Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H.
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Hermite base Bernoulli type polynomials on the umbral algebra
NASA Astrophysics Data System (ADS)
Dere, R.; Simsek, Y.
2015-01-01
The aim of this paper is to construct new generating functions for Hermite base Bernoulli type polynomials, which generalize not only the Milne-Thomson polynomials but also the two-variable Hermite polynomials. We also modify the Milne-Thomson polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. Moreover, by applying the umbral algebra to these generating functions, we derive new identities for the Bernoulli polynomials of higher order, the Hermite polynomials and numbers of higher order, and the Stirling numbers of the second kind.
Affine and deformable registration based on polynomial expansion.
Farnebäck, Gunnar; Westin, Carl-Fredrik
2006-01-01
This paper presents a registration framework based on the polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Starting with observations of how the coefficients of ideal linear and quadratic polynomials change under translation and affine transformation, algorithms are developed to estimate translation and compute affine and deformable registration between a fixed and a moving image, from the polynomial expansion coefficients. All algorithms can be used for signals of any dimensionality. The algorithms are evaluated on medical data. PMID:17354971
An error embedded method based on generalized Chebyshev polynomials
NASA Astrophysics Data System (ADS)
Kim, Philsu; Kim, Junghan; Jung, WonKyu; Bu, Sunyoung
2016-02-01
In this paper, we develop an error embedded method based on generalized Chebyshev polynomials for solving stiff initial value problems. The solution and the error at each integration step are calculated by generalized Chebyshev polynomials of two consecutive degrees having overlapping zeros, which enables us to minimize overall computational costs. Further the errors at each integration step are embedded in the algorithm itself. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 6th order convergence and an almost L-stability. We assess the proposed method with several numerical results, showing that it uses larger time step sizes and is numerically more efficient.
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
Fast complex memory polynomial-based adaptive digital predistorter
NASA Astrophysics Data System (ADS)
Singh Sappal, Amandeep; Singh Patterh, Manjeet; Sharma, Sanjay
2011-07-01
Today's 3G wireless systems require both high linearity and high power amplifier (PA) efficiency. The high peak-to-average ratios of the digital modulation schemes used in 3G wireless systems require that the RF PA maintain high linearity over a large range while maintaining this high efficiency; these two requirements are often at odds with each other with many of the traditional amplifier architectures. In this article, a fast and easy-to-implement adaptive digital predistorter has been presented for Wideband Code Division Multiplexed signals using complex memory polynomial work function. The proposed algorithm has been implemented to test a Motorola LDMOSFET PA. The proposed technique also takes care of the memory effects of the PA, which have been ignored in many proposed techniques in the literature. The results show that the new complex memory polynomial-based adaptive digital predistorter has better linearisation performance than conventional predistortion techniques.
Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials
NASA Astrophysics Data System (ADS)
Shakiba, Ali; Hooshmandasl, Mohammad Reza; Meybodi, Mohsen Alambardar
2016-06-01
In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples.
Enhanced Access Polynomial Based Self-healing Key Distribution
NASA Astrophysics Data System (ADS)
Dutta, Ratna; Mukhopadhyay, Sourav; Dowling, Tom
A fundamental concern of any secure group communication system is that of key management. Wireless environments create new key management problems and requirements to solve these problems. One such core requirement in these emerging networks is that of self-healing. In systems where users can be offline and miss updates self healing allows a user to recover lost keys and get back into the secure communication without putting extra burden on the group manager. Clearly self healing must be only available to authorized users and this creates more challenges in that we must ensure unauthorized or revoked users cannot, themselves or by means of collusion, avail of self healing. To this end we enhance the one-way key chain based self-healing key distribution of Dutta et al. by introducing a collusion resistance property between the revoked users and the newly joined users. Our scheme is based on the concept of access polynomials. These can be loosely thought of as white lists of authorized users as opposed to the more widely used revocation polynomials or black lists of revoked users. We also allow each user a pre-arranged life cycle distributed by the group manager. Our scheme provides better efficiency in terms of storage, and the communication and computation costs do not increase as the number of sessions grows as compared to most current schemes. We analyze our scheme in an appropriate security model and prove that the proposed scheme is computationally secure and not only achieving forward and backward secrecy, but also resisting collusion between the new joined users and the revoked users. Unlike most existing schemes the new scheme allows temporary revocation. Also unlike existing schemes, our construction does not collapse if the number of revoked users crosses a threshold value. This feature increases resilience against revocation based denial of service (DOS) attacks and thus improves availability of communication channel.
Tracking control of piezoelectric actuators using a polynomial-based hysteresis model
NASA Astrophysics Data System (ADS)
Gan, Jinqiang; Zhang, Xianmin; Wu, Heng
2016-06-01
A polynomial-based hysteresis model that describes hysteresis behavior in piezoelectric actuators is presented. The polynomial-based model is validated by comparing with the classic Prandtl-Ishlinskii model. Taking the advantages of the proposed model into consideration, inverse control using the polynomial-based model is proposed. To achieve better tracking performance, a hybrid control combining the developed inverse control and a proportional-integral-differential feedback loop is then proposed. To demonstrate the effectiveness of the proposed tracking controls, several comparative experiments of the polynomial-based model and Prandtl-Ishlinskii model are conducted. The experimental results show that inverse control and hybrid control using the polynomial-based model in trajectory-tracking applications are effective and meaningful.
Gabor-based kernel PCA with fractional power polynomial models for face recognition.
Liu, Chengjun
2004-05-01
This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power
NASA Astrophysics Data System (ADS)
Liang, Xie; Min, Xu; Bin, Zhang; Zihua, Qiu
2015-03-01
To solve hyperbolic conservation laws, a new method is developed based on the spectral difference (SD) algorithm. The new scheme adopts hierarchical polynomials to represent the solution in each cell instead of Lagrange interpolation polynomials used by the original one. The degrees of freedom (DOFs) of the present scheme are the coefficients of these polynomials, which do not represent the states at the solution points like the original method. Therefore, the solution points defined in the original SD scheme are discarded, while the flux points are preserved to construct a Lagrange interpolation polynomial to approximate flux function in each cell. To update the DOFs, differential operators are applied to the governing equation as well as the Lagrange interpolation polynomial of flux function to evaluate first and higher order derivatives of both solution and flux at the centroid of the cell. The stability property of the current scheme is proved to be the same as the original SD method when the same solution space is adopted. One dimensional methods are always stable by the use of zeros of Legendre polynomials as inner flux points. For two dimensional problems, the introduction of Raviart-Thomas spaces for the interpolation of flux function proves stable schemes for triangles. Accuracy studies are performed with one- and two-dimensional problems. p-Multigrid algorithm is implemented with orthogonal hierarchical bases. The results verify the high efficiency and low memory requirements of implementation of p-multigrid algorithm with the proposed scheme.
An Accurate Projector Calibration Method Based on Polynomial Distortion Representation
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
Online segmentation of time series based on polynomial least-squares approximations.
Fuchs, Erich; Gruber, Thiemo; Nitschke, Jiri; Sick, Bernhard
2010-12-01
The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based on a least-squares approximation of time series in sliding and/or growing time windows utilizing a basis of orthogonal polynomials. This allows the definition of fast update steps for the approximating polynomial, where the computational effort depends only on the degree of the approximating polynomial and not on the length of the time window. The coefficients of the orthogonal expansion of the approximating polynomial-obtained by means of the update steps-can be interpreted as optimal (in the least-squares sense) estimators for average, slope, curvature, change of curvature, etc., of the signal in the time window considered. These coefficients, as well as the approximation error, may be used in a very intuitive way to define segmentation criteria. The properties of SwiftSeg are evaluated by means of some artificial and real benchmark time series. It is compared to three different offline and online techniques to assess its accuracy and runtime. It is shown that SwiftSeg-which is suitable for many data streaming applications-offers high accuracy at very low computational costs. PMID:20975120
Aspherical surface profile fitting based on the relationship between polynomial and inner products
NASA Astrophysics Data System (ADS)
Cheng, Xuemin; Yang, Yikang; Hao, Qun
2016-01-01
High-precision aspherical polynomial fitting is essential to image quality evaluation in optical design and optimization. However, conventional fitting methods cannot reach optimal fitting precision and may somehow induce numerical ill-conditioning, such as excessively high coefficients. For this reason, a projection from polynomial equations to vector space was here proposed such that polynomial solutions could be obtained based on matrix and vector operation, so avoiding the problem of excessive coefficients. The Newton-Raphson iteration method was used to search for optimal fitting of the spherical surface. The profile fitting test showed that the proposed approach was able to obtain results with high precision and small value, which solved the numerical ill-conditioning phenomenon effectively.
NASA Astrophysics Data System (ADS)
Wang, Zhengzi
2015-08-01
The influence of ambient temperature is a big challenge to robust infrared face recognition. This paper proposes a new ambient temperature normalization algorithm to improve the performance of infrared face recognition under variable ambient temperatures. Based on statistical regression theory, a second order polynomial model is learned to describe the ambient temperature's impact on infrared face image. Then, infrared image was normalized to reference ambient temperature by the second order polynomial model. Finally, this normalization method is applied to infrared face recognition to verify its efficiency. The experiments demonstrate that the proposed temperature normalization method is feasible and can significantly improve the robustness of infrared face recognition.
A comparison of high-order polynomial and wave-based methods for Helmholtz problems
NASA Astrophysics Data System (ADS)
Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien
2016-09-01
The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.
Coherent orthogonal polynomials
Celeghini, E.; Olmo, M.A. del
2013-08-15
We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relate these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that defines
ISAR Imaging of Maneuvering Targets Based on the Modified Discrete Polynomial-Phase Transform.
Wang, Yong; Abdelkader, Ali Cherif; Zhao, Bin; Wang, Jinxiang
2015-01-01
Inverse synthetic aperture radar (ISAR) imaging of a maneuvering target is a challenging task in the field of radar signal processing. The azimuth echo can be characterized as a multi-component polynomial phase signal (PPS) after the translational compensation, and the high quality ISAR images can be obtained by the parameters estimation of it combined with the Range-Instantaneous-Doppler (RID) technique. In this paper, a novel parameters estimation algorithm of the multi-component PPS with order three (cubic phase signal-CPS) based on the modified discrete polynomial-phase transform (MDPT) is proposed, and the corresponding new ISAR imaging algorithm is presented consequently. This algorithm is efficient and accurate to generate a focused ISAR image, and the results of real data demonstrate the effectiveness of it. PMID:26404299
ISAR Imaging of Maneuvering Targets Based on the Modified Discrete Polynomial-Phase Transform
Wang, Yong; Abdelkader, Ali Cherif; Zhao, Bin; Wang, Jinxiang
2015-01-01
Inverse synthetic aperture radar (ISAR) imaging of a maneuvering target is a challenging task in the field of radar signal processing. The azimuth echo can be characterized as a multi-component polynomial phase signal (PPS) after the translational compensation, and the high quality ISAR images can be obtained by the parameters estimation of it combined with the Range-Instantaneous-Doppler (RID) technique. In this paper, a novel parameters estimation algorithm of the multi-component PPS with order three (cubic phase signal-CPS) based on the modified discrete polynomial-phase transform (MDPT) is proposed, and the corresponding new ISAR imaging algorithm is presented consequently. This algorithm is efficient and accurate to generate a focused ISAR image, and the results of real data demonstrate the effectiveness of it. PMID:26404299
A weighted polynomial based material decomposition method for spectral x-ray CT imaging.
Wu, Dufan; Zhang, Li; Zhu, Xiaohua; Xu, Xiaofei; Wang, Sen
2016-05-21
Currently in photon counting based spectral x-ray computed tomography (CT) imaging, pre-reconstruction basis materials decomposition is an effective way to reconstruct densities of various materials. The iterative maximum-likelihood method requires precise spectrum information and is time-costly. In this paper, a novel non-iterative decomposition method based on polynomials is proposed for spectral CT, whose aim was to optimize the noise performance when there is more energy bins than the number of basis materials. Several subsets were taken from all the energy bins and conventional polynomials were established for each of them. The decomposition results from each polynomial were summed with pre-calculated weighting factors, which were designed to minimize the overall noises. Numerical studies showed that the decomposition noise of the proposed method was close to the Cramer-Rao lower bound under Poisson noises. Furthermore, experiments were carried out with an XCounter Filte X1 photon counting detector for two-material decomposition and three-material decomposition for validation. PMID:27082291
A weighted polynomial based material decomposition method for spectral x-ray CT imaging
NASA Astrophysics Data System (ADS)
Wu, Dufan; Zhang, Li; Zhu, Xiaohua; Xu, Xiaofei; Wang, Sen
2016-05-01
Currently in photon counting based spectral x-ray computed tomography (CT) imaging, pre-reconstruction basis materials decomposition is an effective way to reconstruct densities of various materials. The iterative maximum-likelihood method requires precise spectrum information and is time-costly. In this paper, a novel non-iterative decomposition method based on polynomials is proposed for spectral CT, whose aim was to optimize the noise performance when there is more energy bins than the number of basis materials. Several subsets were taken from all the energy bins and conventional polynomials were established for each of them. The decomposition results from each polynomial were summed with pre-calculated weighting factors, which were designed to minimize the overall noises. Numerical studies showed that the decomposition noise of the proposed method was close to the Cramer–Rao lower bound under Poisson noises. Furthermore, experiments were carried out with an XCounter Filte X1 photon counting detector for two-material decomposition and three-material decomposition for validation.
Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map
2014-01-01
We present a novel image encryption algorithm using Chebyshev polynomial based on permutation and substitution and Duffing map based on substitution. Comprehensive security analysis has been performed on the designed scheme using key space analysis, visual testing, histogram analysis, information entropy calculation, correlation coefficient analysis, differential analysis, key sensitivity test, and speed test. The study demonstrates that the proposed image encryption algorithm shows advantages of more than 10113 key space and desirable level of security based on the good statistical results and theoretical arguments. PMID:25143970
Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices
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
Discrimination Power of Polynomial-Based Descriptors for Graphs by Using Functional Matrices.
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
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device. PMID:21507749
ERIC Educational Resources Information Center
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
Regression-based adaptive sparse polynomial dimensional decomposition for sensitivity analysis
NASA Astrophysics Data System (ADS)
Tang, Kunkun; Congedo, Pietro; Abgrall, Remi
2014-11-01
Polynomial dimensional decomposition (PDD) is employed in this work for global sensitivity analysis and uncertainty quantification of stochastic systems subject to a large number of random input variables. Due to the intimate structure between PDD and Analysis-of-Variance, PDD is able to provide simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to polynomial chaos (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 the standard method unaffordable for real engineering applications. In order to address this problem of curse of dimensionality, this work proposes a variance-based adaptive strategy aiming to build a cheap meta-model by sparse-PDD with PDD coefficients computed by regression. During this adaptive procedure, the model representation by PDD only contains few terms, so that the cost to resolve repeatedly the linear system of the least-square regression problem is negligible. The size of the final sparse-PDD representation is much smaller than the full PDD, since only significant terms are eventually retained. Consequently, a much less number of calls to the deterministic model is required to compute the final PDD coefficients.
NASA Astrophysics Data System (ADS)
Vittaldev, V.; Linares, R.; Godinez, H. C.; Koller, J.; Russell, R. P.
2013-12-01
Recent events in space, including the collision of Russia's Cosmos 2251 satellite with Iridium 33 and China's Feng Yun 1C anti-satellite demonstration, have stressed the capabilities of the Space Surveillance Network and its ability to provide accurate and actionable impact probability estimates. In particular low-Earth orbiting satellites are heavily influenced by upper atmospheric density, due to drag, which is very difficult to model accurately. This work focuses on the generalized Polynomial Chaos (gPC) technique for Uncertainty Quantification (UQ) in physics-based atmospheric models. The advantage of the gPC approach is that it can efficiently model non-Gaussian probability distribution functions (pdfs). The gPC approach is used to create a polynomial chaos in F10.7, AP, and solar wind parameters; this chaos is used to perform UQ on future atmospheric conditions. A number of physics-based models are used as test cases, including GITM and TIE-GCM, and the gPC is shown to have good performance in modeling non-Gaussian pdfs. Los Alamos National Laboratory (LANL) has established a research effort, called IMPACT (Integrated Modeling of Perturbations in Atmospheres for Conjunction Tracking), to improve impact assessment via improved physics-based modeling. A number of atmospheric models exist which can be classified as either empirical or physics-based. Physics-based models can be used to provide a forward prediction which is required for accurate collision assessments. As part of this effort, accurate and consistent UQ is required for the atmospheric models used. One of the primary sources of uncertainty is input parameter uncertainty. These input parameters, which include F10.7, AP, and solar wind parameters, are measured constantly. In turn, these measurements are used to provide a prediction for future parameter values. Therefore, the uncertainty of the atmospheric model forecast, due to potential error in the input parameters, must be correctly characterized to
Solving fuzzy polynomial equation and the dual fuzzy polynomial equation using the ranking method
NASA Astrophysics Data System (ADS)
Rahman, Nurhakimah Ab.; Abdullah, Lazim
2014-06-01
Fuzzy polynomials with trapezoidal and triangular fuzzy numbers have attracted interest among some researchers. Many studies have been done by researchers to obtain real roots of fuzzy polynomials. As a result, there are many numerical methods involved in obtaining the real roots of fuzzy polynomials. In this study, we will present the solution to the fuzzy polynomial equation and dual fuzzy polynomial equation using the ranking method of fuzzy numbers and subsequently transforming fuzzy polynomials to crisp polynomials. This transformation is performed using the ranking method based on three parameters, namely Value, Ambiguity and Fuzziness. Finally, we illustrate our approach with two numerical examples for fuzzy polynomial equation and dual fuzzy polynomial equation.
Azimipour, Mehdi; Atry, Farid; Pashaie, Ramin
2016-04-10
Digital optical phase conjugation (DOPC) has proven to be a promising technique in deep tissue fluorescence imaging. Nonetheless, DOPC optical setups require precise alignment of all optical components to accurately read the wavefront of scattered light in a turbid medium and playback the conjugated beam toward the sample. Minor misalignments and possible imperfections in the arrangement or the structure of the optical components significantly reduce the performance of the method. In this paper, a calibration procedure based on orthogonal rectangular polynomials is introduced to compensate major imperfections including the optical aberration in the wavefront of the reference beam and the substrate curvature of the spatial light modulator without adding extra optical components to the original setup. The proposed algorithm also provides a systematic calibration procedure for mechanical fine tuning of DOPC systems. It is shown experimentally that the proposed calibration process improves the peak-to-background ratio when focusing light after passing through a highly scattering medium. PMID:27139849
Krishnamoorthi, R; Anna Poorani, G
2016-01-01
Iris normalization is an important stage in any iris biometric, as it has a propensity to trim down the consequences of iris distortion. To indemnify the variation in size of the iris owing to the action of stretching or enlarging the pupil in iris acquisition process and camera to eyeball distance, two normalization schemes has been proposed in this work. In the first method, the iris region of interest is normalized by converting the iris into the variable size rectangular model in order to avoid the under samples near the limbus border. In the second method, the iris region of interest is normalized by converting the iris region into a fixed size rectangular model in order to avoid the dimensional discrepancies between the eye images. The performance of the proposed normalization methods is evaluated with orthogonal polynomials based iris recognition in terms of FAR, FRR, GAR, CRR and EER. PMID:27066376
Lee, Joohwi; Kim, Sun Hyung; Oguz, Ipek; Styner, Martin
2016-01-01
The cortical thickness of the mammalian brain is an important morphological characteristic that can be used to investigate and observe the brain’s developmental changes that might be caused by biologically toxic substances such as ethanol or cocaine. Although various cortical thickness analysis methods have been proposed that are applicable for human brain and have developed into well-validated open-source software packages, cortical thickness analysis methods for rodent brains have not yet become as robust and accurate as those designed for human brains. Based on a previously proposed cortical thickness measurement pipeline for rodent brain analysis,1 we present an enhanced cortical thickness pipeline in terms of accuracy and anatomical consistency. First, we propose a Lagrangian-based computational approach in the thickness measurement step in order to minimize local truncation error using the fourth-order Runge-Kutta method. Second, by constructing a line object for each streamline of the thickness measurement, we can visualize the way the thickness is measured and achieve sub-voxel accuracy by performing geometric post-processing. Last, with emphasis on the importance of an anatomically consistent partial differential equation (PDE) boundary map, we propose an automatic PDE boundary map generation algorithm that is specific to rodent brain anatomy, which does not require manual labeling. The results show that the proposed cortical thickness pipeline can produce statistically significant regions that are not observed in the the previous cortical thickness analysis pipeline. PMID:27065047
NASA Astrophysics Data System (ADS)
Lee, Joohwi; Kim, Sun Hyung; Oguz, Ipek; Styner, Martin
2016-03-01
The cortical thickness of the mammalian brain is an important morphological characteristic that can be used to investigate and observe the brain's developmental changes that might be caused by biologically toxic substances such as ethanol or cocaine. Although various cortical thickness analysis methods have been proposed that are applicable for human brain and have developed into well-validated open-source software packages, cortical thickness analysis methods for rodent brains have not yet become as robust and accurate as those designed for human brains. Based on a previously proposed cortical thickness measurement pipeline for rodent brain analysis,1 we present an enhanced cortical thickness pipeline in terms of accuracy and anatomical consistency. First, we propose a Lagrangian-based computational approach in the thickness measurement step in order to minimize local truncation error using the fourth-order Runge-Kutta method. Second, by constructing a line object for each streamline of the thickness measurement, we can visualize the way the thickness is measured and achieve sub-voxel accuracy by performing geometric post-processing. Last, with emphasis on the importance of an anatomically consistent partial differential equation (PDE) boundary map, we propose an automatic PDE boundary map generation algorithm that is specific to rodent brain anatomy, which does not require manual labeling. The results show that the proposed cortical thickness pipeline can produce statistically significant regions that are not observed in the previous cortical thickness analysis pipeline.
Phase demodulation method from a single fringe pattern based on correlation with a polynomial form
Robin, Eric; Valle, Valery; Bremand, 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.
Optimization of LED-based non-imaging optics with orthogonal polynomial shapes
NASA Astrophysics Data System (ADS)
Brick, Peter; Wiesmann, Christopher
2012-10-01
Starting with a seminal paper by Forbes [1], orthogonal polynomials have received considerable interest as descriptors of lens shapes for imaging optics. However, there is little information on the application of orthogonal polynomials in the field of non-imaging optics. Here, we consider fundamental cases related to LED primary and secondary optics. To make it most realistic, we avoid many of the simplifications of non-imaging theory and consider the full complexity of LED optics. In this framework, the benefits of orthogonal polynomial surface description for LED optics are evaluated in comparison to a surface description by widely used monomials.
Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.
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. PMID:16353793
NASA Astrophysics Data System (ADS)
Papila, Nilay Uzgoren
Turbine performance directly affects engine specific impulse, thrust-to-weight ratio, and cost in a rocket propulsion system. This dissertation focuses on methodology and application of employing optimization techniques, with the neural network (NN) and polynomial-based response surface method (RSM), for supersonic turbine optimization. The research is relevant to NASA's reusable launching vehicle initiatives. It is demonstrated that accuracy of the response surface (RS) approximations can be improved with combined utilization of the NN and polynomial techniques, and higher emphases on data in regions of interests. The design of experiment methodology is critical while performing optimization in efficient and effective manners. In physical applications, both preliminary design and detailed shape design optimization are investigated. For preliminary design level, single-, two-, and three-stage turbines are considered with the number of design variables increasing from six to 11 and then to 15, in accordance with the number of stages. A major goal of the preliminary optimization effort is to balance the desire of maximizing aerodynamic performance and minimizing weight. To ascertain required predictive capability of the RSM, a two-level domain refinement approach (windowing) has been adopted. The accuracy of the predicted optimal design points based on this strategy is shown to be satisfactory. The results indicate that the two-stage turbine is the optimum configuration with the higher efficiency corresponding to smaller weights. It is demonstrated that the criteria for selecting the database exhibit significant impact on the efficiency and effectiveness of the construction of the response surface. Based on the optimized preliminary design outcome, shape optimization is performed for vanes and blades of a two-stage supersonic turbine, involving O(10) design variables. It is demonstrated that a major merit of the RS-based optimization approach is that it enables one
Cloning and characterization of a SnRK2 gene from Jatropha curcas L.
Chun, J; Li, F-S; Ma, Y; Wang, S-H; Chen, F
2014-01-01
Although the SnRK2 class of Ser/Thr protein kinases is critical for signal transduction and abiotic stress resistance in plants, there have been no studies to examine SnRK2 in Jatropha curcas L. In the present study, JcSnRK2 was cloned from J. curcas using the rapid amplification of cDNA end technique and characterized. The JcSnRK2 genomic sequence is 2578 base pairs (bp), includes 10 exons and 9 introns, and the 1017-bp open reading frame encodes 338 amino acids. JcSnRK2 was transcribed in all examined tissues, with the highest transcription rate observed in the roots, followed by the leaves and stalks; the lowest rate was observed in flowers and seeds. JcSnRK2 expression increased following abscisic acid treatment, salinity, and drought stress. During a 48-h stress period, the expression of JcSnRK2 showed 2 peaks and periodic up- and downregulation. JcSnRK2 was rapidly activated within 1 h under salt and drought stress, but not under cold stress. Because of the gene sequence and expression similarity of JcSnRK2 to AtSnRK2.8, primarily in the roots, an eukaryotic expression vector containing the JcSnRK2 gene (pBI121-JcSnRK2) was constructed and introduced to the Arabidopsis AtSnRK2.8 mutant snf2.8. JcSnRK2-overexpressing plants exhibited higher salt and drought tolerance, further demonstrating the function of JcSnRK2 in the osmotic stress response. J. curcas is highly resistant to extreme salt and drought conditions and JcSnRK2 was found to be activated under these conditions. Thus, JcSnRK2 is potential candidate for improving crop tolerance to salt and drought stress. PMID:25526217
NASA Astrophysics Data System (ADS)
Erdogan, Eren; Onur Karslioglu, Mahmut; Durmaz, Murat; Aghakarimi, Armin
2014-05-01
In this study, particle filter (PF) which is mainly based on the Monte Carlo simulation technique has been carried out for polynomial modeling of the local ionospheric conditions above the selected ground based stations. Less sensitivity to the errors caused by linearization of models and the effect of unknown or unmodeled components in the system model is one of the advantages of the particle filter as compared to the Kalman filter which is commonly used as a recursive filtering method in VTEC modeling. Besides, probability distribution of the system models is not necessarily required to be Gaussian. In this work third order polynomial function has been incorporated into the particle filter implementation to represent the local VTEC distribution. Coefficients of the polynomial model presenting the ionospheric parameters and the receiver inter frequency biases are the unknowns forming the state vector which has been estimated epoch-wise for each ground station. To consider the time varying characteristics of the regional VTEC distribution, dynamics of the state vector parameters changing permanently have been modeled using the first order Gauss-Markov process. In the processing of the particle filtering, multi-variety probability distribution of the state vector through the time has been approximated by means of randomly selected samples and their associated weights. A known drawback of the particle filtering is that the increasing number of the state vector parameters results in an inefficient filter performance and requires more samples to represent the probability distribution of the state vector. Considering the total number of unknown parameters for all ground stations, estimation of these parameters which were inserted into a single state vector has caused the particle filter to produce inefficient results. To solve this problem, the PF implementation has been carried out separately for each ground station at current time epochs. After estimation of unknown
Polynomial fitting-based shape matching algorithm for multi-sensors remote sensing images
NASA Astrophysics Data System (ADS)
Gu, Yujie; Ren, Kan; Wang, Pengcheng; Gu, Guohua
2016-05-01
According to the characteristics of multi-sensors remote sensing images, a new registration algorithm based on shape contour feature is proposed. Firstly, the edge features of remote sensing images are extracted by Canny operator, and the edge of the main contour is retained. According to the characteristics of the contour pixels, a new feature extraction algorithm based on polynomial fitting is proposed and it is used to determine the principal directions of the feature points. On this basis, we improved the shape context descriptor and completed coarse registration by minimizing the matching cost between the feature points. The shape context has been found to be robust in Simple object registration, and in this paper, it is applied to remote sensing image registration after improving the circular template with rotation invariance. Finally, the fine registration is accomplished by the RANSAC algorithm. Experiments show that this algorithm can realize the automatic registration of multi-sensors remote sensing images with high accuracy, robustness and applicability.
