects the conditions of outer surfaces. The defect detection system is an enhanced feature extraction method that employs this technique to inspect the flatness, waviness, blob, and curvature faults of these surfaces. The proposed method has been performed, tested, and validated on numerous pipes and ceramic tiles. The results illustrate that the physical defects such as abnormal, popped-up blobs are recognized completely, and that flames, waviness, and curvature faults are detected simultaneously. PMID:23202186

Response Surface Modeling Tolerance and Inference Error Risk Specifications: Proposed Industry Standards

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2012-01-01

This paper reviews the derivation of an equation for scaling response surface modeling experiments. The equation represents the smallest number of data points required to fit a linear regression polynomial so as to achieve certain specified model adequacy criteria. Specific criteria are proposed which simplify an otherwise rather complex equation, generating a practical rule of thumb for the minimum volume of data required to adequately fit a polynomial with a specified number of terms in the model. This equation and the simplified rule of thumb it produces can be applied to minimize the cost of wind tunnel testing.

An Accurate Centroiding Algorithm for PSF Reconstruction

NASA Astrophysics Data System (ADS)

Lu, Tianhuan; Luo, Wentao; Zhang, Jun; Zhang, Jiajun; Li, Hekun; Dong, Fuyu; Li, Yingke; Liu, Dezi; Fu, Liping; Li, Guoliang; Fan, Zuhui

2018-07-01

In this work, we present a novel centroiding method based on Fourier space Phase Fitting (FPF) for Point Spread Function (PSF) reconstruction. We generate two sets of simulations to test our method. The first set is generated by GalSim with an elliptical Moffat profile and strong anisotropy that shifts the center of the PSF. The second set of simulations is drawn from CFHT i band stellar imaging data. We find non-negligible anisotropy from CFHT stellar images, which leads to ∼0.08 scatter in units of pixels using a polynomial fitting method (Vakili & Hogg). When we apply the FPF method to estimate the centroid in real space, the scatter reduces to ∼0.04 in S/N = 200 CFHT-like sample. In low signal-to-noise ratio (S/N; 50 and 100) CFHT-like samples, the background noise dominates the shifting of the centroid; therefore, the scatter estimated from different methods is similar. We compare polynomial fitting and FPF using GalSim simulation with optical anisotropy. We find that in all S/N (50, 100, and 200) samples, FPF performs better than polynomial fitting by a factor of ∼3. In general, we suggest that in real observations there exists anisotropy that shifts the centroid, and thus, the FPF method provides a better way to accurately locate it.

An empirical analysis of the quantitative effect of data when fitting quadratic and cubic polynomials

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

A study is made of the extent to which the size of the sample affects the accuracy of a quadratic or a cubic polynomial approximation of an experimentally observed quantity, and the trend with regard to improvement in the accuracy of the approximation as a function of sample size is established. The task is made possible through a simulated analysis carried out by the Monte Carlo method in which data are simulated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to either quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sizes and diminishes drastically for moderate and large amounts of experimental data.

Estimating the Effective Permittivity for Reconstructing Accurate Microwave-Radar Images.

PubMed

Lavoie, Benjamin R; Okoniewski, Michal; Fear, Elise C

2016-01-01

We present preliminary results from a method for estimating the optimal effective permittivity for reconstructing microwave-radar images. Using knowledge of how microwave-radar images are formed, we identify characteristics that are typical of good images, and define a fitness function to measure the relative image quality. We build a polynomial interpolant of the fitness function in order to identify the most likely permittivity values of the tissue. To make the estimation process more efficient, the polynomial interpolant is constructed using a locally and dimensionally adaptive sampling method that is a novel combination of stochastic collocation and polynomial chaos. Examples, using a series of simulated, experimental and patient data collected using the Tissue Sensing Adaptive Radar system, which is under development at the University of Calgary, are presented. These examples show how, using our method, accurate images can be reconstructed starting with only a broad estimate of the permittivity range.

Switching probability of all-perpendicular spin valve nanopillars

NASA Astrophysics Data System (ADS)

Tzoufras, M.

2018-05-01

In all-perpendicular spin valve nanopillars the probability density of the free-layer magnetization is independent of the azimuthal angle and its evolution equation simplifies considerably compared to the general, nonaxisymmetric geometry. Expansion of the time-dependent probability density to Legendre polynomials enables analytical integration of the evolution equation and yields a compact expression for the practically relevant switching probability. This approach is valid when the free layer behaves as a single-domain magnetic particle and it can be readily applied to fitting experimental data.

Prediction of zeolite-cement-sand unconfined compressive strength using polynomial neural network

NASA Astrophysics Data System (ADS)

MolaAbasi, H.; Shooshpasha, I.

2016-04-01

The improvement of local soils with cement and zeolite can provide great benefits, including strengthening slopes in slope stability problems, stabilizing problematic soils and preventing soil liquefaction. Recently, dosage methodologies are being developed for improved soils based on a rational criterion as it exists in concrete technology. There are numerous earlier studies showing the possibility of relating Unconfined Compressive Strength (UCS) and Cemented sand (CS) parameters (voids/cement ratio) as a power function fits. Taking into account the fact that the existing equations are incapable of estimating UCS for zeolite cemented sand mixture (ZCS) well, artificial intelligence methods are used for forecasting them. Polynomial-type neural network is applied to estimate the UCS from more simply determined index properties such as zeolite and cement content, porosity as well as curing time. In order to assess the merits of the proposed approach, a total number of 216 unconfined compressive tests have been done. A comparison is carried out between the experimentally measured UCS with the predictions in order to evaluate the performance of the current method. The results demonstrate that generalized polynomial-type neural network has a great ability for prediction of the UCS. At the end sensitivity analysis of the polynomial model is applied to study the influence of input parameters on model output. The sensitivity analysis reveals that cement and zeolite content have significant influence on predicting UCS.

Introduction to methodology of dose-response meta-analysis for binary outcome: With application on software.

PubMed

Zhang, Chao; Jia, Pengli; Yu, Liu; Xu, Chang

2018-05-01

Dose-response meta-analysis (DRMA) is widely applied to investigate the dose-specific relationship between independent and dependent variables. Such methods have been in use for over 30 years and are increasingly employed in healthcare and clinical decision-making. In this article, we give an overview of the methodology used in DRMA. We summarize the commonly used regression model and the pooled method in DRMA. We also use an example to illustrate how to employ a DRMA by these methods. Five regression models, linear regression, piecewise regression, natural polynomial regression, fractional polynomial regression, and restricted cubic spline regression, were illustrated in this article to fit the dose-response relationship. And two types of pooling approaches, that is, one-stage approach and two-stage approach are illustrated to pool the dose-response relationship across studies. The example showed similar results among these models. Several dose-response meta-analysis methods can be used for investigating the relationship between exposure level and the risk of an outcome. However the methodology of DRMA still needs to be improved. © 2018 Chinese Cochrane Center, West China Hospital of Sichuan University and John Wiley & Sons Australia, Ltd.

Forecasting irregular variations of UT1-UTC and LOD data caused by ENSO

NASA Astrophysics Data System (ADS)

Niedzielski, T.; Kosek, W.

2008-04-01

The research focuses on prediction of LOD and UT1-UTC time series up to one-year in the future with the particular emphasis on the prediction improvement during El Nĩ o or La Nĩ a n n events. The polynomial-harmonic least-squares model is applied to fit the deterministic function to LOD data. The stochastic residuals computed as the difference between LOD data and the polynomial- harmonic model reveal the extreme values driven by El Nĩ o or La Nĩ a. These peaks are modeled by the n n stochastic bivariate autoregressive prediction. This approach focuses on the auto- and cross-correlations between LOD and the axial component of the atmospheric angular momentum. This technique allows one to derive more accurate predictions than purely univariate forecasts, particularly during El Nĩ o/La n Nĩ a events. n

Comparison of random regression models with Legendre polynomials and linear splines for production traits and somatic cell score of Canadian Holstein cows.

PubMed

Bohmanova, J; Miglior, F; Jamrozik, J; Misztal, I; Sullivan, P G

2008-09-01

A random regression model with both random and fixed regressions fitted by Legendre polynomials of order 4 was compared with 3 alternative models fitting linear splines with 4, 5, or 6 knots. The effects common for all models were a herd-test-date effect, fixed regressions on days in milk (DIM) nested within region-age-season of calving class, and random regressions for additive genetic and permanent environmental effects. Data were test-day milk, fat and protein yields, and SCS recorded from 5 to 365 DIM during the first 3 lactations of Canadian Holstein cows. A random sample of 50 herds consisting of 96,756 test-day records was generated to estimate variance components within a Bayesian framework via Gibbs sampling. Two sets of genetic evaluations were subsequently carried out to investigate performance of the 4 models. Models were compared by graphical inspection of variance functions, goodness of fit, error of prediction of breeding values, and stability of estimated breeding values. Models with splines gave lower estimates of variances at extremes of lactations than the model with Legendre polynomials. Differences among models in goodness of fit measured by percentages of squared bias, correlations between predicted and observed records, and residual variances were small. The deviance information criterion favored the spline model with 6 knots. Smaller error of prediction and higher stability of estimated breeding values were achieved by using spline models with 5 and 6 knots compared with the model with Legendre polynomials. In general, the spline model with 6 knots had the best overall performance based upon the considered model comparison criteria.

Algorithm for Compressing Time-Series Data

NASA Technical Reports Server (NTRS)

Hawkins, S. Edward, III; Darlington, Edward Hugo

2012-01-01

An algorithm based on Chebyshev polynomials effects lossy compression of time-series data or other one-dimensional data streams (e.g., spectral data) that are arranged in blocks for sequential transmission. The algorithm was developed for use in transmitting data from spacecraft scientific instruments to Earth stations. In spite of its lossy nature, the algorithm preserves the information needed for scientific analysis. The algorithm is computationally simple, yet compresses data streams by factors much greater than two. The algorithm is not restricted to spacecraft or scientific uses: it is applicable to time-series data in general. The algorithm can also be applied to general multidimensional data that have been converted to time-series data, a typical example being image data acquired by raster scanning. However, unlike most prior image-data-compression algorithms, this algorithm neither depends on nor exploits the two-dimensional spatial correlations that are generally present in images. In order to understand the essence of this compression algorithm, it is necessary to understand that the net effect of this algorithm and the associated decompression algorithm is to approximate the original stream of data as a sequence of finite series of Chebyshev polynomials. For the purpose of this algorithm, a block of data or interval of time for which a Chebyshev polynomial series is fitted to the original data is denoted a fitting interval. Chebyshev approximation has two properties that make it particularly effective for compressing serial data streams with minimal loss of scientific information: The errors associated with a Chebyshev approximation are nearly uniformly distributed over the fitting interval (this is known in the art as the "equal error property"); and the maximum deviations of the fitted Chebyshev polynomial from the original data have the smallest possible values (this is known in the art as the "min-max property").

Learning polynomial feedforward neural networks by genetic programming and backpropagation.

PubMed

Nikolaev, N Y; Iba, H

2003-01-01

This paper presents an approach to learning polynomial feedforward neural networks (PFNNs). The approach suggests, first, finding the polynomial network structure by means of a population-based search technique relying on the genetic programming paradigm, and second, further adjustment of the best discovered network weights by an especially derived backpropagation algorithm for higher order networks with polynomial activation functions. These two stages of the PFNN learning process enable us to identify networks with good training as well as generalization performance. Empirical results show that this approach finds PFNN which outperform considerably some previous constructive polynomial network algorithms on processing benchmark time series.

Polynomial fuzzy observer designs: a sum-of-squares approach.

PubMed

Tanaka, Kazuo; Ohtake, Hiroshi; Seo, Toshiaki; Tanaka, Motoyasu; Wang, Hua O

2012-10-01

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space

PubMed Central

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. PMID:24603904

Monte Carlo based approach to the LS-NaI 4πβ-γ anticoincidence extrapolation and uncertainty

PubMed Central

Fitzgerald, R.

2016-01-01

The 4πβ-γ anticoincidence method is used for the primary standardization of β−, β+, electron capture (EC), α, and mixed-mode radionuclides. Efficiency extrapolation using one or more γ ray coincidence gates is typically carried out by a low-order polynomial fit. The approach presented here is to use a Geant4-based Monte Carlo simulation of the detector system to analyze the efficiency extrapolation. New code was developed to account for detector resolution, direct γ ray interaction with the PMT, and implementation of experimental β-decay shape factors. The simulation was tuned to 57Co and 60Co data, then tested with 99mTc data, and used in measurements of 18F, 129I, and 124I. The analysis method described here offers a more realistic activity value and uncertainty than those indicated from a least-squares fit alone. PMID:27358944

THEORETICAL p-MODE OSCILLATION FREQUENCIES FOR THE RAPIDLY ROTATING {delta} SCUTI STAR {alpha} OPHIUCHI

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

Deupree, Robert G., E-mail: bdeupree@ap.smu.ca

2011-11-20

A rotating, two-dimensional stellar model is evolved to match the approximate conditions of {alpha} Oph. Both axisymmetric and nonaxisymmetric oscillation frequencies are computed for two-dimensional rotating models which approximate the properties of {alpha} Oph. These computed frequencies are compared to the observed frequencies. Oscillation calculations are made assuming the eigenfunction can be fitted with six Legendre polynomials, but comparison calculations with eight Legendre polynomials show the frequencies agree to within about 0.26% on average. The surface horizontal shape of the eigenfunctions for the two sets of assumed number of Legendre polynomials agrees less well, but all calculations show significant departuresmore » from that of a single Legendre polynomial. It is still possible to determine the large separation, although the small separation is more complicated to estimate. With the addition of the nonaxisymmetric modes with |m| {<=} 4, the frequency space becomes sufficiently dense that it is difficult to comment on the adequacy of the fit of the computed to the observed frequencies. While the nonaxisymmetric frequency mode splitting is no longer uniform, the frequency difference between the frequencies for positive and negative values of the same m remains 2m times the rotation rate.« less

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Statistically generated weighted curve fit of residual functions for modal analysis of structures

NASA Technical Reports Server (NTRS)

Bookout, P. S.

1995-01-01

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure for modal testing large structures in an external constraint-free environment to measure the effects of higher order modes and interface stiffness. This test method is applicable to structures with distinct degree-of-freedom interfaces to other system components. A theoretical residual function in the displacement/force domain has the characteristics of a relatively flat line in the lower frequencies and a slight upward curvature in the higher frequency range. In the test residual function, the above-mentioned characteristics can be seen in the data, but due to the present limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of ragged data. A second order polynomial curve fit is required to obtain the residual flexibility term. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure. The residual flexibility modal test method is applied to a straight beam with a trunnion appendage and a space shuttle payload pallet simulator.

Parameter reduction in nonlinear state-space identification of hysteresis

NASA Astrophysics Data System (ADS)

Fakhrizadeh Esfahani, Alireza; Dreesen, Philippe; Tiels, Koen; Noël, Jean-Philippe; Schoukens, Johan

2018-05-01

Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50%, while maintaining a comparable output error level.

Comparison of Three Methods for Wind Turbine Capacity Factor Estimation

PubMed Central

Ditkovich, Y.; Kuperman, A.

2014-01-01

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first “quasiexact” approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second “analytic” approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third “approximate” approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation. PMID:24587755

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Improved Potential Energy Surface of Ozone Constructed Using the Fitting by Permutationally Invariant Polynomial Function

DOE PAGES

Ayouz, Mehdi; Babikov, Dmitri

2012-01-01

New global potential energy surface for the ground electronic state of ozone is constructed at the complete basis set level of the multireference configuration interaction theory. A method of fitting the data points by analytical permutationally invariant polynomial function is adopted. A small set of 500 points is preoptimized using the old surface of ozone. In this procedure the positions of points in the configuration space are chosen such that the RMS deviation of the fit is minimized. New ab initio calculations are carried out at these points and are used to build new surface. Additional points are added tomore » the vicinity of the minimum energy path in order to improve accuracy of the fit, particularly in the region where the surface of ozone exhibits a shallow van der Waals well. New surface can be used to study formation of ozone at thermal energies and its spectroscopy near the dissociation threshold.« less

betaFIT: A computer program to fit pointwise potentials to selected analytic functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.; Pashov, Asen

2017-01-01

This paper describes program betaFIT, which performs least-squares fits of sets of one-dimensional (or radial) potential function values to four different types of sophisticated analytic potential energy functional forms. These families of potential energy functions are: the Expanded Morse Oscillator (EMO) potential [J Mol Spectrosc 1999;194:197], the Morse/Long-Range (MLR) potential [Mol Phys 2007;105:663], the Double Exponential/Long-Range (DELR) potential [J Chem Phys 2003;119:7398], and the "Generalized Potential Energy Function (GPEF)" form introduced by Šurkus et al. [Chem Phys Lett 1984;105:291], which includes a wide variety of polynomial potentials, such as the Dunham [Phys Rev 1932;41:713], Simons-Parr-Finlan [J Chem Phys 1973;59:3229], and Ogilvie-Tipping [Proc R Soc A 1991;378:287] polynomials, as special cases. This code will be useful for providing the realistic sets of potential function shape parameters that are required to initiate direct fits of selected analytic potential functions to experimental data, and for providing better analytical representations of sets of ab initio results.

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials.

PubMed

Mota, L F M; Martins, P G M A; Littiere, T O; Abreu, L R A; Silva, M A; Bonafé, C M

2018-04-01

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.

Automatic bone outer contour extraction from B-modes ultrasound images based on local phase symmetry and quadratic polynomial fitting

NASA Astrophysics Data System (ADS)

Karlita, Tita; Yuniarno, Eko Mulyanto; Purnama, I. Ketut Eddy; Purnomo, Mauridhi Hery

2017-06-01

Analyzing ultrasound (US) images to get the shapes and structures of particular anatomical regions is an interesting field of study since US imaging is a non-invasive method to capture internal structures of a human body. However, bone segmentation of US images is still challenging because it is strongly influenced by speckle noises and it has poor image quality. This paper proposes a combination of local phase symmetry and quadratic polynomial fitting methods to extract bone outer contour (BOC) from two dimensional (2D) B-modes US image as initial steps of three-dimensional (3D) bone surface reconstruction. By using local phase symmetry, the bone is initially extracted from US images. BOC is then extracted by scanning one pixel on the bone boundary in each column of the US images using first phase features searching method. Quadratic polynomial fitting is utilized to refine and estimate the pixel location that fails to be detected during the extraction process. Hole filling method is then applied by utilize the polynomial coefficients to fill the gaps with new pixel. The proposed method is able to estimate the new pixel position and ensures smoothness and continuity of the contour path. Evaluations are done using cow and goat bones by comparing the resulted BOCs with the contours produced by manual segmentation and contours produced by canny edge detection. The evaluation shows that our proposed methods produces an excellent result with average MSE before and after hole filling at the value of 0.65.

Computational algebraic geometry for statistical modeling FY09Q2 progress.

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

Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre

2009-03-01

This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones inmore » more detail; the next section provides an overview of the project and how the current progress fits into it.« less

Modelling local GPS/levelling geoid undulations using artificial neural networks

NASA Astrophysics Data System (ADS)

Kavzoglu, T.; Saka, M. H.

2005-04-01

The use of GPS for establishing height control in an area where levelling data are available can involve the so-called GPS/levelling technique. Modelling of the GPS/levelling geoid undulations has usually been carried out using polynomial surface fitting, least-squares collocation (LSC) and finite-element methods. Artificial neural networks (ANNs) have recently been used for many investigations, and proven to be effective in solving complex problems represented by noisy and missing data. In this study, a feed-forward ANN structure, learning the characteristics of the training data through the back-propagation algorithm, is employed to model the local GPS/levelling geoid surface. The GPS/levelling geoid undulations for Istanbul, Turkey, were estimated from GPS and precise levelling measurements obtained during a field study in the period 1998-99. The results are compared to those produced by two well-known conventional methods, namely polynomial fitting and LSC, in terms of root mean square error (RMSE) that ranged from 3.97 to 5.73 cm. The results show that ANNs can produce results that are comparable to polynomial fitting and LSC. The main advantage of the ANN-based surfaces seems to be the low deviations from the GPS/levelling data surface, which is particularly important for distorted levelling networks.

bcc-to-hcp transformation pathways for iron versus hydrostatic pressure: Coupled shuffle and shear modes

NASA Astrophysics Data System (ADS)

Liu, J. B.; Johnson, D. D.

2009-04-01

Using density-functional theory, we calculate the potential-energy surface (PES), minimum-energy pathway (MEP), and transition state (TS) versus hydrostatic pressure σhyd for the reconstructive transformation in Fe from body-centered cubic (bcc) to hexagonal closed-packed (hcp). At fixed σhyd , the PES is described by coupled shear (γ) and shuffle (η) modes and is determined from structurally minimized hcp-bcc energy differences at a set of (η,γ) . We fit the PES using symmetry-adapted polynomials, permitting the MEP to be found analytically. The MEP is continuous and fully explains the transformation and its associated magnetization and volume discontinuity at TS. We show that σhyd (while not able to induce shear) dramatically alters the MEP to drive reconstruction by a shuffle-only mode at ≤30GPa , as observed. Finally, we relate our polynomial-based results to Landau and nudge-elastic-band approaches and show they yield incorrect MEP in general.

An Accurate Projector Calibration Method Based on Polynomial Distortion Representation

PubMed Central

Liu, Miao; Sun, Changku; Huang, Shujun; Zhang, Zonghua

2015-01-01

In structure light measurement systems or 3D printing systems, the errors caused by optical distortion of a digital projector always affect the precision performance and cannot be ignored. Existing methods to calibrate the projection distortion rely on calibration plate and photogrammetry, so the calibration performance is largely affected by the quality of the plate and the imaging system. This paper proposes a new projector calibration approach that makes use of photodiodes to directly detect the light emitted from a digital projector. By analyzing the output sequence of the photoelectric module, the pixel coordinates can be accurately obtained by the curve fitting method. A polynomial distortion representation is employed to reduce the residuals of the traditional distortion representation model. Experimental results and performance evaluation show that the proposed calibration method is able to avoid most of the disadvantages in traditional methods and achieves a higher accuracy. This proposed method is also practically applicable to evaluate the geometric optical performance of other optical projection system. PMID:26492247

SU-E-J-85: Leave-One-Out Perturbation (LOOP) Fitting Algorithm for Absolute Dose Film Calibration

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

Chu, A; Ahmad, M; Chen, Z

2014-06-01

Purpose: To introduce an outliers-recognition fitting routine for film dosimetry. It cannot only be flexible with any linear and non-linear regression but also can provide information for the minimal number of sampling points, critical sampling distributions and evaluating analytical functions for absolute film-dose calibration. Methods: The technique, leave-one-out (LOO) cross validation, is often used for statistical analyses on model performance. We used LOO analyses with perturbed bootstrap fitting called leave-one-out perturbation (LOOP) for film-dose calibration . Given a threshold, the LOO process detects unfit points (“outliers”) compared to other cohorts, and a bootstrap fitting process follows to seek any possibilitiesmore » of using perturbations for further improvement. After that outliers were reconfirmed by a traditional t-test statistics and eliminated, then another LOOP feedback resulted in the final. An over-sampled film-dose- calibration dataset was collected as a reference (dose range: 0-800cGy), and various simulated conditions for outliers and sampling distributions were derived from the reference. Comparisons over the various conditions were made, and the performance of fitting functions, polynomial and rational functions, were evaluated. Results: (1) LOOP can prove its sensitive outlier-recognition by its statistical correlation to an exceptional better goodness-of-fit as outliers being left-out. (2) With sufficient statistical information, the LOOP can correct outliers under some low-sampling conditions that other “robust fits”, e.g. Least Absolute Residuals, cannot. (3) Complete cross-validated analyses of LOOP indicate that the function of rational type demonstrates a much superior performance compared to the polynomial. Even with 5 data points including one outlier, using LOOP with rational function can restore more than a 95% value back to its reference values, while the polynomial fitting completely failed under the same conditions. Conclusion: LOOP can cooperate with any fitting routine functioning as a “robust fit”. In addition, it can be set as a benchmark for film-dose calibration fitting performance.« less

Stitching interferometry of a full cylinder without using overlap areas

NASA Astrophysics Data System (ADS)

Peng, Junzheng; Chen, Dingfu; Yu, Yingjie

2017-08-01

Traditional stitching interferometry requires finding out the overlap correspondence and computing the discrepancies in the overlap regions, which makes it complex and time-consuming to obtain the 360° form map of a cylinder. In this paper, we develop a cylinder stitching model based on a new set of orthogonal polynomials, termed Legendre Fourier (LF) polynomials. With these polynomials, individual subaperture data can be expanded as a composition of the inherent form of a partial cylinder surface and additional misalignment parameters. Then the 360° form map can be acquired by simultaneously fitting all subaperture data with the LF polynomials. A metal shaft was measured to experimentally verify the proposed method. In contrast to traditional stitching interferometry, our technique does not require overlapping of adjacent subapertures, thus significantly reducing the measurement time and making the stitching algorithm simple.

Polynomial approximations of thermodynamic properties of arbitrary gas mixtures over wide pressure and density ranges

NASA Technical Reports Server (NTRS)

Allison, D. O.

1972-01-01

Computer programs for flow fields around planetary entry vehicles require real-gas equilibrium thermodynamic properties in a simple form which can be evaluated quickly. To fill this need, polynomial approximations were found for thermodynamic properties of air and model planetary atmospheres. A coefficient-averaging technique was used for curve fitting in lieu of the usual least-squares method. The polynomials consist of terms up to the ninth degree in each of two variables (essentially pressure and density) including all cross terms. Four of these polynomials can be joined to cover, for example, a range of about 1000 to 11000 K and 0.00001 to 1 atmosphere (1 atm = 1.0133 x 100,000 N/m sq) for a given thermodynamic property. Relative errors of less than 1 percent are found over most of the applicable range.

Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

NASA Astrophysics Data System (ADS)

Sikora, Roman; Markiewicz, Przemysław; Pabjańczyk, Wiesława

2018-04-01

The power systems usually include a number of nonlinear receivers. Nonlinear receivers are the source of disturbances generated to the power system in the form of higher harmonics. The level of these disturbances describes the total harmonic distortion coefficient THD. Its value depends on many factors. One of them are the deformation and change in RMS value of supply voltage. A modern LED luminaire is a nonlinear receiver as well. The paper presents the results of the analysis of the influence of change in RMS value of supply voltage and the level of dimming of the tested luminaire on the value of the current THD. The analysis was made using a mathematical model based on multivariable polynomial fitting.

A New Navigation Satellite Clock Bias Prediction Method Based on Modified Clock-bias Quadratic Polynomial Model

NASA Astrophysics Data System (ADS)

Wang, Y. P.; Lu, Z. P.; Sun, D. S.; Wang, N.

2016-01-01

In order to better express the characteristics of satellite clock bias (SCB) and improve SCB prediction precision, this paper proposed a new SCB prediction model which can take physical characteristics of space-borne atomic clock, the cyclic variation, and random part of SCB into consideration. First, the new model employs a quadratic polynomial model with periodic items to fit and extract the trend term and cyclic term of SCB; then based on the characteristics of fitting residuals, a time series ARIMA ~(Auto-Regressive Integrated Moving Average) model is used to model the residuals; eventually, the results from the two models are combined to obtain final SCB prediction values. At last, this paper uses precise SCB data from IGS (International GNSS Service) to conduct prediction tests, and the results show that the proposed model is effective and has better prediction performance compared with the quadratic polynomial model, grey model, and ARIMA model. In addition, the new method can also overcome the insufficiency of the ARIMA model in model recognition and order determination.

On-Ground Processing of Yaogan-24 Remote Sensing Satellite Attitude Data and Verification Using Geometric Field Calibration

PubMed Central

Wang, Mi; Fan, Chengcheng; Yang, Bo; Jin, Shuying; Pan, Jun

2016-01-01

Satellite attitude accuracy is an important factor affecting the geometric processing accuracy of high-resolution optical satellite imagery. To address the problem whereby the accuracy of the Yaogan-24 remote sensing satellite’s on-board attitude data processing is not high enough and thus cannot meet its image geometry processing requirements, we developed an approach involving on-ground attitude data processing and digital orthophoto (DOM) and the digital elevation model (DEM) verification of a geometric calibration field. The approach focuses on three modules: on-ground processing based on bidirectional filter, overall weighted smoothing and fitting, and evaluation in the geometric calibration field. Our experimental results demonstrate that the proposed on-ground processing method is both robust and feasible, which ensures the reliability of the observation data quality, convergence and stability of the parameter estimation model. In addition, both the Euler angle and quaternion could be used to build a mathematical fitting model, while the orthogonal polynomial fitting model is more suitable for modeling the attitude parameter. Furthermore, compared to the image geometric processing results based on on-board attitude data, the image uncontrolled and relative geometric positioning result accuracy can be increased by about 50%. PMID:27483287

Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

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

PubMed

Deboeck, Pascal R

2010-08-06

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common approach for estimating derivatives, Local Linear Approximation (LLA), produces estimates with correlated errors. Depending on the specific differential equation model used, such correlated errors can lead to severely biased estimates of differential equation model parameters. This article shows that the fitting of dynamical systems can be improved by estimating derivatives in a manner similar to that used to fit orthogonal polynomials. Two applications using simulated data compare the proposed method and a generalized form of LLA when used to estimate derivatives and when used to estimate differential equation model parameters. A third application estimates the frequency of oscillation in observations of the monthly deaths from bronchitis, emphysema, and asthma in the United Kingdom. These data are publicly available in the statistical program R, and functions in R for the method presented are provided.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

More irregular eye shape in low myopia than in emmetropia.

PubMed

Tabernero, Juan; Schaeffel, Frank

2009-09-01

To improve the description of the peripheral eye shape in myopia and emmetropia by using a new method for continuous measurement of the peripheral refractive state. A scanning photorefractor was designed to record refractive errors in the vertical pupil meridian across the horizontal visual field (up to +/-45 degrees ). The setup consists of a hot mirror that continuously projects the infrared light from a photoretinoscope under different angles of eccentricity into the eye. The movement of the mirror is controlled by using two stepping motors. Refraction in a group of 17 emmetropic subjects and 11 myopic subjects (mean, -4.3 D; SD, 1.7) was measured without spectacle correction. For the analysis of eye shape, the refractive error versus the eccentricity angles was fitted with different polynomials (from second to tenth order). The new setup presents some important advantages over previous techniques: The subject does not have to change gaze during the measurements, and a continuous profile is obtained rather than discrete points. There was a significant difference in the fitting errors between the subjects with myopia and those with emmetropia. Tenth-order polynomials were required in myopic subjects to achieve a quality of fit similar to that in emmetropic subjects fitted with only sixth-order polynomials. Apparently, the peripheral shape of the myopic eye is more "bumpy." A new setup is presented for obtaining continuous peripheral refraction profiles. It was found that the peripheral retinal shape is more irregular even in only moderately myopic eyes, perhaps because the sclera lost some rigidity even at the early stage of myopia.

Error reduction in three-dimensional metrology combining optical and touch probe data

NASA Astrophysics Data System (ADS)

Gerde, Janice R.; Christens-Barry, William A.

2010-08-01

Analysis of footwear under the Harmonized Tariff Schedule of the United States (HTSUS) is partly based on identifying the boundary ("parting line") between the "external surface area upper" (ESAU) and the sample's sole. Often, that boundary is obscured. We establish the parting line as the curved intersection between the sample outer surface and its insole surface. The outer surface is determined by discrete point cloud coordinates obtained using a laser scanner. The insole surface is defined by point cloud data, obtained using a touch probe device-a coordinate measuring machine (CMM). Because these point cloud data sets do not overlap spatially, a polynomial surface is fitted to the insole data and extended to intersect a mesh fitted to the outer surface point cloud. This line of intersection defines the ESAU boundary, permitting further fractional area calculations to proceed. The defined parting line location is sensitive to the polynomial used to fit experimental data. Extrapolation to the intersection with the ESAU can heighten this sensitivity. We discuss a methodology for transforming these data into a common reference frame. Three scenarios are considered: measurement error in point cloud coordinates, from fitting a polynomial surface to a point cloud then extrapolating beyond the data set, and error from reference frame transformation. These error sources can influence calculated surface areas. We describe experiments to assess error magnitude, the sensitivity of calculated results on these errors, and minimizing error impact on calculated quantities. Ultimately, we must ensure that statistical error from these procedures is minimized and within acceptance criteria.

Venus radar mapper attitude reference quaternion

NASA Technical Reports Server (NTRS)

Lyons, D. T.

1986-01-01

Polynomial functions of time are used to specify the components of the quaternion which represents the nominal attitude of the Venus Radar mapper spacecraft during mapping. The following constraints must be satisfied in order to obtain acceptable synthetic array radar data: the nominal attitude function must have a large dynamic range, the sensor orientation must be known very accurately, the attitude reference function must use as little memory as possible, and the spacecraft must operate autonomously. Fitting polynomials to the components of the desired quaternion function is a straightforward method for providing a very dynamic nominal attitude using a minimum amount of on-board computer resources. Although the attitude from the polynomials may not be exactly the one requested by the radar designers, the polynomial coefficients are known, so they do not contribute to the attitude uncertainty. Frequent coefficient updates are not required, so the spacecraft can operate autonomously.

Ultrawideband temperature-dependent dielectric properties of animal liver tissue in the microwave frequency range.

PubMed

Lazebnik, Mariya; Converse, Mark C; Booske, John H; Hagness, Susan C

2006-04-07

The development of ultrawideband (UWB) microwave diagnostic and therapeutic technologies, such as UWB microwave breast cancer detection and hyperthermia treatment, is facilitated by accurate knowledge of the temperature- and frequency-dependent dielectric properties of biological tissues. To this end, we characterize the temperature-dependent dielectric properties of a representative tissue type-animal liver-from 0.5 to 20 GHz. Since discrete-frequency linear temperature coefficients are impractical and inappropriate for applications spanning wide frequency and temperature ranges, we propose a novel and compact data representation technique. A single-pole Cole-Cole model is used to fit the dielectric properties data as a function of frequency, and a second-order polynomial is used to fit the Cole-Cole parameters as a function of temperature. This approach permits rapid estimation of tissue dielectric properties at any temperature and frequency.

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Making a georeferenced mosaic of historical map series using constrained polynomial fit

NASA Astrophysics Data System (ADS)

Molnár, G.

2009-04-01

Present day GIS software packages make it possible to handle several hundreds of rasterised map sheets. For proper usage of such datasets we usually have two requirements: First these map sheets should be georeferenced, secondly these georeferenced maps should fit properly together, without overlap and short. Both requirements can be fulfilled easily, if the geodetic background for the map series is accurate, and the projection of the map series is known. In this case the individual map sheets should be georeferenced in the projected coordinate system of the map series. This means every individual map sheets are georeferenced using overprinted coordinate grid or image corner projected coordinates as ground control points (GCPs). If after this georeferencing procedure the map sheets do not fit together (for example because of using different projection for every map sheet, as it is in the case of Third Military Survey) a common projection can be chosen, and all the georeferenced maps should be transformed to this common projection using a map-to-map transformation. If the geodetic background is not so strong, ie. there are distortions inside the map sheets, a polynomial (linear quadratic or cubic) polynomial fit can be used for georeferencing the map sheets. Finding identical surface objects (as GCPs) on the historical map and on a present day cartographic map, let us to determine a transformation between raw image coordinates (x,y) and the projected coordinates (Easting, Northing, E,N). This means, for all the map sheets, several GCPs should be found, (for linear, quadratic of cubic transformations at least 3, 5 or 10 respectively) and every map sheets should be transformed to a present day coordinate system individually using these GCPs. The disadvantage of this method is that, after the transformation, the individual transformed map sheets not necessarily fit together properly any more. To overcome this problem neither the reverse order of procedure helps: if we make the mosaic first (eg. graphically) and we try the polynomial fit of this mosaic afterwards, neither using this can we reduce the error of internal inaccuracy of the map-sheets. We can overcome this problem by calculating the transformation parameters of polynomial fit with constrains (Mikhail, 1976). The constrain is that the common edge of two neighboring map-sheets should be transformed identically, ie. the right edge of the left image and the left edge of the right image should fit together after the transformation. This condition should fulfill for all the internal (not only the vertical, but also for the horizontal) edges of the mosaic. Constrains are expressed as a relationship between parameters: The parameters of the polynomial transformation should fulfill not only the least squares adjustment criteria but also the constrain: the transformed coordinates should be identical on the image edges. (With the example mentioned above, for image points of the rightmost column of the left image the transformed coordinates should be the same a for the image points of the leftmost column of the right image, and these transformed coordinates can depend on the line number image coordinate of the raster point.) The normal equation system can be calculated with Lagrange-multipliers. The resulting set of parameters for all map-sheets should be applied on the transformation of the images. This parameter set can not been directly applied in GIS software for the transformation. The simplest solution applying this parameters is ‘simulating' GCPs for every image, and applying these simulated GCPs for the georeferencing of the individual map sheets. This method is applied on a set of map-sheets of the First military Survey of the Habsburg Empire with acceptable results. Reference: Mikhail, E. M.: Observations and Least Squares. IEP—A Dun-Donnelley Publisher, New York, 1976. 497 pp.

Polynomial coefficients for calculating O2 Schumann-Runge cross sections at 0.5/cm resolution

NASA Technical Reports Server (NTRS)

Minschwaner, K.; Anderson, G. P.; Hall, L. A.; Yoshino, K.

1992-01-01

O2 cross sections from 49,000 to 57,000/cm have been fitted with temperature dependent polynomial expressions, providing an accurate and efficient means of determining Schumann-Runge band cross sections for temperatures between 130 and 500 K. The least squares fits were carried out on a 0.5/cm spectral grid, using cross sections obtained from a Schumann-Runge line-by-line model that incorporates the most recent spectroscopic data. The O2 cross sections do not include the underlying Herzberg continuum, but they do contain contributions from the temperature dependent Schumann-Runge continuum. The cross sections are suitable for use in UV transmission calculations at high spectral resolution. They should also prove useful for updating existing parameterizations of ultraviolet transmission and O2 photolysis.

Roots of polynomials by ratio of successive derivatives

NASA Technical Reports Server (NTRS)

Crouse, J. E.; Putt, C. W.

1972-01-01

An order of magnitude study of the ratios of successive polynomial derivatives yields information about the number of roots at an approached root point and the approximate location of a root point from a nearby point. The location approximation improves as a root is approached, so a powerful convergence procedure becomes available. These principles are developed into a computer program which finds the roots of polynomials with real number coefficients.

Influence of surface error on electromagnetic performance of reflectors based on Zernike polynomials

NASA Astrophysics Data System (ADS)

Li, Tuanjie; Shi, Jiachen; Tang, Yaqiong

2018-04-01

This paper investigates the influence of surface error distribution on the electromagnetic performance of antennas. The normalized Zernike polynomials are used to describe a smooth and continuous deformation surface. Based on the geometrical optics and piecewise linear fitting method, the electrical performance of reflector described by the Zernike polynomials is derived to reveal the relationship between surface error distribution and electromagnetic performance. Then the relation database between surface figure and electric performance is built for ideal and deformed surfaces to realize rapidly calculation of far-field electric performances. The simulation analysis of the influence of Zernike polynomials on the electrical properties for the axis-symmetrical reflector with the axial mode helical antenna as feed is further conducted to verify the correctness of the proposed method. Finally, the influence rules of surface error distribution on electromagnetic performance are summarized. The simulation results show that some terms of Zernike polynomials may decrease the amplitude of main lobe of antenna pattern, and some may reduce the pointing accuracy. This work extracts a new concept for reflector's shape adjustment in manufacturing process.

Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach.

PubMed

Tanaka, Kazuo; Ohtake, Hiroshi; Wang, Hua O

2009-04-01

This paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi-Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach.

Polynomial dual energy inverse functions for bone Calcium/Phosphorus ratio determination and experimental evaluation.

PubMed

Sotiropoulou, P; Fountos, G; Martini, N; Koukou, V; Michail, C; Kandarakis, I; Nikiforidis, G

2016-12-01

An X-ray dual energy (XRDE) method was examined, using polynomial nonlinear approximation of inverse functions for the determination of the bone Calcium-to-Phosphorus (Ca/P) mass ratio. Inverse fitting functions with the least-squares estimation were used, to determine calcium and phosphate thicknesses. The method was verified by measuring test bone phantoms with a dedicated dual energy system and compared with previously published dual energy data. The accuracy in the determination of the calcium and phosphate thicknesses improved with the polynomial nonlinear inverse function method, introduced in this work, (ranged from 1.4% to 6.2%), compared to the corresponding linear inverse function method (ranged from 1.4% to 19.5%). Copyright © 2016 Elsevier Ltd. All rights reserved.

Mathematics of Zernike polynomials: a review.

PubMed

McAlinden, Colm; McCartney, Mark; Moore, Jonathan

2011-11-01

Monochromatic aberrations of the eye principally originate from the cornea and the crystalline lens. Aberrometers operate via differing principles but function by either analysing the reflected wavefront from the retina or by analysing an image on the retina. Aberrations may be described as lower order or higher order aberrations with Zernike polynomials being the most commonly employed fitting method. The complex mathematical aspects with regards the Zernike polynomial expansion series are detailed in this review. Refractive surgery has been a key clinical application of aberrometers; however, more recently aberrometers have been used in a range of other areas ophthalmology including corneal diseases, cataract and retinal imaging. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

Empirical performance of interpolation techniques in risk-neutral density (RND) estimation

NASA Astrophysics Data System (ADS)

Bahaludin, H.; Abdullah, M. H.

2017-03-01

The objective of this study is to evaluate the empirical performance of interpolation techniques in risk-neutral density (RND) estimation. Firstly, the empirical performance is evaluated by using statistical analysis based on the implied mean and the implied variance of RND. Secondly, the interpolation performance is measured based on pricing error. We propose using the leave-one-out cross-validation (LOOCV) pricing error for interpolation selection purposes. The statistical analyses indicate that there are statistical differences between the interpolation techniques:second-order polynomial, fourth-order polynomial and smoothing spline. The results of LOOCV pricing error shows that interpolation by using fourth-order polynomial provides the best fitting to option prices in which it has the lowest value error.

OMFIT Tokamak Profile Data Fitting and Physics Analysis

DOE PAGES

Logan, N. C.; Grierson, B. A.; Haskey, S. R.; ...

2018-01-22

Here, One Modeling Framework for Integrated Tasks (OMFIT) has been used to develop a consistent tool for interfacing with, mapping, visualizing, and fitting tokamak profile measurements. OMFIT is used to integrate the many diverse diagnostics on multiple tokamak devices into a regular data structure, consistently applying spatial and temporal treatments to each channel of data. Tokamak data are fundamentally time dependent and are treated so from the start, with front-loaded and logic-based manipulations such as filtering based on the identification of edge-localized modes (ELMs) that commonly scatter data. Fitting is general in its approach, and tailorable in its application inmore » order to address physics constraints and handle the multiple spatial and temporal scales involved. Although community standard one-dimensional fitting is supported, including scale length–fitting and fitting polynomial-exponential blends to capture the H-mode pedestal, OMFITprofiles includes two-dimensional (2-D) fitting using bivariate splines or radial basis functions. These 2-D fits produce regular evolutions in time, removing jitter that has historically been smoothed ad hoc in transport applications. Profiles interface directly with a wide variety of models within the OMFIT framework, providing the inputs for TRANSP, kinetic-EFIT 2-D equilibrium, and GPEC three-dimensional equilibrium calculations. he OMFITprofiles tool’s rapid and comprehensive analysis of dynamic plasma profiles thus provides the critical link between raw tokamak data and simulations necessary for physics understanding.« less

OMFIT Tokamak Profile Data Fitting and Physics Analysis

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

Logan, N. C.; Grierson, B. A.; Haskey, S. R.

Here, One Modeling Framework for Integrated Tasks (OMFIT) has been used to develop a consistent tool for interfacing with, mapping, visualizing, and fitting tokamak profile measurements. OMFIT is used to integrate the many diverse diagnostics on multiple tokamak devices into a regular data structure, consistently applying spatial and temporal treatments to each channel of data. Tokamak data are fundamentally time dependent and are treated so from the start, with front-loaded and logic-based manipulations such as filtering based on the identification of edge-localized modes (ELMs) that commonly scatter data. Fitting is general in its approach, and tailorable in its application inmore » order to address physics constraints and handle the multiple spatial and temporal scales involved. Although community standard one-dimensional fitting is supported, including scale length–fitting and fitting polynomial-exponential blends to capture the H-mode pedestal, OMFITprofiles includes two-dimensional (2-D) fitting using bivariate splines or radial basis functions. These 2-D fits produce regular evolutions in time, removing jitter that has historically been smoothed ad hoc in transport applications. Profiles interface directly with a wide variety of models within the OMFIT framework, providing the inputs for TRANSP, kinetic-EFIT 2-D equilibrium, and GPEC three-dimensional equilibrium calculations. he OMFITprofiles tool’s rapid and comprehensive analysis of dynamic plasma profiles thus provides the critical link between raw tokamak data and simulations necessary for physics understanding.« less

A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

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

Kersaudy, Pierric, E-mail: pierric.kersaudy@orange.com; Whist Lab, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux; ESYCOM, Université Paris-Est Marne-la-Vallée, 5 boulevard Descartes, 77700 Marne-la-Vallée

2015-04-01

In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representationmore » of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.« less

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

DOE PAGES

Xu, Yongfeng F.; Zhu, Weidong D.; Smith, Scott A.

2017-07-01

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamagedmore » one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.« less

Non-model-based damage identification of plates using principal, mean and Gaussian curvature mode shapes

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

Xu, Yongfeng F.; Zhu, Weidong D.; Smith, Scott A.

Mode shapes (MSs) have been extensively used to identify structural damage. This paper presents a new non-model-based method that uses principal, mean and Gaussian curvature MSs (CMSs) to identify damage in plates; the method is applicable and robust to MSs associated with low and high elastic modes on dense and coarse measurement grids. A multi-scale discrete differential-geometry scheme is proposed to calculate principal, mean and Gaussian CMSs associated with a MS of a plate, which can alleviate adverse effects of measurement noise on calculating the CMSs. Principal, mean and Gaussian CMSs of a damaged plate and those of an undamagedmore » one are used to yield four curvature damage indices (CDIs), including Maximum-CDIs, Minimum-CDIs, Mean-CDIs and Gaussian-CDIs. Damage can be identified near regions with consistently higher values of the CDIs. It is shown that a MS of an undamaged plate can be well approximated using a polynomial with a properly determined order that fits a MS of a damaged one, provided that the undamaged plate has a smooth geometry and is made of material that has no stiffness and mass discontinuities. New fitting and convergence indices are proposed to quantify the level of approximation of a MS from a polynomial fit to that of a damaged plate and to determine the proper order of the polynomial fit, respectively. A MS of an aluminum plate with damage in the form of a machined thickness reduction area was measured to experimentally investigate the effectiveness of the proposed CDIs in damage identification; the damage on the plate was successfully identified.« less

Comparison of yellow poplar growth models on the basis of derived growth analysis variables

Treesearch

Keith F. Jensen; Daniel A. Yaussy

1986-01-01

Quadratic and cubic polynomials, and Gompertz and Richards asymptotic models were fitted to yellow poplar growth data. These data included height, leaf area, leaf weight and new shoot height for 23 weeks. Seven growth analysis variables were estimated from each function. The Gompertz and Richards models fitted the data best and provided the most accurate derived...

A GENERAL ALGORITHM FOR THE CONSTRUCTION OF CONTOUR PLOTS

NASA Technical Reports Server (NTRS)

Johnson, W.

1994-01-01

The graphical presentation of experimentally or theoretically generated data sets frequently involves the construction of contour plots. A general computer algorithm has been developed for the construction of contour plots. The algorithm provides for efficient and accurate contouring with a modular approach which allows flexibility in modifying the algorithm for special applications. The algorithm accepts as input data values at a set of points irregularly distributed over a plane. The algorithm is based on an interpolation scheme in which the points in the plane are connected by straight line segments to form a set of triangles. In general, the data is smoothed using a least-squares-error fit of the data to a bivariate polynomial. To construct the contours, interpolation along the edges of the triangles is performed, using the bivariable polynomial if data smoothing was performed. Once the contour points have been located, the contour may be drawn. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 series computer with a central memory requirement of approximately 100K of 8-bit bytes. This computer algorithm was developed in 1981.

Fish biomarkers for environmental monitoring: An integrated model supporting enzyme activity and histopathological lesions

NASA Astrophysics Data System (ADS)

Neta, Raimunda Nonata Fortes Carvalho; Torres Junior, Audalio Rebelo

2014-10-01

We present a mathematical model describing the association between glutathione-S-transferase activity and brachial lesions in the catfish, Sciades herzbergii (Ariidae) from a polluted port. The catfish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Brazil. Two biomarkers, hepatic glutathione S-transferase (GST) activity and histopathological lesions, in gills tissue were measured. The values for GST activity were modeled with the occurrence of branchial lesions by fitting a third order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial lesions in both the wet and the dry seasons, but only at the polluted port site. The model developed in this study indicates that branchial and hepatic lesions are initiated when GST activity reaches 2.15 μmol min-1 mg protein-1. Beyond this limit, GST activity decreased to very low levels and irreversible histopathological lesions occurred. This mathematical model provides a realistic approach to analyze predictive biomarkers of environmental health status.

Precision analysis of autonomous orbit determination using star sensor for Beidou MEO satellite

NASA Astrophysics Data System (ADS)

Shang, Lin; Chang, Jiachao; Zhang, Jun; Li, Guotong

2018-04-01

This paper focuses on the autonomous orbit determination accuracy of Beidou MEO satellite using the onboard observations of the star sensors and infrared horizon sensor. A polynomial fitting method is proposed to calibrate the periodic error in the observation of the infrared horizon sensor, which will greatly influence the accuracy of autonomous orbit determination. Test results show that the periodic error can be eliminated using the polynomial fitting method. The User Range Error (URE) of Beidou MEO satellite is less than 2 km using the observations of the star sensors and infrared horizon sensor for autonomous orbit determination. The error of the Right Ascension of Ascending Node (RAAN) is less than 60 μrad and the observations of star sensors can be used as a spatial basis for Beidou MEO navigation constellation.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

Online Removal of Baseline Shift with a Polynomial Function for Hemodynamic Monitoring Using Near-Infrared Spectroscopy.

PubMed

Zhao, Ke; Ji, Yaoyao; Li, Yan; Li, Ting

2018-01-21

Near-infrared spectroscopy (NIRS) has become widely accepted as a valuable tool for noninvasively monitoring hemodynamics for clinical and diagnostic purposes. Baseline shift has attracted great attention in the field, but there has been little quantitative study on baseline removal. Here, we aimed to study the baseline characteristics of an in-house-built portable medical NIRS device over a long time (>3.5 h). We found that the measured baselines all formed perfect polynomial functions on phantom tests mimicking human bodies, which were identified by recent NIRS studies. More importantly, our study shows that the fourth-order polynomial function acted to distinguish performance with stable and low-computation-burden fitting calibration (R-square >0.99 for all probes) among second- to sixth-order polynomials, evaluated by the parameters R-square, sum of squares due to error, and residual. This study provides a straightforward, efficient, and quantitatively evaluated solution for online baseline removal for hemodynamic monitoring using NIRS devices.

The Ponzano-Regge Model and Parametric Representation

NASA Astrophysics Data System (ADS)

Li, Dan

2014-04-01

We give a parametric representation of the effective noncommutative field theory derived from a -deformation of the Ponzano-Regge model and define a generalized Kirchhoff polynomial with -correction terms, obtained in a -linear approximation. We then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature. We look in particular at the tetrahedron graph, which is the basic case of relevance to quantum gravity. With the help of computer calculations, we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients, hence the hypersurface of the tetrahedron is not polynomially countable. This shows that the correction term can change significantly the motivic properties of the hypersurfaces, with respect to the classical case.

Person-city personality fit and entrepreneurial success: An explorative study in China.

PubMed

Zhou, Mingjie; Zhou, Yixin; Zhang, Jianxin; Obschonka, Martin; Silbereisen, Rainer K

2017-08-13

While the study of personality differences is a traditional psychological approach in entrepreneurship research, economic research directs attention towards the entrepreneurial ecosystems in which entrepreneurial activity are embedded. We combine both approaches and quantify the interplay between the individual personality make-up of entrepreneurs and the local personality composition of ecosystems, with a special focus on person-city personality fit. Specifically, we analyse personality data from N = 26,405 Chinese residents across 42 major Chinese cities, including N = 1091 Chinese entrepreneurs. Multi-level polynomial regression and response surface plots revealed that: (a) individual-level conscientiousness had a positive effect and individual-level agreeableness and neuroticism had a negative effect on entrepreneurial success, (b) city-level conscientiousness had a positive, and city-level neuroticism had a negative effect on entrepreneurial success, and (c) additional person-city personality fit effects existed for agreeableness, conscientiousness and neuroticism. For example, entrepreneurs who are high in agreeableness and conduct their business in a city with a low agreeableness level show the lowest entrepreneurial success. In contrast, entrepreneurs who are low in agreeableness and conduct their business in a city with a high agreeableness level show relatively high entrepreneurial success. Implications for research and practice are discussed. © 2017 International Union of Psychological Science.

Quantum algorithm for linear regression

NASA Astrophysics Data System (ADS)

Wang, Guoming

2017-07-01

We present a quantum algorithm for fitting a linear regression model to a given data set using the least-squares approach. Differently from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at little cost. Moreover, our algorithm works in the standard oracle model, and can handle data sets with nonsparse design matrices. It runs in time poly( log2(N ) ,d ,κ ,1 /ɛ ) , where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and ɛ is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit (without computing its parameters explicitly). This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Polynomial expressions of electron depth dose as a function of energy in various materials: application to thermoluminescence (TL) dosimetry

NASA Astrophysics Data System (ADS)

Deogracias, E. C.; Wood, J. L.; Wagner, E. C.; Kearfott, K. J.

1999-02-01

The CEPXS/ONEDANT code package was used to produce a library of depth-dose profiles for monoenergetic electrons in various materials for energies ranging from 500 keV to 5 MeV in 10 keV increments. The various materials for which depth-dose functions were derived include: lithium fluoride (LiF), aluminum oxide (Al 2O 3), beryllium oxide (BeO), calcium sulfate (CaSO 4), calcium fluoride (CaF 2), lithium boron oxide (LiBO), soft tissue, lens of the eye, adiopose, muscle, skin, glass and water. All materials data sets were fit to five polynomials, each covering a different range of electron energies, using a least squares method. The resultant three dimensional, fifth-order polynomials give the dose as a function of depth and energy for the monoenergetic electrons in each material. The polynomials can be used to describe an energy spectrum by summing the doses at a given depth for each energy, weighted by the spectral intensity for that energy. An application of the polynomial is demonstrated by explaining the energy dependence of thermoluminescent detectors (TLDs) and illustrating the relationship between TLD signal and actual shallow dose due to beta particles.

Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

NASA Astrophysics Data System (ADS)

Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

2018-05-01

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

Design of polynomial fuzzy observer-controller for nonlinear systems with state delay: sum of squares approach

NASA Astrophysics Data System (ADS)

Gassara, H.; El Hajjaji, A.; Chaabane, M.

2017-07-01

This paper investigates the problem of observer-based control for two classes of polynomial fuzzy systems with time-varying delay. The first class concerns a special case where the polynomial matrices do not depend on the estimated state variables. The second one is the general case where the polynomial matrices could depend on unmeasurable system states that will be estimated. For the last case, two design procedures are proposed. The first one gives the polynomial fuzzy controller and observer gains in two steps. In the second procedure, the designed gains are obtained using a single-step approach to overcome the drawback of a two-step procedure. The obtained conditions are presented in terms of sum of squares (SOS) which can be solved via the SOSTOOLS and a semi-definite program solver. Illustrative examples show the validity and applicability of the proposed results.

Growth curves for ostriches (Struthio camelus) in a Brazilian population.

PubMed

Ramos, S B; Caetano, S L; Savegnago, R P; Nunes, B N; Ramos, A A; Munari, D P

2013-01-01

The objective of this study was to fit growth curves using nonlinear and linear functions to describe the growth of ostriches in a Brazilian population. The data set consisted of 112 animals with BW measurements from hatching to 383 d of age. Two nonlinear growth functions (Gompertz and logistic) and a third-order polynomial function were applied. The parameters for the models were estimated using the least-squares method and Gauss-Newton algorithm. The goodness-of-fit of the models was assessed using R(2) and the Akaike information criterion. The R(2) calculated for the logistic growth model was 0.945 for hens and 0.928 for cockerels and for the Gompertz growth model, 0.938 for hens and 0.924 for cockerels. The third-order polynomial fit gave R(2) of 0.938 for hens and 0.924 for cockerels. Among the Akaike information criterion calculations, the logistic growth model presented the lowest values in this study, both for hens and for cockerels. Nonlinear models are more appropriate for describing the sigmoid nature of ostrich growth.

An accurate surface topography restoration algorithm for white light interferometry

NASA Astrophysics Data System (ADS)

Yuan, He; Zhang, Xiangchao; Xu, Min

2017-10-01

As an important measuring technique, white light interferometry can realize fast and non-contact measurement, thus it is now widely used in the field of ultra-precision engineering. However, the traditional recovery algorithms of surface topographies have flaws and limits. In this paper, we propose a new algorithm to solve these problems. It is a combination of Fourier transform and improved polynomial fitting method. Because the white light interference signal is usually expressed as a cosine signal whose amplitude is modulated by a Gaussian function, its fringe visibility is not constant and varies with different scanning positions. The interference signal is processed first by Fourier transform, then the positive frequency part is selected and moved back to the center of the amplitude-frequency curve. In order to restore the surface morphology, a polynomial fitting method is used to fit the amplitude curve after inverse Fourier transform and obtain the corresponding topography information. The new method is then compared to the traditional algorithms. It is proved that the aforementioned drawbacks can be effectively overcome. The relative error is less than 0.8%.

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Leak Isolation in Pressurized Pipelines using an Interpolation Function to approximate the Fitting Losses

NASA Astrophysics Data System (ADS)

Badillo-Olvera, A.; Begovich, O.; Peréz-González, A.

2017-01-01

The present paper is motivated by the purpose of detection and isolation of a single leak considering the Fault Model Approach (FMA) focused on pipelines with changes in their geometry. These changes generate a different pressure drop that those produced by the friction, this phenomenon is a common scenario in real pipeline systems. The problem arises, since the dynamical model of the fluid in a pipeline only considers straight geometries without fittings. In order to address this situation, several papers work with a virtual model of a pipeline that generates a equivalent straight length, thus, friction produced by the fittings is taking into account. However, when this method is applied, the leak is isolated in a virtual length, which for practical reasons does not represent a complete solution. This research proposes as a solution to the problem of leak isolation in a virtual length, the use of a polynomial interpolation function in order to approximate the conversion of the virtual position to a real-coordinates value. Experimental results in a real prototype are shown, concluding that the proposed methodology has a good performance.

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

Temperature Effects and Compensation-Control Methods

PubMed Central

Xia, Dunzhu; Chen, Shuling; Wang, Shourong; Li, Hongsheng

2009-01-01

In the analysis of the effects of temperature on the performance of microgyroscopes, it is found that the resonant frequency of the microgyroscope decreases linearly as the temperature increases, and the quality factor changes drastically at low temperatures. Moreover, the zero bias changes greatly with temperature variations. To reduce the temperature effects on the microgyroscope, temperature compensation-control methods are proposed. In the first place, a BP (Back Propagation) neural network and polynomial fitting are utilized for building the temperature model of the microgyroscope. Considering the simplicity and real-time requirements, piecewise polynomial fitting is applied in the temperature compensation system. Then, an integral-separated PID (Proportion Integration Differentiation) control algorithm is adopted in the temperature control system, which can stabilize the temperature inside the microgyrocope in pursuing its optimal performance. Experimental results reveal that the combination of microgyroscope temperature compensation and control methods is both realizable and effective in a miniaturized microgyroscope prototype. PMID:22408509

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Circi, Christian

2018-05-01

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth-Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

An Introduction to Lagrangian Differential Calculus.

ERIC Educational Resources Information Center

Schremmer, Francesca; Schremmer, Alain

1990-01-01

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2003-05-01

A formula expressing the Laguerre coefficients of a general-order derivative of an infinitely differentiable function in terms of its original coefficients is proved, and a formula expressing explicitly the derivatives of Laguerre polynomials of any degree and for any order as a linear combination of suitable Laguerre polynomials is deduced. A formula for the Laguerre coefficients of the moments of one single Laguerre polynomial of certain degree is given. Formulae for the Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Laguerre coefficients are also obtained. A simple approach in order to build and solve recursively for the connection coefficients between Jacobi-Laguerre and Hermite-Laguerre polynomials is described. An explicit formula for these coefficients between Jacobi and Laguerre polynomials is given, of which the ultra-spherical polynomials of the first and second kinds and Legendre polynomials are important special cases. An analytical formula for the connection coefficients between Hermite and Laguerre polynomials is also obtained.

Maximum Marginal Likelihood Estimation of a Monotonic Polynomial Generalized Partial Credit Model with Applications to Multiple Group Analysis.

PubMed

Falk, Carl F; Cai, Li

2016-06-01

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest order polynomial. Our approach extends Liang's (A semi-parametric approach to estimate IRFs, Unpublished doctoral dissertation, 2007) method for dichotomous item responses to the case of polytomous data. Furthermore, item parameter estimation is implemented with maximum marginal likelihood using the Bock-Aitkin EM algorithm, thereby facilitating multiple group analyses useful in operational settings. Our approach is demonstrated on both educational and psychological data. We present simulation results comparing our approach to more standard IRF estimation approaches and other non-parametric and semi-parametric alternatives.

Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N{sub 4}

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

Bender, Jason D.; Doraiswamy, Sriram; Candler, Graham V., E-mail: truhlar@umn.edu, E-mail: candler@aem.umn.edu

2014-02-07

Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with amore » review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N{sub 4}. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.« less

A Linear Algebraic Approach to Teaching Interpolation

ERIC Educational Resources Information Center

Tassa, Tamir

2007-01-01

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

Least-Squares Adaptive Control Using Chebyshev Orthogonal Polynomials

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Burken, John; Ishihara, Abraham

2011-01-01

This paper presents a new adaptive control approach using Chebyshev orthogonal polynomials as basis functions in a least-squares functional approximation. The use of orthogonal basis functions improves the function approximation significantly and enables better convergence of parameter estimates. Flight control simulations demonstrate the effectiveness of the proposed adaptive control approach.

Simulation of aspheric tolerance with polynomial fitting

NASA Astrophysics Data System (ADS)

Li, Jing; Cen, Zhaofeng; Li, Xiaotong

2018-01-01

The shape of the aspheric lens changes caused by machining errors, resulting in a change in the optical transfer function, which affects the image quality. At present, there is no universally recognized tolerance criterion standard for aspheric surface. To study the influence of aspheric tolerances on the optical transfer function, the tolerances of polynomial fitting are allocated on the aspheric surface, and the imaging simulation is carried out by optical imaging software. Analysis is based on a set of aspheric imaging system. The error is generated in the range of a certain PV value, and expressed as a form of Zernike polynomial, which is added to the aspheric surface as a tolerance term. Through optical software analysis, the MTF of optical system can be obtained and used as the main evaluation index. Evaluate whether the effect of the added error on the MTF of the system meets the requirements of the current PV value. Change the PV value and repeat the operation until the acceptable maximum allowable PV value is obtained. According to the actual processing technology, consider the error of various shapes, such as M type, W type, random type error. The new method will provide a certain development for the actual free surface processing technology the reference value.

Geometry Dynamics of α-Helices in Different Class I Major Histocompatibility Complexes

PubMed Central

Karch, Rudolf; Schreiner, Wolfgang

2015-01-01

MHC α-helices form the antigen-binding cleft and are of particular interest for immunological reactions. To monitor these helices in molecular dynamics simulations, we applied a parsimonious fragment-fitting method to trace the axes of the α-helices. Each resulting axis was fitted by polynomials in a least-squares sense and the curvature integral was computed. To find the appropriate polynomial degree, the method was tested on two artificially modelled helices, one performing a bending movement and another a hinge movement. We found that second-order polynomials retrieve predefined parameters of helical motion with minimal relative error. From MD simulations we selected those parts of α-helices that were stable and also close to the TCR/MHC interface. We monitored the curvature integral, generated a ruled surface between the two MHC α-helices, and computed interhelical area and surface torsion, as they changed over time. We found that MHC α-helices undergo rapid but small changes in conformation. The curvature integral of helices proved to be a sensitive measure, which was closely related to changes in shape over time as confirmed by RMSD analysis. We speculate that small changes in the conformation of individual MHC α-helices are part of the intrinsic dynamics induced by engagement with the TCR. PMID:26649324

Correction factors for on-line microprobe analysis of multielement alloy systems

NASA Technical Reports Server (NTRS)

Unnam, J.; Tenney, D. R.; Brewer, W. D.

1977-01-01

An on-line correction technique was developed for the conversion of electron probe X-ray intensities into concentrations of emitting elements. This technique consisted of off-line calculation and representation of binary interaction data which were read into an on-line minicomputer to calculate variable correction coefficients. These coefficients were used to correct the X-ray data without significantly increasing computer core requirements. The binary interaction data were obtained by running Colby's MAGIC 4 program in the reverse mode. The data for each binary interaction were represented by polynomial coefficients obtained by least-squares fitting a third-order polynomial. Polynomial coefficients were generated for most of the common binary interactions at different accelerating potentials and are included. Results are presented for the analyses of several alloy standards to demonstrate the applicability of this correction procedure.

Three-dimensional trend mapping from wire-line logs

USGS Publications Warehouse

Doveton, J.H.; Ke-an, Z.

1985-01-01

Mapping of lithofacies and porosities of stratigraphic units is complicated because these properties vary in three dimensions. The method of moments was proposed by Krumbein and Libby (1957) as a technique to aid in resolving this problem. Moments are easily computed from wireline logs and are simple statistics which summarize vertical variation in a log trace. Combinations of moment maps have proved useful in understanding vertical and lateral changes in lithology of sedimentary rock units. Although moments have meaning both as statistical descriptors and as mechanical properties, they also define polynomial curves which approximate lithologic changes as a function of depth. These polynomials can be fitted by least-squares methods, partitioning major trends in rock properties from finescale fluctuations. Analysis of variance yields the degree of fit of any polynomial and measures the proportion of vertical variability expressed by any moment or combination of moments. In addition, polynomial curves can be differentiated to determine depths at which pronounced expressions of facies occur and to determine the locations of boundaries between major lithologic subdivisions. Moments can be estimated at any location in an area by interpolating from log moments at control wells. A matrix algebra operation then converts moment estimates to coefficients of a polynomial function which describes a continuous curve of lithologic variation with depth. If this procedure is applied to a grid of geographic locations, the result is a model of variability in three dimensions. Resolution of the model is determined largely by number of moments used in its generation. The method is illustrated with an analysis of lithofacies in the Simpson Group of south-central Kansas; the three-dimensional model is shown as cross sections and slice maps. In this study, the gamma-ray log is used as a measure of shaliness of the unit. However, the method is general and can be applied, for example, to suites of neutron, density, or sonic logs to produce three-dimensional models of porosity in reservoir rocks. ?? 1985 Plenum Publishing Corporation.

dPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.

2017-01-01

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the 'Generalized Potential Energy Function' (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the 'Hannover Polynomial' (or "X-expansion") function, and the 'Tang-Toennies' and Scoles-Aziz 'HFD', exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born-Oppenheimer breakdown functions, and singlet-state Λ-doubling, or 2Σ splitting radial strength functions for one or more electronic states. dPotFit always reports both the 95% confidence limit uncertainty and the "sensitivity" of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a "sequential rounding and refitting" procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

A User’s Manual for Fiber Diffraction: The Automated Picker and Huber Diffractometers

DTIC Science & Technology

1990-07-01

17 3. Layer line scan of degummed silk ( Bombyx mori ) ................................. 18...index (arbitrary units) Figure 3. Layer line scan of degummed silk ( Bombyx mori ) showing layers 0 through 6. If the fit is rejected, new values for... originally made at intervals larger than 0.010. The smoothing and interpolation is done by a least-squares polynomial fit to segments of the data. The number

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

Automatic segmentation of lung parenchyma based on curvature of ribs using HRCT images in scleroderma studies

NASA Astrophysics Data System (ADS)

Prasad, M. N.; Brown, M. S.; Ahmad, S.; Abtin, F.; Allen, J.; da Costa, I.; Kim, H. J.; McNitt-Gray, M. F.; Goldin, J. G.

2008-03-01

Segmentation of lungs in the setting of scleroderma is a major challenge in medical image analysis. Threshold based techniques tend to leave out lung regions that have increased attenuation, for example in the presence of interstitial lung disease or in noisy low dose CT scans. The purpose of this work is to perform segmentation of the lungs using a technique that selects an optimal threshold for a given scleroderma patient by comparing the curvature of the lung boundary to that of the ribs. Our approach is based on adaptive thresholding and it tries to exploit the fact that the curvature of the ribs and the curvature of the lung boundary are closely matched. At first, the ribs are segmented and a polynomial is used to represent the ribs' curvature. A threshold value to segment the lungs is selected iteratively such that the deviation of the lung boundary from the polynomial is minimized. A Naive Bayes classifier is used to build the model for selection of the best fitting lung boundary. The performance of the new technique was compared against a standard approach using a simple fixed threshold of -400HU followed by regiongrowing. The two techniques were evaluated against manual reference segmentations using a volumetric overlap fraction (VOF) and the adaptive threshold technique was found to be significantly better than the fixed threshold technique.

Generalized neurofuzzy network modeling algorithms using Bézier-Bernstein polynomial functions and additive decomposition.

PubMed

Hong, X; Harris, C J

2000-01-01

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bézier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bézier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bézier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bézier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

An Empirical Method for Determining 234U Percentage

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

Miko, David K.

2015-11-02

When isotopic information for uranium is provided, the concentration of 234U is frequently neglected. Often the isotopic content is given as a percentage of 235U with the assumption that the remainder consists of 238U. In certain applications, such as heat output, the concentration of 234U can be a significant contributing factor. For situations where only the 235U and 238U values are given, a simple way to calculate the 234U component would be beneficial. The approach taken here is empirical. A series of uranium standards with varying enrichments were analyzed. The 234U and 235U data were fit using a second ordermore » polynomial.« less

Analysis of longitudinal "time series" data in toxicology.

PubMed

Cox, C; Cory-Slechta, D A

1987-02-01

Studies focusing on chronic toxicity or on the time course of toxicant effect often involve repeated measurements or longitudinal observations of endpoints of interest. Experimental design considerations frequently necessitate between-group comparisons of the resulting trends. Typically, procedures such as the repeated-measures analysis of variance have been used for statistical analysis, even though the required assumptions may not be satisfied in some circumstances. This paper describes an alternative analytical approach which summarizes curvilinear trends by fitting cubic orthogonal polynomials to individual profiles of effect. The resulting regression coefficients serve as quantitative descriptors which can be subjected to group significance testing. Randomization tests based on medians are proposed to provide a comparison of treatment and control groups. Examples from the behavioral toxicology literature are considered, and the results are compared to more traditional approaches, such as repeated-measures analysis of variance.

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE PAGES

Jakeman, John D.; Narayan, Akil; Zhou, Tao

2017-06-22

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Cylinder stitching interferometry: with and without overlap regions

NASA Astrophysics Data System (ADS)

Peng, Junzheng; Chen, Dingfu; Yu, Yingjie

2017-06-01

Since the cylinder surface is closed and periodic in the azimuthal direction, existing stitching methods cannot be used to yield the 360° form map. To address this problem, this paper presents two methods for stitching interferometry of cylinder: one requires overlap regions, and the other does not need the overlap regions. For the former, we use the first order approximation of cylindrical coordinate transformation to build the stitching model. With it, the relative parameters between the adjacent sub-apertures can be calculated by the stitching model. For the latter, a set of orthogonal polynomials, termed Legendre Fourier (LF) polynomials, was developed. With these polynomials, individual sub-aperture data can be expanded as composition of inherent form of partial cylinder surface and additional misalignment parameters. Then the 360° form map can be acquired by simultaneously fitting all sub-aperture data with LF polynomials. Finally the two proposed methods are compared under various conditions. The merits and drawbacks of each stitching method are consequently revealed to provide suggestion in acquisition of 360° form map for a precision cylinder.

On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.

2004-01-01

Formulae expressing explicitly the Jacobi coefficients of a general-order derivative (integral) of an infinitely differentiable function in terms of its original expansion coefficients, and formulae for the derivatives (integrals) of Jacobi polynomials in terms of Jacobi polynomials themselves are stated. A formula for the Jacobi coefficients of the moments of one single Jacobi polynomial of certain degree is proved. Another formula for the Jacobi coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its original expanded coefficients is also given. A simple approach in order to construct and solve recursively for the connection coefficients between Jacobi-Jacobi polynomials is described. Explicit formulae for these coefficients between ultraspherical and Jacobi polynomials are deduced, of which the Chebyshev polynomials of the first and second kinds and Legendre polynomials are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Jacobi and Hermite-Jacobi are developed.

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

Direct calculation of modal parameters from matrix orthogonal polynomials

NASA Astrophysics Data System (ADS)

El-Kafafy, Mahmoud; Guillaume, Patrick

2011-10-01

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system. Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems. The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.

Robust stability of fractional order polynomials with complicated uncertainty structure

PubMed Central

Şenol, Bilal; Pekař, Libor

2017-01-01

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. PMID:28662173

Elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation.

PubMed

Li, Yan; Deng, Jianxin; Zhou, Jun; Li, Xueen

2016-11-01

Corresponding to pre-puncture and post-puncture insertion, elastic and viscoelastic mechanical properties of brain tissues on the implanting trajectory of sub-thalamic nucleus stimulation are investigated, respectively. Elastic mechanical properties in pre-puncture are investigated through pre-puncture needle insertion experiments using whole porcine brains. A linear polynomial and a second order polynomial are fitted to the average insertion force in pre-puncture. The Young's modulus in pre-puncture is calculated from the slope of the two fittings. Viscoelastic mechanical properties of brain tissues in post-puncture insertion are investigated through indentation stress relaxation tests for six interested regions along a planned trajectory. A linear viscoelastic model with a Prony series approximation is fitted to the average load trace of each region using Boltzmann hereditary integral. Shear relaxation moduli of each region are calculated using the parameters of the Prony series approximation. The results show that, in pre-puncture insertion, needle force almost increases linearly with needle displacement. Both fitting lines can perfectly fit the average insertion force. The Young's moduli calculated from the slope of the two fittings are worthy of trust to model linearly or nonlinearly instantaneous elastic responses of brain tissues, respectively. In post-puncture insertion, both region and time significantly affect the viscoelastic behaviors. Six tested regions can be classified into three categories in stiffness. Shear relaxation moduli decay dramatically in short time scales but equilibrium is never truly achieved. The regional and temporal viscoelastic mechanical properties in post-puncture insertion are valuable for guiding probe insertion into each region on the implanting trajectory.

Measurement of pediatric regional cerebral blood flow from 6 months to 15 years of age in a clinical population.

PubMed

Carsin-Vu, Aline; Corouge, Isabelle; Commowick, Olivier; Bouzillé, Guillaume; Barillot, Christian; Ferré, Jean-Christophe; Proisy, Maia

2018-04-01

To investigate changes in cerebral blood flow (CBF) in gray matter (GM) between 6 months and 15 years of age and to provide CBF values for the brain, GM, white matter (WM), hemispheres and lobes. Between 2013 and 2016, we retrospectively included all clinical MRI examinations with arterial spin labeling (ASL). We excluded subjects with a condition potentially affecting brain perfusion. For each subject, mean values of CBF in the brain, GM, WM, hemispheres and lobes were calculated. GM CBF was fitted using linear, quadratic and cubic polynomial regression against age. Regression models were compared with Akaike's information criterion (AIC), and Likelihood Ratio tests. 84 children were included (44 females/40 males). Mean CBF values were 64.2 ± 13.8 mL/100 g/min in GM, and 29.3 ± 10.0 mL/100 g/min in WM. The best-fit model of brain perfusion was the cubic polynomial function (AIC = 672.7, versus respectively AIC = 673.9 and AIC = 674.1 with the linear negative function and the quadratic polynomial function). A statistically significant difference between the tested models demonstrating the superiority of the quadratic (p = 0.18) or cubic polynomial model (p = 0.06), over the negative linear regression model was not found. No effect of general anesthesia (p = 0.34) or of gender (p = 0.16) was found. we provided values for ASL CBF in the brain, GM, WM, hemispheres, and lobes over a wide pediatric age range, approximately showing inverted U-shaped changes in GM perfusion over the course of childhood. Copyright © 2018 Elsevier B.V. All rights reserved.

Computer-assisted map projection research

USGS Publications Warehouse

Snyder, John Parr

1985-01-01

Computers have opened up areas of map projection research which were previously too complicated to utilize, for example, using a least-squares fit to a very large number of points. One application has been in the efficient transfer of data between maps on different projections. While the transfer of moderate amounts of data is satisfactorily accomplished using the analytical map projection formulas, polynomials are more efficient for massive transfers. Suitable coefficients for the polynomials may be determined more easily for general cases using least squares instead of Taylor series. A second area of research is in the determination of a map projection fitting an unlabeled map, so that accurate data transfer can take place. The computer can test one projection after another, and include iteration where required. A third area is in the use of least squares to fit a map projection with optimum parameters to the region being mapped, so that distortion is minimized. This can be accomplished for standard conformal, equalarea, or other types of projections. Even less distortion can result if complex transformations of conformal projections are utilized. This bulletin describes several recent applications of these principles, as well as historical usage and background.

Residual stress measurement of PMMA by combining drilling-hole with digital speckle correlation method

NASA Astrophysics Data System (ADS)

Yao, X. F.; Xiong, T. C.; Xu, H. M.; Wan, J. P.; Long, G. R.

2008-11-01

The residual stresses of the PMMA (polymethyl methacrylate) specimens after being drilled, reamed and polished respectively are investigated using the digital speckle correlation experimental method,. According to the displacement fields around the correlated calculated region, the polynomial curve fitting method is used to obtain the continuous displacement fields, and the strain fields can be obtained from the derivative of the displacement fields. Considering the constitutive equation of the material, the expression of the residual stress can be presented. During the data processing, according to the fitting effect of the data, the calculation region of the correlated speckles and the degree of the polynomial fitting curve is decided. These results show that the maximum stress is at the hole-wall of the drilling hole specimen and with the increasing of the diameter of the drilled hole, the residual stress resulting from the hole drilling increases, whereas the process of reaming and polishing hole can reduce the residual stress. The relative large discrete degree of the residual stress is due to the chip removal ability of the drill bit, the cutting feed of the drill and other various reasons.

Photoelectric absorption cross sections with variable abundances

NASA Technical Reports Server (NTRS)

Balucinska-Church, Monika; Mccammon, Dan

1992-01-01

Polynomial fit coefficients have been obtained for the energy dependences of the photoelectric absorption cross sections of 17 astrophysically important elements. These results allow the calculation of X-ray absorption in the energy range 0.03-10 keV in material with noncosmic abundances.

Empirical predictions of hypervelocity impact damage to the space station

NASA Technical Reports Server (NTRS)

Rule, W. K.; Hayashida, K. B.

1991-01-01

A family of user-friendly, DOS PC based, Microsoft BASIC programs written to provide spacecraft designers with empirical predictions of space debris damage to orbiting spacecraft is described. The spacecraft wall configuration is assumed to consist of multilayer insulation (MLI) placed between a Whipple style bumper and the pressure wall. Predictions are based on data sets of experimental results obtained from simulating debris impacts on spacecraft using light gas guns on Earth. A module of the program facilitates the creation of the data base of experimental results that are used by the damage prediction modules of the code. The user has the choice of three different prediction modules to predict damage to the bumper, the MLI, and the pressure wall. One prediction module is based on fitting low order polynomials through subsets of the experimental data. Another prediction module fits functions based on nondimensional parameters through the data. The last prediction technique is a unique approach that is based on weighting the experimental data according to the distance from the design point.

Noninvasive estimation of assist pressure for direct mechanical ventricular actuation

NASA Astrophysics Data System (ADS)

An, Dawei; Yang, Ming; Gu, Xiaotong; Meng, Fan; Yang, Tianyue; Lin, Shujing

2018-02-01

Direct mechanical ventricular actuation is effective to reestablish the ventricular function with non-blood contact. Due to the energy loss within the driveline of the direct cardiac compression device, it is necessary to acquire the accurate value of assist pressure acting on the heart surface. To avoid myocardial trauma induced by invasive sensors, the noninvasive estimation method is developed and the experimental device is designed to measure the sample data for fitting the estimation models. By examining the goodness of fit numerically and graphically, the polynomial model presents the best behavior among the four alternative models. Meanwhile, to verify the effect of the noninvasive estimation, the simplified lumped parameter model is utilized to calculate the pre-support and the post-support left ventricular pressure. Furthermore, by adjusting the driving pressure beyond the range of the sample data, the assist pressure is estimated with the similar waveform and the post-support left ventricular pressure approaches the value of the adult healthy heart, indicating the good generalization ability of the noninvasive estimation method.

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

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

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

Acute effects of static stretching on passive stiffness of the hamstring muscles calculated using different mathematical models.

PubMed

Nordez, Antoine; Cornu, Christophe; McNair, Peter

2006-08-01

The aim of this study was to assess the effects of static stretching on hamstring passive stiffness calculated using different data reduction methods. Subjects performed a maximal range of motion test, five cyclic stretching repetitions and a static stretching intervention that involved five 30-s static stretches. A computerised dynamometer allowed the measurement of torque and range of motion during passive knee extension. Stiffness was then calculated as the slope of the torque-angle relationship fitted using a second-order polynomial, a fourth-order polynomial, and an exponential model. The second-order polynomial and exponential models allowed the calculation of stiffness indices normalized to knee angle and passive torque, respectively. Prior to static stretching, stiffness levels were significantly different across the models. After stretching, while knee maximal joint range of motion increased, stiffness was shown to decrease. Stiffness decreased more at the extended knee joint angle, and the magnitude of change depended upon the model used. After stretching, the stiffness indices also varied according to the model used to fit data. Thus, the stiffness index normalized to knee angle was found to decrease whereas the stiffness index normalized to passive torque increased after static stretching. Stretching has significant effects on stiffness, but the findings highlight the need to carefully assess the effect of different models when analyzing such data.

Investigation on phase transitions of 1-decylammonium hydrochloride as the potential thermal energy storage material

NASA Astrophysics Data System (ADS)

Dan, Wen-Yan; Di, You-Ying; He, Dong-Hua; Liu, Yu-Pu

2011-02-01

1-Decylammonium hydrochloride was synthesized by the method of liquid phase synthesis. Chemical analysis, elemental analysis, and X-ray single crystal diffraction techniques were applied to characterize its composition and structure. Low-temperature heat capacities of the compounds were measured with a precision automated adiabatic calorimeter over the temperature range from 78 to 380 K. Three solid-solid phase transitions have been observed at the peak temperatures of 307.52 ± 0.13, 325.02 ± 0.19, and 327.26 ± 0.07 K. The molar enthalpies and entropies of three phase transitions were determined based on the analysis of heat capacity curves. Experimental molar heat capacities were fitted to two polynomial equations of the heat capacities as a function of temperature by least square method. Smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15 K were calculated and tabulated at intervals of 5 K based on the fitted polynomials.

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

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

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

NASA Astrophysics Data System (ADS)

Milstead, Jonathan

The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

Automatic differentiation for Fourier series and the radii polynomial approach

NASA Astrophysics Data System (ADS)

Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian

2016-11-01

In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

Classical Dynamics of Fullerenes

NASA Astrophysics Data System (ADS)

Sławianowski, Jan J.; Kotowski, Romuald K.

2017-06-01

The classical mechanics of large molecules and fullerenes is studied. The approach is based on the model of collective motion of these objects. The mixed Lagrangian (material) and Eulerian (space) description of motion is used. In particular, the Green and Cauchy deformation tensors are geometrically defined. The important issue is the group-theoretical approach to describing the affine deformations of the body. The Hamiltonian description of motion based on the Poisson brackets methodology is used. The Lagrange and Hamilton approaches allow us to formulate the mechanics in the canonical form. The method of discretization in analytical continuum theory and in classical dynamics of large molecules and fullerenes enable us to formulate their dynamics in terms of the polynomial expansions of configurations. Another approach is based on the theory of analytical functions and on their approximations by finite-order polynomials. We concentrate on the extremely simplified model of affine deformations or on their higher-order polynomial perturbations.

Algebraic approach to solve ttbar dilepton equations

NASA Astrophysics Data System (ADS)

Sonnenschein, Lars

2006-01-01

The set of non-linear equations describing the Standard Model kinematics of the top quark an- tiqark production system in the dilepton decay channel has at most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its most precise and robust solution is of major importance for measurements of top quark properties like the top quark mass and t t spin correlations. Simple algebraic operations allow to transform the non-linear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be an- alytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree sixteen and the coefficients are free of any singularity. The number of its real solutions is determined analytically by means of Sturm’s theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary brack- eting. Further a new Ansatz - exploiting an accidental cancelation in the process of transforming the equations - is presented. It permits to transform the initial system of equations into two poly- nomial equations with two unknowns. These two polynomials of multidegree two can be reduced to one univariate polynomial of degree four by means of resultants. The obtained quartic equation can be solved analytically. The analytical solution has singularities which can be circumvented by the algebraic approach described above.

Simplified curve fits for the thermodynamic properties of equilibrium air

NASA Technical Reports Server (NTRS)

Srinivasan, S.; Tannehill, J. C.; Weilmuenster, K. J.

1987-01-01

New, improved curve fits for the thermodynamic properties of equilibrium air have been developed. The curve fits are for pressure, speed of sound, temperature, entropy, enthalpy, density, and internal energy. These curve fits can be readily incorporated into new or existing computational fluid dynamics codes if real gas effects are desired. The curve fits are constructed from Grabau-type transition functions to model the thermodynamic surfaces in a piecewise manner. The accuracies and continuity of these curve fits are substantially improved over those of previous curve fits. These improvements are due to the incorporation of a small number of additional terms in the approximating polynomials and careful choices of the transition functions. The ranges of validity of the new curve fits are temperatures up to 25 000 K and densities from 10 to the -7 to 10 to the 3d power amagats.

Comparison of random regression test-day models for Polish Black and White cattle.

PubMed

Strabel, T; Szyda, J; Ptak, E; Jamrozik, J

2005-10-01

Test-day milk yields of first-lactation Black and White cows were used to select the model for routine genetic evaluation of dairy cattle in Poland. The population of Polish Black and White cows is characterized by small herd size, low level of production, and relatively early peak of lactation. Several random regression models for first-lactation milk yield were initially compared using the "percentage of squared bias" criterion and the correlations between true and predicted breeding values. Models with random herd-test-date effects, fixed age-season and herd-year curves, and random additive genetic and permanent environmental curves (Legendre polynomials of different orders were used for all regressions) were chosen for further studies. Additional comparisons included analyses of the residuals and shapes of variance curves in days in milk. The low production level and early peak of lactation of the breed required the use of Legendre polynomials of order 5 to describe age-season lactation curves. For the other curves, Legendre polynomials of order 3 satisfactorily described daily milk yield variation. Fitting third-order polynomials for the permanent environmental effect made it possible to adequately account for heterogeneous residual variance at different stages of lactation.

Reducing motion artifacts in 4D MR images using principal component analysis (PCA) combined with linear polynomial fitting model

PubMed Central

Yang, Juan; Yin, Yong; Li, Dengwang

2015-01-01

We have previously developed a retrospective 4D‐MRI technique using body area as the respiratory surrogate, but generally, the reconstructed 4D MR images suffer from severe or mild artifacts mainly caused by irregular motion during image acquisition. Those image artifacts may potentially affect the accuracy of tumor target delineation or the shape representation of surrounding nontarget tissues and organs. So the purpose of this study is to propose an approach employing principal component analysis (PCA), combined with a linear polynomial fitting model, to remodel the displacement vector fields (DVFs) obtained from deformable image registration (DIR), with the main goal of reducing the motion artifacts in 4D MR images. Seven patients with hepatocellular carcinoma (2/7) or liver metastases (5/7) in the liver, as well as a patient with non‐small cell lung cancer (NSCLC), were enrolled in an IRB‐approved prospective study. Both CT and MR simulations were performed for each patient for treatment planning. Multiple‐slice, multiple‐phase, cine‐MRI images were acquired in the axial plane for 4D‐MRI reconstruction. Single‐slice 2D cine‐MR images were acquired across the center of the tumor in axial, coronal, and sagittal planes. For a 4D MR image dataset, the DVFs in three orthogonal direction (inferior–superior (SI), anterior–posterior (AP), and medial–lateral (ML)) relative to a specific reference phase were calculated using an in‐house DIR algorithm. The DVFs were preprocessed in three temporal and spatial dimensions using a polynomial fitting model, with the goal of correcting the potential registration errors introduced by three‐dimensional DIR. Then PCA was used to decompose each fitted DVF into a linear combination of three principal motion bases whose spanned subspaces combined with their projections had been validated to be sufficient to represent the regular respiratory motion. By wrapping the reference MR image using the remodeled DVFs, ‘synthetic’ MR images with reduced motion artifacts were generated at selected phase. Tumor motion trajectories derived from cine‐MRI, 4D CT, original 4D MRI, and ‘synthetic’ 4D MRI were analyzed in the SI, AP, and ML directions, respectively. Their correlation coefficient (CC) and difference (D) in motion amplitude were calculated for comparison. Of all the patients, the means and standard deviations (SDs) of CC comparing ‘synthetic’ 4D MRI and cine‐MRI were 0.98±0.01,0.98±0,01, and 0.99±0.01 in SI, AP, and ML directions, respectively. The mean±SD Ds were 0.59±0.09 mm,0.29±0.10 mm, and 0.15±0.05 mm in SI, AP and ML directions, respectively. The means and SDs of CC comparing ‘synthetic’ 4D MRI and 4D CT were 0.96±0.01,0.95±0.01, and 0.95±0.01 in SI, AP, and ML directions, respectively. The mean±SD Ds were 0.76±0.20 mm,0.33±0.14 mm, and 0.19±0.07 mm in SI, AP, and ML directions, respectively. The means and SDs of CC comparing ‘synthetic’ 4D MRI and original 4D MRI were 0.98±0.01,0.98±0.01, and 0.97±0.01 in SI, AP, and ML directions, respectively. The mean±SD Ds were 0.58±0.10 mm,0.30±0.09 mm, and 0.17±0.04 mm in SI, AP, and ML directions, respectively. In this study we have proposed an approach employing PCA combined with a linear polynomial fitting model to capture the regular respiratory motion from a 4D MR image dataset. And its potential usefulness in reducing motion artifacts and improving image quality has been demonstrated by the preliminary results in oncological patients. PACS numbers: 87.57.cp, 87.57.nj, 87.61.‐c PMID:26103185

Exploring the use of random regression models with legendre polynomials to analyze measures of volume of ejaculate in Holstein bulls.

PubMed

Carabaño, M J; Díaz, C; Ugarte, C; Serrano, M

2007-02-01

Artificial insemination centers routinely collect records of quantity and quality of semen of bulls throughout the animals' productive period. The goal of this paper was to explore the use of random regression models with orthogonal polynomials to analyze repeated measures of semen production of Spanish Holstein bulls. A total of 8,773 records of volume of first ejaculate (VFE) collected between 12 and 30 mo of age from 213 Spanish Holstein bulls was analyzed under alternative random regression models. Legendre polynomial functions of increasing order (0 to 6) were fitted to the average trajectory, additive genetic and permanent environmental effects. Age at collection and days in production were used as time variables. Heterogeneous and homogeneous residual variances were alternatively assumed. Analyses were carried out within a Bayesian framework. The logarithm of the marginal density and the cross-validation predictive ability of the data were used as model comparison criteria. Based on both criteria, age at collection as a time variable and heterogeneous residuals models are recommended to analyze changes of VFE over time. Both criteria indicated that fitting random curves for genetic and permanent environmental components as well as for the average trajector improved the quality of models. Furthermore, models with a higher order polynomial for the permanent environmental (5 to 6) than for the genetic components (4 to 5) and the average trajectory (2 to 3) tended to perform best. High-order polynomials were needed to accommodate the highly oscillating nature of the phenotypic values. Heritability and repeatability estimates, disregarding the extremes of the studied period, ranged from 0.15 to 0.35 and from 0.20 to 0.50, respectively, indicating that selection for VFE may be effective at any stage. Small differences among models were observed. Apart from the extremes, estimated correlations between ages decreased steadily from 0.9 and 0.4 for measures 1 mo apart to 0.4 and 0.2 for most distant measures for additive genetic and phenotypic components, respectively. Further investigation to account for environmental factors that may be responsible for the oscillating observations of VFE is needed.