Lauricella, Marta Alicia; Maidana, Cristina Graciela; Frias, Victoria Fragueiro; Romagosa, Carlo M; Negri, Vanesa; Benedetti, Ruben; Sinagra, Angel J; Luna, Concepcion; Tartaglino, Lilian; Laucella, Susana; Reed, Steven G; Riarte, Adelina R
2016-07-01
Direct observation of Leishmania parasites in tissue aspirates has shown low sensitivity for the detection of canine visceral leishmaniasis (VL). Therefore in the last quarter century immunoenzymatic tests have been developed to improve diagnosis. The purpose of this study was to develop a fast recombinant K28 antigen, naked-eye qualitative enzyme-linked immunosorbent assay (VL Ql-ELISA) and a quantitative version (VL Qt-ELISA), and to display it in a kit format, whose cutoff value (0.156) was selected as the most adequate one to differentiate reactive from nonreactive samples. Considering 167 cases and 300 controls, sensitivity was 91% for both assays and specificity was 100% and 98.7% in Ql-ELISA and Qt-ELISA, respectively. Positive predictive values were 100% and 97.4% for Ql-ELISA and Qt-ELISA, respectively, and negative predictive values were 95.2% for both ELISAs. Reagent stability, reliability studies, including periodic repetitions and retest of samples, cutoff selection, and comparison of rK28 ELISAs with rK39 immunochromatographic test, were the international criteria that supported the quality in both kits. The performance of both ELISA kits in this work confirmed their validity and emphasized their usefulness for low-to-medium complexity laboratories. PMID:27162270
Blind phone segmentation based on spectral change detection using Legendre polynomial approximation.
Hoang, Dac-Thang; Wang, Hsiao-Chuan
2015-02-01
Phone segmentation involves partitioning a continuous speech signal into discrete phone units. In this paper, a method for automatic phone segmentation without prior knowledge of speech content is proposed. The signal spectrum was represented by band-energies. A segment of the band-energy curve was approximated using Legendre polynomial expansion, allowing Legendre polynomial coefficients to describe the properties of the segment. The spectral changes, which imply phone boundaries in the speech signal, were then detected by monitoring the variations of Legendre polynomial coefficients. A two-step algorithm for detecting phone boundaries was derived. The first step was to detect phone boundaries using first-order and second-order coefficients of the Legendre polynomial approximation. The second step was to locate slow spectral changes in the regions of concatenated voiced phones using zero-order coefficients of the Legendre polynomial approximation. This enabled the phone boundaries missed during the first step to be recovered. An evaluation using the TIMIT corpus indicated that the proposed method is comparable to or more accurate than previous methods. PMID:25698014
Papadopoulos, Anthony
2009-01-01
The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined. PMID:19333397
NASA Technical Reports Server (NTRS)
Narkawicz, Anthony J.; Munoz, Cesar A.
2014-01-01
Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semiopen interval. This paper presents a formalization of this theorem in the PVS theorem prover, as well as a decision procedure that checks whether a polynomial is always positive, nonnegative, nonzero, negative, or nonpositive on any input interval. The soundness and completeness of the decision procedure is proven in PVS. The procedure and its correctness properties enable the implementation of a PVS strategy for automatically proving existential and universal univariate polynomial inequalities. Since the decision procedure is formally verified in PVS, the soundness of the strategy depends solely on the internal logic of PVS rather than on an external oracle. The procedure itself uses a combination of Sturm's Theorem, an interval bisection procedure, and the fact that a polynomial with exactly one root in a bounded interval is always nonnegative on that interval if and only if it is nonnegative at both endpoints.
Orthogonal Bases of Hermitean Monogenic Polynomials: An Explicit Construction in Complex Dimension 2
NASA Astrophysics Data System (ADS)
Brackx, F.; De Schepper, H.; Lávička, R.; Souček, V.
2010-09-01
In this contribution we construct an orthogonal basis of Hermitean monogenic polynomials for the specific case of two complex variables. The approach combines group representation theory, see [5], with a Fischer decomposition for the kernels of each of the considered Dirac operators, see [4], and a Cauchy-Kovalevskaya extension principle, see [3].
Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Parker, William D.; Umrigar, C. J.; Alfè, Dario; Petruzielo, F. R.; Hennig, Richard G.; Wilkins, John W.
2015-04-01
The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work by Williamson et al. (2001) [35] and Alfè and Gillan, (2004) [36] has demonstrated the reduction of the O (N3) cost of evaluating the Slater determinant with planewaves to O (N2) using localized basis functions. We compare four polynomial approximations as basis functions - interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO, and smoothing B-splines most closely reproduce the planewave value for of the variational Monte Carlo energy. Using separate approximations for the Laplacian of the orbitals increases the accuracy sufficiently to justify the increased memory requirement, making smoothing B-splines, with separate approximation for the Laplacian, the preferred choice for approximating planewave-represented orbitals in QMC calculations.
Spreading lengths of Hermite polynomials
NASA Astrophysics Data System (ADS)
Sánchez-Moreno, P.; Dehesa, J. S.; Manzano, D.; Yáñez, R. J.
2010-03-01
The Renyi, Shannon and Fisher spreading lengths of the classical or hypergeometric orthogonal polynomials, which are quantifiers of their distribution all over the orthogonality interval, are defined and investigated. These information-theoretic measures of the associated Rakhmanov probability density, which are direct measures of the polynomial spreading in the sense of having the same units as the variable, share interesting properties: invariance under translations and reflections, linear scaling and vanishing in the limit that the variable tends towards a given definite value. The expressions of the Renyi and Fisher lengths for the Hermite polynomials are computed in terms of the polynomial degree. The combinatorial multivariable Bell polynomials, which are shown to characterize the finite power of an arbitrary polynomial, play a relevant role for the computation of these information-theoretic lengths. Indeed these polynomials allow us to design an error-free computing approach for the entropic moments (weighted Lq-norms) of Hermite polynomials and subsequently for the Renyi and Tsallis entropies, as well as for the Renyi spreading lengths. Sharp bounds for the Shannon length of these polynomials are also given by means of an information-theoretic-based optimization procedure. Moreover, the existence of a linear correlation between the Shannon length (as well as the second-order Renyi length) and the standard deviation is computationally proved. Finally, the application to the most popular quantum-mechanical prototype system, the harmonic oscillator, is discussed and some relevant asymptotical open issues related to the entropic moments, mentioned previously, are posed.
Vector quantizer based on brightness maps for image compression with the polynomial transform
NASA Astrophysics Data System (ADS)
Escalante-Ramirez, Boris; Moreno-Gutierrez, Mauricio; Silvan-Cardenas, Jose L.
2002-11-01
We present a vector quantization scheme acting on brightness fields based on distance/distortion criteria correspondent with psycho-visual aspects. These criteria quantify sensorial distortion between vectors that represent either portions of a digital image or alternatively, coefficients of a transform-based coding system. In the latter case, we use an image representation model, namely the Hermite transform, that is based on some of the main perceptual characteristics of the human vision system (HVS) and in their response to light stimulus. Energy coding in the brightness domain, determination of local structure, code-book training and local orientation analysis are all obtained by means of the Hermite transform. This paper, for thematic reasons, is divided in four sections. The first one will shortly highlight the importance of having newer and better compression algorithms. This section will also serve to explain briefly the most relevant characteristics of the HVS, advantages and disadvantages related with the behavior of our vision in front of ocular stimulus. The second section shall go through a quick review of vector quantization techniques, focusing their performance on image treatment, as a preview for the image vector quantizer compressor actually constructed in section 5. Third chapter was chosen to concentrate the most important data gathered on brightness models. The building of this so-called brightness maps (quantification of the human perception on the visible objects reflectance), in a bi-dimensional model, will be addressed here. The Hermite transform, a special case of polynomial transforms, and its usefulness, will be treated, in an applicable discrete form, in the fourth chapter. As we have learned from previous works 1, Hermite transform has showed to be a useful and practical solution to efficiently code the energy within an image block, deciding which kind of quantization is to be used upon them (whether scalar or vector). It will also be
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. PMID:26367882
Complexity and Performance Results for Non FFT-Based Univariate Polynomial Multiplication
NASA Astrophysics Data System (ADS)
Chowdhury, Muhammad F. I.; Maza, Marc Moreno; Pan, Wei; Schost, Eric
2011-11-01
Today's parallel hardware architectures and computer memory hierarchies enforce revisiting fundamental algorithms which were often designed with algebraic complexity as the main complexity measure and with sequential running time as the main performance counter. This study is devoted to two algorithms of univariate polynomial multiplication; that are independent of the coefficient ring: the plain and the Toom-Cook univariate multiplications. We analyze their cache complexity and report on their parallel implementations in Cilk++ [1].
NASA Astrophysics Data System (ADS)
Withers, Christopher S.; Nadarajah, Saralees
2016-07-01
A new class of polynomials pn(x) known as β-reciprocal polynomials is defined. Given a parameter ? that is not a root of -1, we show that the only β-reciprocal polynomials are pn(x) ≡ xn. When β is a root of -1, other polynomials are possible. For example, the Hermite polynomials are i-reciprocal, ?.
Differential Activation of the Wheat SnRK2 Family by Abiotic Stresses
Zhang, Hongying; Li, Weiyu; Mao, Xinguo; Jing, Ruilian; Jia, Hongfang
2016-01-01
Plant responses to stress occur via abscisic acid (ABA) dependent or independent pathways. Sucrose non-fermenting1-related protein kinase 2 (SnRK2) play a key role in plant stress signal transduction pathways. It is known that some SnRK2 members are positive regulators of ABA signal transduction through interaction with group A type 2C protein phosphatases (PP2Cs). Here, 10 SnRK2s were isolated from wheat. Based on phylogenetic analysis using kinase domains or the C-terminus, the 10 SnRK2s were divided into three subclasses. Expression pattern analysis revealed that all TaSnRK2s were involved in the responses to PEG, NaCl, and cold stress. TaSnRK2s in subclass III were strongly induced by ABA. Subclass II TaSnRK2s responded weakly to ABA, whereas TaSnRK2s in subclass I were not activated by ABA treatment. Motif scanning in the C-terminus indicated that motifs 4 and 5 in the C-terminus were unique to subclass III. We further demonstrate the physical and functional interaction between TaSnRK2s and a typical group A PP2C (TaABI1) using Y2H and BiFC assays. The results showed that TaABI1 interacted physically with subclass III TaSnRK2s, while having no interaction with subclasses I and II TaSnRK2s. Together, these findings indicated that subclass III TaSnRK2s were involved in ABA regulated stress responses, whereas subclasses I and II TaSnRK2s responded to various abiotic stressors in an ABA-independent manner. PMID:27066054
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.
A ROM-Less Direct Digital Frequency Synthesizer Based on Hybrid Polynomial Approximation
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
Accelerated Hazards Model based on Parametric Families Generalized with Bernstein Polynomials
Chen, Yuhui; Hanson, Timothy; Zhang, Jiajia
2015-01-01
Summary A transformed Bernstein polynomial that is centered at standard parametric families, such as Weibull or log-logistic, is proposed for use in the accelerated hazards model. This class provides a convenient way towards creating a Bayesian non-parametric prior for smooth densities, blending the merits of parametric and non-parametric methods, that is amenable to standard estimation approaches. For example optimization methods in SAS or R can yield the posterior mode and asymptotic covariance matrix. This novel nonparametric prior is employed in the accelerated hazards model, which is further generalized to time-dependent covariates. The proposed approach fares considerably better than previous approaches in simulations; data on the effectiveness of biodegradable carmustine polymers on recurrent brain malignant gliomas is investigated. PMID:24261450
A ROM-less direct digital frequency synthesizer based on hybrid polynomial approximation.