A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE

NASA Technical Reports Server (NTRS)

Truong, T. K.

1994-01-01

This program utilizes a fast polynomial transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional convolution has many applications, particularly in image processing. Two-dimensional cyclic convolutions can be converted to a one-dimensional convolution in a polynomial ring. Traditional FPT methods decompose the one-dimensional cyclic polynomial into polynomial convolutions of different lengths. This program will decompose a cyclic polynomial into polynomial convolutions of the same length. Thus, only FPTs and Fast Fourier Transforms of the same length are required. This modular approach can save computational resources. To further enhance its appeal, the program is written in the transportable 'C' language. The steps in the algorithm are: 1) formulate the modulus reduction equations, 2) calculate the polynomial transforms, 3) multiply the transforms using a generalized fast Fourier transformation, 4) compute the inverse polynomial transforms, and 5) reconstruct the final matrices using the Chinese remainder theorem. Input to this program is comprised of the row and column dimensions and the initial two matrices. The matrices are printed out at all steps, ending with the final reconstruction. This program is written in 'C' for batch execution and has been implemented on the IBM PC series of computers under DOS with a central memory requirement of approximately 18K of 8 bit bytes. This program was developed in 1986.

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

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

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; Lu, Lu

2013-12-15

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

Spillover in the Academy: Marriage Stability and Faculty Evaluations.

ERIC Educational Resources Information Center

Ludlow, Larry H.; Alvarez-Salvat, Rose M.

2001-01-01

Studied the spillover between family and work by examining the link between marital status and work performance across marriage, divorce, and remarriage. A polynomial regression model was fit to the data from 78 evaluations of an individual professor, and a cubic curve through the 3 periods was statistically significant. (SLD)

Utility of Inferential Norming with Smaller Sample Sizes

ERIC Educational Resources Information Center

Zhu, Jianjun; Chen, Hsin-Yi

2011-01-01

We examined the utility of inferential norming using small samples drawn from the larger "Wechsler Intelligence Scales for Children-Fourth Edition" (WISC-IV) standardization data set. The quality of the norms was estimated with multiple indexes such as polynomial curve fit, percentage of cases receiving the same score, average absolute…

A range-free method to determine antoine vapor-pressure heat transfer-related equation coefficients using the Boubaker polynomial expansion scheme

NASA Astrophysics Data System (ADS)

Koçak, H.; Dahong, Z.; Yildirim, A.

2011-05-01

In this study, a range-free method is proposed in order to determine the Antoine constants for a given material (salicylic acid). The advantage of this method is mainly yielding analytical expressions which fit different temperature ranges.

Cosmographic analysis with Chebyshev polynomials

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

2018-05-01

The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

Low rank approximation methods for MR fingerprinting with large scale dictionaries.

PubMed

Yang, Mingrui; Ma, Dan; Jiang, Yun; Hamilton, Jesse; Seiberlich, Nicole; Griswold, Mark A; McGivney, Debra

2018-04-01

This work proposes new low rank approximation approaches with significant memory savings for large scale MR fingerprinting (MRF) problems. We introduce a compressed MRF with randomized singular value decomposition method to significantly reduce the memory requirement for calculating a low rank approximation of large sized MRF dictionaries. We further relax this requirement by exploiting the structures of MRF dictionaries in the randomized singular value decomposition space and fitting them to low-degree polynomials to generate high resolution MRF parameter maps. In vivo 1.5T and 3T brain scan data are used to validate the approaches. T 1 , T 2 , and off-resonance maps are in good agreement with that of the standard MRF approach. Moreover, the memory savings is up to 1000 times for the MRF-fast imaging with steady-state precession sequence and more than 15 times for the MRF-balanced, steady-state free precession sequence. The proposed compressed MRF with randomized singular value decomposition and dictionary fitting methods are memory efficient low rank approximation methods, which can benefit the usage of MRF in clinical settings. They also have great potentials in large scale MRF problems, such as problems considering multi-component MRF parameters or high resolution in the parameter space. Magn Reson Med 79:2392-2400, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

The Necessity-Concerns-Framework: A Multidimensional Theory Benefits from Multidimensional Analysis

PubMed Central

Phillips, L. Alison; Diefenbach, Michael; Kronish, Ian M.; Negron, Rennie M.; Horowitz, Carol R.

2014-01-01

Background Patients’ medication-related concerns and necessity-beliefs predict adherence. Evaluation of the potentially complex interplay of these two dimensions has been limited because of methods that reduce them to a single dimension (difference scores). Purpose We use polynomial regression to assess the multidimensional effect of stroke-event survivors’ medication-related concerns and necessity-beliefs on their adherence to stroke-prevention medication. Methods Survivors (n=600) rated their concerns, necessity-beliefs, and adherence to medication. Confirmatory and exploratory polynomial regression determined the best-fitting multidimensional model. Results As posited by the Necessity-Concerns Framework (NCF), the greatest and lowest adherence was reported by those with strong necessity-beliefs/weak concerns and strong concerns/weak necessity-beliefs, respectively. However, as could not be assessed using a difference-score model, patients with ambivalent beliefs were less adherent than those exhibiting indifference. Conclusions Polynomial regression allows for assessment of the multidimensional nature of the NCF. Clinicians/Researchers should be aware that concerns and necessity dimensions are not polar opposites. PMID:24500078

The necessity-concerns framework: a multidimensional theory benefits from multidimensional analysis.

PubMed

Phillips, L Alison; Diefenbach, Michael A; Kronish, Ian M; Negron, Rennie M; Horowitz, Carol R

2014-08-01

Patients' medication-related concerns and necessity-beliefs predict adherence. Evaluation of the potentially complex interplay of these two dimensions has been limited because of methods that reduce them to a single dimension (difference scores). We use polynomial regression to assess the multidimensional effect of stroke-event survivors' medication-related concerns and necessity beliefs on their adherence to stroke-prevention medication. Survivors (n = 600) rated their concerns, necessity beliefs, and adherence to medication. Confirmatory and exploratory polynomial regression determined the best-fitting multidimensional model. As posited by the necessity-concerns framework (NCF), the greatest and lowest adherence was reported by those necessity weak concerns and strong concerns/weak Necessity-Beliefs, respectively. However, as could not be assessed using a difference-score model, patients with ambivalent beliefs were less adherent than those exhibiting indifference. Polynomial regression allows for assessment of the multidimensional nature of the NCF. Clinicians/Researchers should be aware that concerns and necessity dimensions are not polar opposites.

Quadratic polynomial interpolation on triangular domain

NASA Astrophysics Data System (ADS)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

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

Gavignet, A.A.; Wick, C.J.

In current practice, pressure drops in the mud circulating system and the settling velocity of cuttings are calculated with simple rheological models and simple equations. Wellsite computers now allow more sophistication in drilling computations. In this paper, experimental results on the settling velocity of spheres in drilling fluids are reported, along with rheograms done over a wide range of shear rates. The flow curves are fitted to polynomials and general methods are developed to predict friction losses and settling velocities as functions of the polynomial coefficients. These methods were incorporated in a software package that can handle any rig configurationmore » system, including riser booster. Graphic displays show the effect of each parameter on the performance of the circulating system.« less

Seasonality in twin birth rates, Denmark, 1936-84.

PubMed

Bonnelykke, B; Søgaard, J; Nielsen, J

1987-12-01

A study was made of seasonality in twin birth rate in Denmark between 1977 and 1984. We studied all twin births (N = 45,550) in all deliveries (N = 3,679,932) during that period. Statistical analysis using a simple harmonic sinusoidal model provided no evidence for seasonality. However, sequential polynomial analysis disclosed a significant fit to a fifth order polynomial curve with peaks in twin birth rates in May-June and December, along with troughs in February and September. A falling trend in twinning rate broke off in Denmark around 1970, and from 1970 to 1984 an increasing trend was found. The results are discussed in terms of possible environmental influences on twinning.

The parameters of death: a consideration of the quantity of information in a life table using a polynomial representation of the survivorship curve.

PubMed

Anson, J

1988-08-01

How much unique information is contained in any life table? The logarithmic survivorship (lx) columns of 360 empirical life tables were fitted by a weighted fifth degree polynomial, and it is shown that six parameters are adequate to reproduce these curves almost flawlessly. However, these parameters are highly intercorrelated, so that a two-dimensional representation would be adequate to express the similarities and differences among life tables. It is thus concluded that a life table contains but two unique pieces of information, these being the level of mortality in the population which it represents, and the relative shape of the underlying mortality curve.

New analysis strategies for micro aspheric lens metrology

NASA Astrophysics Data System (ADS)

Gugsa, Solomon Abebe

Effective characterization of an aspheric micro lens is critical for understanding and improving processing in micro-optic manufacturing. Since most microlenses are plano-convex, where the convex geometry is a conic surface, current practice is often limited to obtaining an estimate of the lens conic constant, which average out the surface geometry that departs from an exact conic surface and any addition surface irregularities. We have developed a comprehensive approach of estimating the best fit conic and its uncertainty, and in addition propose an alternative analysis that focuses on surface errors rather than best-fit conic constant. We describe our new analysis strategy based on the two most dominant micro lens metrology methods in use today, namely, scanning white light interferometry (SWLI) and phase shifting interferometry (PSI). We estimate several parameters from the measurement. The major uncertainty contributors for SWLI are the estimates of base radius of curvature, the aperture of the lens, the sag of the lens, noise in the measurement, and the center of the lens. In the case of PSI the dominant uncertainty contributors are noise in the measurement, the radius of curvature, and the aperture. Our best-fit conic procedure uses least squares minimization to extract a best-fit conic value, which is then subjected to a Monte Carlo analysis to capture combined uncertainty. In our surface errors analysis procedure, we consider the surface errors as the difference between the measured geometry and the best-fit conic surface or as the difference between the measured geometry and the design specification for the lens. We focus on a Zernike polynomial description of the surface error, and again a Monte Carlo analysis is used to estimate a combined uncertainty, which in this case is an uncertainty for each Zernike coefficient. Our approach also allows us to investigate the effect of individual uncertainty parameters and measurement noise on both the best-fit conic constant analysis and the surface errors analysis, and compare the individual contributions to the overall uncertainty.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

Combined Resistivity and Shear Wave Velocity Soil-type Estimation Beneath a Coastal Protection Levee.

NASA Astrophysics Data System (ADS)

Lorenzo, J. M.; Goff, D.; Hayashi, K.

2015-12-01

Unconsolidated Holocene deltaic sediments comprise levee foundation soils in New Orleans, USA. Whereas geotechnical tests at point locations are indispensable for evaluating soil stability, the highly variable sedimentary facies of the Mississippi delta create difficulties to predict soil conditions between test locations. Combined electrical resistivity and seismic shear wave studies, calibrated to geotechnical data, may provide an efficient methodology to predict soil types between geotechnical sites at shallow depths (0- 10 m). The London Avenue Canal levee flank of New Orleans, which failed in the aftermath of Hurricane Katrina, 2005, presents a suitable site in which to pioneer these geophysical relationships. Preliminary cross-plots show electrically resistive, high-shear-wave velocity areas interpreted as low-permeability, resistive silt. In brackish coastal environments, low-resistivity and low-shear-wave-velocity areas may indicate both saturated, unconsolidated sands and low-rigidity clays. Via a polynomial approximation, soil sub-types of sand, silt and clay can be estimated by a cross-plot of S-wave velocity and resistivity. We confirm that existent boring log data fit reasonably well with the polynomial approximation where 2/3 of soil samples fall within their respective bounds—this approach represents a new classification system that could be used for other mid-latitude, fine-grained deltas.

A simple mathematical model based on biomarkers in stress-resistant catfish species, Sciades herzbergii (Pisces, Ariidae), in São Marcos Bay, Brazil.

PubMed

Carvalho Neta, Raimunda Nonata Fortes; Torres Junior, Audalio Rebelo; Silva, Dilson; Cortez, Célia Martins

2014-12-01

We present a refinement of our model describing the association between enzyme activity and histopathological lesions in the catfish, Sciades herzbergii from a polluted port. The fish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Brazil. Two biomarkers, hepatic glutathione S-transferase (GST) activity and histopathological lesions, in gills and liver tissue were measured. The values for GST activity were modeled with the occurrence of branchial and hepatic lesions by fitting a third-order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial and hepatic lesions in both wet and the dry seasons but only at the polluted port site. The model developed in this study indicates that branchial and hepatic lesions are initiated when GST activity reaches 2.17 μmol min(-1) mg protein(-1). Beyond this limit, GST activity decreased to very low levels and irreversible histopathological lesions occurred. This mathematical model based on two biomarkers (histopathological lesions and enzyme activity) in catfish provides a realistic approach to analyze stress induced by contaminants.

Using Strong Solar Coronal Emission Lines as Coronal Flux Proxies

NASA Technical Reports Server (NTRS)

Falconer, David A.; Jordan, Studart D.; Davila, Joseph M.; Thomas, Roger J.; Andretta, Vincenzo; Brosius, Jeffrey W.; Hara, Hirosha

1997-01-01

A comparison of Skylab results with observations of the strong EUV lines of Fe XVI at 335 A and 361 A from the Goddard Solar EUV Rocket Telescope and Spectrograph (SERTS) flight of 1989 suggests that these lines, and perhaps others observed with SERTS, might offer good proxies for estimating the total coronal flux over important wavelength ranges. In this paper, we compare SERTS observations from a later, 1993 flight with simultaneous cospatial Yohkoh soft X-ray observations to test this suggestion over the energy range of the Soft X-ray Telescope (SXT) on Yohkoh. Both polynomial and power-law fits are obtained, and errors are estimated, for the SERTS lines of Fe XVI 335 A and 361 A, Fe XV 284 A and 417 A, and Mg IX 368 A. It is found that the power-law fits best cover the full range of solar conditions from quiet Sun through active region, though not surprisingly the 'cooler' Mg IX 368 A line proves to be a poor proxy. The quadratic polynomial fits yield fair agreement over a large range for all but the Mg IX line, but the linear fits fail conspicuously when extrapolated into the quiet Sun regime. The implications of this work for the He 11 304 A line formation problem are briefly considered. The paper concludes with a discussion of the value of these iron lines observed with SERTS for estimating stellar coronal fluxes, as observed for example with the EUVE satellite.

Selection of Polynomial Chaos Bases via Bayesian Model Uncertainty Methods with Applications to Sparse Approximation of PDEs with Stochastic Inputs

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

Karagiannis, Georgios; Lin, Guang

2014-02-15

Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesianmore » model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.« less

New template family for the detection of gravitational waves from comparable-mass black hole binaries

NASA Astrophysics Data System (ADS)

Porter, Edward K.

2007-11-01

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various resummation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on reexpressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all post-Newtonian orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the last stable orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

Recursive approach to the moment-based phase unwrapping method.

PubMed

Langley, Jason A; Brice, Robert G; Zhao, Qun

2010-06-01

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

A simplified procedure for correcting both errors and erasures of a Reed-Solomon code using the Euclidean algorithm

NASA Technical Reports Server (NTRS)

Truong, T. K.; Hsu, I. S.; Eastman, W. L.; Reed, I. S.

1987-01-01

It is well known that the Euclidean algorithm or its equivalent, continued fractions, can be used to find the error locator polynomial and the error evaluator polynomial in Berlekamp's key equation needed to decode a Reed-Solomon (RS) code. A simplified procedure is developed and proved to correct erasures as well as errors by replacing the initial condition of the Euclidean algorithm by the erasure locator polynomial and the Forney syndrome polynomial. By this means, the errata locator polynomial and the errata evaluator polynomial can be obtained, simultaneously and simply, by the Euclidean algorithm only. With this improved technique the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. As a consequence, decoders for correcting both errors and erasures of RS codes can be made more modular, regular, simple, and naturally suitable for both VLSI and software implementation. An example illustrating this modified decoding procedure is given for a (15, 9) RS code.

Multivariable Hermite polynomials and phase-space dynamics

NASA Technical Reports Server (NTRS)

Dattoli, G.; Torre, Amalia; Lorenzutta, S.; Maino, G.; Chiccoli, C.

1994-01-01

The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.

Control Synthesis of Discrete-Time T-S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach.

PubMed

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Xue, Yusheng

2016-03-01

This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

Fast Legendre moment computation for template matching

NASA Astrophysics Data System (ADS)

Li, Bing C.

2017-05-01

Normalized cross correlation (NCC) based template matching is insensitive to intensity changes and it has many applications in image processing, object detection, video tracking and pattern recognition. However, normalized cross correlation implementation is computationally expensive since it involves both correlation computation and normalization implementation. In this paper, we propose Legendre moment approach for fast normalized cross correlation implementation and show that the computational cost of this proposed approach is independent of template mask sizes which is significantly faster than traditional mask size dependent approaches, especially for large mask templates. Legendre polynomials have been widely used in solving Laplace equation in electrodynamics in spherical coordinate systems, and solving Schrodinger equation in quantum mechanics. In this paper, we extend Legendre polynomials from physics to computer vision and pattern recognition fields, and demonstrate that Legendre polynomials can help to reduce the computational cost of NCC based template matching significantly.

An Exact Formula for Calculating Inverse Radial Lens Distortions

PubMed Central

Drap, Pierre; Lefèvre, Julien

2016-01-01

This article presents a new approach to calculating the inverse of radial distortions. The method presented here provides a model of reverse radial distortion, currently modeled by a polynomial expression, that proposes another polynomial expression where the new coefficients are a function of the original ones. After describing the state of the art, the proposed method is developed. It is based on a formal calculus involving a power series used to deduce a recursive formula for the new coefficients. We present several implementations of this method and describe the experiments conducted to assess the validity of the new approach. Such an approach, non-iterative, using another polynomial expression, able to be deduced from the first one, can actually be interesting in terms of performance, reuse of existing software, or bridging between different existing software tools that do not consider distortion from the same point of view. PMID:27258288

Nonlinear dynamic analysis and optimal trajectory planning of a high-speed macro-micro manipulator

NASA Astrophysics Data System (ADS)

Yang, Yi-ling; Wei, Yan-ding; Lou, Jun-qiang; Fu, Lei; Zhao, Xiao-wei

2017-09-01

This paper reports the nonlinear dynamic modeling and the optimal trajectory planning for a flexure-based macro-micro manipulator, which is dedicated to the large-scale and high-speed tasks. In particular, a macro- micro manipulator composed of a servo motor, a rigid arm and a compliant microgripper is focused. Moreover, both flexure hinges and flexible beams are considered. By combining the pseudorigid-body-model method, the assumed mode method and the Lagrange equation, the overall dynamic model is derived. Then, the rigid-flexible-coupling characteristics are analyzed by numerical simulations. After that, the microscopic scale vibration excited by the large-scale motion is reduced through the trajectory planning approach. Especially, a fitness function regards the comprehensive excitation torque of the compliant microgripper is proposed. The reference curve and the interpolation curve using the quintic polynomial trajectories are adopted. Afterwards, an improved genetic algorithm is used to identify the optimal trajectory by minimizing the fitness function. Finally, the numerical simulations and experiments validate the feasibility and the effectiveness of the established dynamic model and the trajectory planning approach. The amplitude of the residual vibration reduces approximately 54.9%, and the settling time decreases 57.1%. Therefore, the operation efficiency and manipulation stability are significantly improved.

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Pluripotential theory and convex bodies

NASA Astrophysics Data System (ADS)

Bayraktar, T.; Bloom, T.; Levenberg, N.

2018-03-01

A seminal paper by Berman and Boucksom exploited ideas from complex geometry to analyze the asymptotics of spaces of holomorphic sections of tensor powers of certain line bundles L over compact, complex manifolds as the power grows. This yielded results on weighted polynomial spaces in weighted pluripotential theory in {C}^d. Here, motivated by a recent paper by the first author on random sparse polynomials, we work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body in ({R}^+)^d. These classes of polynomials need not occur as sections of tensor powers of a line bundle L over a compact, complex manifold. We follow the approach of Berman and Boucksom to obtain analogous results. Bibliography: 16 titles.

The Heats of Formation of SiCl+n, for n=1-4

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry; Arnold, James O. (Technical Monitor)

1997-01-01

The heats of formation of SiCl(sub n) and SiCl+(sub n), for n=1-4, have been determined using the G2(B3LYP/MP2/CC) approach. The results for the neutral systems are in very good agreement with previous work. High level calibration calculations show that ion results have about the same accuracy as the neutrals, and allow us to refine the G2(B3LYP/MP2/CC) values. The calculations show that the adiabatic IP of SiCl4 is about 7 kcal/mol smaller than the accepted value. Using a rigid rotor/harmonic oscillator approximation, the temperature dependence of the heat of formation, heat capacity, and entropy are computed for 300 to 4000 K and fit to a polynomial.

Accurate wavelength measurements of a putative standard for near-infrared diffuse reflection spectrometry.

PubMed

Isaksson, Tomas; Yang, Husheng; Kemeny, Gabor J; Jackson, Richard S; Wang, Qian; Alam, M Kathleen; Griffiths, Peter R

2003-02-01

The diffuse reflection (DR) spectrum of a sample consisting of a mixture of rare earth oxides and talc was measured at 2 cm-1 resolution, using five different accessories installed on five different Fourier transform near-infrared (FT-NIR) spectrometers from four manufacturers. Peak positions for 37 peaks were determined using two peak-picking algorithms: center-of-mass and polynomial fitting. The wavenumber of the band center reported by either of these techniques was sensitive to the slope of the baseline, and so the baseline of the spectra was corrected using either a polynomial fit or conversion to the second derivative. Significantly different results were obtained with one combination of spectrometer and accessory than the others. Apparently, the beam path through the interferometer and DR accessory was different for this accessory than for any of the other measurements, causing a severe degradation of the resolution. Spectra measured on this instrument were removed as outliers. For measurements made on FT-NIR spectrometers, it is shown that it is important to check the resolution at which the spectrum has been measured using lines in the vibration-rotation spectrum of atmospheric water vapor and to specify the peak-picking and baseline-correction algorithms that are used to process the measured spectra. The variance between the results given by the four different methods of peak-picking and baseline correction was substantially larger than the variance between the remaining five measurements. Certain bands were found to be more suitable than others for use as wavelength standards. A band at 5943.13 cm-1 (1682.62 nm) was found to be the most stable band between the four methods and the six measurements. A band at 5177.04 cm-1 (1931.61 nm) has the highest precision between different measurements when polynomial baseline correction and polynomial peak-picking algorithms are used.

Nonlinear Structured Growth Mixture Models in M"plus" and OpenMx

ERIC Educational Resources Information Center

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2010-01-01

Growth mixture models (GMMs; B. O. Muthen & Muthen, 2000; B. O. Muthen & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models…

The prediction of acoustical particle motion using an efficient polynomial curve fit procedure

NASA Technical Reports Server (NTRS)

Marshall, S. E.; Bernhard, R.

1984-01-01

A procedure is examined whereby the acoustic model parameters, natural frequencies and mode shapes, in the cavities of transportation vehicles are determined experimentally. The acoustic model shapes are described in terms of the particle motion. The acoustic modal analysis procedure is tailored to existing minicomputer based spectral analysis systems.

Wireless Intrusion Detection

DTIC Science & Technology

2007-03-01

32 4.4 Algorithm Pseudo - Code ...................................................................................34 4.5 WIND Interface With a...difference estimates of xc temporal derivatives, or by using a polynomial fit to the previous values of xc. 34 4.4 ALGORITHM PSEUDO - CODE Pseudo ...Phase Shift Keying DQPSK Differential Quadrature Phase Shift Keying EVM Error Vector Magnitude FFT Fast Fourier Transform FPGA Field Programmable

Dynamic Bidirectional Reflectance Distribution Functions: Measurement and Representation

DTIC Science & Technology

2008-02-01

be included in the harmonic fits. Other sets of orthogonal functions such as Zernike polynomials have also been used to characterize BRDF and could...reflectance spectra of 3D objects,” Proc. SPIE 4663, 370–378 2001. 13J. R. Shell II, C. Salvagio, and J. R. Schott, “A novel BRDF measurement technique

Air motion determination by tracking humidity patterns in isentropic layers

NASA Technical Reports Server (NTRS)

Mancuso, R. L.; Hall, D. J.

1975-01-01

Determining air motions by tracking humidity patterns in isentropic layers was investigated. Upper-air rawinsonde data from the NSSL network and from the AVE-II pilot experiment were used to simulate temperature and humidity profile data that will eventually be available from geosynchronous satellites. Polynomial surfaces that move with time were fitted to the mixing-ratio values of the different isentropic layers. The velocity components of the polynomial surfaces are part of the coefficients that are determined in order to give an optimum fitting of the data. In the mid-troposphere, the derived humidity motions were in good agreement with the winds measured by rawinsondes so long as there were few or no clouds and the lapse rate was relatively stable. In the lower troposphere, the humidity motions were unreliable primarily because of nonadiabatic processes and unstable lapse rates. In the upper troposphere, the humidity amounts were too low to be measured with sufficient accuracy to give reliable results. However, it appears that humidity motions could be used to provide mid-tropospheric wind data over large regions of the globe.

Contact angle measurement with a smartphone

NASA Astrophysics Data System (ADS)

Chen, H.; Muros-Cobos, Jesus L.; Amirfazli, A.

2018-03-01

In this study, a smartphone-based contact angle measurement instrument was developed. Compared with the traditional measurement instruments, this instrument has the advantage of simplicity, compact size, and portability. An automatic contact point detection algorithm was developed to allow the instrument to correctly detect the drop contact points. Two different contact angle calculation methods, Young-Laplace and polynomial fitting methods, were implemented in this instrument. The performance of this instrument was tested first with ideal synthetic drop profiles. It was shown that the accuracy of the new system with ideal synthetic drop profiles can reach 0.01% with both Young-Laplace and polynomial fitting methods. Conducting experiments to measure both static and dynamic (advancing and receding) contact angles with the developed instrument, we found that the smartphone-based instrument can provide accurate and practical measurement results as the traditional commercial instruments. The successful demonstration of use of a smartphone (mobile phone) to conduct contact angle measurement is a significant advancement in the field as it breaks the dominate mold of use of a computer and a bench bound setup for such systems since their appearance in 1980s.

Contact angle measurement with a smartphone.

PubMed

Chen, H; Muros-Cobos, Jesus L; Amirfazli, A

2018-03-01

In this study, a smartphone-based contact angle measurement instrument was developed. Compared with the traditional measurement instruments, this instrument has the advantage of simplicity, compact size, and portability. An automatic contact point detection algorithm was developed to allow the instrument to correctly detect the drop contact points. Two different contact angle calculation methods, Young-Laplace and polynomial fitting methods, were implemented in this instrument. The performance of this instrument was tested first with ideal synthetic drop profiles. It was shown that the accuracy of the new system with ideal synthetic drop profiles can reach 0.01% with both Young-Laplace and polynomial fitting methods. Conducting experiments to measure both static and dynamic (advancing and receding) contact angles with the developed instrument, we found that the smartphone-based instrument can provide accurate and practical measurement results as the traditional commercial instruments. The successful demonstration of use of a smartphone (mobile phone) to conduct contact angle measurement is a significant advancement in the field as it breaks the dominate mold of use of a computer and a bench bound setup for such systems since their appearance in 1980s.

A simplified and powerful image processing methods to separate Thai jasmine rice and sticky rice varieties

NASA Astrophysics Data System (ADS)

Khondok, Piyoros; Sakulkalavek, Aparporn; Suwansukho, Kajpanya

2018-03-01

A simplified and powerful image processing procedures to separate the paddy of KHAW DOK MALI 105 or Thai jasmine rice and the paddy of sticky rice RD6 varieties were proposed. The procedures consist of image thresholding, image chain coding and curve fitting using polynomial function. From the fitting, three parameters of each variety, perimeters, area, and eccentricity, were calculated. Finally, the overall parameters were determined by using principal component analysis. The result shown that these procedures can be significantly separate both varieties.

Response Surface Analysis of Experiments with Random Blocks

DTIC Science & Technology

1988-09-01

partitioned into a lack of fit sum of squares, SSLOF, and a pure error sum of squares, SSPE . The latter is obtained by pooling the pure error sums of squares...from the blocks. Tests concerning the polynomial effects can then proceed using SSPE as the error term in the denominators of the F test statistics. 3.2...the center point in each of the three blocks is equal to SSPE = 2.0127 with 5 degrees of freedom. Hence, the lack of fit sum of squares is SSLoF

Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2004-08-01

A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed.

Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture.

PubMed

Muslimov, Eduard; Hugot, Emmanuel; Jahn, Wilfried; Vives, Sebastien; Ferrari, Marc; Chambion, Bertrand; Henry, David; Gaschet, Christophe

2017-06-26

In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

An algorithmic approach to solving polynomial equations associated with quantum circuits

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Zinin, M. V.

2009-12-01

In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Gröbner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Gröbner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Gröbner bases over F 2.

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

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

Konakli, Katerina, E-mail: konakli@ibk.baug.ethz.ch; Sudret, Bruno

2016-09-15

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely themore » exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input dimension, a situation that is often encountered in real-life problems. By introducing the conditional generalization error, we further demonstrate that canonical LRA tend to outperform sparse PCE in the prediction of extreme model responses, which is critical in reliability analysis.« less

A high-order time-accurate interrogation method for time-resolved PIV

NASA Astrophysics Data System (ADS)

Lynch, Kyle; Scarano, Fulvio

2013-03-01

A novel method is introduced for increasing the accuracy and extending the dynamic range of time-resolved particle image velocimetry (PIV). The approach extends the concept of particle tracking velocimetry by multiple frames to the pattern tracking by cross-correlation analysis as employed in PIV. The working principle is based on tracking the patterned fluid element, within a chosen interrogation window, along its individual trajectory throughout an image sequence. In contrast to image-pair interrogation methods, the fluid trajectory correlation concept deals with variable velocity along curved trajectories and non-zero tangential acceleration during the observed time interval. As a result, the velocity magnitude and its direction are allowed to evolve in a nonlinear fashion along the fluid element trajectory. The continuum deformation (namely spatial derivatives of the velocity vector) is accounted for by adopting local image deformation. The principle offers important reductions of the measurement error based on three main points: by enlarging the temporal measurement interval, the relative error becomes reduced; secondly, the random and peak-locking errors are reduced by the use of least-squares polynomial fits to individual trajectories; finally, the introduction of high-order (nonlinear) fitting functions provides the basis for reducing the truncation error. Lastly, the instantaneous velocity is evaluated as the temporal derivative of the polynomial representation of the fluid parcel position in time. The principal features of this algorithm are compared with a single-pair iterative image deformation method. Synthetic image sequences are considered with steady flow (translation, shear and rotation) illustrating the increase of measurement precision. An experimental data set obtained by time-resolved PIV measurements of a circular jet is used to verify the robustness of the method on image sequences affected by camera noise and three-dimensional motions. In both cases, it is demonstrated that the measurement time interval can be significantly extended without compromising the correlation signal-to-noise ratio and with no increase of the truncation error. The increase of velocity dynamic range scales more than linearly with the number of frames included for the analysis, which supersedes by one order of magnitude the pair correlation by window deformation. The main factors influencing the performance of the method are discussed, namely the number of images composing the sequence and the polynomial order chosen to represent the motion throughout the trajectory.

Helical Axis Data Visualization and Analysis of the Knee Joint Articulation.

PubMed

Millán Vaquero, Ricardo Manuel; Vais, Alexander; Dean Lynch, Sean; Rzepecki, Jan; Friese, Karl-Ingo; Hurschler, Christof; Wolter, Franz-Erich

2016-09-01

We present processing methods and visualization techniques for accurately characterizing and interpreting kinematical data of flexion-extension motion of the knee joint based on helical axes. We make use of the Lie group of rigid body motions and particularly its Lie algebra for a natural representation of motion sequences. This allows to analyze and compute the finite helical axis (FHA) and instantaneous helical axis (IHA) in a unified way without redundant degrees of freedom or singularities. A polynomial fitting based on Legendre polynomials within the Lie algebra is applied to provide a smooth description of a given discrete knee motion sequence which is essential for obtaining stable instantaneous helical axes for further analysis. Moreover, this allows for an efficient overall similarity comparison across several motion sequences in order to differentiate among several cases. Our approach combines a specifically designed patient-specific three-dimensional visualization basing on the processed helical axes information and incorporating computed tomography (CT) scans for an intuitive interpretation of the axes and their geometrical relation with respect to the knee joint anatomy. In addition, in the context of the study of diseases affecting the musculoskeletal articulation, we propose to integrate the above tools into a multiscale framework for exploring related data sets distributed across multiple spatial scales. We demonstrate the utility of our methods, exemplarily processing a collection of motion sequences acquired from experimental data involving several surgery techniques. Our approach enables an accurate analysis, visualization and comparison of knee joint articulation, contributing to the evaluation and diagnosis in medical applications.

Estimation of Heat Transfer Coefficient in Squeeze Casting of Magnesium Alloy AM60 by Experimental Polynomial Extrapolation Method

NASA Astrophysics Data System (ADS)

Sun, Zhizhong; Niu, Xiaoping; Hu, Henry

In this work, a different wall-thickness 5-step (with thicknesses as 3, 5, 8, 12, 20 mm) casting mold was designed, and squeeze casting of magnesium alloy AM60 was performed in a hydraulic press. The casting-die interfacial heat transfer coefficients (IHTC) in 5-step casting were determined based on experimental thermal histories data throughout the die and inside the casting which were recorded by fine type-K thermocouples. With measured temperatures, heat flux and IHTC were evaluated using the polynomial curve fitting method. The results show that the wall thickness affects IHTC peak values significantly. The IHTC value for the thick step is higher than that for the thin steps.

Prediction of textural attributes using color values of banana (Musa sapientum) during ripening.

PubMed

Jaiswal, Pranita; Jha, Shyam Narayan; Kaur, Poonam Preet; Bhardwaj, Rishi; Singh, Ashish Kumar; Wadhawan, Vishakha

2014-06-01

Banana is an important sub-tropical fruit in international trade. It undergoes significant textural and color transformations during ripening process, which in turn influence the eating quality of the fruit. In present study, color ('L', 'a' and 'b' value) and textural attributes of bananas (peel, fruit and pulp firmness; pulp toughness; stickiness) were studied simultaneously using Hunter Color Lab and Texture Analyser, respectively, during ripening period of 10 days at ambient atmosphere. There was significant effect of ripening period on all the considered textural characteristics and color properties of bananas except color value 'b'. In general, textural descriptors (peel, fruit and pulp firmness; and pulp toughness) decreased during ripening except stickiness, while color values viz 'a' and 'b' increased with ripening barring 'L' value. Among various textural attributes, peel toughness and pulp firmness showed highest correlation (r) with 'a' value of banana peel. In order to predict textural properties using color values of banana, five types of equations (linear/polynomial/exponential/logarithmic/power) were fitted. Among them, polynomial equation was found to be the best fit (highest coefficient of determination, R(2)) for prediction of texture using color properties for bananas. The pulp firmness, peel toughness and pulp toughness showed R(2) above 0.84 with indicating its potentiality of the fitted equations for prediction of textural profile of bananas non-destructively using 'a' value.

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

PubMed

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Interstellar photoelectric absorption cross sections, 0.03-10 keV

NASA Technical Reports Server (NTRS)

Morrison, R.; Mccammon, D.

1983-01-01

An effective absorption cross section per hydrogen atom has been calculated as a function of energy in the 0.03-10 keV range using the most recent atomic cross section and cosmic abundance data. Coefficients of a piecewise polynomial fit to the numerical results are given to allow convenient application in automated calculations.

Random regression models on Legendre polynomials to estimate genetic parameters for weights from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Albuquerque, L G; Alencar, M M

2010-08-01

The objective of this work was to estimate covariance functions for direct and maternal genetic effects, animal and maternal permanent environmental effects, and subsequently, to derive relevant genetic parameters for growth traits in Canchim cattle. Data comprised 49,011 weight records on 2435 females from birth to adult age. The model of analysis included fixed effects of contemporary groups (year and month of birth and at weighing) and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were allowed to vary and were modelled by a step function with 1, 4 or 11 classes based on animal's age. The model fitting four classes of residual variances was the best. A total of 12 random regression models from second to seventh order were used to model direct and maternal genetic effects, animal and maternal permanent environmental effects. The model with direct and maternal genetic effects, animal and maternal permanent environmental effects fitted by quadric, cubic, quintic and linear Legendre polynomials, respectively, was the most adequate to describe the covariance structure of the data. Estimates of direct and maternal heritability obtained by multi-trait (seven traits) and random regression models were very similar. Selection for higher weight at any age, especially after weaning, will produce an increase in mature cow weight. The possibility to modify the growth curve in Canchim cattle to obtain animals with rapid growth at early ages and moderate to low mature cow weight is limited.

Wavefront reconstruction for multi-lateral shearing interferometry using difference Zernike polynomials fitting

NASA Astrophysics Data System (ADS)

Liu, Ke; Wang, Jiannian; Wang, Hai; Li, Yanqiu

2018-07-01

For the multi-lateral shearing interferometers (multi-LSIs), the measurement accuracy can be enhanced by estimating the wavefront under test with the multidirectional phase information encoded in the shearing interferogram. Usually the multi-LSIs reconstruct the test wavefront from the phase derivatives in multiple directions using the discrete Fourier transforms (DFT) method, which is only suitable to small shear ratios and relatively sensitive to noise. To improve the accuracy of multi-LSIs, wavefront reconstruction from the multidirectional phase differences using the difference Zernike polynomials fitting (DZPF) method is proposed in this paper. For the DZPF method applied in the quadriwave LSI, difference Zernike polynomials in only two orthogonal shear directions are required to represent the phase differences in multiple shear directions. In this way, the test wavefront can be reconstructed from the phase differences in multiple shear directions using a noise-variance weighted least-squares method with almost no extra computational burden, compared with the usual recovery from the phase differences in two orthogonal directions. Numerical simulation results show that the DZPF method can maintain high reconstruction accuracy in a wider range of shear ratios and has much better anti-noise performance than the DFT method. A null test experiment of the quadriwave LSI has been conducted and the experimental results show that the measurement accuracy of the quadriwave LSI can be improved from 0.0054 λ rms to 0.0029 λ rms (λ = 632.8 nm) by substituting the DFT method with the proposed DZPF method in the wavefront reconstruction process.

An Artificial Intelligence Approach to the Symbolic Factorization of Multivariable Polynomials. Technical Report No. CS74019-R.

ERIC Educational Resources Information Center

Claybrook, Billy G.

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

Optimal Robust Motion Controller Design Using Multiobjective Genetic Algorithm

PubMed Central

Svečko, Rajko

2014-01-01

This paper describes the use of a multiobjective genetic algorithm for robust motion controller design. Motion controller structure is based on a disturbance observer in an RIC framework. The RIC approach is presented in the form with internal and external feedback loops, in which an internal disturbance rejection controller and an external performance controller must be synthesised. This paper involves novel objectives for robustness and performance assessments for such an approach. Objective functions for the robustness property of RIC are based on simple even polynomials with nonnegativity conditions. Regional pole placement method is presented with the aims of controllers' structures simplification and their additional arbitrary selection. Regional pole placement involves arbitrary selection of central polynomials for both loops, with additional admissible region of the optimized pole location. Polynomial deviation between selected and optimized polynomials is measured with derived performance objective functions. A multiobjective function is composed of different unrelated criteria such as robust stability, controllers' stability, and time-performance indexes of closed loops. The design of controllers and multiobjective optimization procedure involve a set of the objectives, which are optimized simultaneously with a genetic algorithm—differential evolution. PMID:24987749

New realisation of Preisach model using adaptive polynomial approximation

NASA Astrophysics Data System (ADS)

Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young

2012-09-01

Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.

Fabrication and correction of freeform surface based on Zernike polynomials by slow tool servo

NASA Astrophysics Data System (ADS)

Cheng, Yuan-Chieh; Hsu, Ming-Ying; Peng, Wei-Jei; Hsu, Wei-Yao

2017-10-01

Recently, freeform surface widely using to the optical system; because it is have advance of optical image and freedom available to improve the optical performance. For freeform optical fabrication by integrating freeform optical design, precision freeform manufacture, metrology freeform optics and freeform compensate method, to modify the form deviation of surface, due to production process of freeform lens ,compared and provides more flexibilities and better performance. This paper focuses on the fabrication and correction of the free-form surface. In this study, optical freeform surface using multi-axis ultra-precision manufacturing could be upgrading the quality of freeform. It is a machine equipped with a positioning C-axis and has the CXZ machining function which is also called slow tool servo (STS) function. The freeform compensate method of Zernike polynomials results successfully verified; it is correction the form deviation of freeform surface. Finally, the freeform surface are measured experimentally by Ultrahigh Accurate 3D Profilometer (UA3P), compensate the freeform form error with Zernike polynomial fitting to improve the form accuracy of freeform.

Estimating errors in least-squares fitting

NASA Technical Reports Server (NTRS)

Richter, P. H.

1995-01-01

While least-squares fitting procedures are commonly used in data analysis and are extensively discussed in the literature devoted to this subject, the proper assessment of errors resulting from such fits has received relatively little attention. The present work considers statistical errors in the fitted parameters, as well as in the values of the fitted function itself, resulting from random errors in the data. Expressions are derived for the standard error of the fit, as a function of the independent variable, for the general nonlinear and linear fitting problems. Additionally, closed-form expressions are derived for some examples commonly encountered in the scientific and engineering fields, namely ordinary polynomial and Gaussian fitting functions. These results have direct application to the assessment of the antenna gain and system temperature characteristics, in addition to a broad range of problems in data analysis. The effects of the nature of the data and the choice of fitting function on the ability to accurately model the system under study are discussed, and some general rules are deduced to assist workers intent on maximizing the amount of information obtained form a given set of measurements.

Bell-polynomial approach and Wronskian determinant solutions for three sets of differential-difference nonlinear evolution equations with symbolic computation

NASA Astrophysics Data System (ADS)

Qin, Bo; Tian, Bo; Wang, Yu-Feng; Shen, Yu-Jia; Wang, Ming

2017-10-01

Under investigation in this paper are the Belov-Chaltikian (BC), Leznov and Blaszak-Marciniak (BM) lattice equations, which are associated with the conformal field theory, UToda(m_1,m_2) system and r-matrix, respectively. With symbolic computation, the Bell-polynomial approach is developed to directly bilinearize those three sets of differential-difference nonlinear evolution equations (NLEEs). This Bell-polynomial approach does not rely on any dependent variable transformation, which constitutes the key step and main difficulty of the Hirota bilinear method, and thus has the advantage in the bilinearization of the differential-difference NLEEs. Based on the bilinear forms obtained, the N-soliton solutions are constructed in terms of the N × N Wronskian determinant. Graphic illustrations demonstrate that those solutions, more general than the existing results, permit some new properties, such as the solitonic propagation and interactions for the BC lattice equations, and the nonnegative dark solitons for the BM lattice equations.

Periodicity analysis of tourist arrivals to Banda Aceh using smoothing SARIMA approach

NASA Astrophysics Data System (ADS)

Miftahuddin, Helida, Desri; Sofyan, Hizir

2017-11-01

Forecasting the number of tourist arrivals who enters a region is needed for tourism businesses, economic and industrial policies, so that the statistical modeling needs to be conducted. Banda Aceh is the capital of Aceh province more economic activity is driven by the services sector, one of which is the tourism sector. Therefore, the prediction of the number of tourist arrivals is needed to develop further policies. The identification results indicate that the data arrival of foreign tourists to Banda Aceh to contain the trend and seasonal nature. Allegedly, the number of arrivals is influenced by external factors, such as economics, politics, and the holiday season caused the structural break in the data. Trend patterns are detected by using polynomial regression with quadratic and cubic approaches, while seasonal is detected by a periodic regression polynomial with quadratic and cubic approach. To model the data that has seasonal effects, one of the statistical methods that can be used is SARIMA (Seasonal Autoregressive Integrated Moving Average). The results showed that the smoothing, a method to detect the trend pattern is cubic polynomial regression approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 70.52. While the method for detecting the seasonal pattern is a periodic regression polynomial cubic approach, with the modified model and the multiplicative periodicity of 12 months. The AIC value obtained was 73.37. Furthermore, the best model to predict the number of foreign tourist arrivals to Banda Aceh in 2017 to 2018 is SARIMA (0,1,1)(1,1,0) with MAPE is 26%.

Using polynomials to simplify fixed pattern noise and photometric correction of logarithmic CMOS image sensors.

PubMed

Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

2015-10-16

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient.

Baseline Estimation and Outlier Identification for Halocarbons

NASA Astrophysics Data System (ADS)

Wang, D.; Schuck, T.; Engel, A.; Gallman, F.

2017-12-01

The aim of this paper is to build a baseline model for halocarbons and to statistically identify the outliers under specific conditions. In this paper, time series of regional CFC-11 and Chloromethane measurements was discussed, which taken over the last 4 years at two locations, including a monitoring station at northwest of Frankfurt am Main (Germany) and Mace Head station (Ireland). In addition to analyzing time series of CFC-11 and Chloromethane, more importantly, a statistical approach of outlier identification is also introduced in this paper in order to make a better estimation of baseline. A second-order polynomial plus harmonics are fitted to CFC-11 and chloromethane mixing ratios data. Measurements with large distance to the fitting curve are regard as outliers and flagged. Under specific requirement, the routine is iteratively adopted without the flagged measurements until no additional outliers are found. Both model fitting and the proposed outlier identification method are realized with the help of a programming language, Python. During the period, CFC-11 shows a gradual downward trend. And there is a slightly upward trend in the mixing ratios of Chloromethane. The concentration of chloromethane also has a strong seasonal variation, mostly due to the seasonal cycle of OH. The usage of this statistical method has a considerable effect on the results. This method efficiently identifies a series of outliers according to the standard deviation requirements. After removing the outliers, the fitting curves and trend estimates are more reliable.