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
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.
NASA Astrophysics Data System (ADS)
Bagchi, B.; Grandati, Y.; Quesne, C.
2015-06-01
The possibility for the Jacobi equation to admit, in some cases, general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them para-Jacobi polynomials. Such polynomials are used here to build seed functions of a Darboux-Bäcklund transformation for the trigonometric Darboux-Pöschl-Teller potential. As a result, one-step regular rational extensions of the latter depending both on an integer index n and on a continuously varying parameter λ are constructed. For each n value, the eigenstates of these extended potentials are associated with a novel family of λ-dependent polynomials, which are orthogonal on [-1,1].
Silbar, R.R.
1998-09-28
WhistleSoft, Inc., proposed to convert a successful pedagogical experiment into multimedia software, making it accessible to a much broader audience. A colleague, Richard J. Jacob, has been teaching a workshop course in mathematical methods at Arizona State University (ASU) for lower undergraduate science majors. Students work at their own pace through paper-based tutorials containing many exercises, either with pencil and paper or with computer tools such as spreadsheets. These tutorial modules cry out for conversion into an interactive computer-based tutorial course that is suitable both for the classroom and for self-paced, independent learning. WhistleSoft has made a prototype of one such module, Legendre Polynomials, under Subcontract (No F97440018-35) with the Los Alamos Laboratory`s Technology Commercialization Office for demonstration and marketing purposes.
Ultrafast laser spatial beam shaping based on Zernike polynomials for surface processing.
Houzet, J; Faure, N; Larochette, M; Brulez, A-C; Benayoun, S; Mauclair, C
2016-03-21
In femtosecond laser machining, spatial beam shaping can be achieved with wavefront modulators. The wavefront modulator displays a pre-calculated phase mask that modulates the laser wavefront to generate a target intensity distribution in the processing plane. Due to the non-perfect optical response of wavefront modulators, the experimental distribution may significantly differ from the target, especially for continuous shapes. We propose an alternative phase mask calculation method that can be adapted to the phase modulator optical performance. From an adjustable number of Zernike polynomials according to this performance, a least square fitting algorithm numerically determines their coefficients to obtain the desired wavefront modulation. We illustrate the technique with an optically addressed liquid-crystal light valve to produce continuous intensity distributions matching a desired ablation profile, without the need of a wavefront sensor. The projection of the experimental laser distribution shows a 5% RMS error compared to the calculated one. Ablation of steel is achieved following user-defined micro-dimples and micro-grooves targets on mold surfaces. The profiles of the microgrooves and the injected polycarbonate closely match the target (RMS below 4%). PMID:27136844
Polynomial regression calculation of the Earth's position based on millisecond pulsar timing
NASA Astrophysics Data System (ADS)
Tian, Feng; Tang, Zheng-Hong; Yan, Qing-Zeng; Yu, Yong
2012-02-01
Prior to achieving high precision navigation of a spacecraft using X-ray observations, a pulsar rotation model must be built and analysis of the precise position of the Earth should be performed using ground pulsar timing observations. We can simulate time-of-arrival ground observation data close to actual observed values before using pulsar timing observation data. Considering the correlation between the Earth's position and its short arc section of an orbit, we use polynomial regression to build the correlation. Regression coefficients can be calculated using the least square method, and a coordinate component series can also be obtained; that is, we can calculate Earth's position in the Barycentric Celestial Reference System according to pulse arrival time data and a precise pulsar rotation model. In order to set appropriate parameters before the actual timing observations for Earth positioning, we can calculate the influence of the spatial distribution of pulsars on errors in the positioning result and the influence of error source variation on positioning by simulation. It is significant that the threshold values of the observation and systematic errors can be established before an actual observation occurs; namely, we can determine the observation mode with small errors and reject the observed data with big errors, thus improving the positioning result.
Karagiannis, Georgios Lin, Guang
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, by 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.
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 Bayesian 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.
Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures
Fahrenholtz, S.; Stafford, R. J.; Maier, F.; Hazle, J. D.; Fuentes, D.
2014-01-01
Purpose A generalized polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided Laser Induced Thermal Therapies (MRgLITT). Methods Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n=4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms. Results Within the range of physically meaningful constitutive values relevant to the ablative temperature regime of MRgLITT, the sensitivity study indicated that the optical parameters, particularly the anisotropy factor, created the most variance in the stochastic model's output temperature prediction. Further, within the statistical sense considered, a nonlinear model of the temperature and damage dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data. Conclusions Given parameter uncertainties and mathematical modeling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning. PMID:23692295
A generalized polynomial chaos based ensemble Kalman filter with high accuracy
Li Jia; Xiu Dongbin
2009-08-20
As one of the most adopted sequential data assimilation methods in many areas, especially those involving complex nonlinear dynamics, the ensemble Kalman filter (EnKF) has been under extensive investigation regarding its properties and efficiency. Compared to other variants of the Kalman filter (KF), EnKF is straightforward to implement, as it employs random ensembles to represent solution states. This, however, introduces sampling errors that affect the accuracy of EnKF in a negative manner. Though sampling errors can be easily reduced by using a large number of samples, in practice this is undesirable as each ensemble member is a solution of the system of state equations and can be time consuming to compute for large-scale problems. In this paper we present an efficient EnKF implementation via generalized polynomial chaos (gPC) expansion. The key ingredients of the proposed approach involve (1) solving the system of stochastic state equations via the gPC methodology to gain efficiency; and (2) sampling the gPC approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost, to drastically reduce the sampling errors. The resulting algorithm thus achieves a high accuracy at reduced computational cost, compared to the classical implementations of EnKF. Numerical examples are provided to verify the convergence property and accuracy improvement of the new algorithm. We also prove that for linear systems with Gaussian noise, the first-order gPC Kalman filter method is equivalent to the exact Kalman filter.
Factoring Polynomials and Fibonacci.
ERIC Educational Resources Information Center
Schwartzman, Steven
1986-01-01
Discusses the factoring of polynomials and Fibonacci numbers, offering several challenges teachers can give students. For example, they can give students a polynomial containing large numbers and challenge them to factor it. (JN)
Chaos, Fractals, and Polynomials.
ERIC Educational Resources Information Center
Tylee, J. Louis; Tylee, Thomas B.
1996-01-01
Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)
NASA Astrophysics Data System (ADS)
Ammari, Amara; Karoui, Abderrazek
2012-05-01
In this paper, we build a stable scheme for the solution of a deconvolution problem of the Abel integral equation type. This scheme is obtained by further developing the orthogonal polynomial-based techniques for solving the Abel integral equation of Ammari and Karoui (2010 Inverse Problems 26 105005). More precisely, this method is based on the simultaneous use of the two families of orthogonal polynomials of the Legendre and Jacobi types. In particular, we provide an explicit formula for the computation of the Legendre expansion coefficients of the solution. This explicit formula is based on some known formulae for the exact computation of the integrals of the product of some Jacobi polynomials with the derivatives of the Legendre polynomials. Besides the explicit and the exact computation of the expansion coefficients of the solution, our proposed method has the advantage of ensuring the stability of the solution under a fairly weak condition on the functional space to which the data function belongs. Finally, we provide the reader with some numerical examples that illustrate the results of this work.
Interval polynomial positivity
NASA Technical Reports Server (NTRS)
Bose, N. K.; Kim, K. D.
1989-01-01
It is shown that a univariate interval polynomial is globally positive if and only if two extreme polynomials are globally positive. It is shown that the global positivity property of a bivariate interval polynomial is completely determined by four extreme bivariate polynomials. The cardinality of the determining set for k-variate interval polynomials is 2k. One of many possible generalizations, where vertex implication for global positivity holds, is made by considering the parameter space to be the set dual of a boxed domain.
Shityakov, Sergey; Förster, Carola
2014-01-01
P-glycoprotein (P-gp) is an ATP (adenosine triphosphate)-binding cassette transporter that causes multidrug resistance of various chemotherapeutic substances by active efflux from mammalian cells. P-gp plays a pivotal role in limiting drug absorption and distribution in different organs, including the intestines and brain. Thus, the prediction of P-gp-drug interactions is of vital importance in assessing drug pharmacokinetic and pharmacodynamic properties. To find the strongest P-gp blockers, we performed an in silico structure-based screening of P-gp inhibitor library (1,300 molecules) by the gradient optimization method, using polynomial empirical scoring (POLSCORE) functions. We report a strong correlation (r (2)=0.80, F=16.27, n=6, P<0.0157) of inhibition constants (Kiexp or pKiexp; experimental Ki or negative decimal logarithm of Kiexp) converted from experimental IC50 (half maximal inhibitory concentration) values with POLSCORE-predicted constants (KiPOLSCORE or pKiPOLSCORE), using a linear regression fitting technique. The hydrophobic interactions between P-gp and selected drug substances were detected as the main forces responsible for the inhibition effect. The results showed that this scoring technique might be useful in the virtual screening and filtering of databases of drug-like compounds at the early stage of drug development processes. PMID:24711707
Shityakov, Sergey; Förster, Carola
2014-01-01
P-glycoprotein (P-gp) is an ATP (adenosine triphosphate)-binding cassette transporter that causes multidrug resistance of various chemotherapeutic substances by active efflux from mammalian cells. P-gp plays a pivotal role in limiting drug absorption and distribution in different organs, including the intestines and brain. Thus, the prediction of P-gp–drug interactions is of vital importance in assessing drug pharmacokinetic and pharmacodynamic properties. To find the strongest P-gp blockers, we performed an in silico structure-based screening of P-gp inhibitor library (1,300 molecules) by the gradient optimization method, using polynomial empirical scoring (POLSCORE) functions. We report a strong correlation (r2=0.80, F=16.27, n=6, P<0.0157) of inhibition constants (Kiexp or pKiexp; experimental Ki or negative decimal logarithm of Kiexp) converted from experimental IC50 (half maximal inhibitory concentration) values with POLSCORE-predicted constants (KiPOLSCORE or pKiPOLSCORE), using a linear regression fitting technique. The hydrophobic interactions between P-gp and selected drug substances were detected as the main forces responsible for the inhibition effect. The results showed that this scoring technique might be useful in the virtual screening and filtering of databases of drug-like compounds at the early stage of drug development processes. PMID:24711707
POLYNOMIAL-BASED DISAGGREGATION OF HOURLY RAINFALL FOR CONTINUOUS HYDROLOGIC SIMULATION
Hydrologic modeling of urban watersheds for designs and analyses of stormwater conveyance facilities can be performed in either an event-based or continuous fashion. Continuous simulation requires, among other things, the use of a time series of rainfall amounts. However, for urb...
NASA Technical Reports Server (NTRS)
Wood, C. A.
1974-01-01
For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.
Entanglement conditions and polynomial identities
Shchukin, E.
2011-11-15
We develop a rather general approach to entanglement characterization based on convexity properties and polynomial identities. This approach is applied to obtain simple and efficient entanglement conditions that work equally well in both discrete as well as continuous-variable environments. Examples of violations of our conditions are presented.
Polynomial Algorithms for Item Matching.
ERIC Educational Resources Information Center
Armstrong, Ronald D.; Jones, Douglas H.
1992-01-01
Polynomial algorithms are presented that are used to solve selected problems in test theory, and computational results from sample problems with several hundred decision variables are provided that demonstrate the benefits of these algorithms. The algorithms are based on optimization theory in networks (graphs). (SLD)
Fink, Wolfgang; Micol, Daniel
2006-01-01
We describe a computer eye model that allows for aspheric surfaces and a three-dimensional computer-based ray-tracing technique to simulate optical properties of the human eye and visual perception under various eye defects. Eye surfaces, such as the cornea, eye lens, and retina, are modeled or approximated by a set of Zernike polynomials that are fitted to input data for the respective surfaces. A ray-tracing procedure propagates light rays using Snell's law of refraction from an input object (e.g., digital image) through the eye under investigation (i.e., eye with defects to be modeled) to form a retinal image that is upside down and left-right inverted. To obtain a first-order realistic visual perception without having to model or simulate the retina and the visual cortex, this retinal image is then back-propagated through an emmetropic eye (e.g., Gullstrand exact schematic eye model with no additional eye defects) to an output screen of the same dimensions and at the same distance from the eye as the input object. Visual perception under instances of emmetropia, regular astigmatism, irregular astigmatism, and (central symmetric) keratoconus is simulated and depicted. In addition to still images, the computer ray-tracing tool presented here (simEye) permits the production of animated movies. These developments may have scientific and educational value. This tool may facilitate the education and training of both the public, for example, patients before undergoing eye surgery, and those in the medical field, such as students and professionals. Moreover, simEye may be used as a scientific research tool to investigate optical lens systems in general and the visual perception under a variety of eye conditions and surgical procedures such as cataract surgery and laser assisted in situ keratomileusis (LASIK) in particular. PMID:17092160
NASA Astrophysics Data System (ADS)
Bogner, Christian; Weinzierl, Stefan
The integrand of any multiloop integral is characterized after Feynman parametrization by two polynomials. In this review we summarize the properties of these polynomials. Topics covered in this paper include among others: spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
NASA Astrophysics Data System (ADS)
Duan, Lei; Hui, Mei; Deng, Jiayuan; Gong, Cheng; Zhao, Yuejin
2012-11-01
Annular sub-aperture stitching method was developed for testing large-aperture aspheric surfaces without using of any compensating element for measurement. It is necessary to correct measurement of aspheric optical aberrations and create mathematical description to describe wave-front aberrations. Zernike polynomials are suitable to describe wave aberration functions and data fitting of experimental measurements for the annular sub-aperture stitching system. This paper uses Zernike polynomials to describe the wave-front aberrations of full wave-front and reconstructed wave-front by annular sub-aperture stitching algorithm. At the same time, the imaging quality of the aspheric optical element can be contrasted. The stitching result shows good agreement with the full aperture result.