Molecular Dynamics Analysis of Lysozyme Protein in Ethanol-Water Mixed Solvent Environment

NASA Astrophysics Data System (ADS)

Ochije, Henry Ikechukwu

Effect of protein-solvent interaction on the protein structure is widely studied using both experimental and computational techniques. Despite such extensive studies molecular level understanding of proteins and some simple solvents is still not fully understood. This work focuses on detailed molecular dynamics simulations to study of solvent effect on lysozyme protein, using water, alcohol and different concentrations of water-alcohol mixtures as solvents. The lysozyme protein structure in water, alcohol and alcohol-water mixture (0-12% alcohol) was studied using GROMACS molecular dynamics simulation code. Compared to water environment, the lysozome structure showed remarkable changes in solvents with increasing alcohol concentration. In particular, significant changes were observed in the protein secondary structure involving alpha helices. The influence of alcohol on the lysozyme protein was investigated by studying thermodynamic and structural properties. With increasing ethanol concentration we observed a systematic increase in total energy, enthalpy, root mean square deviation (RMSD), and radius of gyration. a polynomial interpolation approach. Using the resulting polynomial equation, we could determine above quantities for any intermediate alcohol percentage. In order to validate this approach, we selected an intermediate ethanol percentage and carried out full MD simulation. The results from MD simulation were in reasonably good agreement with that obtained using polynomial approach. Hence, the polynomial approach based method proposed here eliminates the need for computationally intensive full MD analysis for the concentrations within the range (0-12%) studied in this work.

Density effects on the electronic contribution to hydrogen Lyman alpha Stark profiles

NASA Astrophysics Data System (ADS)

Motapon, O.

1998-01-01

The quantum unified theory of Stark broadening (Tran Minh et al. 1975, Feautrier et al. 1976) is used to study the density effects on the electronic contribution to the hydrogen Lyman alpha lineshape. The contribution of the first angular momenta to the total profile is obtained by an extrapolation method, and the results agree with other approaches. The comparison made with Vidal et al. (1973) shows a good agreement; and the electronic profile is found to be linear in density for | Delta lambda right | greater than 8 Angstroms for densities below 10(17) cm(-3) , while the density dependence becomes more complex for | Delta lambda right | less than 8 Angstroms. The wing profiles are calculated at various temperatures scaling from 2500 to 40000K and a polynomial fit of these profiles is given.

Numeric model to predict the location of market demand and economic order quantity for retailers of supply chain

NASA Astrophysics Data System (ADS)

Fradinata, Edy; Marli Kesuma, Zurnila

2018-05-01

Polynomials and Spline regression are the numeric model where they used to obtain the performance of methods, distance relationship models for cement retailers in Banda Aceh, predicts the market area for retailers and the economic order quantity (EOQ). These numeric models have their difference accuracy for measuring the mean square error (MSE). The distance relationships between retailers are to identify the density of retailers in the town. The dataset is collected from the sales of cement retailer with a global positioning system (GPS). The sales dataset is plotted of its characteristic to obtain the goodness of fitted quadratic, cubic, and fourth polynomial methods. On the real sales dataset, polynomials are used the behavior relationship x-abscissa and y-ordinate to obtain the models. This research obtains some advantages such as; the four models from the methods are useful for predicting the market area for the retailer in the competitiveness, the comparison of the performance of the methods, the distance of the relationship between retailers, and at last the inventory policy based on economic order quantity. The results, the high-density retail relationship areas indicate that the growing population with the construction project. The spline is better than quadratic, cubic, and four polynomials in predicting the points indicating of small MSE. The inventory policy usages the periodic review policy type.

Aerodynamic database development of the ESA intermediate experimental vehicle

NASA Astrophysics Data System (ADS)

Pezzella, Giuseppe; Marino, Giuliano; Rufolo, Giuseppe C.

2014-01-01

This work deals with the aerodynamic database development of the Intermediate Experiment Vehicle. The aerodynamic analysis, carried out for the whole flight scenario, relies on computational fluid dynamics, wind tunnel test, and engineering-based design data generated during the project phases, from rarefied flow conditions, to hypersonic continuum flow up to reach subsonic speeds regime. Therefore, the vehicle aerodynamic database covers the range of Mach number, angle of attack, sideslip and control surface deflections foreseen for the vehicle nominal re-entry. In particular, the databasing activities are developed in the light of build-up approach. This means that all aerodynamic force and moment coefficients are provided by means of a linear summation over certain number of incremental contributions such as, for example, effect of sideslip angle, aerodynamic control surface effectiveness, etc. Each force and moment coefficient is treated separately and appropriate equation is provided, in which all the pertinent contributions for obtaining the total coefficient for any selected flight conditions appear. To this aim, all the available numerical and experimental aerodynamic data are gathered in order to explicit the functional dependencies from each aerodynamic model addend through polynomial expressions obtained with the least squares method. These polynomials are function of the primary variable that drives the phenomenon whereas secondary dependencies are introduced directly into its unknown coefficients which are determined by means of best-fitting algorithms.

Optical Performance Modeling of FUSE Telescope Mirror

NASA Technical Reports Server (NTRS)

Saha, Timo T.; Ohl, Raymond G.; Friedman, Scott D.; Moos, H. Warren

2000-01-01

We describe the Metrology Data Processor (METDAT), the Optical Surface Analysis Code (OSAC), and their application to the image evaluation of the Far Ultraviolet Spectroscopic Explorer (FUSE) mirrors. The FUSE instrument - designed and developed by the Johns Hopkins University and launched in June 1999 is an astrophysics satellite which provides high resolution spectra (lambda/Delta(lambda) = 20,000 - 25,000) in the wavelength region from 90.5 to 118.7 nm The FUSE instrument is comprised of four co-aligned, normal incidence, off-axis parabolic mirrors, four Rowland circle spectrograph channels with holographic gratings, and delay line microchannel plate detectors. The OSAC code provides a comprehensive analysis of optical system performance, including the effects of optical surface misalignments, low spatial frequency deformations described by discrete polynomial terms, mid- and high-spatial frequency deformations (surface roughness), and diffraction due to the finite size of the aperture. Both normal incidence (traditionally infrared, visible, and near ultraviolet mirror systems) and grazing incidence (x-ray mirror systems) systems can be analyzed. The code also properly accounts for reflectance losses on the mirror surfaces. Low frequency surface errors are described in OSAC by using Zernike polynomials for normal incidence mirrors and Legendre-Fourier polynomials for grazing incidence mirrors. The scatter analysis of the mirror is based on scalar scatter theory. The program accepts simple autocovariance (ACV) function models or power spectral density (PSD) models derived from mirror surface metrology data as input to the scatter calculation. The end product of the program is a user-defined pixel array containing the system Point Spread Function (PSF). The METDAT routine is used in conjunction with the OSAC program. This code reads in laboratory metrology data in a normalized format. The code then fits the data using Zernike polynomials for normal incidence systems or Legendre-Fourier polynomials for grazing incidence systems. It removes low order terms from the metrology data, calculates statistical ACV or PSD functions, and fits these data to OSAC models for the scatter analysis. In this paper we briefly describe the laboratory image testing of FUSE spare mirror performed in the near and vacuum ultraviolet at John Hopkins University and OSAC modeling of the test setup performed at NASA/GSFC. The test setup is a double-pass configuration consisting of a Hg discharge source, the FUSE off-axis parabolic mirror under test, an autocollimating flat mirror, and a tomographic imaging detector. Two additional, small fold flats are used in the optical train to accommodate the light source and the detector. The modeling is based on Zernike fitting and PSD analysis of surface metrology data measured by both the mirror vendor (Tinsley) and JHU. The results of our models agree well with the laboratory imaging data, thus validating our theoretical model. Finally, we predict the imaging performance of FUSE mirrors in their flight configuration at far-ultraviolet wavelengths.

VizieR Online Data Catalog: Optical/NIR photometry of OGLE-2012-SN-006 (Pastorello+, 2015)

NASA Astrophysics Data System (ADS)

Pastorello, A.; Wyrzykowski, L.; Valenti, S.; Prieto, J. L.; Kozlowski, S.; Udalski, A.; Elias-Rosa, N.; Morales-Garoffolo, A.; Anderson, J. P.; Benetti, S.; Bersten, M.; Botticella, M. T.; Cappellaro, E.; Fasano, G.; Fraser, M.; Gal-Yam, A.; Gillone, M.; Graham, M. L.; Greiner, J.; Hachinger, S.; Howell, D. A.; Inserra, C.; Parrent, J.; Rau, A.; Schulze, S.; Smartt, S. J.; Smith, K. W.; Turatto, M.; Yaron, O.; Young, D. R.; Kubiak, M.; Szymanski, M. K.; Pietrzynski, G.; Soszynski, I.; Ulaczyk, K.; Poleski, R.; Pietrukowicz, P.; Skowron, J.; Mroz, P.

2017-11-01

Photometric measurements in the optical and NIR bands were obtained through the PSF-fitting technique. A template PSF was built using stars in the SN field. With this PSF model along with a low-order polynomial surface, we finally performed a fit to the SN and the underlying background. OGLE-IV photometry was obtained using the difference imaging analysis, which is a template subtraction method adapted to the OGLE data and detailed in Wyrzykowski et al. 2014, J/AcA/64/197 (see also Wozniak 2000, J/AcA/50/421). (2 data files).

Linear FBG Temperature Sensor Interrogation with Fabry-Perot ITU Multi-wavelength Reference.

PubMed

Park, Hyoung-Jun; Song, Minho

2008-10-29

The equidistantly spaced multi-passbands of a Fabry-Perot ITU filter are used as an efficient multi-wavelength reference for fiber Bragg grating sensor demodulation. To compensate for the nonlinear wavelength tuning effect in the FBG sensor demodulator, a polynomial fitting algorithm was applied to the temporal peaks of the wavelength-scanned ITU filter. The fitted wavelength values are assigned to the peak locations of the FBG sensor reflections, obtaining constant accuracy, regardless of the wavelength scan range and frequency. A linearity error of about 0.18% against a reference thermocouple thermometer was obtained with the suggested method.

Development of a winter wheat adjustable crop calendar model

NASA Technical Reports Server (NTRS)

Baker, J. R. (Principal Investigator)

1978-01-01

The author has identified the following significant results. After parameter estimation, tests were conducted with variances from the fits, and on independent data. From these tests, it was generally concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson's triquadratic form, in general use for spring wheat, was found to show promise for winter wheat, but special techniques and care were required for its use. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with daily environmental values as independent variables.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

An analytical technique for approximating unsteady aerodynamics in the time domain

NASA Technical Reports Server (NTRS)

Dunn, H. J.

1980-01-01

An analytical technique is presented for approximating unsteady aerodynamic forces in the time domain. The order of elements of a matrix Pade approximation was postulated, and the resulting polynomial coefficients were determined through a combination of least squares estimates for the numerator coefficients and a constrained gradient search for the denominator coefficients which insures stable approximating functions. The number of differential equations required to represent the aerodynamic forces to a given accuracy tends to be smaller than that employed in certain existing techniques where the denominator coefficients are chosen a priori. Results are shown for an aeroelastic, cantilevered, semispan wing which indicate a good fit to the aerodynamic forces for oscillatory motion can be achieved with a matrix Pade approximation having fourth order numerator and second order denominator polynomials.

Enhancing the performance of MOEAs: an experimental presentation of a new fitness guided mutation operator

NASA Astrophysics Data System (ADS)

Liagkouras, K.; Metaxiotis, K.

2017-01-01

Multi-objective evolutionary algorithms (MOEAs) are currently a dynamic field of research that has attracted considerable attention. Mutation operators have been utilized by MOEAs as variation mechanisms. In particular, polynomial mutation (PLM) is one of the most popular variation mechanisms and has been utilized by many well-known MOEAs. In this paper, we revisit the PLM operator and we propose a fitness-guided version of the PLM. Experimental results obtained by non-dominated sorting genetic algorithm II and strength Pareto evolutionary algorithm 2 show that the proposed fitness-guided mutation operator outperforms the classical PLM operator, based on different performance metrics that evaluate both the proximity of the solutions to the Pareto front and their dispersion on it.

Image Processing Language. Phase 1

DTIC Science & Technology

1988-05-01

their entirety. Nonetheless, they can serve as guidelines to which the construction of a useful and comprehensive imaging algebra might aspire. 3. TIH... guidelines to which the construction of a useful and comprehensive imaging algebra might aspire. * It was recognized that any structure which encompasses...Bernstein Polynomial Approximation Best Plane Fit ( BPF , Sobel, Roberts, Prewitt, Gradient) Boundary Finder Boundary Segmenter Chain Code Angle

Compatible taper equation for loblolly pine

Treesearch

J. P. McClure; R. L. Czaplewski

1986-01-01

Cao's compatible, segmented polynomial taper equation (Q. V. Cao, H. E. Burkhart, and T. A. Max. For. Sci. 26: 71-80. 1980) is fitted to a large loblolly pine data set from the southeastern United States. Equations are presented that predict diameter at a given height, height to a given top diameter, and volume below a given position on the main stem. All...

Simplified curve fits for the thermodynamic properties of equilibrium air

NASA Technical Reports Server (NTRS)

Srinivasan, S.; Tannehill, J. C.; Weilmuenster, K. J.

1986-01-01

New improved curve fits for the thermodynamic properties of equilibrium air were developed. The curve fits are for p = p(e,rho), a = a(e,rho), T = T(e,rho), s = s(e,rho), T = T(p,rho), h = h(p,rho), rho = rho(p,s), e = e(p,s) and a = a(p,s). These curve fits can be readily incorporated into new or existing Computational Fluid Dynamics (CFD) codes if real-gas effects are desired. The curve fits were constructed using Grabau-type transition functions to model the thermodynamic surfaces in a piecewise manner. The accuracies and continuity of these curve fits are substantially improved over those of previous curve fits appearing in NASA CR-2470. These improvements were due to the incorporation of a small number of additional terms in the approximating polynomials and careful choices of the transition functions. The ranges of validity of the new curve fits are temperatures up to 25,000 K and densities from 10 to the minus 7th to 100 amagats (rho/rho sub 0).

A fast, automated, polynomial-based cosmic ray spike-removal method for the high-throughput processing of Raman spectra.

PubMed

Schulze, H Georg; Turner, Robin F B

2013-04-01

Raman spectra often contain undesirable, randomly positioned, intense, narrow-bandwidth, positive, unidirectional spectral features generated when cosmic rays strike charge-coupled device cameras. These must be removed prior to analysis, but doing so manually is not feasible for large data sets. We developed a quick, simple, effective, semi-automated procedure to remove cosmic ray spikes from spectral data sets that contain large numbers of relatively homogenous spectra. Although some inhomogeneous spectral data sets can be accommodated--it requires replacing excessively modified spectra with the originals and removing their spikes with a median filter instead--caution is advised when processing such data sets. In addition, the technique is suitable for interpolating missing spectra or replacing aberrant spectra with good spectral estimates. The method is applied to baseline-flattened spectra and relies on fitting a third-order (or higher) polynomial through all the spectra at every wavenumber. Pixel intensities in excess of a threshold of 3× the noise standard deviation above the fit are reduced to the threshold level. Because only two parameters (with readily specified default values) might require further adjustment, the method is easily implemented for semi-automated processing of large spectral sets.

Particle drag history in a subcritical post-shock flow - data analysis method and uncertainty

NASA Astrophysics Data System (ADS)

Ding, Liuyang; Bordoloi, Ankur; Adrian, Ronald; Prestridge, Kathy; Arizona State University Team; Los Alamos National Laboratory Team

2017-11-01

A novel data analysis method for measuring particle drag in an 8-pulse particle tracking velocimetry-accelerometry (PTVA) experiment is described. We represented the particle drag history, CD(t) , using polynomials up to the third order. An analytical model for continuous particle position history was derived by integrating an equation relating CD(t) with particle velocity and acceleration. The coefficients of CD(t) were then calculated by fitting the position history model to eight measured particle locations in the sense of least squares. A preliminary test with experimental data showed that the new method yielded physically more reasonable particle velocity and acceleration history compared to conventionally adopted polynomial fitting. To fully assess and optimize the performance of the new method, we performed a PTVA simulation by assuming a ground truth of particle motion based on an ensemble of experimental data. The results indicated a significant reduction in the RMS error of CD. We also found that for particle locating noise between 0.1 and 3 pixels, a range encountered in our experiment, the lowest RMS error was achieved by using the quadratic CD(t) model. Furthermore, we will also discuss the optimization of the pulse timing configuration.

Goldindec: A Novel Algorithm for Raman Spectrum Baseline Correction

PubMed Central

Liu, Juntao; Sun, Jianyang; Huang, Xiuzhen; Li, Guojun; Liu, Binqiang

2016-01-01

Raman spectra have been widely used in biology, physics, and chemistry and have become an essential tool for the studies of macromolecules. Nevertheless, the raw Raman signal is often obscured by a broad background curve (or baseline) due to the intrinsic fluorescence of the organic molecules, which leads to unpredictable negative effects in quantitative analysis of Raman spectra. Therefore, it is essential to correct this baseline before analyzing raw Raman spectra. Polynomial fitting has proven to be the most convenient and simplest method and has high accuracy. In polynomial fitting, the cost function used and its parameters are crucial. This article proposes a novel iterative algorithm named Goldindec, freely available for noncommercial use as noted in text, with a new cost function that not only conquers the influence of great peaks but also solves the problem of low correction accuracy when there is a high peak number. Goldindec automatically generates parameters from the raw data rather than by empirical choice, as in previous methods. Comparisons with other algorithms on the benchmark data show that Goldindec has a higher accuracy and computational efficiency, and is hardly affected by great peaks, peak number, and wavenumber. PMID:26037638

Reply to ‘No correction for the light propagation within the cube: Comment on Relativistic theory of the falling cube gravimeter’

NASA Astrophysics Data System (ADS)

Ashby, Neil

2018-06-01

The comment (Nagornyi 2018 Metrologia) claims that, notwithstanding the conclusions stated in the paper Relativistic theory of the falling cube gravimeter (Ashby 2008 Metrologia 55 1–10), there is no need to consider the dimensions or refractive index of the cube in fitting data from falling cube absolute gravimeters; additional questions are raised about matching quartic polynomials while determining only three quantities. The comment also suggests errors were made in Ashby (2008 Metrologia 55 1–10) while implementing the fitting routines on which the conclusions were based. The main contention of the comment is shown to be invalid because retarded time was not properly used in constructing a fictitious cube position. Such a fictitious position, fixed relative to the falling cube, is derived and shown to be dependent on cube dimensions and refractive index. An example is given showing how in the present context, polynomials of fourth order can be effectively matched by determining only three quantities, and a new compact characterization of the interference signal arriving at the detector is given. Work of the U.S. government, not subject to copyright.

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

Two-component, ab initio potential energy surface for CO2—H2O, extension to the hydrate clathrate, CO2@(H2O)20, and VSCF/VCI vibrational analyses of both

NASA Astrophysics Data System (ADS)

Wang, Qingfeng Kee; Bowman, Joel M.

2017-10-01

We report an ab initio, full-dimensional, potential energy surface (PES) for CO2—H2O, in which two-body interaction energies are fit using a basis of permutationally invariant polynomials and combined with accurate potentials for the non-interacting monomers. This approach which we have termed "plug and play" is extended here to improve the precision of the 2-body fit in the long range. This is done by combining two separate fits. One is a fit to 47 593 2-body energies in the region of strong interaction and approaching the long range, and the second one is a fit to 6244 2-body energies in the long range. The two fits have a region of overlap which permits a smooth switch from one to the other. All energies are obtained at the CCSD(T)-F12b/aug-cc-pVTZ level of theory. Properties of the full PES, i.e., stationary points, harmonic frequencies of the global minimum, etc., are shown to be in excellent agreement with direct CCSD(T)-F12b/aug-cc-pVTZ results. Diffusion Monte Carlo calculations of the dimer zero-point energy (ZPE) are performed, and a dissociation energy, D0, of 787 cm-1 is obtained using that ZPE, De, and the rigorous ZPEs of the monomers. Using a benchmark De, D0 is 758 cm-1. Vibrational self-consistent field (VSCF)/virtual state configuration interaction (VCI) MULTIMODE calculations of intramolecular fundamentals are reported and are in good agreement with available experimental results. Finally, the full dimer PES is combined with an existing ab initio water potential to develop a potential for the CO2 hydrate clathrate CO2(H2O)20(512 water cage). A full normal-mode analysis of this hydrate clathrate is reported as are local-monomer VSCF/VCI calculations of the fundamentals of CO2.

Two-component, ab initio potential energy surface for CO2-H2O, extension to the hydrate clathrate, CO2@(H2O)20, and VSCF/VCI vibrational analyses of both.

PubMed

Wang, Qingfeng Kee; Bowman, Joel M

2017-10-28

We report an ab initio, full-dimensional, potential energy surface (PES) for CO 2 -H 2 O, in which two-body interaction energies are fit using a basis of permutationally invariant polynomials and combined with accurate potentials for the non-interacting monomers. This approach which we have termed "plug and play" is extended here to improve the precision of the 2-body fit in the long range. This is done by combining two separate fits. One is a fit to 47 593 2-body energies in the region of strong interaction and approaching the long range, and the second one is a fit to 6244 2-body energies in the long range. The two fits have a region of overlap which permits a smooth switch from one to the other. All energies are obtained at the CCSD(T)-F12b/aug-cc-pVTZ level of theory. Properties of the full PES, i.e., stationary points, harmonic frequencies of the global minimum, etc., are shown to be in excellent agreement with direct CCSD(T)-F12b/aug-cc-pVTZ results. Diffusion Monte Carlo calculations of the dimer zero-point energy (ZPE) are performed, and a dissociation energy, D 0 , of 787 cm -1 is obtained using that ZPE, D e , and the rigorous ZPEs of the monomers. Using a benchmark D e , D 0 is 758 cm -1 . Vibrational self-consistent field (VSCF)/virtual state configuration interaction (VCI) MULTIMODE calculations of intramolecular fundamentals are reported and are in good agreement with available experimental results. Finally, the full dimer PES is combined with an existing ab initio water potential to develop a potential for the CO 2 hydrate clathrate CO 2 (H 2 O) 20 (5 12 water cage). A full normal-mode analysis of this hydrate clathrate is reported as are local-monomer VSCF/VCI calculations of the fundamentals of CO 2 .

Assessing the Multidimensional Relationship Between Medication Beliefs and Adherence in Older Adults With Hypertension Using Polynomial Regression.

PubMed

Dillon, Paul; Phillips, L Alison; Gallagher, Paul; Smith, Susan M; Stewart, Derek; Cousins, Gráinne

2018-02-05

The Necessity-Concerns Framework (NCF) is a multidimensional theory describing the relationship between patients' positive and negative evaluations of their medication which interplay to influence adherence. Most studies evaluating the NCF have failed to account for the multidimensional nature of the theory, placing the separate dimensions of medication "necessity beliefs" and "concerns" onto a single dimension (e.g., the Beliefs about Medicines Questionnaire-difference score model). To assess the multidimensional effect of patient medication beliefs (concerns and necessity beliefs) on medication adherence using polynomial regression with response surface analysis. Community-dwelling older adults >65 years (n = 1,211) presenting their own prescription for antihypertensive medication to 106 community pharmacies in the Republic of Ireland rated their concerns and necessity beliefs to antihypertensive medications at baseline and their adherence to antihypertensive medication at 12 months via structured telephone interview. Confirmatory polynomial regression found the difference-score model to be inaccurate; subsequent exploratory analysis identified a quadratic model to be the best-fitting polynomial model. Adherence was lowest among those with strong medication concerns and weak necessity beliefs, and adherence was greatest for those with weak concerns and strong necessity beliefs (slope β = -0.77, p<.001; curvature β = -0.26, p = .004). However, novel nonreciprocal effects were also observed; patients with simultaneously high concerns and necessity beliefs had lower adherence than those with simultaneously low concerns and necessity beliefs (slope β = -0.36, p = .004; curvature β = -0.25, p = .003). The difference-score model fails to account for the potential nonreciprocal effects. Results extend evidence supporting the use of polynomial regression to assess the multidimensional effect of medication beliefs on adherence.

Application of overlay modeling and control with Zernike polynomials in an HVM environment

NASA Astrophysics Data System (ADS)

Ju, JaeWuk; Kim, MinGyu; Lee, JuHan; Nabeth, Jeremy; Jeon, Sanghuck; Heo, Hoyoung; Robinson, John C.; Pierson, Bill

2016-03-01

Shrinking technology nodes and smaller process margins require improved photolithography overlay control. Generally, overlay measurement results are modeled with Cartesian polynomial functions for both intra-field and inter-field models and the model coefficients are sent to an advanced process control (APC) system operating in an XY Cartesian basis. Dampened overlay corrections, typically via exponentially or linearly weighted moving average in time, are then retrieved from the APC system to apply on the scanner in XY Cartesian form for subsequent lot exposure. The goal of the above method is to process lots with corrections that target the least possible overlay misregistration in steady state as well as in change point situations. In this study, we model overlay errors on product using Zernike polynomials with same fitting capability as the process of reference (POR) to represent the wafer-level terms, and use the standard Cartesian polynomials to represent the field-level terms. APC calculations for wafer-level correction are performed in Zernike basis while field-level calculations use standard XY Cartesian basis. Finally, weighted wafer-level correction terms are converted to XY Cartesian space in order to be applied on the scanner, along with field-level corrections, for future wafer exposures. Since Zernike polynomials have the property of being orthogonal in the unit disk we are able to reduce the amount of collinearity between terms and improve overlay stability. Our real time Zernike modeling and feedback evaluation was performed on a 20-lot dataset in a high volume manufacturing (HVM) environment. The measured on-product results were compared to POR and showed a 7% reduction in overlay variation including a 22% terms variation. This led to an on-product raw overlay Mean + 3Sigma X&Y improvement of 5% and resulted in 0.1% yield improvement.

An Analysis of Polynomial Chaos Approximations for Modeling Single-Fluid-Phase Flow in Porous Medium Systems

PubMed Central

Rupert, C.P.; Miller, C.T.

2008-01-01

We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method. PMID:18836519

Integrand reduction for two-loop scattering amplitudes through multivariate polynomial division

NASA Astrophysics Data System (ADS)

Mastrolia, Pierpaolo; Mirabella, Edoardo; Ossola, Giovanni; Peraro, Tiziano

2013-04-01

We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for arbitrary amplitudes, regardless of the number of loops. It allows for the determination of the residue at any multiparticle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure. By using the division modulo Gröbner basis, we can derive a simple integrand recurrence relation that generates the multiparticle pole decomposition for integrands of arbitrary multiloop amplitudes. We apply the new reduction algorithm to the two-loop planar and nonplanar diagrams contributing to the five-point scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity in four dimensions, whose numerator functions contain up to rank-two terms in the integration momenta. We determine all polynomial residues parametrizing the cuts of the corresponding topologies and subtopologies. We obtain the integral basis for the decomposition of each diagram from the polynomial form of the residues. Our approach is well suited for a seminumerical implementation, and its general mathematical properties provide an effective algorithm for the generalization of the integrand-reduction method to all orders in perturbation theory.

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

NASA Astrophysics Data System (ADS)

Yu, Gwo-Ruey; Huang, Yu-Chia; Cheng, Chih-Yung

2016-07-01

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi-Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland W.

1992-01-01

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Revision of the Phenomenological Characteristics of the Algol-Type Stars Using the Nav Algorithm

NASA Astrophysics Data System (ADS)

Tkachenko, M. G.; Andronov, I. L.; Chinarova, L. L.

Phenomenological characteristics of the sample of the Algol-type stars are revised using a recently developed NAV ("New Algol Variable") algorithm (2012Ap.....55..536A, 2012arXiv 1212.6707A) and compared to that obtained using common methods of Trigonometric Polynomial Fit (TP) or local Algebraic Polynomial (A) fit of a fixed or (alternately) statistically optimal degree (1994OAP.....7...49A, 2003ASPC..292..391A). The computer program NAV is introduced, which allows to determine the best fit with 7 "linear" and 5 "nonlinear" parameters and their error estimates. The number of parameters is much smaller than for the TP fit (typically 20-40, depending on the width of the eclipse, and is much smaller (5-20) for the W UMa and β Lyrae-type stars. This causes more smooth approximation taking into account the reflection and ellipsoidal effects (TP2) and generally different shapes of the primary and secondary eclipses. An application of the method to two-color CCD photometry to the recently discovered eclipsing variable 2MASS J18024395 + 4003309 = VSX J180243.9 +400331 (2015JASS...32..101A) allowed to make estimates of the physical parameters of the binary system based on the phenomenological parameters of the light curve. The phenomenological parameters of the light curves were determined for the sample of newly discovered EA and EW-type stars (VSX J223429.3+552903, VSX J223421.4+553013, VSX J223416.2+553424, USNO-B1.0 1347-0483658, UCAC3-191-085589, VSX J180755.6+074711= UCAC3 196-166827). Despite we have used original observations published by the discoverers, the accuracy estimates of the period using the NAV method are typically better than the original ones.

Data Processing Algorithm for Diagnostics of Combustion Using Diode Laser Absorption Spectrometry.

PubMed

Mironenko, Vladimir R; Kuritsyn, Yuril A; Liger, Vladimir V; Bolshov, Mikhail A

2018-02-01

A new algorithm for the evaluation of the integral line intensity for inferring the correct value for the temperature of a hot zone in the diagnostic of combustion by absorption spectroscopy with diode lasers is proposed. The algorithm is based not on the fitting of the baseline (BL) but on the expansion of the experimental and simulated spectra in a series of orthogonal polynomials, subtracting of the first three components of the expansion from both the experimental and simulated spectra, and fitting the spectra thus modified. The algorithm is tested in the numerical experiment by the simulation of the absorption spectra using a spectroscopic database, the addition of white noise, and the parabolic BL. Such constructed absorption spectra are treated as experimental in further calculations. The theoretical absorption spectra were simulated with the parameters (temperature, total pressure, concentration of water vapor) close to the parameters used for simulation of the experimental data. Then, spectra were expanded in the series of orthogonal polynomials and first components were subtracted from both spectra. The value of the correct integral line intensities and hence the correct temperature evaluation were obtained by fitting of the thus modified experimental and simulated spectra. The dependence of the mean and standard deviation of the evaluation of the integral line intensity on the linewidth and the number of subtracted components (first two or three) were examined. The proposed algorithm provides a correct estimation of temperature with standard deviation better than 60 K (for T = 1000 K) for the line half-width up to 0.6 cm -1 . The proposed algorithm allows for obtaining the parameters of a hot zone without the fitting of usually unknown BL.

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference.

PubMed

Breda, F C; Albuquerque, L G; Euclydes, R F; Bignardi, A B; Baldi, F; Torres, R A; Barbosa, L; Tonhati, H

2010-02-01

Random regression models were used to estimate genetic parameters for test-day milk yield in Murrah buffaloes using Bayesian inference. Data comprised 17,935 test-day milk records from 1,433 buffaloes. Twelve models were tested using different combinations of third-, fourth-, fifth-, sixth-, and seventh-order orthogonal polynomials of weeks of lactation for additive genetic and permanent environmental effects. All models included the fixed effects of contemporary group, number of daily milkings and age of cow at calving as covariate (linear and quadratic effect). In addition, residual variances were considered to be heterogeneous with 6 classes of variance. Models were selected based on the residual mean square error, weighted average of residual variance estimates, and estimates of variance components, heritabilities, correlations, eigenvalues, and eigenfunctions. Results indicated that changes in the order of fit for additive genetic and permanent environmental random effects influenced the estimation of genetic parameters. Heritability estimates ranged from 0.19 to 0.31. Genetic correlation estimates were close to unity between adjacent test-day records, but decreased gradually as the interval between test-days increased. Results from mean squared error and weighted averages of residual variance estimates suggested that a model considering sixth- and seventh-order Legendre polynomials for additive and permanent environmental effects, respectively, and 6 classes for residual variances, provided the best fit. Nevertheless, this model presented the largest degree of complexity. A more parsimonious model, with fourth- and sixth-order polynomials, respectively, for these same effects, yielded very similar genetic parameter estimates. Therefore, this last model is recommended for routine applications. Copyright 2010 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Phase analysis for three-dimensional surface reconstruction of apples using structured-illumination reflectance imaging

NASA Astrophysics Data System (ADS)

Lu, Yuzhen; Lu, Renfu

2017-05-01

Three-dimensional (3-D) shape information is valuable for fruit quality evaluation. This study was aimed at developing phase analysis techniques for reconstruction of the 3-D surface of fruit from the pattern images acquired by a structuredillumination reflectance imaging (SIRI) system. Phase-shifted sinusoidal patterns, distorted by the fruit geometry, were acquired and processed through phase demodulation, phase unwrapping and other post-processing procedures to obtain phase difference maps relative to the phase of a reference plane. The phase maps were then transformed into height profiles and 3-D shapes in a world coordinate system based on phase-to-height and in-plane calibrations. A reference plane-based approach, coupled with the curve fitting technique using polynomials of order 3 or higher, was utilized for phase-to-height calibrations, which achieved superior accuracies with the root-mean-squared errors (RMSEs) of 0.027- 0.033 mm for a height measurement range of 0-91 mm. The 3rd-order polynomial curve fitting technique was further tested on two reference blocks with known heights, resulting in relative errors of 3.75% and 4.16%. In-plane calibrations were performed by solving a linear system formed by a number of control points in a calibration object, which yielded a RMSE of 0.311 mm. Tests of the calibrated system for reconstructing the surface of apple samples showed that surface concavities (i.e., stem/calyx regions) could be easily discriminated from bruises from the phase difference maps, reconstructed height profiles and the 3-D shape of apples. This study has laid a foundation for using SIRI for 3-D shape measurement, and thus expanded the capability of the technique for quality evaluation of horticultural products. Further research is needed to utilize the phase analysis techniques for stem/calyx detection of apples, and optimize the phase demodulation and unwrapping algorithms for faster and more reliable detection.

Investigations of black-hole spectra: Purely-imaginary modes and Kerr ringdown radiation

NASA Astrophysics Data System (ADS)

Zalutskiy, Maxim P.

When black holes are perturbed they give rise to characteristic waves that propagate outwards carrying information about the black hole. In the linear regime these waves are described in terms of quasinormal modes (QNM). Studying QNM is an important topic which may provide a connection to the quantum theory of gravity in addition to their astrophysical applications. Quasinormal modes correspond to complex frequencies where the real part represents oscillation and the imaginary part represents damping. We have developed a new code for calculating QNM with high precision and accuracy, which we applied to the Schwarzschild and Kerr geometries. The high accuracy of our calculations was a significant improvement over prior work, allowing us to compute QNM much closer to the negative imaginary axis (NIA) than it was possible before. The existence of QNM on the NIA has remained poorly understood, but our high accuracy studies have highlighted the importance of understanding their nature. In this work we show how the purely-imaginary modes can be calculated with the help of the theory of confluent Heun polynomials with the conclusion that all modes on the NIA correspond to polynomial solutions. We also show that certain types of these modes correspond to Kerr QNM. Finally, using our highly accurate QNM data we model the ringdown, a remnant black hole's decaying radiation. Ringdown occurs in the final stages of such violent astrophysical events as supernovae and black hole collisions. We use our model to analyse the ringdown waveforms from the publicly available binary black hole coalescence catalog maintained by the SXS collaboration. In our analysis we use a number of methods: Fourier transform, multi-mode nonlinear fitting and waveform overlap. Both our fitting and overlap approach allow inclusion of many modes in the ringdown model with the goal being to extract information about the nature of the astrophysical source of the ringdown signal.

Using Polynomials to Simplify Fixed Pattern Noise and Photometric Correction of Logarithmic CMOS Image Sensors

PubMed Central

Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

2015-01-01

An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient. PMID:26501287

Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach.

PubMed

Lam, H K

2012-02-01

This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.

Mixed kernel function support vector regression for global sensitivity analysis

NASA Astrophysics Data System (ADS)

Cheng, Kai; Lu, Zhenzhou; Wei, Yuhao; Shi, Yan; Zhou, Yicheng

2017-11-01

Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on an assigned output response. Amongst the wide sensitivity analyses in literature, the Sobol indices have attracted much attention since they can provide accurate information for most models. In this paper, a mixed kernel function (MKF) based support vector regression (SVR) model is employed to evaluate the Sobol indices at low computational cost. By the proposed derivation, the estimation of the Sobol indices can be obtained by post-processing the coefficients of the SVR meta-model. The MKF is constituted by the orthogonal polynomials kernel function and Gaussian radial basis kernel function, thus the MKF possesses both the global characteristic advantage of the polynomials kernel function and the local characteristic advantage of the Gaussian radial basis kernel function. The proposed approach is suitable for high-dimensional and non-linear problems. Performance of the proposed approach is validated by various analytical functions and compared with the popular polynomial chaos expansion (PCE). Results demonstrate that the proposed approach is an efficient method for global sensitivity analysis.

Rock infromation of the moon revealed by multi-channel microwave radiometer data

NASA Astrophysics Data System (ADS)

Hu, Guo-Ping; Zheng, Yong-Chun; Chan, Kwing Lam; Xu, Ao-Ao

2016-10-01

Rock abundance on lunar surface is an important consideration for understanding the physical properties of the Moon. With the deeper penetration power of the microwave, data from Chang'E (CE) multichannel (3.0-, 7.8-, 19.35-, and 37-GHz) microwave radiometer (MRM) are used to constrain the rock distribution on the Moon. The contrasting thermo-physical properties between rocks and regolith fines cause multiple brightness temperature (TB) to be present within the field of view of CE microwave data. But these variations could be easily masked by the more significant effect of ilmenite on TB, especially in the mare regions which are rich in ilmenite.To highlight the rock effect in TB, the diurnal TB difference, which has the effect of enlarging the TB difference caused by the rock abundance and reducing the absolute error of the CE microwave data, is considered here. The rock information in TB data is distinguished from the ilmenite effect by comparing the diurnal TB difference with a statistical TB model of the mare regions which are relatively low in rock abundance. The employed statistical TB model is a polynomial fitting formula between the selected CE TB data from mare regions and the corresponding TiO2 content data from Clementine UVVIS data. The correlation coefficients of the polynomial fit between TB and TiO2 content are 0.94 at lunar daytime and 0.84 at lunar nighttime, respectively. This polynomial fit forms an approximated relationship between the TiO2 content and TB when rock abundance is zero, with a standard error determined from the regression procedure.Based on the TiO2 map retrieved from Clementine UVVIS data, the TB map that is deflated to a lower TiO2 content shows a distribution trend similar to the rock abundance map retrieved by LRO data, except for the mare regions at the nearside of the Moon. The bigger diurnal TB difference in the mare regions could be either caused by the rich ilmenite rocks or the smaller rocks which cannot be recognized by the LRO data.

Polynomial time blackbox identity testers for depth-3 circuits : the field doesn't matter.

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

Seshadhri, Comandur; Saxena, Nitin

Let C be a depth-3 circuit with n variables, degree d and top fanin k (called {Sigma}{Pi}{Sigma}(k, d, n) circuits) over base field F. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runsmore » in time poly(n)d{sup k}, regardless of the base field. The only field for which polynomial time algorithms were previously known is F = Q (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-3 circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a {Sigma}{Pi}{Sigma}(k, d, n) circuit to k variables, but preserves the identity structure. Polynomial identity testing (PIT) is a major open problem in theoretical computer science. The input is an arithmetic circuit that computes a polynomial p(x{sub 1}, x{sub 2},..., x{sub n}) over a base field F. We wish to check if p is the zero polynomial, or in other words, is identically zero. We may be provided with an explicit circuit, or may only have blackbox access. In the latter case, we can only evaluate the polynomial p at various domain points. The main goal is to devise a deterministic blackbox polynomial time algorithm for PIT.« less

The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation

NASA Astrophysics Data System (ADS)

Filipuk, Galina; Van Assche, Walter; Zhang, Lun

2012-05-01

We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlevé equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also discuss a relation between the recurrence coefficients for the Freud weight and the semi-classical Laguerre weight and show how it arises from the Bäcklund transformation of the fourth Painlevé equation.

Linear decomposition approach for a class of nonconvex programming problems.

PubMed

Shen, Peiping; Wang, Chunfeng

2017-01-01

This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

Polynomial complexity despite the fermionic sign

NASA Astrophysics Data System (ADS)

Rossi, R.; Prokof'ev, N.; Svistunov, B.; Van Houcke, K.; Werner, F.

2017-04-01

It is commonly believed that in unbiased quantum Monte Carlo approaches to fermionic many-body problems, the infamous sign problem generically implies prohibitively large computational times for obtaining thermodynamic-limit quantities. We point out that for convergent Feynman diagrammatic series evaluated with a recently introduced Monte Carlo algorithm (see Rossi R., arXiv:1612.05184), the computational time increases only polynomially with the inverse error on thermodynamic-limit quantities.

Communication: Fitting potential energy surfaces with fundamental invariant neural network

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

Shao, Kejie; Chen, Jun; Zhao, Zhiqiang

A more flexible neural network (NN) method using the fundamental invariants (FIs) as the input vector is proposed in the construction of potential energy surfaces for molecular systems involving identical atoms. Mathematically, FIs finitely generate the permutation invariant polynomial (PIP) ring. In combination with NN, fundamental invariant neural network (FI-NN) can approximate any function to arbitrary accuracy. Because FI-NN minimizes the size of input permutation invariant polynomials, it can efficiently reduce the evaluation time of potential energy, in particular for polyatomic systems. In this work, we provide the FIs for all possible molecular systems up to five atoms. Potential energymore » surfaces for OH{sub 3} and CH{sub 4} were constructed with FI-NN, with the accuracy confirmed by full-dimensional quantum dynamic scattering and bound state calculations.« less

Geometric accuracy of LANDSAT-4 MSS image data

NASA Technical Reports Server (NTRS)

Welch, R.; Usery, E. L.

1983-01-01

Analyses of the LANDSAT-4 MSS image data of North Georgia provided by the EDC in CCT-p formats reveal that errors of approximately + or - 30 m in the raw data can be reduced to about + or - 55 m based on rectification procedures involving the use of 20 to 30 well-distributed GCPs and 2nd or 3rd degree polynomial equations. Higher order polynomials do not appear to improve the rectification accuracy. A subscene area of 256 x 256 pixels was rectified with a 1st degree polynomial to yield an RMSE sub xy value of + or - 40 m, indicating that USGS 1:24,000 scale quadrangle-sized areas of LANDSAT-4 data can be fitted to a map base with relatively few control points and simple equations. The errors in the rectification process are caused by the spatial resolution of the MSS data, by errors in the maps and GCP digitizing process, and by displacements caused by terrain relief. Overall, due to the improved pointing and attitude control of the spacecraft, the geometric quality of the LANDSAT-4 MSS data appears much improved over that of LANDSATS -1, -2 and -3.

[Using fractional polynomials to estimate the safety threshold of fluoride in drinking water].

PubMed

Pan, Shenling; An, Wei; Li, Hongyan; Yang, Min

2014-01-01

To study the dose-response relationship between fluoride content in drinking water and prevalence of dental fluorosis on the national scale, then to determine the safety threshold of fluoride in drinking water. Meta-regression analysis was applied to the 2001-2002 national endemic fluorosis survey data of key wards. First, fractional polynomial (FP) was adopted to establish fixed effect model, determining the best FP structure, after that restricted maximum likelihood (REML) was adopted to estimate between-study variance, then the best random effect model was established. The best FP structure was first-order logarithmic transformation. Based on the best random effect model, the benchmark dose (BMD) of fluoride in drinking water and its lower limit (BMDL) was calculated as 0.98 mg/L and 0.78 mg/L. Fluoride in drinking water can only explain 35.8% of the variability of the prevalence, among other influencing factors, ward type was a significant factor, while temperature condition and altitude were not. Fractional polynomial-based meta-regression method is simple, practical and can provide good fitting effect, based on it, the safety threshold of fluoride in drinking water of our country is determined as 0.8 mg/L.

Efficient scheme for parametric fitting of data in arbitrary dimensions.

PubMed

Pang, Ning-Ning; Tzeng, Wen-Jer; Kao, Hisen-Ching

2008-07-01

We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

Investigations into the shape-preserving interpolants using symbolic computation

NASA Technical Reports Server (NTRS)

Lam, Maria

1988-01-01

Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines.

Sixth-order wave aberration theory of ultrawide-angle optical systems.

PubMed

Lu, Lijun; Cao, Yiqing

2017-10-20

In this paper, we develop sixth-order wave aberration theory of ultrawide-angle optical systems like fisheye lenses. Based on the concept and approach to develop wave aberration theory of plane-symmetric optical systems, we first derive the sixth-order intrinsic wave aberrations and the fifth-order ray aberrations; second, we present a method to calculate the pupil aberration of such kind of optical systems to develop the extrinsic aberrations; third, the relation of aperture-ray coordinates between adjacent optical surfaces is fitted with the second-order polynomial to improve the calculation accuracy of the wave aberrations of a fisheye lens with a large acceptance aperture. Finally, the resultant aberration expressions are applied to calculate the aberrations of two design examples of fisheye lenses; the calculation results are compared with the ray-tracing ones with Zemax software to validate the aberration expressions.

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.

PubMed

Kulkarni, Rishikesh; Rastogi, Pramod

2018-02-01

A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Maximal blood flow acceleration analysis in the early diastolic phase for aortocoronary artery bypass grafts: a new transit-time flow measurement predictor of graft failure following coronary artery bypass grafting.

PubMed

Handa, Takemi; Orihashi, Kazumasa; Nishimori, Hideaki; Yamamoto, Masaki

2016-11-01

Maximal graft flow acceleration (max df/dt) determined using transit-time flowmetry (TTFM) in the diastolic phase was assessed as a potential predictor of graft failure for aortocoronary artery (AC) bypass grafts in coronary artery bypass patients. Max df/dt was retrospectively measured in 114 aortocoronary artery bypass grafts. TTFM data were fitted to a 9-polynomial curve, which was derived from the first-derivative curve, to measure max df/dt (9-polynomial max df/dt). Abnormal TTFM was defined as a mean flow of <15 ml/min, a pulsatility index of >5 or a diastolic filling ratio of <50 %. Postoperative assessments were routinely performed by coronary artery angiography (CAG) at 1 year after surgery. Using TTFM, 68 grafts were normal, 4 of which were failing on CAG, and 46 grafts were abnormal, 21 of which were failing on CAG. 9-polynomial max df/dt was significantly lower in abnormal TTFM/failing by the CAG group compared with abnormal TTFM/patent by the CAG group (1.08 ± 0.89 vs. 2.05 ± 1.51 ml/s(2), respectively; P < 0.01, Mann-Whitney U test, Holm adjustment). TTFM 9-polynomial max df/dt in the early diastolic phase may be a promising predictor of future graft failure for AC bypass grafts, particularly in abnormal TTFM grafts.

Myocardial strains from 3D displacement encoded magnetic resonance imaging

PubMed Central

2012-01-01

Background The ability to measure and quantify myocardial motion and deformation provides a useful tool to assist in the diagnosis, prognosis and management of heart disease. The recent development of magnetic resonance imaging methods, such as harmonic phase analysis of tagging and displacement encoding with stimulated echoes (DENSE), make detailed non-invasive 3D kinematic analyses of human myocardium possible in the clinic and for research purposes. A robust analysis method is required, however. Methods We propose to estimate strain using a polynomial function which produces local models of the displacement field obtained with DENSE. Given a specific polynomial order, the model is obtained as the least squares fit of the acquired displacement field. These local models are subsequently used to produce estimates of the full strain tensor. Results The proposed method is evaluated on a numerical phantom as well as in vivo on a healthy human heart. The evaluation showed that the proposed method produced accurate results and showed low sensitivity to noise in the numerical phantom. The method was also demonstrated in vivo by assessment of the full strain tensor and to resolve transmural strain variations. Conclusions Strain estimation within a 3D myocardial volume based on polynomial functions yields accurate and robust results when validated on an analytical model. The polynomial field is capable of resolving the measured material positions from the in vivo data, and the obtained in vivo strains values agree with previously reported myocardial strains in normal human hearts. PMID:22533791

Response Surface Methodology Using a Fullest Balanced Model: A Re-Analysis of a Dataset in the Korean Journal for Food Science of Animal Resources.

PubMed

Rheem, Sungsue; Rheem, Insoo; Oh, Sejong

2017-01-01

Response surface methodology (RSM) is a useful set of statistical techniques for modeling and optimizing responses in research studies of food science. In the analysis of response surface data, a second-order polynomial regression model is usually used. However, sometimes we encounter situations where the fit of the second-order model is poor. If the model fitted to the data has a poor fit including a lack of fit, the modeling and optimization results might not be accurate. In such a case, using a fullest balanced model, which has no lack of fit, can fix such problem, enhancing the accuracy of the response surface modeling and optimization. This article presents how to develop and use such a model for the better modeling and optimizing of the response through an illustrative re-analysis of a dataset in Park et al. (2014) published in the Korean Journal for Food Science of Animal Resources .

Model Robust Calibration: Method and Application to Electronically-Scanned Pressure Transducers

NASA Technical Reports Server (NTRS)

Walker, Eric L.; Starnes, B. Alden; Birch, Jeffery B.; Mays, James E.

2010-01-01

This article presents the application of a recently developed statistical regression method to the controlled instrument calibration problem. The statistical method of Model Robust Regression (MRR), developed by Mays, Birch, and Starnes, is shown to improve instrument calibration by reducing the reliance of the calibration on a predetermined parametric (e.g. polynomial, exponential, logarithmic) model. This is accomplished by allowing fits from the predetermined parametric model to be augmented by a certain portion of a fit to the residuals from the initial regression using a nonparametric (locally parametric) regression technique. The method is demonstrated for the absolute scale calibration of silicon-based pressure transducers.

Linear FBG Temperature Sensor Interrogation with Fabry-Perot ITU Multi-wavelength Reference

PubMed Central

Park, Hyoung-Jun; Song, Minho

2008-01-01

The equidistantly spaced multi-passbands of a Fabry-Perot ITU filter are used as an efficient multi-wavelength reference for fiber Bragg grating sensor demodulation. To compensate for the nonlinear wavelength tuning effect in the FBG sensor demodulator, a polynomial fitting algorithm was applied to the temporal peaks of the wavelength-scanned ITU filter. The fitted wavelength values are assigned to the peak locations of the FBG sensor reflections, obtaining constant accuracy, regardless of the wavelength scan range and frequency. A linearity error of about 0.18% against a reference thermocouple thermometer was obtained with the suggested method. PMID:27873898

LMI-based stability analysis of fuzzy-model-based control systems using approximated polynomial membership functions.

PubMed

Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles

2011-06-01

Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.

Polynomial chaos expansion with random and fuzzy variables

NASA Astrophysics Data System (ADS)

Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.

2016-06-01

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.

Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam Carlitz I polynomials

NASA Astrophysics Data System (ADS)

Doha, E. H.; Ahmed, H. M.

2005-12-01

Two formulae expressing explicitly the derivatives and moments of Al-Salam-Carlitz I polynomials of any degree and for any order in terms of Al-Salam-Carlitz I themselves are proved. Two other formulae for the expansion coefficients of general-order derivatives Dpqf(x), and for the moments xellDpqf(x), of an arbitrary function f(x) in terms of its original expansion coefficients are also obtained. Application of these formulae for solving q-difference equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Al-Salam-Carlitz I polynomials and any system of basic hypergeometric orthogonal polynomials, belonging to the q-Hahn class, is described.

Kurtosis Approach for Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

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

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

Work domain constraints for modelling surgical performance.

PubMed

Morineau, Thierry; Riffaud, Laurent; Morandi, Xavier; Villain, Jonathan; Jannin, Pierre

2015-10-01

Three main approaches can be identified for modelling surgical performance: a competency-based approach, a task-based approach, both largely explored in the literature, and a less known work domain-based approach. The work domain-based approach first describes the work domain properties that constrain the agent's actions and shape the performance. This paper presents a work domain-based approach for modelling performance during cervical spine surgery, based on the idea that anatomical structures delineate the surgical performance. This model was evaluated through an analysis of junior and senior surgeons' actions. Twenty-four cervical spine surgeries performed by two junior and two senior surgeons were recorded in real time by an expert surgeon. According to a work domain-based model describing an optimal progression through anatomical structures, the degree of adjustment of each surgical procedure to a statistical polynomial function was assessed. Each surgical procedure showed a significant suitability with the model and regression coefficient values around 0.9. However, the surgeries performed by senior surgeons fitted this model significantly better than those performed by junior surgeons. Analysis of the relative frequencies of actions on anatomical structures showed that some specific anatomical structures discriminate senior from junior performances. The work domain-based modelling approach can provide an overall statistical indicator of surgical performance, but in particular, it can highlight specific points of interest among anatomical structures that the surgeons dwelled on according to their level of expertise.

Considering body mass differences, who are the world's strongest women?

PubMed

Vanderburgh, P M; Dooman, C

2000-01-01

Allometric modeling (AM) has been used to determine the world's strongest body mass-adjusted man. Recently, however, AM was shown to demonstrate body mass bias in elite Olympic weightlifting performance. A second order polynomial (2OP) provided a better fit than AM with no body mass bias for men and women. The purpose of this study was to apply both AM and 2OP models to women's world powerlifting records (more a function of pure strength and less power than Olympic lifts) to determine the optimal model approach as well as the strongest body mass-adjusted woman in each event. Subjects were the 36 (9 per event) current women world record holders (as of Nov., 1997) for bench press (BP), deadlift (DL), squat (SQ), and total (TOT) lift (BP + DL + SQ) according to the International Powerlifting Federation (IPF). The 2OP model demonstrated the superior fit and no body mass bias as indicated by the coefficient of variation and residuals scatterplot inspection, respectively, for DL, SQ, and TOT. The AM for these three lifts, however, showed favorable bias toward the middle weight classes. The 2OP and AM yielded an essentially identical fit for BP. Although body mass-adjusted world records were dependent on the model used, Carrie Boudreau (U.S., 56-kg weight class), who received top scores in TOT and DL with both models, is arguably the world's strongest woman overall. Furthermore, although the 2OP model provides a better fit than AM for this elite population, a case can still be made for AM use, particularly in light of theoretical superiority.

SPSS macros to compare any two fitted values from a regression model.

PubMed

Weaver, Bruce; Dubois, Sacha

2012-12-01

In regression models with first-order terms only, the coefficient for a given variable is typically interpreted as the change in the fitted value of Y for a one-unit increase in that variable, with all other variables held constant. Therefore, each regression coefficient represents the difference between two fitted values of Y. But the coefficients represent only a fraction of the possible fitted value comparisons that might be of interest to researchers. For many fitted value comparisons that are not captured by any of the regression coefficients, common statistical software packages do not provide the standard errors needed to compute confidence intervals or carry out statistical tests-particularly in more complex models that include interactions, polynomial terms, or regression splines. We describe two SPSS macros that implement a matrix algebra method for comparing any two fitted values from a regression model. The !OLScomp and !MLEcomp macros are for use with models fitted via ordinary least squares and maximum likelihood estimation, respectively. The output from the macros includes the standard error of the difference between the two fitted values, a 95% confidence interval for the difference, and a corresponding statistical test with its p-value.

New approach to calculate the true-coincidence effect of HpGe detector

NASA Astrophysics Data System (ADS)

Alnour, I. A.; Wagiran, H.; Ibrahim, N.; Hamzah, S.; Siong, W. B.; Elias, M. S.

2016-01-01

The corrections for true-coincidence effects in HpGe detector are important, especially at low source-to-detector distances. This work established an approach to calculate the true-coincidence effects experimentally for HpGe detectors of type Canberra GC3018 and Ortec GEM25-76-XLB-C, which are in operation at neutron activation analysis lab in Malaysian Nuclear Agency (NM). The correction for true-coincidence effects was performed close to detector at distances 2 and 5 cm using 57Co, 60Co, 133Ba and 137Cs as standard point sources. The correction factors were ranged between 0.93-1.10 at 2 cm and 0.97-1.00 at 5 cm for Canberra HpGe detector; whereas for Ortec HpGe detector ranged between 0.92-1.13 and 0.95-100 at 2 and 5 cm respectively. The change in efficiency calibration curve of the detector at 2 and 5 cm after correction was found to be less than 1%. Moreover, the polynomial parameters functions were simulated through a computer program, MATLAB in order to find an accurate fit to the experimental data points.

Models for Estimating Genetic Parameters of Milk Production Traits Using Random Regression Models in Korean Holstein Cattle

PubMed Central

Cho, C. I.; Alam, M.; Choi, T. J.; Choy, Y. H.; Choi, J. G.; Lee, S. S.; Cho, K. H.

2016-01-01

The objectives of the study were to estimate genetic parameters for milk production traits of Holstein cattle using random regression models (RRMs), and to compare the goodness of fit of various RRMs with homogeneous and heterogeneous residual variances. A total of 126,980 test-day milk production records of the first parity Holstein cows between 2007 and 2014 from the Dairy Cattle Improvement Center of National Agricultural Cooperative Federation in South Korea were used. These records included milk yield (MILK), fat yield (FAT), protein yield (PROT), and solids-not-fat yield (SNF). The statistical models included random effects of genetic and permanent environments using Legendre polynomials (LP) of the third to fifth order (L3–L5), fixed effects of herd-test day, year-season at calving, and a fixed regression for the test-day record (third to fifth order). The residual variances in the models were either homogeneous (HOM) or heterogeneous (15 classes, HET15; 60 classes, HET60). A total of nine models (3 orders of polynomials×3 types of residual variance) including L3-HOM, L3-HET15, L3-HET60, L4-HOM, L4-HET15, L4-HET60, L5-HOM, L5-HET15, and L5-HET60 were compared using Akaike information criteria (AIC) and/or Schwarz Bayesian information criteria (BIC) statistics to identify the model(s) of best fit for their respective traits. The lowest BIC value was observed for the models L5-HET15 (MILK; PROT; SNF) and L4-HET15 (FAT), which fit the best. In general, the BIC values of HET15 models for a particular polynomial order was lower than that of the HET60 model in most cases. This implies that the orders of LP and types of residual variances affect the goodness of models. Also, the heterogeneity of residual variances should be considered for the test-day analysis. The heritability estimates of from the best fitted models ranged from 0.08 to 0.15 for MILK, 0.06 to 0.14 for FAT, 0.08 to 0.12 for PROT, and 0.07 to 0.13 for SNF according to days in milk of first lactation. Genetic variances for studied traits tended to decrease during the earlier stages of lactation, which were followed by increases in the middle and decreases further at the end of lactation. With regards to the fitness of the models and the differential genetic parameters across the lactation stages, we could estimate genetic parameters more accurately from RRMs than from lactation models. Therefore, we suggest using RRMs in place of lactation models to make national dairy cattle genetic evaluations for milk production traits in Korea. PMID:26954184

Models for Estimating Genetic Parameters of Milk Production Traits Using Random Regression Models in Korean Holstein Cattle.

PubMed

Cho, C I; Alam, M; Choi, T J; Choy, Y H; Choi, J G; Lee, S S; Cho, K H

2016-05-01

The objectives of the study were to estimate genetic parameters for milk production traits of Holstein cattle using random regression models (RRMs), and to compare the goodness of fit of various RRMs with homogeneous and heterogeneous residual variances. A total of 126,980 test-day milk production records of the first parity Holstein cows between 2007 and 2014 from the Dairy Cattle Improvement Center of National Agricultural Cooperative Federation in South Korea were used. These records included milk yield (MILK), fat yield (FAT), protein yield (PROT), and solids-not-fat yield (SNF). The statistical models included random effects of genetic and permanent environments using Legendre polynomials (LP) of the third to fifth order (L3-L5), fixed effects of herd-test day, year-season at calving, and a fixed regression for the test-day record (third to fifth order). The residual variances in the models were either homogeneous (HOM) or heterogeneous (15 classes, HET15; 60 classes, HET60). A total of nine models (3 orders of polynomials×3 types of residual variance) including L3-HOM, L3-HET15, L3-HET60, L4-HOM, L4-HET15, L4-HET60, L5-HOM, L5-HET15, and L5-HET60 were compared using Akaike information criteria (AIC) and/or Schwarz Bayesian information criteria (BIC) statistics to identify the model(s) of best fit for their respective traits. The lowest BIC value was observed for the models L5-HET15 (MILK; PROT; SNF) and L4-HET15 (FAT), which fit the best. In general, the BIC values of HET15 models for a particular polynomial order was lower than that of the HET60 model in most cases. This implies that the orders of LP and types of residual variances affect the goodness of models. Also, the heterogeneity of residual variances should be considered for the test-day analysis. The heritability estimates of from the best fitted models ranged from 0.08 to 0.15 for MILK, 0.06 to 0.14 for FAT, 0.08 to 0.12 for PROT, and 0.07 to 0.13 for SNF according to days in milk of first lactation. Genetic variances for studied traits tended to decrease during the earlier stages of lactation, which were followed by increases in the middle and decreases further at the end of lactation. With regards to the fitness of the models and the differential genetic parameters across the lactation stages, we could estimate genetic parameters more accurately from RRMs than from lactation models. Therefore, we suggest using RRMs in place of lactation models to make national dairy cattle genetic evaluations for milk production traits in Korea.

An Interpolation Approach to Optimal Trajectory Planning for Helicopter Unmanned Aerial Vehicles

DTIC Science & Technology

2012-06-01

Armament Data Line DOF Degree of Freedom PS Pseudospectral LGL Legendre -Gauss-Lobatto quadrature nodes ODE Ordinary Differential Equation xiv...low order polynomials patched together in such away so that the resulting trajectory has several continuous derivatives at all points. In [7], Murray...claims that splines are ideal for optimal control problems because each segment of the spline’s piecewise polynomials approximate the trajectory

Finding higher order Darboux polynomials for a family of rational first order ordinary differential equations

NASA Astrophysics Data System (ADS)

Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.

2015-10-01

For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.

Integration of epidemiology into the genetic analysis of mastitis in Swedish Holstein.

PubMed

Windig, Jack J; Urioste, Jorge I; Strandberg, Erling

2013-04-01

Heritability of mastitis (and diseases in general) tends to be low. One possible cause is that no clear distinction can be made between resistant and nonresistant animals, because healthy animals include animals that have not been exposed to pathogens and resistant animals. To account for this, we quantified the prevalence of clinical mastitis (CM) and subclinical mastitis (SCM) in 2,069 Swedish Holstein herds as a measure of exposure. Herd prevalence averaged 26.5% for SCM and 6.4% for CM; 61% of the first lactations of 177,309 cows were classified as having at least one case of SCM and 10% as having CM. In a reaction norm approach, heritability of (S)CM was quantified as a function of herd prevalence of (S)CM. The best-fitting model was a second-order polynomial of first-lactation cow SCM as a function of herd prevalence SCM, and a first-order (linear) polynomial of first-lactation cow CM as a function of CM herd prevalence. Heritability for SCM ranged from 0.069 to 0.105 and for CM from 0.016 to 0.032. For both, we found no clear effect of herd prevalence on their heritability. Genetic correlations within traits across herd prevalences were all greater than 0.92. Whether relationships among prevalence, exposure, disease, and genetics were as expected is a matter of discussion, but reaction norm analyses may be a valuable tool for epidemiological genetics. Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

A Bayesian analysis of trends in ozone sounding data series from 9 Nordic stations

NASA Astrophysics Data System (ADS)

Christiansen, Bo; Jepsen, Nis; Larsen, Niels; Korsholm, Ulrik S.

2016-04-01

Ozone soundings from 9 Nordic stations have been homogenized and interpolated to standard pressure levels. The different stations have very different data coverage; the longest period with data is from the end of the 1980ies to 2013. We apply a model which includes both low-frequency variability in form of a polynomial, an annual cycle with harmonics, the possibility for low-frequency variability in the annual amplitude and phasing, and either white noise or AR1 noise. The fitting of the parameters is performed with a Bayesian approach not only giving the posterior mean values but also credible intervals. We find that all stations agree on an well-defined annual cycle in the free troposphere with a relatively confined maximum in the early summer. Regarding the low-frequency variability we find that Scoresbysund, Ny Aalesund, and Sodankyla show similar structures with a maximum near 2005 followed by a decrease. However, these results are only weakly significant. A significant change in the amplitude of the annual cycle was only found for Ny Aalesund. Here the peak-to-peak amplitude changes from 0.9 to 0.8 mhPa between 1995-2000 and 2007-2012. The results are shown to be robust to the different settings of the model parameters (order of the polynomial, number of harmonics in the annual cycle, type of noise, etc). The results are also shown to be characteristic for all pressure levels in the free troposphere.

A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems

DOE PAGES

Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; ...

2016-08-16

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a thick-restart version of the Lanczos algorithm with deflation ("locking'') and a new type of polynomial filter obtained from a least-squares technique. Furthermore, the resulting algorithm can be utilized in a “spectrum-slicing” approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different subintervals independently from onemore » another.« less

Enhanced Interferometry with Programmable Spatial Light Modulator

DTIC Science & Technology

2010-06-07

metrolaserinc.com6-7-2010-Monday 6 Simulated by Zemax  Lenslet diameters, d, define spatial resolution over the wavefront being measured.  (sensitivity...MetroLaser Irvine, California Fitted Zernike Polynomials upto 36 terms, found and put into Zemax Simulated Cats’ eye wavefronts by ZEMAX Experimental...measurement Simulated Fringes Leftover < 0.1λ 23 Cat’s eye wavefronts by ZEMAX based on Experimental results Jtrolinger@metrolaserinc.com6-7-2010

A Photometric redshift galaxy catalog from the Red-Sequence Cluster Survey

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

Hsieh, Bau-Ching; /Taiwan, Natl. Central U. /Taipei, Inst. Astron. Astrophys.; Yee, H.K.C.

2005-02-01

The Red-Sequence Cluster Survey (RCS) provides a large and deep photometric catalog of galaxies in the z' and R{sub c} bands for 90 square degrees of sky, and supplemental V and B data have been obtained for 33.6 deg{sup 2}. They compile a photometric redshift catalog from these 4-band data by utilizing the empirical quadratic polynomial photometric redshift fitting technique in combination with CNOC2 and GOODS/HDF-N redshift data. The training set includes 4924 spectral redshifts. The resulting catalog contains more than one million galaxies with photometric redshifts < 1.5 and R{sub c} < 24, giving an rms scatter {delta}({Delta}z)

Random regression analyses using B-splines to model growth of Australian Angus cattle

PubMed Central

Meyer, Karin

2005-01-01

Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights with age were modelled through B-splines of age at recording. A total of thirteen analyses, considering different combinations of linear, quadratic and cubic B-splines and up to six knots, were carried out. Results showed good agreement for all ages with many records, but fluctuated where data were sparse. On the whole, analyses using B-splines appeared more robust against "end-of-range" problems and yielded more consistent and accurate estimates of the first eigenfunctions than previous, polynomial analyses. A model fitting quadratic B-splines, with knots at 0, 200, 400, 600 and 821 days and a total of 91 covariance components, appeared to be a good compromise between detailedness of the model, number of parameters to be estimated, plausibility of results, and fit, measured as residual mean square error. PMID:16093011

Performance analysis of 60-min to 1-min integration time rain rate conversion models in Malaysia

NASA Astrophysics Data System (ADS)

Ng, Yun-Yann; Singh, Mandeep Singh Jit; Thiruchelvam, Vinesh

2018-01-01

Utilizing the frequency band above 10 GHz is in focus nowadays as a result of the fast expansion of radio communication systems in Malaysia. However, rain fade is the critical factor in attenuation of signal propagation for frequencies above 10 GHz. Malaysia is located in a tropical and equatorial region with high rain intensity throughout the year, and this study will review rain distribution and evaluate the performance of 60-min to 1-min integration time rain rate conversion methods for Malaysia. Several conversion methods such as Segal, Chebil & Rahman, Burgeono, Emiliani, Lavergnat and Gole (LG), Simplified Moupfouma, Joo et al., fourth order polynomial fit and logarithmic model have been chosen to evaluate the performance to predict 1-min rain rate for 10 sites in Malaysia. After the completion of this research, the results show that Chebil & Rahman model, Lavergnat & Gole model, Fourth order polynomial fit and Logarithmic model have shown the best performances in 60-min to 1-min rain rate conversion over 10 sites. In conclusion, it is proven that there is no single model which can claim to perform the best across 10 sites. By averaging RMSE and SC-RMSE over 10 sites, Chebil and Rahman model is the best method.

Modeling the effect of temperature on survival rate of Salmonella Enteritidis in yogurt.

PubMed

Szczawiński, J; Szczawińska, M E; Łobacz, A; Jackowska-Tracz, A

2014-01-01

The aim of the study was to determine the inactivation rates of Salmonella Enteritidis in commercially produced yogurt and to generate primary and secondary mathematical models to predict the behaviour of these bacteria during storage at different temperatures. The samples were inoculated with the mixture of three S. Enteritidis strains and stored at 5 degrees C, 10 degrees C, 15 degrees C, 20 degrees C and 25 degrees C for 24 h. The number of salmonellae was determined every two hours. It was found that the number of bacteria decreased linearly with storage time in all samples. Storage temperature and pH of yogurt significantly influenced survival rate of S. Enteritidis (p < 0.05). In samples kept at 5 degrees C the number of salmonellae decreased at the lowest rate, whereas at 25 degrees C the reduction in number of bacteria was the most dynamic. The natural logarithm of mean inactivation rates of Salmonella calculated from primary model was fitted to two secondary models: linear and polynomial. Equations obtained from both secondary models can be applied as a tool for prediction of inactivation rate of Salmonella in yogurt stored under temperature range from 5 to 25 degrees C; however, polynomial model gave the better fit to the experimental data.

Low-Temperature Heat Capacities and Standard Molar Enthalpy of Formation of Potassium Benzoate C7H5O2K(s)

NASA Astrophysics Data System (ADS)

Yang, Wei-Wei; di, You-Ying; Yin, Zhen-Fen; Kong, Yu-Xia; Tan, Zhi-Cheng

2009-04-01

Potassium benzoate C7H5O2K (CAS Registry No. 582-25-2) was synthesized by the method of liquid phase reaction. Chemical and elemental analyses, FTIR, and X-ray powder diffraction (XRD) techniques were applied to characterize the composition and structure of the compound. Low-temperature heat capacities of the compound were measured by a precision automated adiabatic calorimeter over the temperature range from 78 K to 398 K. A polynomial equation of the heat capacities as a function of temperature was fitted by the least-squares method. Smoothed heat capacities and thermodynamic functions of the compound were calculated based on the fitted polynomial. In accordance with Hess’s law, a reasonable thermochemical cycle was designed, and 100 mL of 1 mol · dm-3 NaOH solution was chosen as the calorimetric solvent. The standard molar enthalpies of dissolution for the reactants and products of the supposed reaction in the selected solvent were measured by an isoperibol solution-reaction calorimeter. Finally, the standard molar enthalpy of formation of the title compound C7H5O2K (s) was derived to be -(610.94 ± 0.77) kJ · mol-1.

Thermal Output of WK-Type Strain Gauges on Various Materials at Cryogenic and Elevated Temperatures

NASA Technical Reports Server (NTRS)

Kowalkowski, Matthew K.; Rivers, H. Kevin; Smith, Russell W.

1998-01-01

Strain gage apparent strain (thermal output) is one of the largest sources of error associated with the measurement of strain when temperatures and mechanical loads are varied. In this paper, experimentally determined apparent strains of WK-type strain gages, installed on both metallic and composite-laminate materials of various lay-ups and resin systems for temperatures ranging from -450 F to 230 F are presented. For the composite materials apparent strain in both the 0 ply orientation angle and the 90 ply orientation angle were measured. Metal specimens tested included: aluminum-lithium alloy (Al-LI 2195-T87), aluminum alloy (Al 2219-T87), and titanium alloy. Composite materials tested include: graphite-toughened-epoxy (IM7/997- 2), graphite-bismaleimide (IM7/5260), and graphite-K3 (IM7/K3B). The experimentally determined apparent strain data are curve fit with a fourth-order polynomial for each of the materials studied. The apparent strain data and the polynomials that are fit to the data are compared with those produced by the strain gage manufacturer, and the results and comparisons are presented. Unacceptably high errors between the manufacture's data and the experimentally determined data were observed (especially at temperatures below - 270-F).

Multiple and Single Green Area Measurements and Classification Using Phantom Images in Comparison with Derived Experimental Law

NASA Astrophysics Data System (ADS)

Abu-Zaid, N. A. M.

2017-11-01

In many circumstances, it is difficult for humans to reach some areas, due to its topography, personal safety, or security regulations in the country. Governments and persons need to calculate those areas and classify the green parts for reclamation to benefit from it.To solve this problem, this research proposes to use a phantom air plane to capture a digital image for the targeted area, then use a segmentation algorithm to separate the green space and calculate it's area. It was necessary to deal with two problems. The first is the variable elevation at which an image was taken, which leads to a change in the physical area of each pixel. To overcome this problem a fourth degree polynomial was fit to some experimental data. The second problem was the existence of different unconnected pieces of green areas in a single image, but we might be interested only in one of them. To solve this problem, the probability of classifying the targeted area as green was increased, while the probability of other untargeted sections was decreased by the inclusion of parts of it as non-green. A practical law was also devised to measure the target area in the digital image for comparison purposes with practical measurements and the polynomial fit.

Light field creating and imaging with different order intensity derivatives

NASA Astrophysics Data System (ADS)

Wang, Yu; Jiang, Huan

2014-10-01

Microscopic image restoration and reconstruction is a challenging topic in the image processing and computer vision, which can be widely applied to life science, biology and medicine etc. A microscopic light field creating and three dimensional (3D) reconstruction method is proposed for transparent or partially transparent microscopic samples, which is based on the Taylor expansion theorem and polynomial fitting. Firstly the image stack of the specimen is divided into several groups in an overlapping or non-overlapping way along the optical axis, and the first image of every group is regarded as reference image. Then different order intensity derivatives are calculated using all the images of every group and polynomial fitting method based on the assumption that the structure of the specimen contained by the image stack in a small range along the optical axis are possessed of smooth and linear property. Subsequently, new images located any position from which to reference image the distance is Δz along the optical axis can be generated by means of Taylor expansion theorem and the calculated different order intensity derivatives. Finally, the microscopic specimen can be reconstructed in 3D form using deconvolution technology and all the images including both the observed images and the generated images. The experimental results show the effectiveness and feasibility of our method.

A gradient-based model parametrization using Bernstein polynomials in Bayesian inversion of surface wave dispersion

NASA Astrophysics Data System (ADS)

Gosselin, Jeremy M.; Dosso, Stan E.; Cassidy, John F.; Quijano, Jorge E.; Molnar, Sheri; Dettmer, Jan

2017-10-01

This paper develops and applies a Bernstein-polynomial parametrization to efficiently represent general, gradient-based profiles in nonlinear geophysical inversion, with application to ambient-noise Rayleigh-wave dispersion data. Bernstein polynomials provide a stable parametrization in that small perturbations to the model parameters (basis-function coefficients) result in only small perturbations to the geophysical parameter profile. A fully nonlinear Bayesian inversion methodology is applied to estimate shear wave velocity (VS) profiles and uncertainties from surface wave dispersion data extracted from ambient seismic noise. The Bayesian information criterion is used to determine the appropriate polynomial order consistent with the resolving power of the data. Data error correlations are accounted for in the inversion using a parametric autoregressive model. The inversion solution is defined in terms of marginal posterior probability profiles for VS as a function of depth, estimated using Metropolis-Hastings sampling with parallel tempering. This methodology is applied to synthetic dispersion data as well as data processed from passive array recordings collected on the Fraser River Delta in British Columbia, Canada. Results from this work are in good agreement with previous studies, as well as with co-located invasive measurements. The approach considered here is better suited than `layered' modelling approaches in applications where smooth gradients in geophysical parameters are expected, such as soil/sediment profiles. Further, the Bernstein polynomial representation is more general than smooth models based on a fixed choice of gradient type (e.g. power-law gradient) because the form of the gradient is determined objectively by the data, rather than by a subjective parametrization choice.

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

Singh, M.; Al-Dayeh, L.; Patel, P.

It is well known that even small movements of the head can lead to artifacts in fMRI. Corrections for these movements are usually made by a registration algorithm which accounts for translational and rotational motion of the head under a rigid body assumption. The brain, however, is not entirely rigid and images are prone to local deformations due to CSF motion, susceptibility effects, local changes in blood flow and inhomogeneities in the magnetic and gradient fields. Since nonrigid body motion is not adequately corrected by approaches relying on simple rotational and translational corrections, we have investigated a general approach wheremore » an n{sup th} order polynomial is used to map all images onto a common reference image. The coefficients of the polynomial transformation were determined through minimization of the ratio of the variance to the mean of each pixel. Simulation studies were conducted to validate the technique. Results of experimental studies using polynomial transformation for 2D and 3D registration show lower variance to mean ratio compared to simple rotational and translational corrections.« less

A Small and Slim Coaxial Probe for Single Rice Grain Moisture Sensing

PubMed Central

You, Kok Yeow; Mun, Hou Kit; You, Li Ling; Salleh, Jamaliah; Abbas, Zulkifly

2013-01-01

A moisture detection of single rice grains using a slim and small open-ended coaxial probe is presented. The coaxial probe is suitable for the nondestructive measurement of moisture values in the rice grains ranging from from 9.5% to 26%. Empirical polynomial models are developed to predict the gravimetric moisture content of rice based on measured reflection coefficients using a vector network analyzer. The relationship between the reflection coefficient and relative permittivity were also created using a regression method and expressed in a polynomial model, whose model coefficients were obtained by fitting the data from Finite Element-based simulation. Besides, the designed single rice grain sample holder and experimental set-up were shown. The measurement of single rice grains in this study is more precise compared to the measurement in conventional bulk rice grains, as the random air gap present in the bulk rice grains is excluded. PMID:23493127

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

DOE PAGES

Huang, Lei; Xue, Junpeng; Gao, Bo; ...

2016-12-21

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Viabilty of atomistic potentials for thermodynamic properties of carbon dioxide at low temperatures.

PubMed

Kuznetsova, Tatyana; Kvamme, Bjørn

2001-11-30

Investigation into volumetric and energetic properties of several atomistic models mimicking carbon dioxide geometry and quadrupole momentum covered the liquid-vapor coexistence curve. Thermodynamic integration over a polynomial and an exponential-polynomial path was used to calculate free energy. Computational results showed that model using GROMOS Lennard-Jones parameters was unsuitable for bulk CO(2) simulations. On the other hand, model with potential fitted to reproduce only correct density-pressure relationship in the supercritical region proved to yield correct enthalpy of vaporization and free energy of liquid CO(2) in the low-temperature region. Except for molar volume at the upper part of the vapor-liquid equilibrium line, the bulk properties of exp-6-1 parametrization of ab initio CO(2) potential were in a close agreement with the experimental results. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1772-1781, 2001

Spline based least squares integration for two-dimensional shape or wavefront reconstruction

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

Huang, Lei; Xue, Junpeng; Gao, Bo

In this paper, we present a novel method to handle two-dimensional shape or wavefront reconstruction from its slopes. The proposed integration method employs splines to fit the measured slope data with piecewise polynomials and uses the analytical polynomial functions to represent the height changes in a lateral spacing with the pre-determined spline coefficients. The linear least squares method is applied to estimate the height or wavefront as a final result. Numerical simulations verify that the proposed method has less algorithm errors than two other existing methods used for comparison. Especially at the boundaries, the proposed method has better performance. Themore » noise influence is studied by adding white Gaussian noise to the slope data. Finally, experimental data from phase measuring deflectometry are tested to demonstrate the feasibility of the new method in a practical measurement.« less

Method for Constructing Composite Response Surfaces by Combining Neural Networks with other Interpolation or Estimation Techniques

NASA Technical Reports Server (NTRS)

Rai, Man Mohan (Inventor); Madavan, Nateri K. (Inventor)

2003-01-01

A method and system for design optimization that incorporates the advantages of both traditional response surface methodology (RSM) and neural networks is disclosed. The present invention employs a unique strategy called parameter-based partitioning of the given design space. In the design procedure, a sequence of composite response surfaces based on both neural networks and polynomial fits is used to traverse the design space to identify an optimal solution. The composite response surface has both the power of neural networks and the economy of low-order polynomials (in terms of the number of simulations needed and the network training requirements). The present invention handles design problems with many more parameters than would be possible using neural networks alone and permits a designer to rapidly perform a variety of trade-off studies before arriving at the final design.

Feasibility study on the least square method for fitting non-Gaussian noise data

NASA Astrophysics Data System (ADS)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

Kurtosis Approach Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Computers and the Rational-Root Theorem--Another View.

ERIC Educational Resources Information Center

Waits, Bert K.; Demana, Franklin

1989-01-01

An approach to finding the rational roots of polynomial equations based on computer graphing is given. It integrates graphing with the purely algebraic approach. Either computers or graphing calculators can be used. (MNS)

Strong stabilization servo controller with optimization of performance criteria.

PubMed

Sarjaš, Andrej; Svečko, Rajko; Chowdhury, Amor

2011-07-01

Synthesis of a simple robust controller with a pole placement technique and a H(∞) metrics is the method used for control of a servo mechanism with BLDC and BDC electric motors. The method includes solving a polynomial equation on the basis of the chosen characteristic polynomial using the Manabe standard polynomial form and parametric solutions. Parametric solutions are introduced directly into the structure of the servo controller. On the basis of the chosen parametric solutions the robustness of a closed-loop system is assessed through uncertainty models and assessment of the norm ‖•‖(∞). The design procedure and the optimization are performed with a genetic algorithm differential evolution - DE. The DE optimization method determines a suboptimal solution throughout the optimization on the basis of a spectrally square polynomial and Šiljak's absolute stability test. The stability of the designed controller during the optimization is being checked with Lipatov's stability condition. Both utilized approaches: Šiljak's test and Lipatov's condition, check the robustness and stability characteristics on the basis of the polynomial's coefficients, and are very convenient for automated design of closed-loop control and for application in optimization algorithms such as DE. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

BGFit: management and automated fitting of biological growth curves.

PubMed

Veríssimo, André; Paixão, Laura; Neves, Ana Rute; Vinga, Susana

2013-09-25

Existing tools to model cell growth curves do not offer a flexible integrative approach to manage large datasets and automatically estimate parameters. Due to the increase of experimental time-series from microbiology and oncology, the need for a software that allows researchers to easily organize experimental data and simultaneously extract relevant parameters in an efficient way is crucial. BGFit provides a web-based unified platform, where a rich set of dynamic models can be fitted to experimental time-series data, further allowing to efficiently manage the results in a structured and hierarchical way. The data managing system allows to organize projects, experiments and measurements data and also to define teams with different editing and viewing permission. Several dynamic and algebraic models are already implemented, such as polynomial regression, Gompertz, Baranyi, Logistic and Live Cell Fraction models and the user can add easily new models thus expanding current ones. BGFit allows users to easily manage their data and models in an integrated way, even if they are not familiar with databases or existing computational tools for parameter estimation. BGFit is designed with a flexible architecture that focus on extensibility and leverages free software with existing tools and methods, allowing to compare and evaluate different data modeling techniques. The application is described in the context of bacterial and tumor cells growth data fitting, but it is also applicable to any type of two-dimensional data, e.g. physical chemistry and macroeconomic time series, being fully scalable to high number of projects, data and model complexity.

The XMM-Newton View of Stellar Coronae: High-Resolution X-Ray Spectroscopy of Capella

NASA Technical Reports Server (NTRS)

Audard, M.; Behar, E.; Guedel, M.; Raassen, A. J. J.; Porquet, D.; Mewe, R.; Foley, C. A.; Bromage, G. E.

2000-01-01

We present the high-resolution RGS spectrum of the bright stellar binary Capella observed by the XMM-Newton satellite. A multi-thermal approach has been applied to fit the data and derive elemental abundances. The differential emission measure distribution is reconstructed using a Chebychev polynomial fit. The DEM shape is found to display a sharp peak around 7 MK, consistent with previous EUVE and ASCA results. A small but significant amount of emission measure is required around 1.8 MK in order to explain the O VII He-like triplet and the C VI Ly(alpha) line. Using the sensitivity to temperature of dielectronic recombination lines from O VI around 22 A, we confirm that the cool plasma temperature needs to be higher than 1.2 MK. In the approximation of a cool plasma described by one temperature, we used line ratios from the forbidden, intercombination, and resonance lines of the O VII triplet and derived an average density for the cool coronal plasma at the low density limit. A tentative study of line ratios from the M XI triplet gives an average temperature close to the sharp peak in emission measure and an average density of the order of 10(exp 12)cu cm, three orders of magnitude higher than for O VII. Implications for the coronal physics of Capella are discussed. We complement this paper with a discussion of the importance of the atomic code uncertainties on the spectral fitting procedure.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models.

PubMed

Bignardi, A B; El Faro, L; Cardoso, V L; Machado, P F; Albuquerque, L G

2009-09-01

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Random regression models using Legendre orthogonal polynomials to evaluate the milk production of Alpine goats.

PubMed

Silva, F G; Torres, R A; Brito, L F; Euclydes, R F; Melo, A L P; Souza, N O; Ribeiro, J I; Rodrigues, M T

2013-12-11

The objective of this study was to identify the best random regression model using Legendre orthogonal polynomials to evaluate Alpine goats genetically and to estimate the parameters for test day milk yield. On the test day, we analyzed 20,710 records of milk yield of 667 goats from the Goat Sector of the Universidade Federal de Viçosa. The evaluated models had combinations of distinct fitting orders for polynomials (2-5), random genetic (1-7), and permanent environmental (1-7) fixed curves and a number of classes for residual variance (2, 4, 5, and 6). WOMBAT software was used for all genetic analyses. A random regression model using the best Legendre orthogonal polynomial for genetic evaluation of milk yield on the test day of Alpine goats considered a fixed curve of order 4, curve of genetic additive effects of order 2, curve of permanent environmental effects of order 7, and a minimum of 5 classes of residual variance because it was the most economical model among those that were equivalent to the complete model by the likelihood ratio test. Phenotypic variance and heritability were higher at the end of the lactation period, indicating that the length of lactation has more genetic components in relation to the production peak and persistence. It is very important that the evaluation utilizes the best combination of fixed, genetic additive and permanent environmental regressions, and number of classes of heterogeneous residual variance for genetic evaluation using random regression models, thereby enhancing the precision and accuracy of the estimates of parameters and prediction of genetic values.

Dielectric and conformational studies of hydrogen bonded 2-ethoxyethanol and ethyl methyl ketone system

NASA Astrophysics Data System (ADS)

Pattebahadur, Kanchan. L.; Deshmukh, S. D.; Mohod, A. G.; Undre, P. B.; Patil, S. S.; Khirade, P. W.

2018-05-01

The Dielectric constant, density and refractive index of binary mixture of 2-ethoxy ethanol (2-EE) with ethyl methyl ketone (EMK) including those of the pure liquids were measured for 11 concentrations at 25°C temperature. The experimental data is used to calculate the Excess molar volume, Excess dielectric constant, Kirkwood correlation factor and Bruggemann factor. The excess parameters results were fitted to the Redlich-Kister type polynomial equation to derive its fitting coefficient. The Kirkwood correlation factor of the mixture has been discussed to yield information about solute solvent interaction. The Bruggeman plot shows a deviation from linearity. The FT-IR spectra of pure and their binary mixtures are also studied.

Peak Doctor v 1.0.0 Labview Version

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

Garner, Scott

2014-05-29

PeakDoctor software works interactively with its user to analyze raw gamma-ray spectroscopic data. The goal of the software is to produce a list of energies and areas of all of the peaks in the spectrum, as accurately as possible. It starts by performing an energy calibration, creating a function that describes how energy can be related to channel number. Next, the software determines which channels in the raw histogram are in the Compton continuum and which channels are parts of a peak. Then the software fits the Compton continuum with cubic polynomials. The last step is to fit all ofmore » the peaks with Gaussian functions, thus producing the list.« less

Minimizing Higgs potentials via numerical polynomial homotopy continuation

NASA Astrophysics Data System (ADS)

Maniatis, M.; Mehta, D.

2012-08-01

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like non-linearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gröbner basis approach.

Primary decomposition of zero-dimensional ideals over finite fields

NASA Astrophysics Data System (ADS)

Gao, Shuhong; Wan, Daqing; Wang, Mingsheng

2009-03-01

A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp's algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a complete decomposition. Unlike previous approaches for decomposing multivariate polynomial systems, the new method does not need primality testing nor any generic projection, instead it reduces the general decomposition problem directly to root finding of univariate polynomials over the ground field. Also, it is shown how Groebner basis structure can be used to get partial primary decomposition without any root finding.

Homogenous polynomially parameter-dependent H∞ filter designs of discrete-time fuzzy systems.

PubMed

Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng

2011-10-01

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Chain mapping approach of Hamiltonian for FMO complex using associated, generalized and exceptional Jacobi polynomials

NASA Astrophysics Data System (ADS)

Mahdian, M.; Arjmandi, M. B.; Marahem, F.

2016-06-01

The excitation energy transfer (EET) in photosynthesis complex has been widely investigated in recent years. However, one of the main problems is simulation of this complex under realistic condition. In this paper by using the associated, generalized and exceptional Jacobi polynomials, firstly, we introduce the spectral density of Fenna-Matthews-Olson (FMO) complex. Afterward, we obtain a map that transforms the Hamiltonian of FMO complex as an open quantum system to a one-dimensional chain of oscillatory modes with only nearest neighbor interaction in which the system is coupled only to first mode of chain. The frequency and coupling strength of each mode can be analytically obtained from recurrence coefficient of mentioned orthogonal polynomials.

Maximal aggregation of polynomial dynamical systems

PubMed Central

Cardelli, Luca; Tschaikowski, Max

2017-01-01

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory. PMID:28878023

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

Sevast'yanov, E A; Sadekova, E Kh

The Bulgarian mathematicians Sendov, Popov, and Boyanov have well-known results on the asymptotic behaviour of the least deviations of 2{pi}-periodic functions in the classes H{sup {omega}} from trigonometric polynomials in the Hausdorff metric. However, the asymptotics they give are not adequate to detect a difference in, for example, the rate of approximation of functions f whose moduli of continuity {omega}(f;{delta}) differ by factors of the form (log(1/{delta})){sup {beta}}. Furthermore, a more detailed determination of the asymptotic behaviour by traditional methods becomes very difficult. This paper develops an approach based on using trigonometric snakes as approximating polynomials. The snakes of ordermore » n inscribed in the Minkowski {delta}-neighbourhood of the graph of the approximated function f provide, in a number of cases, the best approximation for f (for the appropriate choice of {delta}). The choice of {delta} depends on n and f and is based on constructing polynomial kernels adjusted to the Hausdorff metric and polynomials with special oscillatory properties. Bibliography: 19 titles.« less

The Kinetics of Dissolution Revisited

NASA Astrophysics Data System (ADS)

Antonel, Paula S.; Hoijemberg, Pablo A.; Maiante, Leandro M.; Lagorio, M. Gabriela

2003-09-01

An experiment analyzing the kinetics of dissolution of a solid with cylindrical geometry in water is presented. The dissolution process is followed by measuring the solid mass and its size parameters (thickness and diameter) as a function of time. It is verified that the dissolution rate follows the Nernst model. Data treatment is compared with the dissolution of a spherical solid previously described. Kinetics, diffusion concepts, and polynomial fitting of experimental data are combined in this simple experiment.

Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface.