NASA Astrophysics Data System (ADS)
Mironov, A.; Mkrtchyan, R.; Morozov, A.
2016-02-01
We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.
Efficient Multiplication of Polynomials on Graphics Hardware
NASA Astrophysics Data System (ADS)
Emeliyanenko, Pavel
We present the algorithm to multiply univariate polynomials with integer coefficients efficiently using the Number Theoretic transform (NTT) on Graphics Processing Units (GPU). The same approach can be used to multiply large integers encoded as polynomials. Our algorithm exploits fused multiply-add capabilities of the graphics hardware. NTT multiplications are executed in parallel for a set of distinct primes followed by reconstruction using the Chinese Remainder theorem (CRT) on the GPU. Our benchmarking experiences show the NTT multiplication performance up to 77 GMul/s. We compared our approach with CPU-based implementations of polynomial and large integer multiplication provided by NTL and GMP libraries.
Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang
2016-03-01
An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS. PMID:26810185
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 radiation 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.
Distortion theorems for polynomials on a circle
Dubinin, V N
2000-12-31
Inequalities for the derivatives with respect to {phi}=arg z the functions ReP(z), |P(z)|{sup 2} and arg P(z) are established for an algebraic polynomial P(z) at points on the circle |z|=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.
Tutte Polynomial of Scale-Free Networks
NASA Astrophysics Data System (ADS)
Chen, Hanlin; Deng, Hanyuan
2016-05-01
The Tutte polynomial of a graph, or equivalently the q-state Potts model partition function, is a two-variable polynomial graph invariant of considerable importance in both statistical physics and combinatorics. The computation of this invariant for a graph is NP-hard in general. In this paper, we focus on two iteratively growing scale-free networks, which are ubiquitous in real-life systems. Based on their self-similar structures, we mainly obtain recursive formulas for the Tutte polynomials of two scale-free networks (lattices), one is fractal and "large world", while the other is non-fractal but possess the small-world property. Furthermore, we give some exact analytical expressions of the Tutte polynomial for several special points at ( x, y)-plane, such as, the number of spanning trees, the number of acyclic orientations, etc.
Polynomials with small Mahler measure
NASA Astrophysics Data System (ADS)
Mossinghoff, M. J.
1998-10-01
We describe several searches for polynomials with integer coefficients and small Mahler measure. We describe the algorithm used to test Mahler measures. We determine all polynomials with degree at most 24 and Mahler measure less than 1.3, test all reciprocal and antireciprocal polynomials with height 1 and degree at most 40, and check certain sparse polynomials with height 1 and degree as large as 181. We find a new limit point of Mahler measures near 1.309, four new Salem numbers less than 1.3, and many new polynomials with small Mahler measure. None has measure smaller than that of Lehmer's degree 10 polynomial.
Chen, Huifang; Xie, Lei
2014-01-01
Self-healing group key distribution (SGKD) aims to deal with the key distribution problem over an unreliable wireless network. In this paper, we investigate the SGKD issue in resource-constrained wireless networks. We propose two improved SGKD schemes using the one-way hash chain (OHC) and the revocation polynomial (RP), the OHC&RP-SGKD schemes. In the proposed OHC&RP-SGKD schemes, by introducing the unique session identifier and binding the joining time with the capability of recovering previous session keys, the problem of the collusion attack between revoked users and new joined users in existing hash chain-based SGKD schemes is resolved. Moreover, novel methods for utilizing the one-way hash chain and constructing the personal secret, the revocation polynomial and the key updating broadcast packet are presented. Hence, the proposed OHC&RP-SGKD schemes eliminate the limitation of the maximum allowed number of revoked users on the maximum allowed number of sessions, increase the maximum allowed number of revoked/colluding users, and reduce the redundancy in the key updating broadcast packet. Performance analysis and simulation results show that the proposed OHC&RP-SGKD schemes are practical for resource-constrained wireless networks in bad environments, where a strong collusion attack resistance is required and many users could be revoked. PMID:25529204
ERIC Educational Resources Information Center
Gordon, Sheldon P.
1992-01-01
Demonstrates how the uniqueness and anonymity of a student's Social Security number can be utilized to create individualized polynomial equations that students can investigate using computers or graphing calculators. Students write reports of their efforts to find and classify all real roots of their equation. (MDH)
Calculators and Polynomial Evaluation.
ERIC Educational Resources Information Center
Weaver, J. F.
The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized.…
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.
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…
Determinants and Polynomial Root Structure
ERIC Educational Resources Information Center
De Pillis, L. G.
2005-01-01
A little known property of determinants is developed in a manner accessible to beginning undergraduates in linear algebra. Using the language of matrix theory, a classical result by Sylvester that describes when two polynomials have a common root is recaptured. Among results concerning the structure of polynomial roots, polynomials with pairs of…
Interpolation algorithm of Leverrier?Faddev type for polynomial matrices
NASA Astrophysics Data System (ADS)
Petkovic, Marko; Stanimirovic, Predrag
2006-07-01
We investigated an interpolation algorithm for computing outer inverses of a given polynomial matrix, based on the Leverrier?Faddeev method. This algorithm is a continuation of the finite algorithm for computing generalized inverses of a given polynomial matrix, introduced in [11]. Also, a method for estimating the degrees of polynomial matrices arising from the Leverrier?Faddeev algorithm is given as the improvement of the interpolation algorithm. Based on similar idea, we introduced methods for computing rank and index of polynomial matrix. All algorithms are implemented in the symbolic programming language MATHEMATICA , and tested on several different classes of test examples.
NASA Astrophysics Data System (ADS)
Wong-Loya, J. A.; Andaverde, J.; Santoyo, E.
2012-12-01
A new practical method based on rational polynomial (RP) functions to estimate the static formation temperatures (SFT) in geothermal and petroleum boreholes is described. Thermal recovery processes involved during borehole drilling and completion operations were represented by mathematical asymptotic trends. Measurements of bottom-hole temperature and shut-in times (at least three or more) have been used both to obtain a mathematical function that describes the thermal recovery process of drilled boreholes, and to estimate the SFT. Using build-up temperature logs, the SFT have been reliably estimated with precision and accuracy. With these results, it was successfully demonstrated that the new RP method provides a practical tool for the reliable prediction of SFT in geothermal and petroleum boreholes.
Some discrete multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
Independence polynomial and matching polynomial of the Koch network
NASA Astrophysics Data System (ADS)
Liao, Yunhua; Xie, Xiaoliang
2015-11-01
The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “#P-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.
Orthogonal polynomials and tolerancing
NASA Astrophysics Data System (ADS)
Rogers, John R.
2011-10-01
Previous papers have established the inadvisability of applying tolerances directly to power-series aspheric coefficients. The basic reason is that the individual terms are far from orthogonal. Zernike surfaces and the new Forbes surface types have certain orthogonality properties over the circle described by the "normalization radius." However, at surfaces away from the stop, the optical beam is smaller than the surface, and the polynomials are not orthogonal over the area sampled by the beam. In this paper, we investigate the breakdown of orthogonality as the surface moves away from the aperture stop, and the implications of this to tolerancing.
NASA Astrophysics Data System (ADS)
Laksâ, Arne
2015-11-01
B-splines are the de facto industrial standard for surface modelling in Computer Aided design. It is comparable to bend flexible rods of wood or metal. A flexible rod minimize the energy when bending, a third degree polynomial spline curve minimize the second derivatives. B-spline is a nice way of representing polynomial splines, it connect polynomial splines to corner cutting techniques, which induces many nice and useful properties. However, the B-spline representation can be expanded to something we can call general B-splines, i.e. both polynomial and non-polynomial splines. We will show how this expansion can be done, and the properties it induces, and examples of non-polynomial B-spline.
NASA Astrophysics Data System (ADS)
Chaves, Rafael
2016-01-01
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
NASA Astrophysics Data System (ADS)
Zhang, Xu
This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange attractors, and shows that some maps are chaotic in the sense of Li-Yorke or Devaney. This type of maps includes both the Logistic map and the Hénon map. For some diffeomorphisms with the expansion dimension equal to one or two in three-dimensional spaces, the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets on which the systems are topologically conjugate to the two-sided fullshift on finite alphabet are obtained; for some expanding maps, the chaotic region is analyzed by using the coupled-expansion theory and the Brouwer degree theory. For three types of higher-dimensional polynomial maps with degree two, the conditions under which there are Smale horseshoes and uniformly hyperbolic invariant sets are given, and the topological conjugacy between the maps on the invariant sets and the two-sided fullshift on finite alphabet is obtained. Some interesting maps with chaotic attractors and positive Lyapunov exponents in three-dimensional spaces are found by using computer simulations. In the end, two examples are provided to illustrate the theoretical results.
Molecular Insights into the Enigmatic Metabolic Regulator, SnRK1.
Emanuelle, Shane; Doblin, Monika S; Stapleton, David I; Bacic, Antony; Gooley, Paul R
2016-04-01
Sucrose non-fermenting-1 (SNF1)-related kinase 1 (SnRK1) lies at the heart of metabolic homeostasis in plants and is crucial for normal development and response to stress. Evolutionarily related to SNF1 in yeast and AMP-activated kinase (AMPK) in mammals, SnRK1 acts protectively to maintain homeostasis in the face of fluctuations in energy status. Despite a conserved function, the structure and regulation of the plant kinase differ considerably from its relatively well-understood opisthokont orthologues. In this review, we highlight the known plant-specific modes of regulation involving SnRK1 together with new insights based on a 3D molecular model of the kinase. We also summarise how these differences from other orthologues may be specific adaptations to plant metabolism, and offer insights into possible avenues of future inquiry into this enigmatic enzyme. PMID:26642889
Satellite Orbital Interpolation using Tchebychev Polynomials
NASA Astrophysics Data System (ADS)
Richard, Jean-Yves; Deleflie, Florent; Edorh, Sémého
2014-05-01
A satellite or artificial probe orbit is made of time series of orbital elements such as state vectors (position and velocities, keplerian orbital elements) given at regular or irregular time intervals. These time series are fitted to observations, so that differences between observations (distance, radial velocity) and the theoretical quantity be minimal, according to a statistical criterion, mostly based on the least-squared algorithm. These computations are carried out using dedicated software, such as the GINS used by GRGS, mainly at CNES Toulouse and Paris Observatory. From an operational point of view, time series of orbital elements are 7-day long. Depending on the dynamical configurations, more generally, they can typically vary from a couple of days to some weeks. One of the fundamental parameters to be adjusted is the initial state vector. This can lead to time gaps, at the level of a few dozen of centimetres between the last point of a time series to the first one of the following data set. The objective of this presentation consists in the improvement of an interpolation method freed itself of such possible "discontinuities" resulting between satellite's orbit arcs when a new initial bulletin is adjusted. We compare solutions of different Satellite Laser Ranging using interpolation methods such as Lagrange polynomial, spline cubic, Tchebychev orthogonal polynomial and cubic Hermite polynomial. These polynomial coefficients are used to reconstruct and interpolate the satellite orbits without time gaps and discontinuities and requiring a weak memory size. In this approach, we have tested the orbital reconstruction using Tchebychev polynomial coefficients for the LAGEOS and Starlette satellites. In this presentation, it is showed that Tchebychev's polynomial interpolation can achieve accuracy in the orbit reconstruction at the sub-centimetre level and allowing a gain of a factor 5 of memory size of the satellite orbit with respect to the Cartesian
On a Perplexing Polynomial Puzzle
ERIC Educational Resources Information Center
Richmond, Bettina
2010-01-01
It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…
Graphical Solution of Polynomial Equations
ERIC Educational Resources Information Center
Grishin, Anatole
2009-01-01
Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…
Pollok, Jill R; Johnson, Charles S; Eisenback, J D; Reed, T David
2016-06-01
Most commercial tobacco cultivars possess the Rk1 resistance gene to races 1 and 3 of Meloidogyne incognita and race 1 of Meloidogyne arenaria, which has caused a shift in population prevalence in Virginia tobacco fields toward other species and races. A number of cultivars now also possess the Rk2 gene for root-knot resistance. Experiments were conducted in 2013 to 2014 to examine whether possessing both Rk1 and Rk2 increases resistance to a variant of M. incognita race 3 compared to either gene alone. Greenhouse trials were arranged in a completely randomized design with Coker 371-Gold (C371G; susceptible), NC 95 and SC 72 (Rk1Rk1), T-15-1-1 (Rk2Rk2), and STNCB-2-28 and NOD 8 (Rk1Rk1 and Rk2Rk2). Each plant was inoculated with 5,000 root-knot nematode eggs; data were collected 60 d postinoculation. Percent galling and numbers of egg masses and eggs were counted, the latter being used to calculate the reproductive index on each host. Despite variability, entries with both Rk1 and Rk2 conferred greater resistance to a variant of M. incognita race 3 than plants with Rk1 or Rk2 alone. Entries with Rk1 alone were successful in reducing root galling and nematode reproduction compared to the susceptible control. Entry T-15-1-1 did not reduce galling compared to the susceptible control but often suppressed reproduction. PMID:27418700
Pollok, Jill R.; Johnson, Charles S.; Eisenback, J. D.; Reed, T. David
2016-01-01
Most commercial tobacco cultivars possess the Rk1 resistance gene to races 1 and 3 of Meloidogyne incognita and race 1 of Meloidogyne arenaria, which has caused a shift in population prevalence in Virginia tobacco fields toward other species and races. A number of cultivars now also possess the Rk2 gene for root-knot resistance. Experiments were conducted in 2013 to 2014 to examine whether possessing both Rk1 and Rk2 increases resistance to a variant of M. incognita race 3 compared to either gene alone. Greenhouse trials were arranged in a completely randomized design with Coker 371-Gold (C371G; susceptible), NC 95 and SC 72 (Rk1Rk1), T-15-1-1 (Rk2Rk2), and STNCB-2-28 and NOD 8 (Rk1Rk1 and Rk2Rk2). Each plant was inoculated with 5,000 root-knot nematode eggs; data were collected 60 d postinoculation. Percent galling and numbers of egg masses and eggs were counted, the latter being used to calculate the reproductive index on each host. Despite variability, entries with both Rk1 and Rk2 conferred greater resistance to a variant of M. incognita race 3 than plants with Rk1 or Rk2 alone. Entries with Rk1 alone were successful in reducing root galling and nematode reproduction compared to the susceptible control. Entry T-15-1-1 did not reduce galling compared to the susceptible control but often suppressed reproduction. PMID:27418700
NASA Astrophysics Data System (ADS)
Wong-Loya, J. A.; Santoyo, E.; Andaverde, J. A.; Quiroz-Ruiz, A.