PubMed

Zhuang, Zhenfeng; Chen, Yanting; Yu, Feihong; Sun, Xiaowei

2014-08-01

This paper presents a field curvature correction method of designing an ultrashort throw ratio (TR) projection lens for an imaging system. The projection lens is composed of several refractive optical elements and an odd polynomial mirror surface. A curved image is formed in a direction away from the odd polynomial mirror surface by the refractive optical elements from the image formed on the digital micromirror device (DMD) panel, and the curved image formed is its virtual image. Then the odd polynomial mirror surface enlarges the curved image and a plane image is formed on the screen. Based on the relationship between the chief ray from the exit pupil of each field of view (FOV) and the corresponding predescribed position on the screen, the initial profile of the freeform mirror surface is calculated by using segments of the hyperbolic according to the laws of reflection. For further optimization, the value of the high-order odd polynomial surface is used to express the freeform mirror surface through a least-squares fitting method. As an example, an ultrashort TR projection lens that realizes projection onto a large 50 in. screen at a distance of only 510 mm is presented. The optical performance for the designed projection lens is analyzed by ray tracing method. Results show that an ultrashort TR projection lens modulation transfer function of over 60% at 0.5 cycles/mm for all optimization fields is achievable with f-number of 2.0, 126° full FOV, <1% distortion, and 0.46 TR. Moreover, in comparing the proposed projection lens' optical specifications to that of traditional projection lenses, aspheric mirror projection lenses, and conventional short TR projection lenses, results indicate that this projection lens has the advantages of ultrashort TR, low f-number, wide full FOV, and small distortion.

Experimental characterization of the AFIT neutron facility. Master's thesis

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

Lessard, O.J.

1993-09-01

AFIT's Neutron Facility was characterized for room-return neutrons using a (252)Cf source and a Bonner sphere spectrometer with three experimental models, the shadow shield, the Eisenhauer, Schwartz, and Johnson (ESJ), and the polynomial models. The free-field fluences at one meter from the ESJ and polynomial models were compared to the equivalent value from the accepted experimental shadow shield model to determine the suitability of the models in the AFIT facility. The polynomial model behaved erratically, as expected, while the ESJ model compared to within 4.8% of the shadow shield model results for the four Bonner sphere calibration. The ratio ofmore » total fluence to free-field fluence at one meter for the ESJ model was then compared to the equivalent ratio obtained by a Monte Cario Neutron-Photon transport code (MCNP), an accepted computational model. The ESJ model compared to within 6.2% of the MCNP results. AFIT's fluence ratios were compared to equivalent ratios reported by three other neutron facilities which verified that AFIT's results fit previously published trends based on room volumes. The ESJ model appeared adequate for health physics applications and was chosen was chosen for calibration of the AFIT facility. Neutron Detector, Bonner Sphere, Neutron Dosimetry, Room Characterization.« less

Optimization of torrefaction conditions of coffee industry residues using desirability function approach.

PubMed

Buratti, C; Barbanera, M; Lascaro, E; Cotana, F

2018-03-01

The aim of the present study is to analyze the influence of independent process variables such as temperature, residence time, and heating rate on the torrefaction process of coffee chaff (CC) and spent coffee grounds (SCGs). Response surface methodology and a three-factor and three-level Box-Behnken design were used in order to evaluate the effects of the process variables on the weight loss (W L ) and the Higher Heating Value (HHV) of the torrefied materials. Results showed that the effects of the three factors on both responses were sequenced as follows: temperature>residence time>heating rate. Data obtained from the experiments were analyzed by analysis of variance (ANOVA) and fitted to second-order polynomial models by using multiple regression analysis. Predictive models were determined, able to obtain satisfactory fittings of the experimental data, with coefficient of determination (R 2 ) values higher than 0.95. An optimization study using Derringer's desired function methodology was also carried out and the optimal torrefaction conditions were found: temperature 271.7°C, residence time 20min, heating rate 5°C/min for CC and 256.0°C, 20min, 25°C/min for SCGs. The experimental values closely agree with the corresponding predicted values. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

Adigun, Babatunde John; Fensin, Michael Lorne; Galloway, Jack D.

Our burnup study examined the effect of a predicted critical control rod position on the nuclide predictability of several axial and radial locations within a 4×4 graphite moderated gas cooled reactor fuel cluster geometry. To achieve this, a control rod position estimator (CRPE) tool was developed within the framework of the linkage code Monteburns between the transport code MCNP and depletion code CINDER90, and four methodologies were proposed within the tool for maintaining criticality. Two of the proposed methods used an inverse multiplication approach - where the amount of fissile material in a set configuration is slowly altered until criticalitymore » is attained - in estimating the critical control rod position. Another method carried out several MCNP criticality calculations at different control rod positions, then used a linear fit to estimate the critical rod position. The final method used a second-order polynomial fit of several MCNP criticality calculations at different control rod positions to guess the critical rod position. The results showed that consistency in prediction of power densities as well as uranium and plutonium isotopics was mutual among methods within the CRPE tool that predicted critical position consistently well. Finall, while the CRPE tool is currently limited to manipulating a single control rod, future work could be geared toward implementing additional criticality search methodologies along with additional features.« less

Improving reliability of aggregation, numerical simulation and analysis of complex systems by empirical data

NASA Astrophysics Data System (ADS)

Dobronets, Boris S.; Popova, Olga A.

2018-05-01

The paper considers a new approach of regression modeling that uses aggregated data presented in the form of density functions. Approaches to Improving the reliability of aggregation of empirical data are considered: improving accuracy and estimating errors. We discuss the procedures of data aggregation as a preprocessing stage for subsequent to regression modeling. An important feature of study is demonstration of the way how represent the aggregated data. It is proposed to use piecewise polynomial models, including spline aggregate functions. We show that the proposed approach to data aggregation can be interpreted as the frequency distribution. To study its properties density function concept is used. Various types of mathematical models of data aggregation are discussed. For the construction of regression models, it is proposed to use data representation procedures based on piecewise polynomial models. New approaches to modeling functional dependencies based on spline aggregations are proposed.

Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells

NASA Astrophysics Data System (ADS)

Marchuk, A. V.; Gnedash, S. V.; Levkovskii, S. A.

2017-03-01

Two approaches to studying the free and forced axisymmetric vibrations of cylindrical shell are proposed. They are based on the three-dimensional theory of elasticity and division of the original cylindrical shell with concentric cross-sectional circles into several coaxial cylindrical shells. One approach uses linear polynomials to approximate functions defined in plan and across the thickness. The other approach also uses linear polynomials to approximate functions defined in plan, but their variation with thickness is described by the analytical solution of a system of differential equations. Both approaches have approximation and arithmetic errors. When determining the natural frequencies by the semi-analytical finite-element method in combination with the divide and conqure method, it is convenient to find the initial frequencies by the finite-element method. The behavior of the shell during free and forced vibrations is analyzed in the case where the loading area is half the shell thickness

An Approach to Stable Gradient-Descent Adaptation of Higher Order Neural Units.

PubMed

Bukovsky, Ivo; Homma, Noriyasu

2017-09-01

Stability evaluation of a weight-update system of higher order neural units (HONUs) with polynomial aggregation of neural inputs (also known as classes of polynomial neural networks) for adaptation of both feedforward and recurrent HONUs by a gradient descent method is introduced. An essential core of the approach is based on the spectral radius of a weight-update system, and it allows stability monitoring and its maintenance at every adaptation step individually. Assuring the stability of the weight-update system (at every single adaptation step) naturally results in the adaptation stability of the whole neural architecture that adapts to the target data. As an aside, the used approach highlights the fact that the weight optimization of HONU is a linear problem, so the proposed approach can be generally extended to any neural architecture that is linear in its adaptable parameters.

Measurement of the n-p elastic scattering angular distribution at E{sub n}=14.9 MeV

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

Boukharouba, N.; Bateman, F. B.; Carlson, A. D.

2010-07-15

The relative differential cross section for the elastic scattering of neutrons by protons was measured at an incident neutron energy E{sub n}=14.9 MeV and for center-of-mass scattering angles ranging from about 60 deg. to 180 deg. Angular distribution values were obtained from the normalization of the integrated data to the n-p total elastic scattering cross section. Comparisons of the normalized data to the predictions of the Arndt et al. phase-shift analysis, those of the Nijmegen group, and with the ENDF/B-VII.0 evaluation are sensitive to the value of the total elastic scattering cross section used to normalize the data. The resultsmore » of a fit to a first-order Legendre polynomial expansion are in good agreement in the backward scattering hemisphere with the predictions of the Arndt et al. phase-shift analysis, those of the Nijmegen group, and to a lesser extent, with the ENDF/B-VII.0 evaluation. A fit to a second-order expansion is in better agreement with the ENDF/B-VII.0 evaluation than with the other predictions, in particular when the total elastic scattering cross section given by Arndt et al. and the Nijmegen group is used to normalize the data. A Legendre polynomial fit to the existing n-p scattering data in the 14 MeV energy region, excluding the present measurement, showed that a best fit is obtained for a second-order expansion. Furthermore, the Kolmogorov-Smirnov test confirms the general agreement in the backward scattering hemisphere and shows that significant differences between the database and the predictions occur in the angular range between 60 deg. and 120 deg. and below 20 deg. Although there is good overall agreement in the backward scattering hemisphere, more precision small-angle scattering data and a better definition of the total elastic cross section are needed for an accurate determination of the shape and magnitude of the angular distribution.« less

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle.

PubMed

Baldi, F; Alencar, M M; Albuquerque, L G

2010-12-01

The objective of this work was to estimate covariance functions using random regression models on B-splines functions of animal age, for weights from birth to adult age in Canchim cattle. Data comprised 49,011 records on 2435 females. The model of analysis included fixed effects of contemporary groups, age of dam as quadratic covariable and the population mean trend taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were modelled through a step function with four classes. The direct and maternal additive genetic effects, and animal and maternal permanent environmental effects were included as random effects in the model. A total of seventeen analyses, considering linear, quadratic and cubic B-splines functions and up to seven knots, were carried out. B-spline functions of the same order were considered for all random effects. Random regression models on B-splines functions were compared to a random regression model on Legendre polynomials and with a multitrait model. Results from different models of analyses were compared using the REML form of the Akaike Information criterion and Schwarz' Bayesian Information criterion. In addition, the variance components and genetic parameters estimated for each random regression model were also used as criteria to choose the most adequate model to describe the covariance structure of the data. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most adequate to describe the covariance structure of the data. Random regression models using B-spline functions as base functions fitted the data better than Legendre polynomials, especially at mature ages, but higher number of parameters need to be estimated with B-splines functions. © 2010 Blackwell Verlag GmbH.

A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

NASA Astrophysics Data System (ADS)

Kewlani, Gaurav; Crawford, Justin; Iagnemma, Karl

2012-05-01

The ability of ground vehicles to quickly and accurately analyse their dynamic response to a given input is critical to their safety and efficient autonomous operation. In field conditions, significant uncertainty is associated with terrain and/or vehicle parameter estimates, and this uncertainty must be considered in the analysis of vehicle motion dynamics. Here, polynomial chaos approaches that explicitly consider parametric uncertainty during modelling of vehicle dynamics are presented. They are shown to be computationally more efficient than the standard Monte Carlo scheme, and experimental results compared with the simulation results performed on ANVEL (a vehicle simulator) indicate that the method can be utilised for efficient and accurate prediction of vehicle motion in realistic scenarios.

Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels

PubMed Central

Camacho-Bello, César; Padilla-Vivanco, Alfonso; Toxqui-Quitl, Carina; Báez-Rojas, José Javier

2016-01-01

Abstract. A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters α and β of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented. PMID:27014716

Heat transfer of phase-change materials in two-dimensional cylindrical coordinates

NASA Technical Reports Server (NTRS)

Labdon, M. B.; Guceri, S. I.

1981-01-01

Two-dimensional phase-change problem is numerically solved in cylindrical coordinates (r and z) by utilizing two Taylor series expansions for the temperature distributions in the neighborhood of the interface location. These two expansions form two polynomials in r and z directions. For the regions sufficiently away from the interface the temperature field equations are numerically solved in the usual way and the results are coupled with the polynomials. The main advantages of this efficient approach include ability to accept arbitrarily time dependent boundary conditions of all types and arbitrarily specified initial temperature distributions. A modified approach using a single Taylor series expansion in two variables is also suggested.

Getting what you want: How fit between desired and received leader sensitivity influences emotion and counterproductive work behavior.

PubMed

Rupprecht, Elizabeth A; Kueny, Clair Reynolds; Shoss, Mindy K; Metzger, Andrew J

2016-10-01

We challenge the intuitive belief that greater leader sensitivity is always associated with desirable outcomes for employees and organizations. Specifically, we argue that followers' idiosyncratic desires for, and perceptions of, leader sensitivity behaviors play a key role in how followers react to their leader's sensitivity. Moreover, these resulting affective experiences are likely to have important consequences for organizations, specifically as they relate to employee counterproductive work behavior (CWB). Drawing from supplies-values (S-V) fit theory and the stressor-emotion model of CWB, the current study focuses on the affective and behavioral consequences of fit between subordinates' ideal leader sensitivity behavior preferences and subordinates' perceptions of their actual leader's sensitivity behaviors. Polynomial regression analyses reveal that congruence between ideal and actual leader sensitivity influences employee negative affect and, consequently, engagement in counterproductive work behavior. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

PubMed Central

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2014-01-01

Growth mixture models (GMMs; Muthén & Muthén, 2000; Muthén & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models because of their common use, flexibility in modeling many types of change patterns, the availability of statistical programs to fit such models, and the ease of programming. In this paper, we present additional ways of modeling nonlinear change patterns with GMMs. Specifically, we show how LCMs that follow specific nonlinear functions can be extended to examine the presence of multiple latent classes using the Mplus and OpenMx computer programs. These models are fit to longitudinal reading data from the Early Childhood Longitudinal Study-Kindergarten Cohort to illustrate their use. PMID:25419006

Efficient computer algebra algorithms for polynomial matrices in control design

NASA Technical Reports Server (NTRS)

Baras, J. S.; Macenany, D. C.; Munach, R.

1989-01-01

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

An updated PREDICT breast cancer prognostication and treatment benefit prediction model with independent validation.

PubMed

Candido Dos Reis, Francisco J; Wishart, Gordon C; Dicks, Ed M; Greenberg, David; Rashbass, Jem; Schmidt, Marjanka K; van den Broek, Alexandra J; Ellis, Ian O; Green, Andrew; Rakha, Emad; Maishman, Tom; Eccles, Diana M; Pharoah, Paul D P

2017-05-22

PREDICT is a breast cancer prognostic and treatment benefit model implemented online. The overall fit of the model has been good in multiple independent case series, but PREDICT has been shown to underestimate breast cancer specific mortality in women diagnosed under the age of 40. Another limitation is the use of discrete categories for tumour size and node status resulting in 'step' changes in risk estimates on moving between categories. We have refitted the PREDICT prognostic model using the original cohort of cases from East Anglia with updated survival time in order to take into account age at diagnosis and to smooth out the survival function for tumour size and node status. Multivariable Cox regression models were used to fit separate models for ER negative and ER positive disease. Continuous variables were fitted using fractional polynomials and a smoothed baseline hazard was obtained by regressing the baseline cumulative hazard for each patients against time using fractional polynomials. The fit of the prognostic models were then tested in three independent data sets that had also been used to validate the original version of PREDICT. In the model fitting data, after adjusting for other prognostic variables, there is an increase in risk of breast cancer specific mortality in younger and older patients with ER positive disease, with a substantial increase in risk for women diagnosed before the age of 35. In ER negative disease the risk increases slightly with age. The association between breast cancer specific mortality and both tumour size and number of positive nodes was non-linear with a more marked increase in risk with increasing size and increasing number of nodes in ER positive disease. The overall calibration and discrimination of the new version of PREDICT (v2) was good and comparable to that of the previous version in both model development and validation data sets. However, the calibration of v2 improved over v1 in patients diagnosed under the age of 40. The PREDICT v2 is an improved prognostication and treatment benefit model compared with v1. The online version should continue to aid clinical decision making in women with early breast cancer.

Toward Continuous GPS Carrier-Phase Time Transfer: Eliminating the Time Discontinuity at an Anomaly

PubMed Central

Yao, Jian; Levine, Judah; Weiss, Marc

2015-01-01

The wide application of Global Positioning System (GPS) carrier-phase (CP) time transfer is limited by the problem of boundary discontinuity (BD). The discontinuity has two categories. One is “day boundary discontinuity,” which has been studied extensively and can be solved by multiple methods [1–8]. The other category of discontinuity, called “anomaly boundary discontinuity (anomaly-BD),” comes from a GPS data anomaly. The anomaly can be a data gap (i.e., missing data), a GPS measurement error (i.e., bad data), or a cycle slip. Initial study of the anomaly-BD shows that we can fix the discontinuity if the anomaly lasts no more than 20 min, using the polynomial curve-fitting strategy to repair the anomaly [9]. However, sometimes, the data anomaly lasts longer than 20 min. Thus, a better curve-fitting strategy is in need. Besides, a cycle slip, as another type of data anomaly, can occur and lead to an anomaly-BD. To solve these problems, this paper proposes a new strategy, i.e., the satellite-clock-aided curve fitting strategy with the function of cycle slip detection. Basically, this new strategy applies the satellite clock correction to the GPS data. After that, we do the polynomial curve fitting for the code and phase data, as before. Our study shows that the phase-data residual is only ~3 mm for all GPS satellites. The new strategy also detects and finds the number of cycle slips by searching the minimum curve-fitting residual. Extensive examples show that this new strategy enables us to repair up to a 40-min GPS data anomaly, regardless of whether the anomaly is due to a data gap, a cycle slip, or a combination of the two. We also find that interference of the GPS signal, known as “jamming”, can possibly lead to a time-transfer error, and that this new strategy can compensate for jamming outages. Thus, the new strategy can eliminate the impact of jamming on time transfer. As a whole, we greatly improve the robustness of the GPS CP time transfer. PMID:26958451

TU-CD-207-11: Patient-Driven Automatic Exposure Control for Dedicated Breast CT

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

Hernandez, A; Gazi, P; Department of Radiology, UC Davis Medical Center, Sacramento, CA

Purpose: To implement automatic exposure control (AEC) in dedicated breast CT (bCT) on a patient-specific basis using only the pre-scan scout views. Methods: Using a large cohort (N=153) of bCT data sets, the breast effective diameter (D) and width in orthogonal planes (Wa,Wb) were calculated from the reconstructed bCT image and pre-scan scout views, respectively. D, Wa, and Wb were measured at the breast center-of-mass (COM), making use of the known geometry of our bCT system. These data were then fit to a second-order polynomial “D=F(Wa,Wb)” in a least squares sense in order to provide a functional form for determiningmore » the breast diameter. The coefficient of determination (R{sup 2}) and mean percent error between the measured breast diameter and fit breast diameter were used to evaluate the overall robustness of the polynomial fit. Lastly, previously-reported bCT technique factors derived from Monte Carlo simulations were used to determine the tube current required for each breast diameter in order to match two-view mammographic dose levels. Results: F(Wa,Wb) provided fitted breast diameters in agreement with the measured breast diameters resulting in R{sup 2} values ranging from 0.908 to 0.929 and mean percent errors ranging from 3.2% to 3.7%. For all 153 bCT data sets used in this study, the fitted breast diameters ranged from 7.9 cm to 15.7 cm corresponding to tube current values ranging from 0.6 mA to 4.9 mA in order to deliver the same dose as two-view mammography in a 50% glandular breast with a 80 kV x-ray beam and 16.6 second scan time. Conclusion: The present work provides a robust framework for AEC in dedicated bCT using only the width measurements derived from the two orthogonal pre-scan scout views. Future work will investigate how these automatically chosen exposure levels affect the quality of the reconstructed image.« less

Comparison of volatility function technique for risk-neutral densities estimation

NASA Astrophysics Data System (ADS)

Bahaludin, Hafizah; Abdullah, Mimi Hafizah

2017-08-01

Volatility function technique by using interpolation approach plays an important role in extracting the risk-neutral density (RND) of options. The aim of this study is to compare the performances of two interpolation approaches namely smoothing spline and fourth order polynomial in extracting the RND. The implied volatility of options with respect to strike prices/delta are interpolated to obtain a well behaved density. The statistical analysis and forecast accuracy are tested using moments of distribution. The difference between the first moment of distribution and the price of underlying asset at maturity is used as an input to analyze forecast accuracy. RNDs are extracted from the Dow Jones Industrial Average (DJIA) index options with a one month constant maturity for the period from January 2011 until December 2015. The empirical results suggest that the estimation of RND using a fourth order polynomial is more appropriate to be used compared to a smoothing spline in which the fourth order polynomial gives the lowest mean square error (MSE). The results can be used to help market participants capture market expectations of the future developments of the underlying asset.

Scaling Property of Period-n-Tupling Sequences in One-Dimensional Mappings

NASA Astrophysics Data System (ADS)

Zeng, Wan-Zhen; Hao, Bai-Lin; Wang, Guang-Rui; Chen, Shi-Gang

1984-05-01

We calculated the universal scaling function g(x) and the scaling factor α as well as the convergence rate δ for periodtripling, -quadrapling and-quintupling sequences of RL, RL^2, RLR^2, RL2 R and RL^3 types. The superstable periods are closely connected to a set of polynomial P_n defined recursively by the original mapping. Some notable properties of these polynomials are studied. Several approaches to solving the renormalization group equation and estimating the scaling factors are suggested.

Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices.

PubMed

Dehmer, Matthias; Emmert-Streib, Frank; Shi, Yongtang; Stefu, Monica; Tripathi, Shailesh

2015-01-01

In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164-168]. We demonstrate that by using the new functional matrix approach, exhaustively generated graphs can be discriminated more uniquely than shown in the mentioned previous work.

Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices

PubMed Central

Dehmer, Matthias; Emmert-Streib, Frank; Shi, Yongtang; Stefu, Monica; Tripathi, Shailesh

2015-01-01

In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164–168]. We demonstrate that by using the new functional matrix approach, exhaustively generated graphs can be discriminated more uniquely than shown in the mentioned previous work. PMID:26479495

Modeling lactation curves and estimation of genetic parameters in Holstein cows using multiple-trait random regression models.

PubMed

Kheirabadi, Khabat; Rashidi, Amir; Alijani, Sadegh; Imumorin, Ikhide

2014-11-01

We compared the goodness of fit of three mathematical functions (including: Legendre polynomials, Lidauer-Mäntysaari function and Wilmink function) for describing the lactation curve of primiparous Iranian Holstein cows by using multiple-trait random regression models (MT-RRM). Lactational submodels provided the largest daily additive genetic (AG) and permanent environmental (PE) variance estimates at the end and at the onset of lactation, respectively, as well as low genetic correlations between peripheral test-day records. For all models, heritability estimates were highest at the end of lactation (245 to 305 days) and ranged from 0.05 to 0.26, 0.03 to 0.12 and 0.04 to 0.24 for milk, fat and protein yields, respectively. Generally, the genetic correlations between traits depend on how far apart they are or whether they are on the same day in any two traits. On average, genetic correlations between milk and fat were the lowest and those between fat and protein were intermediate, while those between milk and protein were the highest. Results from all criteria (Akaike's and Schwarz's Bayesian information criterion, and -2*logarithm of the likelihood function) suggested that a model with 2 and 5 coefficients of Legendre polynomials for AG and PE effects, respectively, was the most adequate for fitting the data. © 2014 Japanese Society of Animal Science.

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

2016-08-01

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

Genetic Parameters for Milk Yield and Lactation Persistency Using Random Regression Models in Girolando Cattle

PubMed Central

Canaza-Cayo, Ali William; Lopes, Paulo Sávio; da Silva, Marcos Vinicius Gualberto Barbosa; de Almeida Torres, Robledo; Martins, Marta Fonseca; Arbex, Wagner Antonio; Cobuci, Jaime Araujo

2015-01-01

A total of 32,817 test-day milk yield (TDMY) records of the first lactation of 4,056 Girolando cows daughters of 276 sires, collected from 118 herds between 2000 and 2011 were utilized to estimate the genetic parameters for TDMY via random regression models (RRM) using Legendre’s polynomial functions whose orders varied from 3 to 5. In addition, nine measures of persistency in milk yield (PSi) and the genetic trend of 305-day milk yield (305MY) were evaluated. The fit quality criteria used indicated RRM employing the Legendre’s polynomial of orders 3 and 5 for fitting the genetic additive and permanent environment effects, respectively, as the best model. The heritability and genetic correlation for TDMY throughout the lactation, obtained with the best model, varied from 0.18 to 0.23 and from −0.03 to 1.00, respectively. The heritability and genetic correlation for persistency and 305MY varied from 0.10 to 0.33 and from −0.98 to 1.00, respectively. The use of PS7 would be the most suitable option for the evaluation of Girolando cattle. The estimated breeding values for 305MY of sires and cows showed significant and positive genetic trends. Thus, the use of selection indices would be indicated in the genetic evaluation of Girolando cattle for both traits. PMID:26323397

Characteristic of entire corneal topography and tomography for the detection of sub-clinical keratoconus with Zernike polynomials using Pentacam.

PubMed

Xu, Zhe; Li, Weibo; Jiang, Jun; Zhuang, Xiran; Chen, Wei; Peng, Mei; Wang, Jianhua; Lu, Fan; Shen, Meixiao; Wang, Yuanyuan

2017-11-28

The study aimed to characterize the entire corneal topography and tomography for the detection of sub-clinical keratoconus (KC) with a Zernike application method. Normal subjects (n = 147; 147 eyes), sub-clinical KC patients (n = 77; 77 eyes), and KC patients (n = 139; 139 eyes) were imaged with the Pentacam HR system. The entire corneal data of pachymetry and elevation of both the anterior and posterior surfaces were exported from the Pentacam HR software. Zernike polynomials fitting was used to quantify the 3D distribution of the corneal thickness and surface elevation. The root mean square (RMS) values for each order and the total high-order irregularity were calculated. Multimeric discriminant functions combined with individual indices were built using linear step discriminant analysis. Receiver operating characteristic curves determined the diagnostic accuracy (area under the curve, AUC). The 3rd-order RMS of the posterior surface (AUC: 0.928) obtained the highest discriminating capability in sub-clinical KC eyes. The multimeric function, which consisted of the Zernike fitting indices of corneal posterior elevation, showed the highest discriminant ability (AUC: 0.951). Indices generated from the elevation of posterior surface and thickness measurements over the entire cornea using the Zernike method based on the Pentacam HR system were able to identify very early KC.

Bounding the Failure Probability Range of Polynomial Systems Subject to P-box Uncertainties

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2012-01-01

This paper proposes a reliability analysis framework for systems subject to multiple design requirements that depend polynomially on the uncertainty. Uncertainty is prescribed by probability boxes, also known as p-boxes, whose distribution functions have free or fixed functional forms. An approach based on the Bernstein expansion of polynomials and optimization is proposed. In particular, we search for the elements of a multi-dimensional p-box that minimize (i.e., the best-case) and maximize (i.e., the worst-case) the probability of inner and outer bounding sets of the failure domain. This technique yields intervals that bound the range of failure probabilities. The offset between this bounding interval and the actual failure probability range can be made arbitrarily tight with additional computational effort.

Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.

PubMed

Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko

2014-04-01

The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.

A Christoffel function weighted least squares algorithm for collocation approximations

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

Narayan, Akil; Jakeman, John D.; Zhou, Tao

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

A Christoffel function weighted least squares algorithm for collocation approximations

DOE PAGES

Narayan, Akil; Jakeman, John D.; Zhou, Tao

2016-11-28

Here, we propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the (weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. We present theoretical analysis tomore » motivate the algorithm, and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest.« less

Adaptive surrogate modeling by ANOVA and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Congedo, Pietro M.; Abgrall, Rémi

2016-06-01

The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable for real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.

An efficient algorithm for building locally refined hp - adaptive H-PCFE: Application to uncertainty quantification

NASA Astrophysics Data System (ADS)

Chakraborty, Souvik; Chowdhury, Rajib

2017-12-01

Hybrid polynomial correlated function expansion (H-PCFE) is a novel metamodel formulated by coupling polynomial correlated function expansion (PCFE) and Kriging. Unlike commonly available metamodels, H-PCFE performs a bi-level approximation and hence, yields more accurate results. However, till date, it is only applicable to medium scaled problems. In order to address this apparent void, this paper presents an improved H-PCFE, referred to as locally refined hp - adaptive H-PCFE. The proposed framework computes the optimal polynomial order and important component functions of PCFE, which is an integral part of H-PCFE, by using global variance based sensitivity analysis. Optimal number of training points are selected by using distribution adaptive sequential experimental design. Additionally, the formulated model is locally refined by utilizing the prediction error, which is inherently obtained in H-PCFE. Applicability of the proposed approach has been illustrated with two academic and two industrial problems. To illustrate the superior performance of the proposed approach, results obtained have been compared with those obtained using hp - adaptive PCFE. It is observed that the proposed approach yields highly accurate results. Furthermore, as compared to hp - adaptive PCFE, significantly less number of actual function evaluations are required for obtaining results of similar accuracy.

Trends and annual cycles in soundings of Arctic tropospheric ozone

NASA Astrophysics Data System (ADS)

Christiansen, Bo; Jepsen, Nis; Kivi, Rigel; Hansen, Georg; Larsen, Niels; Smith Korsholm, Ulrik

2017-08-01

Ozone soundings from nine Nordic stations have been homogenized and interpolated to standard pressure levels. The different stations have very different data coverage; the longest period with data is from the end of the 1980s to 2014. At each pressure level the homogenized ozone time series have been analysed with a model that includes both low-frequency variability in the form of a polynomial, an annual cycle with harmonics, the possibility for low-frequency variability in the annual amplitude and phasing, and either white noise or noise given by a first-order autoregressive process. The fitting of the parameters is performed with a Bayesian approach not only giving the mean values but also confidence intervals. The results show that all stations agree on a well-defined annual cycle in the free troposphere with a relatively confined maximum in the early summer. Regarding the low-frequency variability, it is found that Scoresbysund, Ny Ålesund, Sodankylä, Eureka, and Ørland show similar, significant signals with a maximum near 2005 followed by a decrease. This change is characteristic for all pressure levels in the free troposphere. A significant change in the annual cycle was found for Ny Ålesund, Scoresbysund, and Sodankylä. The changes at these stations are in agreement with the interpretation that the early summer maximum is appearing earlier in the year. The results are shown to be robust to the different settings of the model parameters such as the order of the polynomial, number of harmonics in the annual cycle, and the type of noise.

Multifidelity, Multidisciplinary Design Under Uncertainty with Non-Intrusive Polynomial Chaos

NASA Technical Reports Server (NTRS)

West, Thomas K., IV; Gumbert, Clyde

2017-01-01

The primary objective of this work is to develop an approach for multifidelity uncertainty quantification and to lay the framework for future design under uncertainty efforts. In this study, multifidelity is used to describe both the fidelity of the modeling of the physical systems, as well as the difference in the uncertainty in each of the models. For computational efficiency, a multifidelity surrogate modeling approach based on non-intrusive polynomial chaos using the point-collocation technique is developed for the treatment of both multifidelity modeling and multifidelity uncertainty modeling. Two stochastic model problems are used to demonstrate the developed methodologies: a transonic airfoil model and multidisciplinary aircraft analysis model. The results of both showed the multifidelity modeling approach was able to predict the output uncertainty predicted by the high-fidelity model as a significant reduction in computational cost.

The Extrapolar SWIFT model (version 1.0): fast stratospheric ozone chemistry for global climate models

NASA Astrophysics Data System (ADS)

Kreyling, Daniel; Wohltmann, Ingo; Lehmann, Ralph; Rex, Markus

2018-03-01

The Extrapolar SWIFT model is a fast ozone chemistry scheme for interactive calculation of the extrapolar stratospheric ozone layer in coupled general circulation models (GCMs). In contrast to the widely used prescribed ozone, the SWIFT ozone layer interacts with the model dynamics and can respond to atmospheric variability or climatological trends.The Extrapolar SWIFT model employs a repro-modelling approach, in which algebraic functions are used to approximate the numerical output of a full stratospheric chemistry and transport model (ATLAS). The full model solves a coupled chemical differential equation system with 55 initial and boundary conditions (mixing ratio of various chemical species and atmospheric parameters). Hence the rate of change of ozone over 24 h is a function of 55 variables. Using covariances between these variables, we can find linear combinations in order to reduce the parameter space to the following nine basic variables: latitude, pressure altitude, temperature, overhead ozone column and the mixing ratio of ozone and of the ozone-depleting families (Cly, Bry, NOy and HOy). We will show that these nine variables are sufficient to characterize the rate of change of ozone. An automated procedure fits a polynomial function of fourth degree to the rate of change of ozone obtained from several simulations with the ATLAS model. One polynomial function is determined per month, which yields the rate of change of ozone over 24 h. A key aspect for the robustness of the Extrapolar SWIFT model is to include a wide range of stratospheric variability in the numerical output of the ATLAS model, also covering atmospheric states that will occur in a future climate (e.g. temperature and meridional circulation changes or reduction of stratospheric chlorine loading).For validation purposes, the Extrapolar SWIFT model has been integrated into the ATLAS model, replacing the full stratospheric chemistry scheme. Simulations with SWIFT in ATLAS have proven that the systematic error is small and does not accumulate during the course of a simulation. In the context of a 10-year simulation, the ozone layer simulated by SWIFT shows a stable annual cycle, with inter-annual variations comparable to the ATLAS model. The application of Extrapolar SWIFT requires the evaluation of polynomial functions with 30-100 terms. Computers can currently calculate such polynomial functions at thousands of model grid points in seconds. SWIFT provides the desired numerical efficiency and computes the ozone layer 104 times faster than the chemistry scheme in the ATLAS CTM.

Uncertainty quantification of reaction mechanisms accounting for correlations introduced by rate rules and fitted Arrhenius parameters

DOE PAGES

Prager, Jens; Najm, Habib N.; Sargsyan, Khachik; ...

2013-02-23

We study correlations among uncertain Arrhenius rate parameters in a chemical model for hydrocarbon fuel-air combustion. We consider correlations induced by the use of rate rules for modeling reaction rate constants, as well as those resulting from fitting rate expressions to empirical measurements arriving at a joint probability density for all Arrhenius parameters. We focus on homogeneous ignition in a fuel-air mixture at constant-pressure. We also outline a general methodology for this analysis using polynomial chaos and Bayesian inference methods. Finally, we examine the uncertainties in both the Arrhenius parameters and in predicted ignition time, outlining the role of correlations,more » and considering both accuracy and computational efficiency.« less

Analysis of the impacts of horizontal translation and scaling on wavefront approximation coefficients with rectangular pupils for Chebyshev and Legendre polynomials.

PubMed

Sun, Wenqing; Chen, Lei; Tuya, Wulan; He, Yong; Zhu, Rihong

2013-12-01

Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.

Trajectory control of an articulated robot with a parallel drive arm based on splines under tension

NASA Astrophysics Data System (ADS)

Yi, Seung-Jong

Today's industrial robots controlled by mini/micro computers are basically simple positioning devices. The positioning accuracy depends on the mathematical description of the robot configuration to place the end-effector at the desired position and orientation within the workspace and on following the specified path which requires the trajectory planner. In addition, the consideration of joint velocity, acceleration, and jerk trajectories are essential for trajectory planning of industrial robots to obtain smooth operation. The newly designed 6 DOF articulated robot with a parallel drive arm mechanism which permits the joint actuators to be placed in the same horizontal line to reduce the arm inertia and to increase load capacity and stiffness is selected. First, the forward kinematic and inverse kinematic problems are examined. The forward kinematic equations are successfully derived based on Denavit-Hartenberg notation with independent joint angle constraints. The inverse kinematic problems are solved using the arm-wrist partitioned approach with independent joint angle constraints. Three types of curve fitting methods used in trajectory planning, i.e., certain degree polynomial functions, cubic spline functions, and cubic spline functions under tension, are compared to select the best possible method to satisfy both smooth joint trajectories and positioning accuracy for a robot trajectory planner. Cubic spline functions under tension is the method selected for the new trajectory planner. This method is implemented for a 6 DOF articulated robot with a parallel drive arm mechanism to improve the smoothness of the joint trajectories and the positioning accuracy of the manipulator. Also, this approach is compared with existing trajectory planners, 4-3-4 polynomials and cubic spline functions, via circular arc motion simulations. The new trajectory planner using cubic spline functions under tension is implemented into the microprocessor based robot controller and motors to produce combined arc and straight-line motion. The simulation and experiment show interesting results by demonstrating smooth motion in both acceleration and jerk and significant improvements of positioning accuracy in trajectory planning.

WE-E-18A-04: Precision In-Vivo Dosimetry Using Optically Stimulated Luminescence Dosimeters and a Pulsed-Stimulating Dose Reader

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

Chen, Q; Herrick, A; Hoke, S

Purpose: A new readout technology based on pulsed optically stimulating luminescence is introduced (microSTARii, Landauer, Inc, Glenwood, IL60425). This investigation searches for approaches that maximizes the dosimetry accuracy in clinical applications. Methods: The sensitivity of each optically stimulated luminescence dosimeter (OSLD) was initially characterized by exposing it to a given radiation beam. After readout, the luminescence signal stored in the OSLD was erased by exposing its sensing area to a 21W white LED light for 24 hours. A set of OSLDs with consistent sensitivities was selected to calibrate the dose reader. Higher order nonlinear curves were also derived from themore » calibration readings. OSLDs with cumulative doses below 15 Gy were reused. Before an in-vivo dosimetry, the OSLD luminescence signal was erased with the white LED light. Results: For a set of 68 manufacturer-screened OSLDs, the measured sensitivities vary in a range of 17.3%. A sub-set of the OSLDs with sensitivities within ±1% was selected for the reader calibration. Three OSLDs in a group were exposed to a given radiation. Nine groups were exposed to radiation doses ranging from 0 to 13 Gy. Additional verifications demonstrated that the reader uncertainty is about 3%. With an external calibration function derived by fitting the OSLD readings to a 3rd-order polynomial, the dosimetry uncertainty dropped to 0.5%. The dose-luminescence response curves of individual OSLDs were characterized. All curves converge within 1% after the sensitivity correction. With all uncertainties considered, the systematic uncertainty is about 2%. Additional tests emulating in-vivo dosimetry by exposing the OSLDs under different radiation sources confirmed the claim. Conclusion: The sensitivity of individual OSLD should be characterized initially. A 3rd-order polynomial function is a more accurate representation of the dose-luminescence response curve. The dosimetry uncertainty specified by the manufacturer is 4%. Following the proposed approach, it can be controlled to 2%.« less

Meta-analytic approaches to determine gender differences in the age-incidence characteristics of schizophrenia and related psychoses.

PubMed

Jackson, Dan; Kirkbride, James; Croudace, Tim; Morgan, Craig; Boydell, Jane; Errazuriz, Antonia; Murray, Robin M; Jones, Peter B

2013-03-01

A recent systematic review and meta-analysis of the incidence and prevalence of schizophrenia and other psychoses in England investigated the variation in the rates of psychotic disorders. However, some of the questions of interest, and the data collected to answer these, could not be adequately addressed using established meta-analysis techniques. We developed a novel statistical method, which makes combined use of fractional polynomials and meta-regression. This was used to quantify the evidence of gender differences and a secondary peak onset in women, where the outcome of interest is the incidence of schizophrenia. Statistically significant and epidemiologically important effects were obtained using our methods. Our analysis is based on data from four studies that provide 50 incidence rates, stratified by age and gender. We describe several variations of our method, in particular those that might be used where more data is available, and provide guidance for assessing the model fit. Copyright © 2013 John Wiley & Sons, Ltd.

Integrating uniform design and response surface methodology to optimize thiacloprid suspension

PubMed Central

Li, Bei-xing; Wang, Wei-chang; Zhang, Xian-peng; Zhang, Da-xia; Mu, Wei; Liu, Feng

2017-01-01

A model 25% suspension concentrate (SC) of thiacloprid was adopted to evaluate an integrative approach of uniform design and response surface methodology. Tersperse2700, PE1601, xanthan gum and veegum were the four experimental factors, and the aqueous separation ratio and viscosity were the two dependent variables. Linear and quadratic polynomial models of stepwise regression and partial least squares were adopted to test the fit of the experimental data. Verification tests revealed satisfactory agreement between the experimental and predicted data. The measured values for the aqueous separation ratio and viscosity were 3.45% and 278.8 mPa·s, respectively, and the relative errors of the predicted values were 9.57% and 2.65%, respectively (prepared under the proposed conditions). Comprehensive benefits could also be obtained by appropriately adjusting the amount of certain adjuvants based on practical requirements. Integrating uniform design and response surface methodology is an effective strategy for optimizing SC formulas. PMID:28383036

Empirical dual energy calibration (EDEC) for cone-beam computed tomography.

PubMed

Stenner, Philip; Berkus, Timo; Kachelriess, Marc

2007-09-01

Material-selective imaging using dual energy CT (DECT) relies heavily on well-calibrated material decomposition functions. These require the precise knowledge of the detected x-ray spectra, and even if they are exactly known the reliability of DECT will suffer from scattered radiation. We propose an empirical method to determine the proper decomposition function. In contrast to other decomposition algorithms our empirical dual energy calibration (EDEC) technique requires neither knowledge of the spectra nor of the attenuation coefficients. The desired material-selective raw data p1 and p2 are obtained as functions of the measured attenuation data q1 and q2 (one DECT scan = two raw data sets) by passing them through a polynomial function. The polynomial's coefficients are determined using a general least squares fit based on thresholded images of a calibration phantom. The calibration phantom's dimension should be of the same order of magnitude as the test object, but other than that no assumptions on its exact size or positioning are made. Once the decomposition coefficients are determined DECT raw data can be decomposed by simply passing them through the polynomial. To demonstrate EDEC simulations of an oval CTDI phantom, a lung phantom, a thorax phantom and a mouse phantom were carried out. The method was further verified by measuring a physical mouse phantom, a half-and-half-cylinder phantom and a Yin-Yang phantom with a dedicated in vivo dual source micro-CT scanner. The raw data were decomposed into their components, reconstructed, and the pixel values obtained were compared to the theoretical values. The determination of the calibration coefficients with EDEC is very robust and depends only slightly on the type of calibration phantom used. The images of the test phantoms (simulations and measurements) show a nearly perfect agreement with the theoretical micro values and density values. Since EDEC is an empirical technique it inherently compensates for scatter components. The empirical dual energy calibration technique is a pragmatic, simple, and reliable calibration approach that produces highly quantitative DECT images.

Generalized Hill-stability criteria for hierarchical three-body systems at arbitrary inclinations

NASA Astrophysics Data System (ADS)

Grishin, Evgeni; Perets, Hagai B.; Zenati, Yossef; Michaely, Erez

2017-04-01

A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasi-stable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (˜120°), beyond which the agreement is marginal. At such high inclinations, the stability radius is larger, the ratio between the outer and inner periods becomes comparable and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non-co-planar systems, our results have direct implications for any triple systems and, in particular, binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.

Determination of localization accuracy based on experimentally acquired image sets: applications to single molecule microscopy

PubMed Central

Tahmasbi, Amir; Ward, E. Sally; Ober, Raimund J.

2015-01-01

Fluorescence microscopy is a photon-limited imaging modality that allows the study of subcellular objects and processes with high specificity. The best possible accuracy (standard deviation) with which an object of interest can be localized when imaged using a fluorescence microscope is typically calculated using the Cramér-Rao lower bound, that is, the inverse of the Fisher information. However, the current approach for the calculation of the best possible localization accuracy relies on an analytical expression for the image of the object. This can pose practical challenges since it is often difficult to find appropriate analytical models for the images of general objects. In this study, we instead develop an approach that directly uses an experimentally collected image set to calculate the best possible localization accuracy for a general subcellular object. In this approach, we fit splines, i.e. smoothly connected piecewise polynomials, to the experimentally collected image set to provide a continuous model of the object, which can then be used for the calculation of the best possible localization accuracy. Due to its practical importance, we investigate in detail the application of the proposed approach in single molecule fluorescence microscopy. In this case, the object of interest is a point source and, therefore, the acquired image set pertains to an experimental point spread function. PMID:25837101

Evaluation of Analytical Modeling Functions for the Phonation Onset Process.

PubMed

Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael

2016-01-01

The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW.

Gen-2 hand-held optical imager towards cancer imaging: reflectance and transillumination phantom studies.

PubMed

Gonzalez, Jean; Roman, Manuela; Hall, Michael; Godavarty, Anuradha

2012-01-01

Hand-held near-infrared (NIR) optical imagers are developed by various researchers towards non-invasive clinical breast imaging. Unlike these existing imagers that can perform only reflectance imaging, a generation-2 (Gen-2) hand-held optical imager has been recently developed to perform both reflectance and transillumination imaging. The unique forked design of the hand-held probe head(s) allows for reflectance imaging (as in ultrasound) and transillumination or compressed imaging (as in X-ray mammography). Phantom studies were performed to demonstrate two-dimensional (2D) target detection via reflectance and transillumination imaging at various target depths (1-5 cm deep) and using simultaneous multiple point illumination approach. It was observed that 0.45 cc targets were detected up to 5 cm deep during transillumination, but limited to 2.5 cm deep during reflectance imaging. Additionally, implementing appropriate data post-processing techniques along with a polynomial fitting approach, to plot 2D surface contours of the detected signal, yields distinct target detectability and localization. The ability of the gen-2 imager to perform both reflectance and transillumination imaging allows its direct comparison to ultrasound and X-ray mammography results, respectively, in future clinical breast imaging studies.

New approach to calculate the true-coincidence effect of HpGe detector

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

Alnour, I. A., E-mail: aaibrahim3@live.utm.my, E-mail: ibrahim.elnour@yahoo.com; Wagiran, H.; Ibrahim, N.

The corrections for true-coincidence effects in HpGe detector are important, especially at low source-to-detector distances. This work established an approach to calculate the true-coincidence effects experimentally for HpGe detectors of type Canberra GC3018 and Ortec GEM25-76-XLB-C, which are in operation at neutron activation analysis lab in Malaysian Nuclear Agency (NM). The correction for true-coincidence effects was performed close to detector at distances 2 and 5 cm using {sup 57}Co, {sup 60}Co, {sup 133}Ba and {sup 137}Cs as standard point sources. The correction factors were ranged between 0.93-1.10 at 2 cm and 0.97-1.00 at 5 cm for Canberra HpGe detector; whereas for Ortec HpGemore » detector ranged between 0.92-1.13 and 0.95-100 at 2 and 5 cm respectively. The change in efficiency calibration curve of the detector at 2 and 5 cm after correction was found to be less than 1%. Moreover, the polynomial parameters functions were simulated through a computer program, MATLAB in order to find an accurate fit to the experimental data points.« less

Assessment of the pseudo-tracking approach for the calculation of material acceleration and pressure fields from time-resolved PIV: part I. Error propagation

NASA Astrophysics Data System (ADS)

van Gent, P. L.; Schrijer, F. F. J.; van Oudheusden, B. W.

2018-04-01

Pseudo-tracking refers to the construction of imaginary particle paths from PIV velocity fields and the subsequent estimation of the particle (material) acceleration. In view of the variety of existing and possible alternative ways to perform the pseudo-tracking method, it is not straightforward to select a suitable combination of numerical procedures for its implementation. To address this situation, this paper extends the theoretical framework for the approach. The developed theory is verified by applying various implementations of pseudo-tracking to a simulated PIV experiment. The findings of the investigations allow us to formulate the following insights and practical recommendations: (1) the velocity errors along the imaginary particle track are primarily a function of velocity measurement errors and spatial velocity gradients; (2) the particle path may best be calculated with second-order accurate numerical procedures while ensuring that the CFL condition is met; (3) least-square fitting of a first-order polynomial is a suitable method to estimate the material acceleration from the track; and (4) a suitable track length may be selected on the basis of the variation in material acceleration with track length.

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation

NASA Astrophysics Data System (ADS)

Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar

2018-05-01

In this paper, we present SMKA18 analysis, which is a first attempt to extract the set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach. Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NNLO approximation. The results are extracted using a wide range of proton g1p(x ,Q2) , neutron g1n(x ,Q2) , and deuteron g1d(x ,Q2) spin-dependent structure functions data set including the most recent high-precision measurements from COMPASS16 experiments at CERN, which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been done using the standard Hessian error propagation. We will compare our results with the available spin-dependent inclusive deep inelastic scattering data set and other results for the spin-dependent PDFs in literature. The results obtained for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of x .

Wavefront reconstruction algorithm based on Legendre polynomials for radial shearing interferometry over a square area and error analysis.

PubMed

Kewei, E; Zhang, Chen; Li, Mengyang; Xiong, Zhao; Li, Dahai

2015-08-10

Based on the Legendre polynomials expressions and its properties, this article proposes a new approach to reconstruct the distorted wavefront under test of a laser beam over square area from the phase difference data obtained by a RSI system. And the result of simulation and experimental results verifies the reliability of the method proposed in this paper. The formula of the error propagation coefficients is deduced when the phase difference data of overlapping area contain noise randomly. The matrix T which can be used to evaluate the impact of high-orders Legendre polynomial terms on the outcomes of the low-order terms due to mode aliasing is proposed, and the magnitude of impact can be estimated by calculating the F norm of the T. In addition, the relationship between ratio shear, sampling points, terms of polynomials and noise propagation coefficients, and the relationship between ratio shear, sampling points and norms of the T matrix are both analyzed, respectively. Those research results can provide an optimization design way for radial shearing interferometry system with the theoretical reference and instruction.

A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation

NASA Astrophysics Data System (ADS)

Oruç, Ömer

2018-04-01

In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.

Design of reinforced areas of concrete column using quadratic polynomials

NASA Astrophysics Data System (ADS)

Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

2017-11-01

Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

An Adaptive Prediction-Based Approach to Lossless Compression of Floating-Point Volume Data.

PubMed

Fout, N; Ma, Kwan-Liu

2012-12-01

In this work, we address the problem of lossless compression of scientific and medical floating-point volume data. We propose two prediction-based compression methods that share a common framework, which consists of a switched prediction scheme wherein the best predictor out of a preset group of linear predictors is selected. Such a scheme is able to adapt to different datasets as well as to varying statistics within the data. The first method, called APE (Adaptive Polynomial Encoder), uses a family of structured interpolating polynomials for prediction, while the second method, which we refer to as ACE (Adaptive Combined Encoder), combines predictors from previous work with the polynomial predictors to yield a more flexible, powerful encoder that is able to effectively decorrelate a wide range of data. In addition, in order to facilitate efficient visualization of compressed data, our scheme provides an option to partition floating-point values in such a way as to provide a progressive representation. We compare our two compressors to existing state-of-the-art lossless floating-point compressors for scientific data, with our data suite including both computer simulations and observational measurements. The results demonstrate that our polynomial predictor, APE, is comparable to previous approaches in terms of speed but achieves better compression rates on average. ACE, our combined predictor, while somewhat slower, is able to achieve the best compression rate on all datasets, with significantly better rates on most of the datasets.

Injection molding lens metrology using software configurable optical test system

NASA Astrophysics Data System (ADS)

Zhan, Cheng; Cheng, Dewen; Wang, Shanshan; Wang, Yongtian

2016-10-01

Optical plastic lens produced by injection molding machine possesses numerous advantages of light quality, impact resistance, low cost, etc. The measuring methods in the optical shop are mainly interferometry, profile meter. However, these instruments are not only expensive, but also difficult to alignment. The software configurable optical test system (SCOTS) is based on the geometry of the fringe refection and phase measuring deflectometry method (PMD), which can be used to measure large diameter mirror, aspheric and freeform surface rapidly, robustly, and accurately. In addition to the conventional phase shifting method, we propose another data collection method called as dots matrix projection. We also use the Zernike polynomials to correct the camera distortion. This polynomials fitting mapping distortion method has not only simple operation, but also high conversion precision. We simulate this test system to measure the concave surface using CODE V and MATLAB. The simulation results show that the dots matrix projection method has high accuracy and SCOTS has important significance for on-line detection in optical shop.

Modeling and control for closed environment plant production systems

NASA Technical Reports Server (NTRS)

Fleisher, David H.; Ting, K. C.; Janes, H. W. (Principal Investigator)

2002-01-01

A computer program was developed to study multiple crop production and control in controlled environment plant production systems. The program simulates crop growth and development under nominal and off-nominal environments. Time-series crop models for wheat (Triticum aestivum), soybean (Glycine max), and white potato (Solanum tuberosum) are integrated with a model-based predictive controller. The controller evaluates and compensates for effects of environmental disturbances on crop production scheduling. The crop models consist of a set of nonlinear polynomial equations, six for each crop, developed using multivariate polynomial regression (MPR). Simulated data from DSSAT crop models, previously modified for crop production in controlled environments with hydroponics under elevated atmospheric carbon dioxide concentration, were used for the MPR fitting. The model-based predictive controller adjusts light intensity, air temperature, and carbon dioxide concentration set points in response to environmental perturbations. Control signals are determined from minimization of a cost function, which is based on the weighted control effort and squared-error between the system response and desired reference signal.

A model to environmental monitoring based on glutathione-S-transferase activity and branchial lesions in catfish

NASA Astrophysics Data System (ADS)

Neta, Raimunda Nonata Fortes Carvalho; Torres, Audalio Rebelo

2017-11-01

In this work, we validate the glutathione-S-transferase and branchial lesions as biomarkers in catfish Sciades herzbergii to obtain a predictive model of the environmental impact effects in a harbor of Brazil. The catfish were sampled from a port known to be contaminated with heavy metals and organic compounds and from a natural reserve in São Marcos Bay, Maranhão. Two biomarkers, hepatic glutathione S-transferase (GST) activity and branchial lesions were analyzed. The values for GST activity were modeled with the occurrence of branchial lesions by fitting a third order polynomial. Results from the mathematical model indicate that GST activity has a strong polynomial relationship with the occurrence of branchial lesions in both the wet and the dry seasons, but only at the polluted port site. Our mathematic model indicates that when the GST ceases to act, serious branchial lesions are observed in the catfish of the contaminated port area.

Synthesized tissue-equivalent dielectric phantoms using salt and polyvinylpyrrolidone solutions.

PubMed

Ianniello, Carlotta; de Zwart, Jacco A; Duan, Qi; Deniz, Cem M; Alon, Leeor; Lee, Jae-Seung; Lattanzi, Riccardo; Brown, Ryan

2018-07-01

To explore the use of polyvinylpyrrolidone (PVP) for simulated materials with tissue-equivalent dielectric properties. PVP and salt were used to control, respectively, relative permittivity and electrical conductivity in a collection of 63 samples with a range of solute concentrations. Their dielectric properties were measured with a commercial probe and fitted to a 3D polynomial in order to establish an empirical recipe. The material's thermal properties and MR spectra were measured. The empirical polynomial recipe (available at https://www.amri.ninds.nih.gov/cgi-bin/phantomrecipe) provides the PVP and salt concentrations required for dielectric materials with permittivity and electrical conductivity values between approximately 45 and 78, and 0.1 to 2 siemens per meter, respectively, from 50 MHz to 4.5 GHz. The second- (solute concentrations) and seventh- (frequency) order polynomial recipe provided less than 2.5% relative error between the measured and target properties. PVP side peaks in the spectra were minor and unaffected by temperature changes. PVP-based phantoms are easy to prepare and nontoxic, and their semitransparency makes air bubbles easy to identify. The polymer can be used to create simulated material with a range of dielectric properties, negligible spectral side peaks, and long T 2 relaxation time, which are favorable in many MR applications. Magn Reson Med 80:413-419, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

FIREFLY (Fitting IteRativEly For Likelihood analYsis): a full spectral fitting code

NASA Astrophysics Data System (ADS)

Wilkinson, David M.; Maraston, Claudia; Goddard, Daniel; Thomas, Daniel; Parikh, Taniya

2017-12-01

We present a new spectral fitting code, FIREFLY, for deriving the stellar population properties of stellar systems. FIREFLY is a chi-squared minimization fitting code that fits combinations of single-burst stellar population models to spectroscopic data, following an iterative best-fitting process controlled by the Bayesian information criterion. No priors are applied, rather all solutions within a statistical cut are retained with their weight. Moreover, no additive or multiplicative polynomials are employed to adjust the spectral shape. This fitting freedom is envisaged in order to map out the effect of intrinsic spectral energy distribution degeneracies, such as age, metallicity, dust reddening on galaxy properties, and to quantify the effect of varying input model components on such properties. Dust attenuation is included using a new procedure, which was tested on Integral Field Spectroscopic data in a previous paper. The fitting method is extensively tested with a comprehensive suite of mock galaxies, real galaxies from the Sloan Digital Sky Survey and Milky Way globular clusters. We also assess the robustness of the derived properties as a function of signal-to-noise ratio (S/N) and adopted wavelength range. We show that FIREFLY is able to recover age, metallicity, stellar mass, and even the star formation history remarkably well down to an S/N ∼ 5, for moderately dusty systems. Code and results are publicly available.1

New approach to wireless data communication in a propagation environment

NASA Astrophysics Data System (ADS)

Hunek, Wojciech P.; Majewski, Paweł

2017-10-01

This paper presents a new idea of perfect signal reconstruction in multivariable wireless communications systems including a different number of transmitting and receiving antennas. The proposed approach is based on the polynomial matrix S-inverse associated with Smith factorization. Crucially, the above mentioned inverse implements the so-called degrees of freedom. It has been confirmed by simulation study that the degrees of freedom allow to minimalize the negative impact of the propagation environment in terms of increasing the robustness of whole signal reconstruction process. Now, the parasitic drawbacks in form of dynamic ISI and ICI effects can be eliminated in framework described by polynomial calculus. Therefore, the new method guarantees not only reducing the financial impact but, more importantly, provides potentially the lower consumption energy systems than other classical ones. In order to show the potential of new approach, the simulation studies were performed by author's simulator based on well-known OFDM technique.

Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling

NASA Astrophysics Data System (ADS)

Dobronets, B. S.; Popova, O. A.

2018-05-01

Data aggregation issues for numerical modeling are reviewed in the present study. The authors discuss data aggregation procedures as preprocessing for subsequent numerical modeling. To calculate the data aggregation, the authors propose using numerical probabilistic analysis (NPA). An important feature of this study is how the authors represent the aggregated data. The study shows that the offered approach to data aggregation can be interpreted as the frequency distribution of a variable. To study its properties, the density function is used. For this purpose, the authors propose using the piecewise polynomial models. A suitable example of such approach is the spline. The authors show that their approach to data aggregation allows reducing the level of data uncertainty and significantly increasing the efficiency of numerical calculations. To demonstrate the degree of the correspondence of the proposed methods to reality, the authors developed a theoretical framework and considered numerical examples devoted to time series aggregation.

Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

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

Balondo Iyela, Daddy; Centre for Cosmology, Particle Physics and Phenomenology; Département de Physique, Université de Kinshasa

2013-09-15

Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristicmore » of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies.« less

Weighted spline based integration for reconstruction of freeform wavefront.

PubMed

Pant, Kamal K; Burada, Dali R; Bichra, Mohamed; Ghosh, Amitava; Khan, Gufran S; Sinzinger, Stefan; Shakher, Chandra

2018-02-10

In the present work, a spline-based integration technique for the reconstruction of a freeform wavefront from the slope data has been implemented. The slope data of a freeform surface contain noise due to their machining process and that introduces reconstruction error. We have proposed a weighted cubic spline based least square integration method (WCSLI) for the faithful reconstruction of a wavefront from noisy slope data. In the proposed method, the measured slope data are fitted into a piecewise polynomial. The fitted coefficients are determined by using a smoothing cubic spline fitting method. The smoothing parameter locally assigns relative weight to the fitted slope data. The fitted slope data are then integrated using the standard least squares technique to reconstruct the freeform wavefront. Simulation studies show the improved result using the proposed technique as compared to the existing cubic spline-based integration (CSLI) and the Southwell methods. The proposed reconstruction method has been experimentally implemented to a subaperture stitching-based measurement of a freeform wavefront using a scanning Shack-Hartmann sensor. The boundary artifacts are minimal in WCSLI which improves the subaperture stitching accuracy and demonstrates an improved Shack-Hartmann sensor for freeform metrology application.

An adaptive least-squares global sensitivity method and application to a plasma-coupled combustion prediction with parametric correlation

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Massa, Luca; Wang, Jonathan; Freund, Jonathan B.

2018-05-01

We introduce an efficient non-intrusive surrogate-based methodology for global sensitivity analysis and uncertainty quantification. Modified covariance-based sensitivity indices (mCov-SI) are defined for outputs that reflect correlated effects. The overall approach is applied to simulations of a complex plasma-coupled combustion system with disparate uncertain parameters in sub-models for chemical kinetics and a laser-induced breakdown ignition seed. The surrogate is based on an Analysis of Variance (ANOVA) expansion, such as widely used in statistics, with orthogonal polynomials representing the ANOVA subspaces and a polynomial dimensional decomposition (PDD) representing its multi-dimensional components. The coefficients of the PDD expansion are obtained using a least-squares regression, which both avoids the direct computation of high-dimensional integrals and affords an attractive flexibility in choosing sampling points. This facilitates importance sampling using a Bayesian calibrated posterior distribution, which is fast and thus particularly advantageous in common practical cases, such as our large-scale demonstration, for which the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense. Effort, instead, is focused on efficient finite-resolution sampling. Standard covariance-based sensitivity indices (Cov-SI) are employed to account for correlation of the uncertain parameters. Magnitude of Cov-SI is unfortunately unbounded, which can produce extremely large indices that limit their utility. Alternatively, mCov-SI are then proposed in order to bound this magnitude ∈ [ 0 , 1 ]. The polynomial expansion is coupled with an adaptive ANOVA strategy to provide an accurate surrogate as the union of several low-dimensional spaces, avoiding the typical computational cost of a high-dimensional expansion. It is also adaptively simplified according to the relative contribution of the different polynomials to the total variance. The approach is demonstrated for a laser-induced turbulent combustion simulation model, which includes parameters with correlated effects.

Efficiently approximating the Pareto frontier: Hydropower dam placement in the Amazon basin

USGS Publications Warehouse

Wu, Xiaojian; Gomes-Selman, Jonathan; Shi, Qinru; Xue, Yexiang; Garcia-Villacorta, Roosevelt; Anderson, Elizabeth; Sethi, Suresh; Steinschneider, Scott; Flecker, Alexander; Gomes, Carla P.

2018-01-01

Real–world problems are often not fully characterized by a single optimal solution, as they frequently involve multiple competing objectives; it is therefore important to identify the so-called Pareto frontier, which captures solution trade-offs. We propose a fully polynomial-time approximation scheme based on Dynamic Programming (DP) for computing a polynomially succinct curve that approximates the Pareto frontier to within an arbitrarily small > 0 on treestructured networks. Given a set of objectives, our approximation scheme runs in time polynomial in the size of the instance and 1/. We also propose a Mixed Integer Programming (MIP) scheme to approximate the Pareto frontier. The DP and MIP Pareto frontier approaches have complementary strengths and are surprisingly effective. We provide empirical results showing that our methods outperform other approaches in efficiency and accuracy. Our work is motivated by a problem in computational sustainability concerning the proliferation of hydropower dams throughout the Amazon basin. Our goal is to support decision-makers in evaluating impacted ecosystem services on the full scale of the Amazon basin. Our work is general and can be applied to approximate the Pareto frontier of a variety of multiobjective problems on tree-structured networks.

Modeling Source Water TOC Using Hydroclimate Variables and Local Polynomial Regression.

PubMed

Samson, Carleigh C; Rajagopalan, Balaji; Summers, R Scott

2016-04-19

To control disinfection byproduct (DBP) formation in drinking water, an understanding of the source water total organic carbon (TOC) concentration variability can be critical. Previously, TOC concentrations in water treatment plant source waters have been modeled using streamflow data. However, the lack of streamflow data or unimpaired flow scenarios makes it difficult to model TOC. In addition, TOC variability under climate change further exacerbates the problem. Here we proposed a modeling approach based on local polynomial regression that uses climate, e.g. temperature, and land surface, e.g., soil moisture, variables as predictors of TOC concentration, obviating the need for streamflow. The local polynomial approach has the ability to capture non-Gaussian and nonlinear features that might be present in the relationships. The utility of the methodology is demonstrated using source water quality and climate data in three case study locations with surface source waters including river and reservoir sources. The models show good predictive skill in general at these locations, with lower skills at locations with the most anthropogenic influences in their streams. Source water TOC predictive models can provide water treatment utilities important information for making treatment decisions for DBP regulation compliance under future climate scenarios.

Uncertainty Quantification for Polynomial Systems via Bernstein Expansions

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2012-01-01

This paper presents a unifying framework to uncertainty quantification for systems having polynomial response metrics that depend on both aleatory and epistemic uncertainties. The approach proposed, which is based on the Bernstein expansions of polynomials, enables bounding the range of moments and failure probabilities of response metrics as well as finding supersets of the extreme epistemic realizations where the limits of such ranges occur. These bounds and supersets, whose analytical structure renders them free of approximation error, can be made arbitrarily tight with additional computational effort. Furthermore, this framework enables determining the importance of particular uncertain parameters according to the extent to which they affect the first two moments of response metrics and failure probabilities. This analysis enables determining the parameters that should be considered uncertain as well as those that can be assumed to be constants without incurring significant error. The analytical nature of the approach eliminates the numerical error that characterizes the sampling-based techniques commonly used to propagate aleatory uncertainties as well as the possibility of under predicting the range of the statistic of interest that may result from searching for the best- and worstcase epistemic values via nonlinear optimization or sampling.

Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application

PubMed Central

Tutty, O.

2015-01-01

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterizing the magnitude of the Coriolis force. By converting the original Navier–Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares of polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterizing the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study, several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach. PMID:26730219

Well-conditioning global-local analysis using stable generalized/extended finite element method for linear elastic fracture mechanics

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felicio Bruzzi

2016-11-01

Using the locally-enriched strategy to enrich a small/local part of the problem by generalized/extended finite element method (G/XFEM) leads to non-optimal convergence rate and ill-conditioning system of equations due to presence of blending elements. The local enrichment can be chosen from polynomial, singular, branch or numerical types. The so-called stable version of G/XFEM method provides a well-conditioning approach when only singular functions are used in the blending elements. This paper combines numeric enrichment functions obtained from global-local G/XFEM method with the polynomial enrichment along with a well-conditioning approach, stable G/XFEM, in order to show the robustness and effectiveness of the approach. In global-local G/XFEM, the enrichment functions are constructed numerically from the solution of a local problem. Furthermore, several enrichment strategies are adopted along with the global-local enrichment. The results obtained with these enrichments strategies are discussed in detail, considering convergence rate in strain energy, growth rate of condition number, and computational processing. Numerical experiments show that using geometrical enrichment along with stable G/XFEM for global-local strategy improves the convergence rate and the conditioning of the problem. In addition, results shows that using polynomial enrichment for global problem simultaneously with global-local enrichments lead to ill-conditioned system matrices and bad convergence rate.

NFIRAOS beamsplitters subsystems optomechanical design

NASA Astrophysics Data System (ADS)

Lamontagne, Frédéric; Desnoyers, Nichola; Nash, Reston; Boucher, Marc-André; Martin, Olivier; Buteau-Vaillancourt, Louis; Châteauneuf, François; Atwood, Jenny; Hill, Alexis; Byrnes, Peter W. G.; Herriot, Glen; Véran, Jean-Pierre

2016-07-01

The early-light facility adaptive optics system for the Thirty Meter Telescope (TMT) is the Narrow-Field InfraRed Adaptive Optics System (NFIRAOS). The science beam splitter changer mechanism and the visible light beam splitter are subsystems of NFIRAOS. This paper presents the opto-mechanical design of the NFIRAOS beam splitters subsystems (NBS). In addition to the modal and the structural analyses, the beam splitters surface deformations are computed considering the environmental constraints during operation. Surface deformations are fit to Zernike polynomials using SigFit software. Rigid body motion as well as residual RMS and peak-to-valley surface deformations are calculated. Finally, deformed surfaces are exported to Zemax to evaluate the transmitted and reflected wave front error. The simulation results of this integrated opto-mechanical analysis have shown compliance with all optical requirements.

Temperature dependent lattice constant of InSb above room temperature

NASA Astrophysics Data System (ADS)

Breivik, Magnus; Nilsen, Tron Arne; Fimland, Bjørn-Ove

2013-10-01

Using temperature dependent X-ray diffraction on two InSb single crystalline substrates, the bulk lattice constant of InSb was determined between 32 and 325 °C. A polynomial function was fitted to the data: a(T)=6.4791+3.28×10-5×T+1.02×10-8×T2 Å (T in °C), which gives slightly higher values than previously published (which go up to 62 °C). From the fit, the thermal expansion of InSb was calculated to be α(T)=5.062×10-6+3.15×10-9×T K-1 (T in °C). We found that the thermal expansion coefficient is higher than previously published values above 100 °C (more than 10% higher at 325 °C).

mfpa: Extension of mfp using the ACD covariate transformation for enhanced parametric multivariable modeling.

PubMed

Royston, Patrick; Sauerbrei, Willi

2016-01-01

In a recent article, Royston (2015, Stata Journal 15: 275-291) introduced the approximate cumulative distribution (acd) transformation of a continuous covariate x as a route toward modeling a sigmoid relationship between x and an outcome variable. In this article, we extend the approach to multivariable modeling by modifying the standard Stata program mfp. The result is a new program, mfpa, that has all the features of mfp plus the ability to fit a new model for user-selected covariates that we call fp1( p 1 , p 2 ). The fp1( p 1 , p 2 ) model comprises the best-fitting combination of a dimension-one fractional polynomial (fp1) function of x and an fp1 function of acd ( x ). We describe a new model-selection algorithm called function-selection procedure with acd transformation, which uses significance testing to attempt to simplify an fp1( p 1 , p 2 ) model to a submodel, an fp1 or linear model in x or in acd ( x ). The function-selection procedure with acd transformation is related in concept to the fsp (fp function-selection procedure), which is an integral part of mfp and which is used to simplify a dimension-two (fp2) function. We describe the mfpa command and give univariable and multivariable examples with real data to demonstrate its use.

Maintaining a Critical Spectra within Monteburns for a Gas-Cooled Reactor Array by Way of Control Rod Manipulation

DOE PAGES

Adigun, Babatunde John; Fensin, Michael Lorne; Galloway, Jack D.; ...

2016-10-01

Our burnup study examined the effect of a predicted critical control rod position on the nuclide predictability of several axial and radial locations within a 4×4 graphite moderated gas cooled reactor fuel cluster geometry. To achieve this, a control rod position estimator (CRPE) tool was developed within the framework of the linkage code Monteburns between the transport code MCNP and depletion code CINDER90, and four methodologies were proposed within the tool for maintaining criticality. Two of the proposed methods used an inverse multiplication approach - where the amount of fissile material in a set configuration is slowly altered until criticalitymore » is attained - in estimating the critical control rod position. Another method carried out several MCNP criticality calculations at different control rod positions, then used a linear fit to estimate the critical rod position. The final method used a second-order polynomial fit of several MCNP criticality calculations at different control rod positions to guess the critical rod position. The results showed that consistency in prediction of power densities as well as uranium and plutonium isotopics was mutual among methods within the CRPE tool that predicted critical position consistently well. Finall, while the CRPE tool is currently limited to manipulating a single control rod, future work could be geared toward implementing additional criticality search methodologies along with additional features.« less

Improving the Depth-Time Fit of Holocene Climate Proxy Measures by Increasing Coherence with a Reference Time-Series

NASA Astrophysics Data System (ADS)

Rahim, K. J.; Cumming, B. F.; Hallett, D. J.; Thomson, D. J.

2007-12-01

An accurate assessment of historical local Holocene data is important in making future climate predictions. Holocene climate is often obtained through proxy measures such as diatoms or pollen using radiocarbon dating. Wiggle Match Dating (WMD) uses an iterative least squares approach to tune a core with a large amount of 14C dates to the 14C calibration curve. This poster will present a new method of tuning a time series with when only a modest number of 14C dates are available. The method presented uses the multitaper spectral estimation, and it specifically makes use of a multitaper spectral coherence tuning technique. Holocene climate reconstructions are often based on a simple depth-time fit such as a linear interpolation, splines, or low order polynomials. Many of these models make use of only a small number of 14C dates, each of which is a point estimate with a significant variance. This technique attempts to tune the 14C dates to a reference series, such as tree rings, varves, or the radiocarbon calibration curve. The amount of 14C in the atmosphere is not constant, and a significant source of variance is solar activity. A decrease in solar activity coincides with an increase in cosmogenic isotope production, and an increase in cosmogenic isotope production coincides with a decrease in temperature. The method presented uses multitaper coherence estimates and adjusts the phase of the time series to line up significant line components with that of the reference series in attempt to obtain a better depth-time fit then the original model. Given recent concerns and demonstrations of the variation in estimated dates from radiocarbon labs, methods to confirm and tune the depth-time fit can aid climate reconstructions by improving and serving to confirm the accuracy of the underlying depth-time fit. Climate reconstructions can then be made on the improved depth-time fit. This poster presents a run though of this process using Chauvin Lake in the Canadian prairies and Mt. Barr Cirque Lake located in British Columbia as examples.

Design of measuring system for wire diameter based on sub-pixel edge detection algorithm

NASA Astrophysics Data System (ADS)

Chen, Yudong; Zhou, Wang

2016-09-01

Light projection method is often used in measuring system for wire diameter, which is relatively simpler structure and lower cost, and the measuring accuracy is limited by the pixel size of CCD. Using a CCD with small pixel size can improve the measuring accuracy, but will increase the cost and difficulty of making. In this paper, through the comparative analysis of a variety of sub-pixel edge detection algorithms, polynomial fitting method is applied for data processing in measuring system for wire diameter, to improve the measuring accuracy and enhance the ability of anti-noise. In the design of system structure, light projection method with orthogonal structure is used for the detection optical part, which can effectively reduce the error caused by line jitter in the measuring process. For the electrical part, ARM Cortex-M4 microprocessor is used as the core of the circuit module, which can not only drive double channel linear CCD but also complete the sampling, processing and storage of the CCD video signal. In addition, ARM microprocessor can complete the high speed operation of the whole measuring system for wire diameter in the case of no additional chip. The experimental results show that sub-pixel edge detection algorithm based on polynomial fitting can make up for the lack of single pixel size and improve the precision of measuring system for wire diameter significantly, without increasing hardware complexity of the entire system.

[Colorimetric characterization of LCD based on wavelength partition spectral model].

PubMed

Liu, Hao-Xue; Cui, Gui-Hua; Huang, Min; Wu, Bing; Xu, Yan-Fang; Luo, Ming

2013-10-01

To establish a colorimetrical characterization model of LCDs, an experiment with EIZO CG19, IBM 19, DELL 19 and HP 19 LCDs was designed and carried out to test the interaction between RGB channels, and then to test the spectral additive property of LCDs. The RGB digital values of single channel and two channels were given and the corresponding tristimulus values were measured, then a chart was plotted and calculations were made to test the independency of RGB channels. The results showed that the interaction between channels was reasonably weak and spectral additivity property was held well. We also found that the relations between radiations and digital values at different wavelengths varied, that is, they were the functions of wavelength. A new calculation method based on piecewise spectral model, in which the relation between radiations and digital values was fitted by a cubic polynomial in each piece of wavelength with measured spectral radiation curves, was proposed and tested. The spectral radiation curves of RGB primaries with any digital values can be found out with only a few measurements and fitted cubic polynomial in this way and then any displayed color can be turned out by the spectral additivity property of primaries at given digital values. The algorithm of this method was discussed in detail in this paper. The computations showed that the proposed method was simple and the number of measurements needed was reduced greatly while keeping a very high computation precision. This method can be used as a colorimetrical characterization model.

Constructing a polynomial whose nodal set is the three-twist knot 52

NASA Astrophysics Data System (ADS)

Dennis, Mark R.; Bode, Benjamin

2017-06-01

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot 52. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other simple knots and links. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.

Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

NASA Astrophysics Data System (ADS)

Grolet, Aurelien; Thouverez, Fabrice

2015-02-01

This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Control Synthesis of Discrete-Time T-S Fuzzy Systems: Reducing the Conservatism Whilst Alleviating the Computational Burden.

PubMed

Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Peng, Chen

2017-09-01

The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi-Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix approach in the literature, we aim to design a more efficient slack variable approach under a general framework of homogenous matrix polynomials. Thanks to the introduction of a new extended representation for homogeneous matrix polynomials, related matrices with the same coefficient are collected together into one sole set and thus those redundant terms of the augmented multi-indexed matrix approach can be removed, i.e., the computational burden can be alleviated in this paper. More importantly, due to the fact that more useful information is involved into control design, the conservatism of the proposed approach as well is less than the counterpart of the augmented multi-indexed matrix approach. Finally, numerical experiments are given to show the effectiveness of the proposed approach.

Secure message authentication system for node to node network

NASA Astrophysics Data System (ADS)

Sindhu, R.; Vanitha, M. M.; Norman, J.

2017-10-01

The Message verification remains some of the best actual methods for prevent the illegal and dis honored communication after presence progressed to WSNs (Wireless Sensor Networks). Intend for this purpose, several message verification systems must stand established, created on both symmetric key cryptography otherwise public key cryptosystems. Best of them will have some limits for great computational then statement above in count of deficiency of climb ability then flexibility in node settlement occurrence. In a polynomial based system was newly presented for these problems. Though, this system then situations delay will must the dimness of integral limitation firm in the point of polynomial: once the amount of message transferred remains the greater than the limitation then the opponent will completely improve the polynomial approaches. This paper suggests using ECC (Elliptic Curve Cryptography). Though using the node verification the technique in this paper permits some nodes to transfer a limitless amount of messages lacking misery in the limit problem. This system will have the message cause secrecy. Equally theoretic study then model effects show our planned system will be effective than the polynomial based method in positions of calculation then statement above in privacy points though message basis privacy.

An interactive graphics program to retrieve, display, compare, manipulate, curve fit, difference and cross plot wind tunnel data

NASA Technical Reports Server (NTRS)

Elliott, R. D.; Werner, N. M.; Baker, W. M.

1975-01-01

The Aerodynamic Data Analysis and Integration System (ADAIS), developed as a highly interactive computer graphics program capable of manipulating large quantities of data such that addressable elements of a data base can be called up for graphic display, compared, curve fit, stored, retrieved, differenced, etc., was described. The general nature of the system is evidenced by the fact that limited usage has already occurred with data bases consisting of thermodynamic, basic loads, and flight dynamics data. Productivity using ADAIS of five times that for conventional manual methods of wind tunnel data analysis is routinely achieved. In wind tunnel data analysis, data from one or more runs of a particular test may be called up and displayed along with data from one or more runs of a different test. Curves may be faired through the data points by any of four methods, including cubic spline and least squares polynomial fit up to seventh order.

Research on Al-alloy sheet forming formability during warm/hot sheet hydroforming based on elliptical warm bulging test

NASA Astrophysics Data System (ADS)

Cai, Gaoshen; Wu, Chuanyu; Gao, Zepu; Lang, Lihui; Alexandrov, Sergei

2018-05-01

An elliptical warm/hot sheet bulging test under different temperatures and pressure rates was carried out to predict Al-alloy sheet forming limit during warm/hot sheet hydroforming. Using relevant formulas of ultimate strain to calculate and dispose experimental data, forming limit curves (FLCS) in tension-tension state of strain (TTSS) area are obtained. Combining with the basic experimental data obtained by uniaxial tensile test under the equivalent condition with bulging test, complete forming limit diagrams (FLDS) of Al-alloy are established. Using a quadratic polynomial curve fitting method, material constants of fitting function are calculated and a prediction model equation for sheet metal forming limit is established, by which the corresponding forming limit curves in TTSS area can be obtained. The bulging test and fitting results indicated that the sheet metal FLCS obtained were very accurate. Also, the model equation can be used to instruct warm/hot sheet bulging test.

Bayesian Revision of Residual Detection Power

NASA Technical Reports Server (NTRS)

DeLoach, Richard

2013-01-01

This paper addresses some issues with quality assessment and quality assurance in response surface modeling experiments executed in wind tunnels. The role of data volume on quality assurance for response surface models is reviewed. Specific wind tunnel response surface modeling experiments are considered for which apparent discrepancies exist between fit quality expectations based on implemented quality assurance tactics, and the actual fit quality achieved in those experiments. These discrepancies are resolved by using Bayesian inference to account for certain imperfections in the assessment methodology. Estimates of the fraction of out-of-tolerance model predictions based on traditional frequentist methods are revised to account for uncertainty in the residual assessment process. The number of sites in the design space for which residuals are out of tolerance is seen to exceed the number of sites where the model actually fails to fit the data. A method is presented to estimate how much of the design space in inadequately modeled by low-order polynomial approximations to the true but unknown underlying response function.

Training Data Requirement for a Neural Network to Predict Aerodynamic Coefficients

NASA Technical Reports Server (NTRS)

Korsmeyer, David (Technical Monitor); Rajkumar, T.; Bardina, Jorge

2003-01-01

Basic aerodynamic coefficients are modeled as functions of angle of attack, speed brake deflection angle, Mach number, and side slip angle. Most of the aerodynamic parameters can be well-fitted using polynomial functions. We previously demonstrated that a neural network is a fast, reliable way of predicting aerodynamic coefficients. We encountered few under fitted and/or over fitted results during prediction. The training data for the neural network are derived from wind tunnel test measurements and numerical simulations. The basic questions that arise are: how many training data points are required to produce an efficient neural network prediction, and which type of transfer functions should be used between the input-hidden layer and hidden-output layer. In this paper, a comparative study of the efficiency of neural network prediction based on different transfer functions and training dataset sizes is presented. The results of the neural network prediction reflect the sensitivity of the architecture, transfer functions, and training dataset size.

Statistical modelling of growth using a mixed model with orthogonal polynomials.

PubMed

Suchocki, T; Szyda, J

2011-02-01

In statistical modelling, the effects of single-nucleotide polymorphisms (SNPs) are often regarded as time-independent. However, for traits recorded repeatedly, it is very interesting to investigate the behaviour of gene effects over time. In the analysis, simulated data from the 13th QTL-MAS Workshop (Wageningen, The Netherlands, April 2009) was used and the major goal was the modelling of genetic effects as time-dependent. For this purpose, a mixed model which describes each effect using the third-order Legendre orthogonal polynomials, in order to account for the correlation between consecutive measurements, is fitted. In this model, SNPs are modelled as fixed, while the environment is modelled as random effects. The maximum likelihood estimates of model parameters are obtained by the expectation-maximisation (EM) algorithm and the significance of the additive SNP effects is based on the likelihood ratio test, with p-values corrected for multiple testing. For each significant SNP, the percentage of the total variance contributed by this SNP is calculated. Moreover, by using a model which simultaneously incorporates effects of all of the SNPs, the prediction of future yields is conducted. As a result, 179 from the total of 453 SNPs covering 16 out of 18 true quantitative trait loci (QTL) were selected. The correlation between predicted and true breeding values was 0.73 for the data set with all SNPs and 0.84 for the data set with selected SNPs. In conclusion, we showed that a longitudinal approach allows for estimating changes of the variance contributed by each SNP over time and demonstrated that, for prediction, the pre-selection of SNPs plays an important role.

Predicting Subnational Ebola Virus Disease Epidemic Dynamics from Sociodemographic Indicators

PubMed Central

Valeri, Linda; Patterson-Lomba, Oscar; Gurmu, Yared; Ablorh, Akweley; Bobb, Jennifer; Townes, F. William; Harling, Guy

2016-01-01

Background The recent Ebola virus disease (EVD) outbreak in West Africa has spread wider than any previous human EVD epidemic. While individual-level risk factors that contribute to the spread of EVD have been studied, the population-level attributes of subnational regions associated with outbreak severity have not yet been considered. Methods To investigate the area-level predictors of EVD dynamics, we integrated time series data on cumulative reported cases of EVD from the World Health Organization and covariate data from the Demographic and Health Surveys. We first estimated the early growth rates of epidemics in each second-level administrative district (ADM2) in Guinea, Sierra Leone and Liberia using exponential, logistic and polynomial growth models. We then evaluated how these growth rates, as well as epidemic size within ADM2s, were ecologically associated with several demographic and socio-economic characteristics of the ADM2, using bivariate correlations and multivariable regression models. Results The polynomial growth model appeared to best fit the ADM2 epidemic curves, displaying the lowest residual standard error. Each outcome was associated with various regional characteristics in bivariate models, however in stepwise multivariable models only mean education levels were consistently associated with a worse local epidemic. Discussion By combining two common methods—estimation of epidemic parameters using mathematical models, and estimation of associations using ecological regression models—we identified some factors predicting rapid and severe EVD epidemics in West African subnational regions. While care should be taken interpreting such results as anything more than correlational, we suggest that our approach of using data sources that were publicly available in advance of the epidemic or in real-time provides an analytic framework that may assist countries in understanding the dynamics of future outbreaks as they occur. PMID:27732614

Cosmic acceleration in non-flat f( T) cosmology

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; Luongo, Orlando; Pincak, Richard; Ravanpak, Arvin

2018-05-01

We study f( T) cosmological models inserting a non-vanishing spatial curvature and discuss its consequences on cosmological dynamics. To figure this out, a polynomial f( T) model and a double torsion model are considered. We first analyze those models with cosmic data, employing the recent surveys of Union 2.1, baryonic acoustic oscillation and cosmic microwave background measurements. We then emphasize that the two popular f( T) models enable the crossing of the phantom divide line due to dark torsion. Afterwards, we compute numerical bounds up to 3-σ confidence level, emphasizing the fact that Ω _{k0} turns out to be non-compatible with zero at least at 1σ . Moreover, we underline that, even increasing the accuracy, one cannot remove the degeneracy between our models and the Λ CDM paradigm. So that, we show that our treatments contain the concordance paradigm and we analyze the equation of state behaviors at different redshift domains. We also take into account gamma ray bursts and we describe the evolution of both the f( T) models with high redshift data. We calibrate the gamma ray burst measurements through small redshift surveys of data and we thus compare the main differences between non-flat and flat f( T) cosmology at different redshift ranges. We finally match the corresponding outcomes with small redshift bounds provided by cosmography. To do so, we analyze the deceleration parameters and their variations, proportional to the jerk term. Even though the two models well fit late-time data, we notice that the polynomial f( T) approach provides an effective de-Sitter phase, whereas the second f( T) framework shows analogous results compared with the Λ CDM predictions.

Theoretical Analysis of Local Search and Simple Evolutionary Algorithms for the Generalized Travelling Salesperson Problem.

PubMed

Pourhassan, Mojgan; Neumann, Frank

2018-06-22

The generalized travelling salesperson problem is an important NP-hard combinatorial optimization problem for which meta-heuristics, such as local search and evolutionary algorithms, have been used very successfully. Two hierarchical approaches with different neighbourhood structures, namely a Cluster-Based approach and a Node-Based approach, have been proposed by Hu and Raidl (2008) for solving this problem. In this paper, local search algorithms and simple evolutionary algorithms based on these approaches are investigated from a theoretical perspective. For local search algorithms, we point out the complementary abilities of the two approaches by presenting instances where they mutually outperform each other. Afterwards, we introduce an instance which is hard for both approaches when initialized on a particular point of the search space, but where a variable neighbourhood search combining them finds the optimal solution in polynomial time. Then we turn our attention to analysing the behaviour of simple evolutionary algorithms that use these approaches. We show that the Node-Based approach solves the hard instance of the Cluster-Based approach presented in Corus et al. (2016) in polynomial time. Furthermore, we prove an exponential lower bound on the optimization time of the Node-Based approach for a class of Euclidean instances.

The Use of Transformations in Solving Equations

ERIC Educational Resources Information Center

Libeskind, Shlomo

2010-01-01

Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

Orbital component extraction by time-variant sinusoidal modeling.

NASA Astrophysics Data System (ADS)

Sinnesael, Matthias; Zivanovic, Miroslav; De Vleeschouwer, David; Claeys, Philippe; Schoukens, Johan

2016-04-01

Accurately deciphering periodic variations in paleoclimate proxy signals is essential for cyclostratigraphy. Classical spectral analysis often relies on methods based on the (Fast) Fourier Transformation. This technique has no unique solution separating variations in amplitude and frequency. This characteristic makes it difficult to correctly interpret a proxy's power spectrum or to accurately evaluate simultaneous changes in amplitude and frequency in evolutionary analyses. Here, we circumvent this drawback by using a polynomial approach to estimate instantaneous amplitude and frequency in orbital components. This approach has been proven useful to characterize audio signals (music and speech), which are non-stationary in nature (Zivanovic and Schoukens, 2010, 2012). Paleoclimate proxy signals and audio signals have in nature similar dynamics; the only difference is the frequency relationship between the different components. A harmonic frequency relationship exists in audio signals, whereas this relation is non-harmonic in paleoclimate signals. However, the latter difference is irrelevant for the problem at hand. Using a sliding window approach, the model captures time variations of an orbital component by modulating a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters that determine the model are the mean frequency of the orbital component and the polynomial coefficients. The first parameter depends on geologic interpretation, whereas the latter are estimated by means of linear least-squares. As an output, the model provides the orbital component waveform, either in the depth or time domain. Furthermore, it allows for a unique decomposition of the signal into its instantaneous amplitude and frequency. Frequency modulation patterns can be used to reconstruct changes in accumulation rate, whereas amplitude modulation can be used to reconstruct e.g. eccentricity-modulated precession. The time-variant sinusoidal model is applied to well-established Pleistocene benthic isotope records to evaluate its performance. Zivanovic M. and Schoukens J. (2010) On The Polynomial Approximation for Time-Variant Harmonic Signal Modeling. IEEE Transactions On Audio, Speech, and Language Processing vol. 19, no. 3, pp. 458-467. Doi: 10.1109/TASL.2010.2049673. Zivanovic M. and Schoukens J. (2012) Single and Piecewise Polynomials for Modeling of Pitched Sounds. IEEE Transactions On Audio, Speech, and Language Processing vol. 20, no. 4, pp. 1270-1281. Doi: 10.1109/TASL.2011.2174228.

SU-G-IeP2-12: The Effect of Iterative Reconstruction and CT Tube Voltage On Hounsfield Unit Values of Iodinated Contrast

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

Ogden, K; Greene-Donnelly, K; Vallabhaneni, D

Purpose: To investigate the effects of changing iterative reconstruction strength and tube voltage on Hounsfield Unit (HU) values of varying concentrations of Iodinated contrast medium in a phantom. Method: Iodinated contrast (Omnipaque 300, GE Healthcare, Princeton NJ) was diluted with distilled water to concentrations of 0.6, 0.9, 1.8, 3.6, 7.2, and 10.8 mg/mL of Iodine. The solutions were scanned in a patient equivalent water phantom on two MDCT scanners: VCT 64 slice (GE Medical Systems, Waukesha, WI) and an Aquilion One 320 slice scanner (Toshiba America Medical Systems, Tustin CA). The phantom was scanned at 80, 100, 120, 140 kVmore » using 400, 255, 180, and 130 mAs, respectively, for the VCT scanner, and 80, 100, 120, and 135 kV using 400, 250, 200, and 150 mAs, respectively, on the Aquilion One. Images were reconstructed at 2.5 mm (VCT) and 0.5 mm (Aquilion One). The VCT images were reconstructed using Advanced Statistical Iterative Reconstruction (ASIR) at 6 different strengths: 0%, 20%, 40%, 60%, 80%, and 100%. Aquilion One images were reconstructed using Adaptive Iterative Dose Reduction (AIDR) at 4 strengths: no AIDR, Weak AIDR, Standard AIDR, and Strong AIDR. Regions of interest (ROIs) were drawn on the images to measure the HU values and standard deviations of the diluted contrast. Second order polynomials were used to fit the HU values as a function of Iodine concentration. Results: For both scanners, there was no significant effect of changing the iterative reconstruction strength. The polynomial fits yielded goodness-of-fit (R2) values averaging 0.997. Conclusion: Changing the strength of the iterative reconstruction has no significant effect on the HU values of Iodinated contrast in a tissue-equivalent phantom. Fit values of HU vs Iodine concentration are useful in quantitative imaging protocols such as the determination of cardiac output from time-density curves in the main pulmonary artery.« less

Experimental injury study of children seated behind collapsing front seats in rear impacts.