2015-12-01
A Web-Based Computer System (RPM-WEBBSYS) has been developed for the application of the Rational Polynomial Method (RPM) to estimate static formation temperatures (SFT) of geothermal and petroleum wells. The system is also capable to reproduce the full thermal recovery processes occurred during the well completion. RPM-WEBBSYS has been programmed using advances of the information technology to perform more efficiently computations of SFT. RPM-WEBBSYS may be friendly and rapidly executed by using any computing device (e.g., personal computers and portable computing devices such as tablets or smartphones) with Internet access and a web browser. The computer system was validated using bottomhole temperature (BHT) measurements logged in a synthetic heat transfer experiment, where a good matching between predicted and true SFT was achieved. RPM-WEBBSYS was finally applied to BHT logs collected from well drilling and shut-in operations, where the typical problems of the under- and over-estimation of the SFT (exhibited by most of the existing analytical methods) were effectively corrected.
Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials.
Lombardo, Rosaria; Beh, Eric J; Kroonenberg, Pieter M
2016-06-01
The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display-the polynomial biplot. PMID:25791164
NASA Astrophysics Data System (ADS)
Oh, Jaehong; Lee, Changno
2015-02-01
As the need for efficient methods to accurately update and refine geospatial satellite image databases is increasing, we have proposed the use of 3-dimensional digital maps for the fully-automated RPCs bias compensation of high resolution satellite imagery. The basic idea is that the map features are scaled and aligned to the image features, except for the local shift, through the RPCs-based image projection, and then the shifts are automatically determined over the entire image space by template-based edge matching of the heterogeneous data set. This enables modeling of RPCs bias compensation parameters for accurate georeferencing. The map features are selected based on four suggested rules. Experiments were carried out for three Kompsat-2 images and stereo IKONOS images with 1:5000 scale Korean national topographic maps. Image matching performance is discussed with justification of the parameter selection, and the georeferencing accuracy is analyzed. The experimental results showed the automated approach can achieve one-pixel level of georeferencing accuracy, enabling economical hybrid map creation as well as large scale map updates.
Thermodynamic characterization of networks using graph polynomials
NASA Astrophysics Data System (ADS)
Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.
2015-09-01
In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.
Hadamard Factorization of Stable Polynomials
NASA Astrophysics Data System (ADS)
Loredo-Villalobos, Carlos Arturo; Aguirre-Hernández, Baltazar
2011-11-01
The stable (Hurwitz) polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p,q ∈ R[x]:p(x) = anxn+an-1xn-1+...+a1x+a0q(x) = bmx m+bm-1xm-1+...+b1x+b0the Hadamard product (p × q) is defined as (p×q)(x) = akbkxk+ak-1bk-1xk-1+...+a1b1x+a0b0where k = min(m,n). Some results (see [16]) shows that if p,q ∈R[x] are stable polynomials then (p×q) is stable, also, i.e. the Hadamard product is closed; however, the reciprocal is not always true, that is, not all stable polynomial has a factorization into two stable polynomials the same degree n, if n> 4 (see [15]).In this work we will give some conditions to Hadamard factorization existence for stable polynomials.
Orthogonal polynomials and deformed oscillators
NASA Astrophysics Data System (ADS)
Borzov, V. V.; Damaskinsky, E. V.
2015-10-01
In the example of the Fibonacci oscillator, we discuss the construction of oscillator-like systems associated with orthogonal polynomials. We also consider the question of the dimensions of the corresponding Lie algebras.
NASA Astrophysics Data System (ADS)
Rochoux, M. C.; Ricci, S.; Lucor, D.; Cuenot, B.; Trouvé, A.
2014-05-01
This paper is the first part in a series of two articles and presents a data-driven wildfire simulator for forecasting wildfire spread scenarios, at a reduced computational cost that is consistent with operational systems. The prototype simulator features the following components: a level-set-based fire propagation solver FIREFLY that adopts a regional-scale modeling viewpoint, treats wildfires as surface propagating fronts, and uses a description of the local rate of fire spread (ROS) as a function of environmental conditions based on Rothermel's model; a series of airborne-like observations of the fire front positions; and a data assimilation algorithm based on an ensemble Kalman filter (EnKF) for parameter estimation. This stochastic algorithm partly accounts for the non-linearities between the input parameters of the semi-empirical ROS model and the fire front position, and is sequentially applied to provide a spatially-uniform correction to wind and biomass fuel parameters as observations become available. A wildfire spread simulator combined with an ensemble-based data assimilation algorithm is therefore a promising approach to reduce uncertainties in the forecast position of the fire front and to introduce a paradigm-shift in the wildfire emergency response. In order to reduce the computational cost of the EnKF algorithm, a surrogate model based on a polynomial chaos (PC) expansion is used in place of the forward model FIREFLY in the resulting hybrid PC-EnKF algorithm. The performance of EnKF and PC-EnKF is assessed on synthetically-generated simple configurations of fire spread to provide valuable information and insight on the benefits of the PC-EnKF approach as well as on a controlled grassland fire experiment. The results indicate that the proposed PC-EnKF algorithm features similar performance to the standard EnKF algorithm, but at a much reduced computational cost. In particular, the re-analysis and forecast skills of data assimilation strongly relate
NASA Astrophysics Data System (ADS)
Rochoux, M. C.; Ricci, S.; Lucor, D.; Cuenot, B.; Trouvé, A.
2014-11-01
This paper is the first part in a series of two articles and presents a data-driven wildfire simulator for forecasting wildfire spread scenarios, at a reduced computational cost that is consistent with operational systems. The prototype simulator features the following components: an Eulerian front propagation solver FIREFLY that adopts a regional-scale modeling viewpoint, treats wildfires as surface propagating fronts, and uses a description of the local rate of fire spread (ROS) as a function of environmental conditions based on Rothermel's model; a series of airborne-like observations of the fire front positions; and a data assimilation (DA) algorithm based on an ensemble Kalman filter (EnKF) for parameter estimation. This stochastic algorithm partly accounts for the nonlinearities between the input parameters of the semi-empirical ROS model and the fire front position, and is sequentially applied to provide a spatially uniform correction to wind and biomass fuel parameters as observations become available. A wildfire spread simulator combined with an ensemble-based DA algorithm is therefore a promising approach to reduce uncertainties in the forecast position of the fire front and to introduce a paradigm-shift in the wildfire emergency response. In order to reduce the computational cost of the EnKF algorithm, a surrogate model based on a polynomial chaos (PC) expansion is used in place of the forward model FIREFLY in the resulting hybrid PC-EnKF algorithm. The performance of EnKF and PC-EnKF is assessed on synthetically generated simple configurations of fire spread to provide valuable information and insight on the benefits of the PC-EnKF approach, as well as on a controlled grassland fire experiment. The results indicate that the proposed PC-EnKF algorithm features similar performance to the standard EnKF algorithm, but at a much reduced computational cost. In particular, the re-analysis and forecast skills of DA strongly relate to the spatial and temporal
ERIC Educational Resources Information Center
Young, Forrest W.
A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…
Constructing general partial differential equations using polynomial and neural networks.
Zjavka, Ladislav; Pedrycz, Witold
2016-01-01
Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. PMID:26547244
Zernike polynomials for photometric characterization of LEDs
NASA Astrophysics Data System (ADS)
Velázquez, J. L.; Ferrero, A.; Pons, A.; Campos, J.; Hernanz, M. L.
2016-02-01
We propose a method based on Zernike polynomials to characterize photometric quantities and descriptors of light emitting diodes (LEDs) from measurements of the angular distribution of the luminous intensity, such as total luminous flux, BA, inhomogeneity, anisotropy, direction of the optical axis and Lambertianity of the source. The performance of this method was experimentally tested for 18 high-power LEDs from different manufacturers and with different photometric characteristics. A small set of Zernike coefficients can be used to calculate all the mentioned photometric quantities and descriptors. For applications not requiring a great accuracy such as those of lighting design, the angular distribution of the luminous intensity of most of the studied LEDs can be interpolated with only two Zernike polynomials.
On the formulae for the colored HOMFLY polynomials
NASA Astrophysics Data System (ADS)
Kawagoe, Kenichi
2016-08-01
We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and links, and we study a generalization of the volume conjecture by means of numerical calculations. In these examples, we observe that asymptotic behaviors of invariants seem to have relations to the volume conjecture.
Using Tutte polynomials to analyze the structure of the benzodiazepines
NASA Astrophysics Data System (ADS)
Cadavid Muñoz, Juan José
2014-05-01
Graph theory in general and Tutte polynomials in particular, are implemented for analyzing the chemical structure of the benzodiazepines. Similarity analysis are used with the Tutte polynomials for finding other molecules that are similar to the benzodiazepines and therefore that might show similar psycho-active actions for medical purpose, in order to evade the drawbacks associated to the benzodiazepines based medicine. For each type of benzodiazepines, Tutte polynomials are computed and some numeric characteristics are obtained, such as the number of spanning trees and the number of spanning forests. Computations are done using the computer algebra Maple's GraphTheory package. The obtained analytical results are of great importance in pharmaceutical engineering. As a future research line, the usage of the chemistry computational program named Spartan, will be used to extent and compare it with the obtained results from the Tutte polynomials of benzodiazepines.
Georeferencing CAMS data: Polynomial rectification and beyond
NASA Astrophysics Data System (ADS)
Yang, Xinghe
The Calibrated Airborne Multispectral Scanner (CAMS) is a sensor used in the commercial remote sensing program at NASA Stennis Space Center. In geographic applications of the CAMS data, accurate geometric rectification is essential for the analysis of the remotely sensed data and for the integration of the data into Geographic Information Systems (GIS). The commonly used rectification techniques such as the polynomial transformation and ortho rectification have been very successful in the field of remote sensing and GIS for most remote sensing data such as Landsat imagery, SPOT imagery and aerial photos. However, due to the geometric nature of the airborne line scanner which has high spatial frequency distortions, the polynomial model and the ortho rectification technique in current commercial software packages such as Erdas Imagine are not adequate for obtaining sufficient geometric accuracy. In this research, the geometric nature, especially the major distortions, of the CAMS data has been described. An analytical step-by-step geometric preprocessing has been utilized to deal with the potential high frequency distortions of the CAMS data. A generic sensor-independent photogrammetric model has been developed for the ortho-rectification of the CAMS data. Three generalized kernel classes and directional elliptical basis have been formulated into a rectification model of summation of multisurface functions, which is a significant extension to the traditional radial basis functions. The preprocessing mechanism has been fully incorporated into the polynomial, the triangle-based finite element analysis as well as the summation of multisurface functions. While the multisurface functions and the finite element analysis have the characteristics of localization, piecewise logic has been applied to the polynomial and photogrammetric methods, which can produce significant accuracy improvement over the global approach. A software module has been implemented with full
General complex polynomial root solver
NASA Astrophysics Data System (ADS)
Skowron, J.; Gould, A.
2012-12-01
This general complex polynomial root solver, implemented in Fortran and further optimized for binary microlenses, uses a new algorithm to solve polynomial equations and is 1.6-3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement, when compared to naive solvers, comes from a fail-safe procedure that permits skipping the majority of the calculations in the great majority of cases, without risking catastrophic failure in the few cases that these are actually required.
On the minimum polynomial of supermatrices
NASA Astrophysics Data System (ADS)
Fellouris, Anargyros G.; Matiadou, Lina K.
2002-11-01
In this paper, a new selection of factors for the construction of the minimum polynomial of a supermatrix M is proposed, leading to null polynomials of M of lower degree than the degree of the corresponding polynomial obtained by using the method proposed in the work of Urrutia and Morales [1]. The case of (1 + 1) × (1 + 1) supermatrices has been completely discussed. Moreover, the main theorem concerning the construction of the minimum polynomial as a product of factors from the characteristic polynomial in the general case of (m + n) × (m + n) supermatrices is given. Finally, we prove that the minimum polynomial of a supermatrix M, in general, is not unique.
Polynomial Beam Element Analysis Module
Energy Science and Technology Software Center (ESTSC)
2013-05-01
pBEAM (Polynomial Beam Element Analysis Module) is a finite element code for beam-like structures. The methodology uses Euler? Bernoulli beam elements with 12 degrees of freedom (3 translation and 3 rotational at each end of the element).
Optical homodyne tomography with polynomial series expansion
Benichi, Hugo; Furusawa, Akira
2011-09-15
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner function and the marginal distribution, and discretize Fourier space. We show that this technique solves most technical difficulties encountered with kernel deconvolution-based methods and reconstructs overall better and smoother Wigner functions. We also give estimators of the reconstruction errors for both methods and show improvement in noise handling properties and resilience to statistical errors.
SymRK and the nodule vascular system
Sanchez-Lopez, Rosana; Jáuregui, David; Quinto, Carmen
2012-01-01
Symbiotic legume-rhizobia relationship leads to the formation of nitrogen-fixing nodules. Successful nodulation depends on the expression and cross-talk of a batttery of genes, among them SymRK (symbiosis receptor-like kinase), a leucine-rich repeat receptor-like kinase. SymRK is required for the rhizobia invasion of root hairs, as well as for the infection thread and symbiosome formation. Using immunolocalization and downregulation strategies we have recently provided evidence of a new function of PvSymRK in nodulation. We have found that a tight regulation of PvSymRK expression is required for the accurate development of the vascular bundle system in Phaseolus vulgaris nodules. PMID:22580688
A Summation Formula for Macdonald Polynomials
NASA Astrophysics Data System (ADS)
de Gier, Jan; Wheeler, Michael
2016-03-01
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases {t = 1} and {q = 0}, we recover known expressions for the monomial symmetric and Hall-Littlewood polynomials, respectively. Other specializations of our formula give new expressions for the Jack and q-Whittaker polynomials.
Nodal Statistics for the Van Vleck Polynomials
NASA Astrophysics Data System (ADS)
Bourget, Alain
The Van Vleck polynomials naturally arise from the generalized Lamé equation
Restricted Schur polynomials and finite N counting
Collins, Storm
2009-01-15
Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from N=4 SYM to type IIB string theory. In this paper we briefly expound the relationship between the restricted Schur polynomials and the operators forwarded by Brown, Heslop, and Ramgoolam. We then briefly examine the finite N counting of the restricted Schur polynomials.
Modal wavefront reconstruction over general shaped aperture by numerical orthogonal polynomials
NASA Astrophysics Data System (ADS)
Ye, Jingfei; Li, Xinhua; Gao, Zhishan; Wang, Shuai; Sun, Wenqing; Wang, Wei; Yuan, Qun
2015-03-01
In practical optical measurements, the wavefront data are recorded by pixelated imaging sensors. The closed-form analytical base polynomial will lose its orthogonality in the discrete wavefront database. For a wavefront with an irregularly shaped aperture, the corresponding analytical base polynomials are laboriously derived. The use of numerical orthogonal polynomials for reconstructing a wavefront with a general shaped aperture over the discrete data points is presented. Numerical polynomials are orthogonal over the discrete data points regardless of the boundary shape of the aperture. The performance of numerical orthogonal polynomials is confirmed by theoretical analysis and experiments. The results demonstrate the adaptability, validity, and accuracy of numerical orthogonal polynomials for estimating the wavefront over a general shaped aperture from regular boundary to an irregular boundary.
Measuring polynomial invariants of multiparty quantum states
Leifer, M.S.; Linden, N.; Winter, A.
2004-05-01
We present networks for directly estimating the polynomial invariants of multiparty quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multiparty states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multiqubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.
Quadratic-Like Dynamics of Cubic Polynomials
NASA Astrophysics Data System (ADS)
Blokh, Alexander; Oversteegen, Lex; Ptacek, Ross; Timorin, Vladlen
2016-02-01
A small perturbation of a quadratic polynomial f with a non-repelling fixed point gives a polynomial g with an attracting fixed point and a Jordan curve Julia set, on which g acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.
NASA Astrophysics Data System (ADS)
Leont'ev, V. K.
2015-11-01
A pseudo-Boolean function is an arbitrary mapping of the set of binary n-tuples to the real line. Such functions are a natural generalization of classical Boolean functions and find numerous applications in various applied studies. Specifically, the Fourier transform of a Boolean function is a pseudo-Boolean function. A number of facts associated with pseudo-Boolean polynomials are presented, and their applications to well-known discrete optimization problems are described.
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.
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.
Solutions of interval type-2 fuzzy polynomials using a new ranking method
NASA Astrophysics Data System (ADS)
Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani
2015-10-01
A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.
Properties of convergence for [omega],q-Bernstein polynomials
NASA Astrophysics Data System (ADS)
Wang, Heping
2008-04-01
In this paper, we discuss properties of the [omega],q-Bernstein polynomials introduced by S. Lewanowicz and P. Wozny in [S. Lewanowicz, P. Wozny, Generalized Bernstein polynomials, BIT 44 (1) (2004) 63-78], where f[set membership, variant]C[0,1], [omega],q>0, [omega][not equal to]1,q-1,...,q-n+1. When [omega]=0, we recover the q-Bernstein polynomials introduced by [G.M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511-518]; when q=1, we recover the classical Bernstein polynomials. We compute the second moment of , and demonstrate that if f is convex and [omega],q[set membership, variant](0,1) or (1,[infinity]), then are monotonically decreasing in n for all x[set membership, variant][0,1]. We prove that for [omega][set membership, variant](0,1), qn[set membership, variant](0,1], the sequence converges to f uniformly on [0,1] for each f[set membership, variant]C[0,1] if and only if limn-->[infinity]qn=1. For fixed [omega],q[set membership, variant](0,1), we prove that the sequence converges for each f[set membership, variant]C[0,1] and obtain the estimates for the rate of convergence of by the modulus of continuity of f, and the estimates are sharp in the sense of order for Lipschitz continuous functions.
Point estimation of simultaneous methods for solving polynomial equations
NASA Astrophysics Data System (ADS)
Petkovic, Miodrag S.; Petkovic, Ljiljana D.; Rancic, Lidija Z.
2007-08-01
The construction of computationally verifiable initial conditions which provide both the guaranteed and fast convergence of the numerical root-finding algorithm is one of the most important problems in solving nonlinear equations. Smale's "point estimation theory" from 1981 was a great advance in this topic; it treats convergence conditions and the domain of convergence in solving an equation f(z)=0 using only the information of f at the initial point z0. The study of a general problem of the construction of initial conditions of practical interest providing guaranteed convergence is very difficult, even in the case of algebraic polynomials. In the light of Smale's point estimation theory, an efficient approach based on some results concerning localization of polynomial zeros and convergent sequences is applied in this paper to iterative methods for the simultaneous determination of simple zeros of polynomials. We state new, improved initial conditions which provide the guaranteed convergence of frequently used simultaneous methods for solving algebraic equations: Ehrlich-Aberth's method, Ehrlich-Aberth's method with Newton's correction, Borsch-Supan's method with Weierstrass' correction and Halley-like (or Wang-Zheng) method. The introduced concept offers not only a clear insight into the convergence analysis of sequences generated by the considered methods, but also explicitly gives their order of convergence. The stated initial conditions are of significant practical importance since they are computationally verifiable; they depend only on the coefficients of a given polynomial, its degree n and initial approximations to polynomial zeros.
Orbifold E-functions of dual invertible polynomials
NASA Astrophysics Data System (ADS)
Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi
2016-08-01
An invertible polynomial is a weighted homogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search for mirror symmetric orbifold Landau-Ginzburg models, P. Berglund and M. Henningson considered a pair (f , G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f ˜ , G ˜) . We consider the so-called orbifold E-function of such a pair (f , G) which is a generating function for the exponents of the monodromy action on an orbifold version of the mixed Hodge structure on the Milnor fibre of f. We prove that the orbifold E-functions of Berglund-Henningson dual pairs coincide up to a sign depending on the number of variables and a simple change of variables. The proof is based on a relation between monomials (say, elements of a monomial basis of the Milnor algebra of an invertible polynomial) and elements of the whole symmetry group of the dual polynomial.
A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories
NASA Technical Reports Server (NTRS)
Narkawicz, Anthony; Munoz, Cesar
2015-01-01
In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.
A new Arnoldi approach for polynomial eigenproblems
Raeven, F.A.
1996-12-31
In this paper we introduce a new generalization of the method of Arnoldi for matrix polynomials. The new approach is compared with the approach of rewriting the polynomial problem into a linear eigenproblem and applying the standard method of Arnoldi to the linearised problem. The algorithm that can be applied directly to the polynomial eigenproblem turns out to be more efficient, both in storage and in computation.
From Jack polynomials to minimal model spectra
NASA Astrophysics Data System (ADS)
Ridout, David; Wood, Simon
2015-01-01
In this note, a deep connection between free field realizations of conformal field theories and symmetric polynomials is presented. We give a brief introduction into the necessary prerequisites of both free field realizations and symmetric polynomials, in particular Jack symmetric polynomials. Then we combine these two fields to classify the irreducible representations of the minimal model vertex operator algebras as an illuminating example of the power of these methods. While these results on the representation theory of the minimal models are all known, this note exploits the full power of Jack polynomials to present significant simplifications of the original proofs in the literature.
The q-Laguerre matrix polynomials.
Salem, Ahmed
2016-01-01
The Laguerre polynomials have been extended to Laguerre matrix polynomials by means of studying certain second-order matrix differential equation. In this paper, certain second-order matrix q-difference equation is investigated and solved. Its solution gives a generalized of the q-Laguerre polynomials in matrix variable. Four generating functions of this matrix polynomials are investigated. Two slightly different explicit forms are introduced. Three-term recurrence relation, Rodrigues-type formula and the q-orthogonality property are given. PMID:27190749
Song, Xueqing; Yu, Xiang; Hori, Chiaki; Demura, Taku; Ohtani, Misato; Zhuge, Qiang
2016-01-01
Subfamily 2 of SNF1-related protein kinase (SnRK2) plays important roles in plant abiotic stress responses as a global positive regulator of abscisic acid signaling. In the genome of the model tree Populus trichocarpa, 12 SnRK2 genes have been identified, and some are upregulated by abiotic stresses. In this study, we heterologously overexpressed the PtSnRK2 genes in Arabidopsis thaliana and found that overexpression of PtSnRK2.5 and PtSnRK2.7 genes enhanced stress tolerance. In the PtSnRK2.5 and PtSnRK2.7 overexpressors, chlorophyll content, and root elongation were maintained under salt stress conditions, leading to higher survival rates under salt stress compared with those in the wild type. Transcriptomic analysis revealed that PtSnRK2.7 overexpression affected stress-related metabolic genes, including lipid metabolism and flavonoid metabolism, even under normal growth conditions. However, the stress response genes reported to be upregulated in Arabidopsis SRK2C/SnRK2.6 and wheat SnRK2.8 overexpressors were not changed by PtSnRK2.7 overexpression. Furthermore, PtSnRK2.7 overexpression widely and largely influenced the transcriptome in response to salt stress; genes related to transport activity, including anion transport-related genes, were characteristically upregulated, and a variety of metabolic genes were specifically downregulated. We also found that the salt stress response genes were greatly upregulated in the PtSnRK2.7 overexpressor. Taken together, poplar subclass 2 PtSnRK2 genes can modulate salt stress tolerance in Arabidopsis, through the activation of cellular signaling pathways in a different manner from that by herbal subclass 2 SnRK2 genes. PMID:27242819
Network meta-analysis of survival data with fractional polynomials
2011-01-01
Background Pairwise meta-analysis, indirect treatment comparisons and network meta-analysis for aggregate level survival data are often based on the reported hazard ratio, which relies on the proportional hazards assumption. This assumption is implausible when hazard functions intersect, and can have a huge impact on decisions based on comparisons of expected survival, such as cost-effectiveness analysis. Methods As an alternative to network meta-analysis of survival data in which the treatment effect is represented by the constant hazard ratio, a multi-dimensional treatment effect approach is presented. With fractional polynomials the hazard functions of interventions compared in a randomized controlled trial are modeled, and the difference between the parameters of these fractional polynomials within a trial are synthesized (and indirectly compared) across studies. Results The proposed models are illustrated with an analysis of survival data in non-small-cell lung cancer. Fixed and random effects first and second order fractional polynomials were evaluated. Conclusion (Network) meta-analysis of survival data with models where the treatment effect is represented with several parameters using fractional polynomials can be more closely fitted to the available data than meta-analysis based on the constant hazard ratio. PMID:21548941
Do r/K reproductive strategies apply to human differences?