PubMed

Saczalski, Kenneth J; Sances, Anthony; Kumaresan, Srirangam; Burton, Joseph L; Lewis, Paul R

2003-01-01

In the mid 1990's the U.S. Department of Transportation made recommendations to place children and infants into the rear seating areas of motor vehicles to avoid front seat airbag induced injuries and fatalities. In most rear-impacts, however, the adult occupied front seats will collapse into the rear occupant area and pose another potentially serious injury hazard to the rear-seated children. Since rear-impacts involve a wide range of speeds, impact severity, and various sizes of adults in collapsing front seats, a multi-variable experimental method was employed in conjunction with a multi-level "factorial analysis" technique to study injury potential of rear-seated children. Various sizes of Hybrid III adult surrogates, seated in a "typical" average strength collapsing type of front seat, and a three-year-old Hybrid III child surrogate, seated on a built-in booster seat located directly behind the front adult occupant, were tested at various impact severity levels in a popular "minivan" sled-buck test set up. A total of five test configurations were utilized in this study. Three levels of velocity changes ranging from 22.5 to 42.5 kph were used. The average of peak accelerations on the sled-buck tests ranged from approximately 8.2 G's up to about 11.1 G's, with absolute peak values of just over 14 G's at the higher velocity change. The parameters of the test configuration enabled the experimental data to be combined into a polynomial "injury" function of the two primary independent variables (i.e. front seat adult occupant weight and velocity change) so that the "likelihood" of rear child "injury potential" could be determined over a wide range of the key parameters. The experimentally derived head injury data was used to obtain a preliminary HIC (Head Injury Criteria) polynomial fit at the 900 level for the rear-seated child. Several actual accident cases were compared with the preliminary polynomial fit. This study provides a test efficient, multi-variable, method to compare the injury biomechanical data with actual accident cases.

A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.

PubMed

Rørvik, Eivind; Thörnqvist, Sara; Stokkevåg, Camilla H; Dahle, Tordis J; Fjaera, Lars Fredrik; Ytre-Hauge, Kristian S

2017-06-01

The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LET d ) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model. The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LET d based models for a simulated spread out Bragg peak (SOBP) scenario. The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22). The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LET d based models should be further evaluated in clinically realistic scenarios. © 2017 American Association of Physicists in Medicine.

Finding the Best-Fit Polynomial Approximation in Evaluating Drill Data: the Application of a Generalized Inverse Matrix / Poszukiwanie Najlepszej ZGODNOŚCI W PRZYBLIŻENIU Wielomianowym Wykorzystanej do Oceny Danych Z ODWIERTÓW - Zastosowanie UOGÓLNIONEJ Macierzy Odwrotnej

NASA Astrophysics Data System (ADS)

Karakus, Dogan

2013-12-01

In mining, various estimation models are used to accurately assess the size and the grade distribution of an ore body. The estimation of the positional properties of unknown regions using random samples with known positional properties was first performed using polynomial approximations. Although the emergence of computer technologies and statistical evaluation of random variables after the 1950s rendered the polynomial approximations less important, theoretically the best surface passing through the random variables can be expressed as a polynomial approximation. In geoscience studies, in which the number of random variables is high, reliable solutions can be obtained only with high-order polynomials. Finding the coefficients of these types of high-order polynomials can be computationally intensive. In this study, the solution coefficients of high-order polynomials were calculated using a generalized inverse matrix method. A computer algorithm was developed to calculate the polynomial degree giving the best regression between the values obtained for solutions of different polynomial degrees and random observational data with known values, and this solution was tested with data derived from a practical application. In this application, the calorie values for data from 83 drilling points in a coal site located in southwestern Turkey were used, and the results are discussed in the context of this study. W górnictwie wykorzystuje się rozmaite modele estymacji do dokładnego określenia wielkości i rozkładu zawartości pierwiastka użytecznego w rudzie. Estymację położenia i właściwości skał w nieznanych obszarach z wykorzystaniem próbek losowych o znanym położeniu przeprowadzano na początku z wykorzystaniem przybliżenia wielomianowego. Pomimo tego, że rozwój technik komputerowych i statystycznych metod ewaluacji próbek losowych sprawiły, że po roku 1950 metody przybliżenia wielomianowego straciły na znaczeniu, nadal teoretyczna powierzchnia najlepszej zgodności przechodząca przez zmienne losowe wyrażana jest właśnie poprzez przybliżenie wielomianowe. W geofizyce, gdzie liczba próbek losowych jest zazwyczaj bardzo wysoka, wiarygodne rozwiązania uzyskać można jedynie przy wykorzystaniu wielomianów wyższych stopni. Określenie współczynników w tego typu wielomia nach jest skomplikowaną procedurą obliczeniową. W pracy tej poszukiwane współczynniki wielomianu wyższych stopni obliczono przy zastosowaniu metody uogólnionej macierzy odwrotnej. Opracowano odpowiedni algorytm komputerowy do obliczania stopnia wielomianu, zapewniający najlepszą regresję pomiędzy wartościami otrzymanymi z rozwiązań bazujących na wielomianach różnych stopni i losowymi danymi z obserwacji, o znanych wartościach. Rozwiązanie to przetestowano z użyciem danych uzyskanych z zastosowań praktycznych. W tym zastosowaniu użyto danych o wartości opałowej pochodzących z 83 odwiertów wykonanych w zagłębiu węglowym w południowo- zachodniej Turcji, wyniki obliczeń przedyskutowano w kontekście zagadnień uwzględnionych w niniejszej pracy.

A subset polynomial neural networks approach for breast cancer diagnosis.

PubMed

O'Neill, T J; Penm, Jack; Penm, Jonathan

2007-01-01

Breast cancer is a very common and serious cancer for women that is diagnosed in one of every eight Australian women before the age of 85. The conventional method of breast cancer diagnosis is mammography. However, mammography has been reported to have poor diagnostic capability. In this paper we have used subset polynomial neural network techniques in conjunction with fine needle aspiration cytology to undertake this difficult task of predicting breast cancer. The successful findings indicate that adoption of NNs is likely to lead to increased survival of women with breast cancer, improved electronic healthcare, and enhanced quality of life.

Temperature Dependence of Mineral Solubility in Water. Part 3. Alkaline and Alkaline Earth Sulfates

NASA Astrophysics Data System (ADS)

Krumgalz, B. S.

2018-06-01

The databases of alkaline and alkaline earth sulfate solubilities in water at various temperatures were created using experimental data from the publications over about the last two centuries. Statistical critical evaluation of the created databases was produced since there were enough independent data sources to justify such evaluation. The reliable experimental data were adequately described by polynomial expressions over various temperature ranges. Using the Pitzer approach for ionic activity and osmotic coefficients, the thermodynamic solubility products for the discussed minerals have been calculated at various temperatures and represented by polynomial expressions.

Temperature Dependence of Mineral Solubility in Water. Part 2. Alkaline and Alkaline Earth Bromides

NASA Astrophysics Data System (ADS)

Krumgalz, B. S.

2018-03-01

Databases of alkaline and alkaline earth bromide solubilities in water at various temperatures were created using experimental data from publications over about the last two centuries. Statistical critical evaluation of the created databases was produced since there were enough independent data sources to justify such evaluation. The reliable experimental data were adequately described by polynomial expressions over various temperature ranges. Using the Pitzer approach for ionic activity and osmotic coefficients, the thermodynamic solubility products for the discussed bromide minerals have been calculated at various temperature intervals and also represented by polynomial expressions.

Optical solver of combinatorial problems: nanotechnological approach.

PubMed

Cohen, Eyal; Dolev, Shlomi; Frenkel, Sergey; Kryzhanovsky, Boris; Palagushkin, Alexandr; Rosenblit, Michael; Zakharov, Victor

2013-09-01

We present an optical computing system to solve NP-hard problems. As nano-optical computing is a promising venue for the next generation of computers performing parallel computations, we investigate the application of submicron, or even subwavelength, computing device designs. The system utilizes a setup of exponential sized masks with exponential space complexity produced in polynomial time preprocessing. The masks are later used to solve the problem in polynomial time. The size of the masks is reduced to nanoscaled density. Simulations were done to choose a proper design, and actual implementations show the feasibility of such a system.

Finding Limit Cycles in self-excited oscillators with infinite-series damping functions

NASA Astrophysics Data System (ADS)

Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.

2015-03-01

In this paper we present a simple method for finding the location of limit cycles of self excited oscillators whose damping functions can be represented by some infinite convergent series. We have used standard results of first-order perturbation theory to arrive at amplitude equations. The approach has been kept pedagogic by first working out the cases of finite polynomials using elementary algebra. Then the method has been extended to various infinite polynomials, where the fixed points of the corresponding amplitude equations cannot be found out. Hopf bifurcations for systems with nonlinear powers in velocities have also been discussed.

Radiometer Calibrations: Saving Time by Automating the Gathering and Analysis Procedures

NASA Technical Reports Server (NTRS)

Sadino, Jeffrey L.

2005-01-01

Mr. Abtahi custom-designs radiometers for Mr. Hook's research group. Inherently, when the radiometers report the temperature of arbitrary surfaces, the results are affected by errors in accuracy. This problem can be reduced if the errors can be accounted for in a polynomial. This is achieved by pointing the radiometer at a constant-temperature surface. We have been using a Hartford Scientific WaterBath. The measurements from the radiometer are collected at many different temperatures and compared to the measurements made by a Hartford Chubb thermometer with a four-decimal point resolution. The data is analyzed and fit to a fifth-order polynomial. This formula is then uploaded into the radiometer software, enabling accurate data gathering. Traditionally, Mr. Abtahi has done this by hand, spending several hours of his time setting the temperature, waiting for stabilization, taking measurements, and then repeating for other temperatures. My program, written in the Python language, has enabled the data gathering and analysis process to be handed off to a less-senior member of the team. Simply by entering several initial settings, the program will simultaneously control all three instruments and organize the data suitable for computer analyses, thus giving the desired fifth-order polynomial. This will save time, allow for a more complete calibration data set, and allow for base calibrations to be developed. The program is expandable to simultaneously take any type of measurement from up to nine distinct instruments.

Comparison of parametric methods for modeling corneal surfaces

NASA Astrophysics Data System (ADS)

Bouazizi, Hala; Brunette, Isabelle; Meunier, Jean

2017-02-01

Corneal topography is a medical imaging technique to get the 3D shape of the cornea as a set of 3D points of its anterior and posterior surfaces. From these data, topographic maps can be derived to assist the ophthalmologist in the diagnosis of disorders. In this paper, we compare three different mathematical parametric representations of the corneal surfaces leastsquares fitted to the data provided by corneal topography. The parameters obtained from these models reduce the dimensionality of the data from several thousand 3D points to only a few parameters and could eventually be useful for diagnosis, biometry, implant design etc. The first representation is based on Zernike polynomials that are commonly used in optics. A variant of these polynomials, named Bhatia-Wolf will also be investigated. These two sets of polynomials are defined over a circular domain which is convenient to model the elevation (height) of the corneal surface. The third representation uses Spherical Harmonics that are particularly well suited for nearly-spherical object modeling, which is the case for cornea. We compared the three methods using the following three criteria: the root-mean-square error (RMSE), the number of parameters and the visual accuracy of the reconstructed topographic maps. A large dataset of more than 2000 corneal topographies was used. Our results showed that Spherical Harmonics were superior with a RMSE mean lower than 2.5 microns with 36 coefficients (order 5) for normal corneas and lower than 5 microns for two diseases affecting the corneal shapes: keratoconus and Fuchs' dystrophy.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

Application of Polynomial Neural Networks to Classification of Acoustic Warfare Signals

DTIC Science & Technology

1993-04-01

on Neural Networks, Vol. II, Jun’e, 1987. [66] Shynk, J.J., "Adaptive IIR filtering," IEEE ASSP Magazine, Vol. 6, No. 2, Apr. 1989. 175 I [67] Specht ...rows This is the size of the yellow capture window which will be displayed on the screen. The best setting for pixel-rows is two greater than exemplar...exemplar size of 4 to be captured by the PNN. The pixel-rows setting is 6, which allows all four rows of I the retina data to fit inside yellow capture

Thermal Energy Storage and Heat Transfer Support Program. Task 4. Thermionic Energy Conversion Studies. Volume 2

DTIC Science & Technology

1991-03-01

Target Temperature as a Function of the Py erot Temperature ........ .... ............. 13 2.4 Emitter Temperature as a Functio of th Liode Target...Temperatm .. ........................ 14 2.5 Experimental Calibration Data and Polynomial Fit for ASTAR-811C Diode ... . ......... . ...... 18 2.6 Actual...12.2152(V) - 0.0099 (5.2) Maximum error a 0.0093% C) TR = 420 K P = 4.5541(V)3 - 23.58 18 (V)2 + 18.1602(V) + 0.002 (5.3) Maximum error =.1.632% d) TR = 450

Two smart spectrophotometric methods for the simultaneous estimation of Simvastatin and Ezetimibe in combined dosage form

NASA Astrophysics Data System (ADS)

Magdy, Nancy; Ayad, Miriam F.

2015-02-01

Two simple, accurate, precise, sensitive and economic spectrophotometric methods were developed for the simultaneous determination of Simvastatin and Ezetimibe in fixed dose combination products without prior separation. The first method depends on a new chemometrics-assisted ratio spectra derivative method using moving window polynomial least square fitting method (Savitzky-Golay filters). The second method is based on a simple modification for the ratio subtraction method. The suggested methods were validated according to USP guidelines and can be applied for routine quality control testing.

Use of high-order spectral moments in Doppler weather radar

NASA Astrophysics Data System (ADS)

di Vito, A.; Galati, G.; Veredice, A.

Three techniques to estimate the skewness and curtosis of measured precipitation spectra are evaluated. These are: (1) an extension of the pulse-pair technique, (2) fitting the autocorrelation function with a least square polynomial and differentiating it, and (3) the autoregressive spectral estimation. The third technique provides the best results but has an exceedingly large computation burden. The first technique does not supply any useful results due to the crude approximation of the derivatives of the ACF. The second technique requires further study to reduce its variance.

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

NASA Technical Reports Server (NTRS)

Lei, Ning; Chiang, Kwo-Fu; Oudrari, Hassan; Xiong, Xiaoxiong

2011-01-01

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Robust algebraic image enhancement for intelligent control systems

NASA Technical Reports Server (NTRS)

Lerner, Bao-Ting; Morrelli, Michael

1993-01-01

Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

Meteoroid and debris special investigation group; status of 3-D crater analysis from binocular imagery

NASA Technical Reports Server (NTRS)

Sapp, Clyde A.; See, Thomas H.; Zolensky, Michael E.

1992-01-01

During the 3 month deintegration of the LDEF, the M&D SIG generated approximately 5000 digital color stereo image pairs of impact related features from all space exposed surfaces. Currently, these images are being processed at JSC to yield more accurate feature information. Work is currently underway to determine the minimum number of data points necessary to parametrically define impact crater morphologies in order to minimize the man-hour intensive task of tie point selection. Initial attempts at deriving accurate crater depth and diameter measurements from binocular imagery were based on the assumption that the crater geometries were best defined by paraboloid. We made no assumptions regarding the crater depth/diameter ratios but instead allowed each crater to define its own coefficients by performing a least-squares fit based on user-selected tiepoints. Initial test cases resulted in larger errors than desired, so it was decided to test our basic assumptions that the crater geometries could be parametrically defined as paraboloids. The method for testing this assumption was to carefully slice test craters (experimentally produced in an appropriate aluminum alloy) vertically through the center resulting in a readily visible cross-section of the crater geometry. Initially, five separate craters were cross-sectioned in this fashion. A digital image of each cross-section was then created, and the 2-D crater geometry was then hand-digitized to create a table of XY position for each crater. A 2nd order polynomial (parabolic) was fitted to the data using a least-squares approach. The differences between the fit equation and the actual data were fairly significant, and easily large enough to account for the errors found in the 3-D fits. The differences between the curve fit and the actual data were consistent between the caters. This consistency suggested that the differences were due to the fact that a parabola did not sufficiently define the generic crater geometry. Fourth and 6th order equations were then fitted to each crater cross-section, and significantly better estimates of the crater geometry were obtained with each fit. Work is presently underway to determine the best way to make use of this new parametric crater definition.

Body Size of Male Youth Soccer Players: 1978-2015.

PubMed

Malina, Robert M; Figueiredo, António J; Coelho-E-Silva, Manuel J

2017-10-01

Studies of the body size and proportions of athletes have a long history. Comparisons of athletes within specific sports across time, though not extensive, indicate both positive and negative trends. To evaluate secular variation in heights and weights of male youth soccer players reported in studies between 1978 and 2015. Reported mean ages, heights, and weights of male soccer players 9-18 years of age were extracted from the literature and grouped into two intervals: 1978-99 and 2000-15. A third-order polynomial was fitted to the mean heights and weights across the age range for each interval, while the Preece-Baines model 1 was fitted to the grand means of mean heights and mean weights within each chronological year to estimate ages at peak height velocity and peak weight velocity for each time interval. Third-order polynomials applied to all data points and estimates based on the Preece-Baines model applied to grand means for each age group provided similar fits. Both indicated secular changes in body size between the two intervals. Secular increases in height and weight between 1978-99 and 2000-15 were especially apparent between 13 and 16 years of age, but estimated ages at peak height velocity (13.01 and 12.91 years) and peak weight velocity (13.86 and 13.77 years) did not differ between the time intervals. Although the body size of youth soccer players increased between 1978-99 and 2000-15, estimated ages at peak height velocity and peak weight velocity did not change. The increase in height and weight likely reflected improved health and nutritional conditions, in addition to the selectivity of soccer reflected in systematic selection and retention of players advanced in maturity status, and exclusion of late maturing players beginning at about 12-13 years of age. Enhanced training programs aimed at the development of strength and power are probably an additional factor contributing to secular increases in body weight.

A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure

NASA Astrophysics Data System (ADS)

Albertazzi, A.; Viotti, M. R.; Veiga, C. L. N.; Fantin, A. V.

2016-08-01

Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.

Fitting relationship between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam

NASA Astrophysics Data System (ADS)

Ji, Zhong-Ye; Zhang, Xiao-Fang

2018-01-01

The mathematical relation between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam is important in beam quality control theory of the high-energy laser weapon system. In order to obtain this mathematical relation, numerical simulation is used in the research. Firstly, the Zernike representations of typically distorted atmospheric wavefront aberrations caused by the Kolmogoroff turbulence are generated. And then, the corresponding beam quality β factors of the different distorted wavefronts are calculated numerically through fast Fourier transform. Thus, the statistical distribution rule between the beam quality β factors of high-energy laser and the wavefront aberrations of the beam can be established by the calculated results. Finally, curve fitting method is chosen to establish the mathematical fitting relationship of these two parameters. And the result of the curve fitting shows that there is a quadratic curve relation between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam. And in this paper, 3 fitting curves, in which the wavefront aberrations are consisted of Zernike Polynomials of 20, 36, 60 orders individually, are established to express the relationship between the beam quality β factor and atmospheric wavefront aberrations with different spatial frequency.

SU-E-T-614: Derivation of Equations to Define Inflection Points and Its Analysis in Flattening Filter Free Photon Beams Based On the Principle of Polynomial function

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

Muralidhar, K Raja; Komanduri, K

2014-06-01

Purpose: The objective of this work is to present a mechanism for calculating inflection points on profiles at various depths and field sizes and also a significant study on the percentage of doses at the inflection points for various field sizes and depths for 6XFFF and 10XFFF energy profiles. Methods: Graphical representation was done on Percentage of dose versus Inflection points. Also using the polynomial function, the authors formulated equations for calculating spot-on inflection point on the profiles for 6X FFF and 10X FFF energies for all field sizes and at various depths. Results: In a flattening filter free radiationmore » beam which is not like in Flattened beams, the dose at inflection point of the profile decreases as field size increases for 10XFFF. Whereas in 6XFFF, the dose at the inflection point initially increases up to 10x10cm2 and then decreases. The polynomial function was fitted for both FFF beams for all field sizes and depths. For small fields less than 5x5 cm2 the inflection point and FWHM are almost same and hence analysis can be done just like in FF beams. A change in 10% of dose can change the field width by 1mm. Conclusion: The present study, Derivative of equations based on the polynomial equation to define inflection point concept is precise and accurate way to derive the inflection point dose on any FFF beam profile at any depth with less than 1% accuracy. Corrections can be done in future studies based on the multiple number of machine data. Also a brief study was done to evaluate the inflection point positions with respect to dose in FFF energies for various field sizes and depths for 6XFFF and 10XFFF energy profiles.« less

Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality

ERIC Educational Resources Information Center

Cattaneo, Matias D.; Titiunik, Rocío; Vazquez-Bare, Gonzalo

2017-01-01

The regression discontinuity (RD) design is a popular quasi-experimental design for causal inference and policy evaluation. The most common inference approaches in RD designs employ "flexible" parametric and nonparametric local polynomial methods, which rely on extrapolation and large-sample approximations of conditional expectations…

Critical frontier of the triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Qian, Xiaofeng; Wegewijs, Maarten; Blöte, Henk W.

2004-03-01

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.

[Application of an Adaptive Inertia Weight Particle Swarm Algorithm in the Magnetic Resonance Bias Field Correction].

PubMed

Wang, Chang; Qin, Xin; Liu, Yan; Zhang, Wenchao

2016-06-01

An adaptive inertia weight particle swarm algorithm is proposed in this study to solve the local optimal problem with the method of traditional particle swarm optimization in the process of estimating magnetic resonance(MR)image bias field.An indicator measuring the degree of premature convergence was designed for the defect of traditional particle swarm optimization algorithm.The inertia weight was adjusted adaptively based on this indicator to ensure particle swarm to be optimized globally and to avoid it from falling into local optimum.The Legendre polynomial was used to fit bias field,the polynomial parameters were optimized globally,and finally the bias field was estimated and corrected.Compared to those with the improved entropy minimum algorithm,the entropy of corrected image was smaller and the estimated bias field was more accurate in this study.Then the corrected image was segmented and the segmentation accuracy obtained in this research was 10% higher than that with improved entropy minimum algorithm.This algorithm can be applied to the correction of MR image bias field.

Water equivalent path length measurement in proton radiotherapy using time resolved diode dosimetry

PubMed Central

Gottschalk, B.; Tang, S.; Bentefour, E. H.; Cascio, E. W.; Prieels, D.; Lu, H.-M.

2011-01-01

Purpose: To verify water equivalent path length (WEPL) before treatment in proton radiotherapy using time resolved in vivo diode dosimetry. Methods: Using a passively scattered range modulated proton beam, the output of a diode driving a fast current-to-voltage amplifier is recorded at a number of depths in a water tank. At each depth, a burst of overlapping single proton pulses is observed. The rms duration of the burst is computed and the resulting data set is fitted with a cubic polynomial. Results: When the diode is subsequently set to an arbitrary depth and the polynomial is used as a calibration curve, the “unknown” depth is determined within 0.3 mm rms. Conclusions: A diode or a diode array, placed (for instance) in the rectum in conjunction with a rectal balloon, can potentially determine the WEPL at that point, just prior to treatment, with submillimeter accuracy, allowing the beam energy to be adjusted. The associated unwanted dose is about 0.2% of a typical single fraction treatment dose. PMID:21626963

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

NASA Astrophysics Data System (ADS)

Buonocore, R. J.; Aste, T.; Di Matteo, T.

2017-04-01

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

Electrical Conductivity of Molten DyCl3-NaCl and DyCl3-KCl Systems: An Approach to Structural Interpretations of Rare Earth Chloride Melts

NASA Astrophysics Data System (ADS)

Iwadate, Yasuhiko; Ohkubo, Takahiro

2017-11-01

Electrical conductivities (κs) of molten DyCl3-NaCl and DyCl3-KCl systems were estimated by measuring the impedances of each mixture melt at any temperature and/or frequency. The molar volumes (Vms) were measured by dilatometry and represented as a polynomial empirical equation of temperature and composition. Due to both the properties, the molar conductivities (Λms) were calculated and their temperature and/or composition dependences were discussed from the standpoint of structural features as well. The κs increased curvilinearly with increasing temperature across the whole composition ranges. This trend was also applied to the Λms which was fitted by an Arrhenius-type equation. The relationship of Λms with melt composition was studied and the Λms were found to decrease with increasing composition of DyCl3. These findings were interpreted based on the results of structural science so far reported, and finally, the relationship between Λms and the structures of pure rare earth chloride melts was discussed.

Rapid computation of photoacoustic fields from normal and pathological red blood cells using a Green's function method

NASA Astrophysics Data System (ADS)

Saha, Ratan K.; Fadhel, Muhannad N.; Lawrence, Aamna; Karmakar, Subhajit; Adhikari, Arunabha; Kolios, Michael C.

2017-03-01

Photoacoustic (PA) field calculations using a Green's function approach is presented. The method has been applied to predict PA spectra generated by normal (discocyte) and pathological (stomatocyte) red blood cells (RBCs). The contours of normal and pathological RBCs were generated by employing a popular parametric model and accordingly, fitted with the Legendre polynomial expansions for surface parametrization. The first frequency minimum of theoretical PA spectrum approximately appears at 607 MHz for a discocyte and 410 MHz for a stomatocyte when computed from the direction of symmetry axis. The same feature occurs nearly at 247 and 331 MHz, respectively, for those particles when measured along the perpendicular direction. The average experimental spectrum for normal RBCs is found to be flat over a bandwidth of 150-500 MHz when measured along the direction of symmetry axis. For spherical RBCs, both the theoretical and experimental spectra demonstrate negative slope over a bandwidth of 250-500 MHz. Using the Green's function method discussed, it may be possible to rapidly characterize cellular morphology from single-particle PA spectra.

A Computational Algorithm for Functional Clustering of Proteome Dynamics During Development

PubMed Central

Wang, Yaqun; Wang, Ningtao; Hao, Han; Guo, Yunqian; Zhen, Yan; Shi, Jisen; Wu, Rongling

2014-01-01

Phenotypic traits, such as seed development, are a consequence of complex biochemical interactions among genes, proteins and metabolites, but the underlying mechanisms that operate in a coordinated and sequential manner remain elusive. Here, we address this issue by developing a computational algorithm to monitor proteome changes during the course of trait development. The algorithm is built within the mixture-model framework in which each mixture component is modeled by a specific group of proteins that display a similar temporal pattern of expression in trait development. A nonparametric approach based on Legendre orthogonal polynomials was used to fit dynamic changes of protein expression, increasing the power and flexibility of protein clustering. By analyzing a dataset of proteomic dynamics during early embryogenesis of the Chinese fir, the algorithm has successfully identified several distinct types of proteins that coordinate with each other to determine seed development in this forest tree commercially and environmentally important to China. The algorithm will find its immediate applications for the characterization of mechanistic underpinnings for any other biological processes in which protein abundance plays a key role. PMID:24955031

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

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

Yang, Xiu; Lei, Huan; Gao, Peiyuan

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many moremore » types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.« less

Estimation of 3-D conduction velocity vector fields from cardiac mapping data.

PubMed

Barnette, A R; Bayly, P V; Zhang, S; Walcott, G P; Ideker, R E; Smith, W M

2000-08-01

A method to estimate three-dimensional (3-D) conduction velocity vector fields in cardiac tissue is presented. The speed and direction of propagation are found from polynomial "surfaces" fitted to space-time (x, y, z, t) coordinates of cardiac activity. The technique is applied to sinus rhythm and paced rhythm mapped with plunge needles at 396-466 sites in the canine myocardium. The method was validated on simulated 3-D plane and spherical waves. For simulated data, conduction velocities were estimated with an accuracy of 1%-2%. In experimental data, estimates of conduction speeds during paced rhythm were slower than those found during normal sinus rhythm. Vector directions were also found to differ between different types of beats. The technique was able to distinguish between premature ventricular contractions and sinus beats and between sinus and paced beats. The proposed approach to computing velocity vector fields provides an automated, physiological, and quantitative description of local electrical activity in 3-D tissue. This method may provide insight into abnormal conduction associated with fatal ventricular arrhythmias.

Classification of resistance to passive motion using minimum probability of error criterion.

PubMed

Chan, H C; Manry, M T; Kondraske, G V

1987-01-01

Neurologists diagnose many muscular and nerve disorders by classifying the resistance to passive motion of patients' limbs. Over the past several years, a computer-based instrument has been developed for automated measurement and parameterization of this resistance. In the device, a voluntarily relaxed lower extremity is moved at constant velocity by a motorized driver. The torque exerted on the extremity by the machine is sampled, along with the angle of the extremity. In this paper a computerized technique is described for classifying a patient's condition as 'Normal' or 'Parkinson disease' (rigidity), from the torque versus angle curve for the knee joint. A Legendre polynomial, fit to the curve, is used to calculate a set of eight normally distributed features of the curve. The minimum probability of error approach is used to classify the curve as being from a normal or Parkinson disease patient. Data collected from 44 different subjects was processes and the results were compared with an independent physician's subjective assessment of rigidity. There is agreement in better than 95% of the cases, when all of the features are used.

Investigations of interference between electromagnetic transponders and wireless MOSFET dosimeters: a phantom study.

PubMed

Su, Zhong; Zhang, Lisha; Ramakrishnan, V; Hagan, Michael; Anscher, Mitchell

2011-05-01

To evaluate both the Calypso Systems' (Calypso Medical Technologies, Inc., Seattle, WA) localization accuracy in the presence of wireless metal-oxide-semiconductor field-effect transistor (MOSFET) dosimeters of dose verification system (DVS, Sicel Technologies, Inc., Morrisville, NC) and the dosimeters' reading accuracy in the presence of wireless electromagnetic transponders inside a phantom. A custom-made, solid-water phantom was fabricated with space for transponders and dosimeters. Two inserts were machined with positioning grooves precisely matching the dimensions of the transponders and dosimeters and were arranged in orthogonal and parallel orientations, respectively. To test the transponder localization accuracy with/without presence of dosimeters (hypothesis 1), multivariate analyses were performed on transponder-derived localization data with and without dosimeters at each preset distance to detect statistically significant localization differences between the control and test sets. To test dosimeter dose-reading accuracy with/without presence of transponders (hypothesis 2), an approach of alternating the transponder presence in seven identical fraction dose (100 cGy) deliveries and measurements was implemented. Two-way analysis of variance was performed to examine statistically significant dose-reading differences between the two groups and the different fractions. A relative-dose analysis method was also used to evaluate transponder impact on dose-reading accuracy after dose-fading effect was removed by a second-order polynomial fit. Multivariate analysis indicated that hypothesis 1 was false; there was a statistically significant difference between the localization data from the control and test sets. However, the upper and lower bounds of the 95% confidence intervals of the localized positional differences between the control and test sets were less than 0.1 mm, which was significantly smaller than the minimum clinical localization resolution of 0.5 mm. For hypothesis 2, analysis of variance indicated that there was no statistically significant difference between the dosimeter readings with and without the presence of transponders. Both orthogonal and parallel configurations had difference of polynomial-fit dose to measured dose values within 1.75%. The phantom study indicated that the Calypso System's localization accuracy was not affected clinically due to the presence of DVS wireless MOSFET dosimeters and the dosimeter-measured doses were not affected by the presence of transponders. Thus, the same patients could be implanted with both transponders and dosimeters to benefit from improved accuracy of radiotherapy treatments offered by conjunctional use of the two systems.

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1987-01-01

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Unconditional reference values for the amniotic fluid index measurement between 26w0d and 41w6d of gestation in low-risk pregnancies.

PubMed

Peixoto, Alberto Borges; Caldas, Taciana Mara Rodrigues da Cunha; Martins, Wellington P; Da Silva Costa, Fabricio; Araujo Júnior, Edward

2016-10-01

To establish reference values for the amniotic fluid index (AFI) measurement between 26w0d and 41w6d of gestation in a Brazilian population. We performed a cross-sectional study with 1984 low-risk singleton pregnant women between 26w0d and 41w6d of gestation. AFI was measured according to the technique proposed by Phelan et al. Maternal abdomen was divided into four quadrants using the umbilicus and linea nigra as landmarks. Single vertical pocket in each quadrant was measured and the AFI was generated by the sum of these four values without umbilical cord or fetal parts. All ultrasound exams were performed by only two experienced examiners. AFI was expressed as median, interquartile range, mean and ranges in each gestational age (GA) interval. Polynomial regressions were performed to obtain the best fit with adjustment by the determination coefficient (R(2)). Mean of AFI ranged from 14.0 ± 4.1 cm (range, 9.7-14.0) at 26w0d to 8.3 ± 4.7 cm (range, 1.9-16.5) at 41w6d, respectively. The best polynomial regression fit curve was a first-degree: AFI = 16.29-0.125*GA (R(2) = 0.01). According the scatterplot, AFI values practically did not vary with advancing GA. Reference values for the AFI measurement between 26w0d and 41w6d of gestation in a low-risk Brazilian population were established.

Spectral colors capture and reproduction based on digital camera

NASA Astrophysics Data System (ADS)

Chen, Defen; Huang, Qingmei; Li, Wei; Lu, Yang

2018-01-01

The purpose of this work is to develop a method for the accurate reproduction of the spectral colors captured by digital camera. The spectral colors being the purest color in any hue, are difficult to reproduce without distortion on digital devices. In this paper, we attempt to achieve accurate hue reproduction of the spectral colors by focusing on two steps of color correction: the capture of the spectral colors and the color characterization of digital camera. Hence it determines the relationship among the spectral color wavelength, the RGB color space of the digital camera device and the CIEXYZ color space. This study also provides a basis for further studies related to the color spectral reproduction on digital devices. In this paper, methods such as wavelength calibration of the spectral colors and digital camera characterization were utilized. The spectrum was obtained through the grating spectroscopy system. A photo of a clear and reliable primary spectrum was taken by adjusting the relative parameters of the digital camera, from which the RGB values of color spectrum was extracted in 1040 equally-divided locations. Calculated using grating equation and measured by the spectrophotometer, two wavelength values were obtained from each location. The polynomial fitting method for the camera characterization was used to achieve color correction. After wavelength calibration, the maximum error between the two sets of wavelengths is 4.38nm. According to the polynomial fitting method, the average color difference of test samples is 3.76. This has satisfied the application needs of the spectral colors in digital devices such as display and transmission.

A New Precession Formula

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2003-07-01

We adapt J. G. Williams' expression of the precession and nutation using the 3-1-3-1 rotation to an arbitrary inertial frame of reference. The modified formulation avoids a singularity caused by finite pole offsets near the epoch. By adopting the planetary precession formula numerically determined from DE405 and by using a recent theory of the forced nutation of the nonrigid Earth by Shirai & Fukishima, we analyze the celestial pole offsets observed by VLBI for 1979-2000 and determine the best-fit polynomials of the lunisolar precession angles. We then translate the results into classical precession quantities and evaluate the difference due to the difference in the ecliptic definition. The combination of these formulae and the periodic part of the Shirai-Fukishima nutation theory serves as a good approximation of the precession-nutation matrix in the International Celestial Reference Frame. As a by-product, we determine the mean celestial pole offset at J2000.0 as X0=-(17.12+/-0.01) mas and Y0=-(5.06+/-0.02) mas. Also, we estimate the speed of general precession in longitude at J2000.0 as p=5028.7955"+/-0.0003" per Julian century, the mean obliquity at J2000.0 in the inertial sense as (ɛ0)I=84381.40621"+/-0.00001" and in the rotational sense as (ɛ0)R=84381.40955"+/-0.00001", and the dynamical flattening of Earth as Hd=(3.2737804+/-0.0000003)×10-3. Furthermore, we establish a fast way to compute the precession-nutation matrix and provide a best-fit polynomial of an angle to specify the mean Celestial Ephemeris Origin.

A Mathematical Model to Predict Endothelial Cell Density Following Penetrating Keratoplasty With Selective Dropout From Graft Failure

PubMed Central

Riddlesworth, Tonya D.; Kollman, Craig; Lass, Jonathan H.; Patel, Sanjay V.; Stulting, R. Doyle; Benetz, Beth Ann; Gal, Robin L.; Beck, Roy W.

2014-01-01

Purpose. We constructed several mathematical models that predict endothelial cell density (ECD) for patients after penetrating keratoplasty (PK) for a moderate-risk condition (principally Fuchs' dystrophy or pseudophakic/aphakic corneal edema). Methods. In a subset (n = 591) of Cornea Donor Study participants, postoperative ECD was determined by a central reading center. Various statistical models were considered to estimate the ECD trend longitudinally over 10 years of follow-up. A biexponential model with and without a logarithm transformation was fit using the Gauss-Newton nonlinear least squares algorithm. To account for correlated data, a log-polynomial model was fit using the restricted maximum likelihood method. A sensitivity analysis for the potential bias due to selective dropout was performed using Bayesian analysis techniques. Results. The three models using a logarithm transformation yield similar trends, whereas the model without the transform predicts higher ECD values. The adjustment for selective dropout turns out to be negligible. However, this is possibly due to the relatively low rate of graft failure in this cohort (19% at 10 years). Fuchs' dystrophy and pseudophakic/aphakic corneal edema (PACE) patients had similar ECD decay curves, with the PACE group having slightly higher cell densities by 10 years. Conclusions. Endothelial cell loss after PK can be modeled via a log-polynomial model, which accounts for the correlated data from repeated measures on the same subject. This model is not significantly affected by the selective dropout due to graft failure. Our findings warrant further study on how this may extend to ECD following endothelial keratoplasty. PMID:25425307

Needle localization using a moving stylet/catheter in ultrasound-guided regional anesthesia: a feasibility study

NASA Astrophysics Data System (ADS)

Beigi, Parmida; Rohling, Robert

2014-03-01

Despite the wide range and long history of ultrasound guided needle insertions, an unresolved issue in many cases is clear needle visibility. A well-known ad hoc technique to detect the needle is to move the stylet and look for changes in the needle appearance. We present a new method to automatically locate a moving stylet/catheter within a stationary cannula using motion detection. We then use this information to detect the needle trajectory and the tip. The differences between the current frame and the previous frame are detected and localized, to minimize the influence of tissue global motions. A polynomial fit based on the detected needle axis determines the estimated stylet shaft trajectory, and the extent of the differences along the needle axis represents the tip. Over a few periodic movements of the stylet including its full insertion into the cannula to the tip, a combination of polynomial fits determines the needle trajectory and the last detected point represents the needle tip. Experiments are conducted in water bath and bovine muscle tissue for several stylet/catheter materials. Results show that a plastic stylet has the best needle shaft and tip localization accuracy in the water bath with RMSE = 0:16 mm and RMSE = 0:51 mm, respectively. In the bovine tissue, the needle tip was best localized with the plastic catheter with RMSE = 0:33 mm. The stylet tip localization was most accurate with the steel stylet, with RMSE = 2:81 mm and the shaft was best localized with the plastic catheter, with RMSE = 0:32 mm.

Processing short-term and long-term information with a combination of polynomial approximation techniques and time-delay neural networks.

PubMed

Fuchs, Erich; Gruber, Christian; Reitmaier, Tobias; Sick, Bernhard

2009-09-01

Neural networks are often used to process temporal information, i.e., any kind of information related to time series. In many cases, time series contain short-term and long-term trends or behavior. This paper presents a new approach to capture temporal information with various reference periods simultaneously. A least squares approximation of the time series with orthogonal polynomials will be used to describe short-term trends contained in a signal (average, increase, curvature, etc.). Long-term behavior will be modeled with the tapped delay lines of a time-delay neural network (TDNN). This network takes the coefficients of the orthogonal expansion of the approximating polynomial as inputs such considering short-term and long-term information efficiently. The advantages of the method will be demonstrated by means of artificial data and two real-world application examples, the prediction of the user number in a computer network and online tool wear classification in turning.

Exploiting structure: Introduction and motivation

NASA Technical Reports Server (NTRS)

Xu, Zhong Ling

1993-01-01

Research activities performed during the period of 29 June 1993 through 31 Aug. 1993 are summarized. The Robust Stability of Systems where transfer function or characteristic polynomial are multilinear affine functions of parameters of interest in two directions, Algorithmic and Theoretical, was developed. In the algorithmic direction, a new approach that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty is found. This technique is called 'Stability by linear process.' In fact, the 'Stability by linear process' described gives an algorithm. In analysis, we obtained a robustness criterion for the family of polynomials with coefficients of multilinear affine function in the coefficient space and obtained the result for the robust stability of diamond families of polynomials with complex coefficients also. We obtained the limited results for SPR design and we provide a framework for solving ACS. Finally, copies of the outline of our results are provided in the appendix. Also, there is an administration issue in the appendix.

Improving Kepler Pipeline Sensitivity with Pixel Response Function Photometry.

NASA Astrophysics Data System (ADS)

Morris, Robert L.; Bryson, Steve; Jenkins, Jon Michael; Smith, Jeffrey C

2014-06-01

We present the results of our investigation into the feasibility and expected benefits of implementing PRF-fitting photometry in the Kepler Science Processing Pipeline. The Kepler Pixel Response Function (PRF) describes the expected system response to a point source at infinity and includes the effects of the optical point spread function, the CCD detector responsivity function, and spacecraft pointing jitter. Planet detection in the Kepler pipeline is currently based on simple aperture photometry (SAP), which is most effective when applied to uncrowded bright stars. Its effectiveness diminishes rapidly as target brightness decreases relative to the effects of noise sources such as detector electronics, background stars, and image motion. In contrast, PRF photometry is based on fitting an explicit model of image formation to the data and naturally accounts for image motion and contributions of background stars. The key to obtaining high-quality photometry from PRF fitting is a high-quality model of the system's PRF, while the key to efficiently processing the large number of Kepler targets is an accurate catalog and accurate mapping of celestial coordinates onto the focal plane. If the CCD coordinates of stellar centroids are known a priori then the problem of PRF fitting becomes linear. A model of the Kepler PRF was constructed at the time of spacecraft commissioning by fitting piecewise polynomial surfaces to data from dithered full frame images. While this model accurately captured the initial state of the system, the PRF has evolved dynamically since then and has been seen to deviate significantly from the initial (static) model. We construct a dynamic PRF model which is then used to recover photometry for all targets of interest. Both simulation tests and results from Kepler flight data demonstrate the effectiveness of our approach. Kepler was selected as the 10th mission of the Discovery Program. Funding for this mission is provided by NASA’s Science Mission Directorate.Kepler was selected as the 10th mission of the Discovery Program. Funding for this mission is provided by NASA’s Science Mission Directorate.

Generation of hollow Gaussian beams by spatial filtering

NASA Astrophysics Data System (ADS)

Liu, Zhengjun; Zhao, Haifa; Liu, Jianlong; Lin, Jie; Ashfaq Ahmad, Muhammad; Liu, Shutian

2007-08-01

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

Generation of hollow Gaussian beams by spatial filtering.

PubMed

Liu, Zhengjun; Zhao, Haifa; Liu, Jianlong; Lin, Jie; Ahmad, Muhammad Ashfaq; Liu, Shutian

2007-08-01

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.

Acoustic wave propagation in continuous functionally graded plates: an extension of the Legendre polynomial approach.

PubMed

Lefebvre, J E; Zhang, V; Gazalet, J; Gryba, T; Sadaune, V

2001-09-01

The propagation of guided waves in continuous functionally graded plates is studied by using Legendre polynomials. Dispersion curves, and power and field profiles are easily obtained. Our computer program is validated by comparing our results against other calculations from the literature. Numerical results are also given for a graded semiconductor plate. It is felt that the present method could be of quite practical interest in waveguiding engineering, non-destructive testing of functionally graded materials (FGMs) to identify the best inspection strategies, or by means of a numerical inversion algorithm to determine through-thickness gradients in material parameters.

Schur polynomials and biorthogonal random matrix ensembles

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

Tierz, Miguel

The study of the average of Schur polynomials over a Stieltjes-Wigert ensemble has been carried out by Dolivet and Tierz [J. Math. Phys. 48, 023507 (2007); e-print arXiv:hep-th/0609167], where it was shown that it is equal to quantum dimensions. Using the same approach, we extend the result to the biorthogonal case. We also study, using the Littlewood-Richardson rule, some particular cases of the quantum dimension result. Finally, we show that the notion of Giambelli compatibility of Schur averages, introduced by Borodin et al. [Adv. Appl. Math. 37, 209 (2006); e-print arXiv:math-ph/0505021], also holds in the biorthogonal setting.

A sequential method for spline approximation with variable knots. [recursive piecewise polynomial signal processing

NASA Technical Reports Server (NTRS)

Mier Muth, A. M.; Willsky, A. S.

1978-01-01

In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.

Demodulation of moire fringes in digital holographic interferometry using an extended Kalman filter.

PubMed

Ramaiah, Jagadesh; Rastogi, Pramod; Rajshekhar, Gannavarpu

2018-03-10

This paper presents a method for extracting multiple phases from a single moire fringe pattern in digital holographic interferometry. The method relies on component separation using singular value decomposition and an extended Kalman filter for demodulating the moire fringes. The Kalman filter is applied by modeling the interference field locally as a multi-component polynomial phase signal and extracting the associated multiple polynomial coefficients using the state space approach. In addition to phase, the corresponding multiple phase derivatives can be simultaneously extracted using the proposed method. The applicability of the proposed method is demonstrated using simulation and experimental results.

Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

DTIC Science & Technology

2002-07-25

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.

PubMed

Mahajan, Virendra N

2012-06-20

In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as they do not represent balanced aberrations for such a system.

Uncertainty Analysis via Failure Domain Characterization: Polynomial Requirement Functions

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Munoz, Cesar A.; Narkawicz, Anthony J.; Kenny, Sean P.; Giesy, Daniel P.

2011-01-01

This paper proposes an uncertainty analysis framework based on the characterization of the uncertain parameter space. This characterization enables the identification of worst-case uncertainty combinations and the approximation of the failure and safe domains with a high level of accuracy. Because these approximations are comprised of subsets of readily computable probability, they enable the calculation of arbitrarily tight upper and lower bounds to the failure probability. A Bernstein expansion approach is used to size hyper-rectangular subsets while a sum of squares programming approach is used to size quasi-ellipsoidal subsets. These methods are applicable to requirement functions whose functional dependency on the uncertainty is a known polynomial. Some of the most prominent features of the methodology are the substantial desensitization of the calculations from the uncertainty model assumed (i.e., the probability distribution describing the uncertainty) as well as the accommodation for changes in such a model with a practically insignificant amount of computational effort.