Rushton, J P
1988-01-01
This article discusses the r/K theory of Social Biology and how it relates to humans. The symbols r and K originate in the mathematics of population biology and refer to 2 ends of a continuum in which a compensatory exchange occurs between gamete production (the r-strategy) and longevity (the K-strategy). Both across and within species, r and K strategists differ in a suite of correlated characteristics. Humans are the most K of all. K's supposedly have a longer gestation period, a higher birthweight, a more delayed sexual maturation, a lower sex drive, and a longer life. Studies providing evidence for the expected covariation among K attributes are presented. Additional evidence for r/K theory comes from the comparison of human population known to differ in gamete production. The pattern of racial differences observed to occur in sexual behavior has also been found to exist on numerous other indices of K. For instance, there are racial differences in brain size, intelligence, and maturation rate, among others. The findings suggest that, on the average, Mongoloids are more K than Caucasoids, who in turn, are more K than Negroids. Recently conducted studies have extended the data in favor of r/K theory, and further research is currently underway, including whether r/K attributes underlie individual and social class differences in health and longevity. PMID:3241997
On polynomial-time testable combinational circuits
Rao, N.S.V.; Toida, Shunichi
1994-11-01
The problems of identifying several nontrivial classes of Polynomial-Time Testable (PTT) circuits are shown to be NP-complete or harder. First, PTT classes obtained by using circuit decompositions proposed by Fujiwara and Chakradhar et al. are considered. Another type of decompositions, based on fanout-reconvergent (f-r) pairs, which also lead to PTT classes are proposed. The problems of obtaining these decompositions, and also some structurally similar general graph decompositions, are shown to be NP-complete or harder. Then, the problems of recognizing PTT classes formed by the Boolean formulae belonging to the weakly positive, weakly negative, bijunctive and affine classes (proposed by Schaefer) are shown to be NP-complete.
Polynomial chaotic inflation in supergravity
Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T. E-mail: fumi@tuhep.phys.tohoku.ac.jp
2013-08-01
We present a general polynomial chaotic inflation model in supergravity, for which the predicted spectral index and tensor-to-scalar ratio can lie within the 1σ region allowed by the Planck results. Most importantly, the predicted tensor-to-scalar ratio is large enough to be probed in the on-going and future B-mode experiments. We study the inflaton dynamics and the subsequent reheating process in a couple of specific examples. The non-thermal gravitino production from the inflaton decay can be suppressed in a case with a discrete Z{sub 2} symmetry. We find that the reheating temperature can be naturally as high as O(10{sup 9−10}) GeV, sufficient for baryon asymmetry generation through (non-)thermal leptogenesis.
On the Waring problem for polynomial rings
Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris
2012-01-01
In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in . Noticeably, kn coincides with the number obtained by naive dimension count. PMID:22460787
Fractal Trigonometric Polynomials for Restricted Range Approximation
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Point vortex equilibria related to Bessel polynomials
NASA Astrophysics Data System (ADS)
O'Neil, Kevin A.
2016-05-01
The method of polynomials is used to construct two families of stationary point vortex configurations. The vortices are placed at the reciprocals of the zeroes of Bessel polynomials. Configurations that translate uniformly, and configurations that are completely stationary, are obtained in this way.
Wang, Lianzhe; Hu, Wei; Sun, Jiutong; Liang, Xiaoyu; Yang, Xiaoyue; Wei, Shuya; Wang, Xiatian; Zhou, Yi; Xiao, Qiang; Yang, Guangxiao; He, Guangyuan
2015-08-01
The sucrose non-fermenting 1 (SNF1)-related protein kinases (SnRKs) play key roles in plant signaling pathways including responses to biotic and abiotic stresses. Although SnRKs have been systematically studied in Arabidopsis and rice, there is no information concerning SnRKs in the new Poaceae model plant Brachypodium distachyon. In the present study, a total of 44 BdSnRKs were identified and classified into three subfamilies, including three members of BdSnRK1, 10 of BdSnRK2 and 31 of BdSnRK3 (CIPK) subfamilies. Phylogenetic reconstruction, chromosome distribution and synteny analyses suggested that BdSnRK family had been established before the dicot-monocot lineage parted, and had experienced rapid expansion during the process of plant evolution since then. Expression analysis of the BdSnRK2 subfamily showed that the majority of them could respond to abiotic stress and related signal molecules treatments. Protein-protein interaction and co-expression analyses of BdSnRK2s network showed that SnRK2s might be involved in biological pathway different from that of dicot model plant Arabidopsis. Expression of BdSnRK2.9 in tobacco resulted in increased tolerance to drought and salt stresses through activation of NtABF2. Taken together, comprehensive analyses of BdSnRKs would provide a basis for understanding of evolution and function of BdSnRK family. PMID:26089150
PLGA nanoparticle formulation of RK-33: an RNA helicase inhibitor against DDX3
Bol, Guus Martinus; Khan, Raheela; van Voss, Marise Rosa Heerma; Tantravedi, Saritha; Korz, Dorian
2016-01-01
Background The DDX3 helicase inhibitor RK-33 is a newly developed anticancer agent that showed promising results in preclinical research (Bol et al. EMBO Mol Med, 7(5):648–649, 2015). However, due to the physicochemical and pharmacological characteristics of RK-33, we initiated development of alternative formulations of RK-33 by preparing sustained release nanoparticles that can be administered intravenously. Methods In this study, RK-33 was encapsulated in poly(lactic-co-glycolic acid) (PLGA), one of the most well-developed biodegradable polymers, using the emulsion solvent evaporation method. Results Hydrodynamic diameter of RK-33-PLGA nanoparticles was about 245 nm with a negative charge, and RK-33-PLGA nanoparticles had a payload of 1.4 % RK-33. RK-33 was released from the PLGA nanoparticles over 7 days (90 ± 5.7 % released by day 7) and exhibited cytotoxicity to human breast carcinoma MCF-7 cells in a time-dependent manner. Moreover, RK-33-PLGA nanoparticles were well tolerated, and systemic retention of RK-33 was markedly improved in normal mice. Conclusions PLGA nanoparticles have a potential as a parenteral formulation of RK-33. PMID:26330329
Matrix product formula for Macdonald polynomials
NASA Astrophysics Data System (ADS)
Cantini, Luigi; de Gier, Jan; Wheeler, Michael
2015-09-01
We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik-Zamolodchikov equations, which arise by considering representations of the Zamolodchikov-Faddeev and Yang-Baxter algebras in terms of t-deformed bosonic operators. These solutions are generalized probabilities for particle configurations of the multi-species asymmetric exclusion process, and form a basis of the ring of polynomials in n variables whose elements are indexed by compositions. For weakly increasing compositions (anti-dominant weights), these basis elements coincide with non-symmetric Macdonald polynomials. Our formulas imply a natural combinatorial interpretation in terms of solvable lattice models. They also imply that normalizations of stationary states of multi-species exclusion processes are obtained as Macdonald polynomials at q = 1.
Tutte polynomial in functional magnetic resonance imaging
NASA Astrophysics Data System (ADS)
García-Castillón, Marlly V.
2015-09-01
Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.
DIFFERENTIAL CROSS SECTION ANALYSIS IN KAON PHOTOPRODUCTION USING ASSOCIATED LEGENDRE POLYNOMIALS
P. T. P. HUTAURUK, D. G. IRELAND, G. ROSNER
2009-04-01
Angular distributions of differential cross sections from the latest CLAS data sets,6 for the reaction γ + p→K+ + Λ have been analyzed using associated Legendre polynomials. This analysis is based upon theoretical calculations in Ref. 1 where all sixteen observables in kaon photoproduction can be classified into four Legendre classes. Each observable can be described by an expansion of associated Legendre polynomial functions. One of the questions to be addressed is how many associated Legendre polynomials are required to describe the data. In this preliminary analysis, we used data models with different numbers of associated Legendre polynomials. We then compared these models by calculating posterior probabilities of the models. We found that the CLAS data set needs no more than four associated Legendre polynomials to describe the differential cross section data. In addition, we also show the extracted coefficients of the best model.
An algorithm for constructing polynomial systems whose solution space characterizes quantum circuits
NASA Astrophysics Data System (ADS)
Gerdt, Vladimir P.; Severyanov, Vasily M.
2006-05-01
An algorithm and its first implementation in C# are presented for assembling arbitrary quantum circuits on the base of Hadamard and Toffoli gates and for constructing multivariate polynomial systems over the finite field Z II arising when applying the Feynman's sum-over-paths approach to quantum circuits. The matrix elements determined by a circuit can be computed by counting the number of common roots in Z II for the polynomial system associated with the circuit. To determine the number of solutions in Z II for the output polynomial system, one can use the Grobner bases method and the relevant algorithms for computing Grobner bases.
Temperature dependence of gas properties in polynomial form
NASA Astrophysics Data System (ADS)
Andrews, J. R.; Biblarz, O.
1981-01-01
Based on a least-squares polynomial approximation, a procedure is introduced for calculating existing tabular values of thermodynamic and transport properties for common gases. The specific heat at constant pressure is given for 238 gases, the thermal conductivity for 55 gases, the dynamic viscocity for 58 gases, and the second and third virial coefficients for 14 gases. At sufficiently low pressures, ideal gas behavior prevails and temperature may be used as the single independent variable. The algorithm for nested multiplication is presented, optimized for hand-held or desktop electronic calculators. Using the polynomial approximations and a suitable calculator, it is possible to duplicate existing reference source tabular values directly, obviating the need for interpolation or further reference to the tables per se. The accuracy of the calculated values can be within 0.5% of the tabular values. The polynomial coefficients are given in the International System of Units (SI). Methods are presented to calculate the temperature corresponding to a given property value. Extrapolation features of the polynomials are discussed.
The Translated Dowling Polynomials and Numbers
Mangontarum, Mahid M.; Macodi-Ringia, Amila P.; Abdulcarim, Normalah S.
2014-01-01
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.
Heisenberg algebra, umbral calculus and orthogonal polynomials
Dattoli, G.; Levi, D.; Winternitz, P.
2008-05-15
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation [P,M]=1. In ordinary quantum mechanics, P is the derivative and M the coordinate operator. Here, we shall realize P as a second order differential operator and M as a first order integral one. We show that this makes it possible to solve large classes of differential and integrodifferential equations and to introduce new classes of orthogonal polynomials, related to Laguerre polynomials. These polynomials are particularly well suited for describing the so-called flatenned beams in laser theory.
More on rotations as spin matrix polynomials
Curtright, Thomas L.
2015-09-15
Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.
NASA Astrophysics Data System (ADS)
Konakli, Katerina; Sudret, Bruno
2016-09-01
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 the 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
Uncertainty quantification in simulations of epidemics using polynomial chaos.
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
Zhao, Chunyu; Burge, James H
2013-12-16
Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials. PMID:24514717
Inequalities for a polynomial and its derivative
NASA Astrophysics Data System (ADS)
Chanam, Barchand; Dewan, K. K.
2007-12-01
Let , 1[less-than-or-equals, slant][mu][less-than-or-equals, slant]n, be a polynomial of degree n such that p(z)[not equal to]0 in z
Schur Stability Regions for Complex Quadratic Polynomials
ERIC Educational Resources Information Center
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Adapted polynomial chaos expansion for failure detection
Paffrath, M. Wever, U.
2007-09-10
In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem.
Hermite polynomials and quasi-classical asymptotics
Ali, S. Twareque; Engliš, Miroslav
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
Combinatorial and algorithm aspects of hyperbolic polynomials
Gurvits, Leonid I.
2004-01-01
Univariate polynomials with real roots appear quite often in modern combinatorics, especially in the context of integer polytopes. We discovered in this paper rather unexpected and very likely far-reaching connections between hyperbolic polynomials and many classical combinatorial and algorithmic problems. There are still several open problems. The most interesting is a hyperbolic generalization of the van der Waerden conjecture for permanents of doubly stochastic matrices.
Stochastic processes with orthogonal polynomial eigenfunctions
NASA Astrophysics Data System (ADS)
Griffiths, Bob
2009-12-01
Markov processes which are reversible with either Gamma, Normal, Poisson or Negative Binomial stationary distributions in the Meixner class and have orthogonal polynomial eigenfunctions are characterized as being processes subordinated to well-known diffusion processes for the Gamma and Normal, and birth and death processes for the Poisson and Negative Binomial. A characterization of Markov processes with Beta stationary distributions and Jacobi polynomial eigenvalues is also discussed.
ERIC Educational Resources Information Center
Schweizer, Karl
2006-01-01
A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…
On the cardinality of twelfth degree polynomial
NASA Astrophysics Data System (ADS)
Lasaraiya, S.; Sapar, S. H.; Johari, M. A. Mohamat
2016-06-01
Let p be a prime and f (x, y) be a polynomial in Zp[x, y]. It is defined that the exponential sums associated with f modulo a prime pα is S (f :q )= ∑ e2/π i f (x ) q for α >1 , where f (x) is in Z[x] and the sum is taken over a complete set of residues x modulo positive integer q. Previous studies has shown that estimation of S (f; pα) is depends on the cardinality of the set of solutions to congruence equation associated with the polynomial. In order to estimate the cardinality, we need to have the value of p-adic sizes of common zeros of partial derivative polynomials associated with polynomial. Hence, p-adic method and newton polyhedron technique will be applied to this approach. After that, indicator diagram will be constructed and analyzed. The cardinality will in turn be used to estimate the exponential sums of the polynomials. This paper concentrates on the cardinality of the set of solutions to congruence equation associated with polynomial in the form of f (x, y) = ax12 + bx11y + cx10y2 + sx + ty + k.
Frameworks for Logically Classifying Polynomial-Time Optimisation Problems
NASA Astrophysics Data System (ADS)
Gate, James; Stewart, Iain A.
We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P ≠ NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision versions are NP-complete. We propose an alternative logical framework, based around inflationary fixed-point logic, and show that we can capture the above classes of optimisation problems. We use the inductive depth of an inflationary fixed-point as a means to describe the objective functions of the instances of our optimisation problems.
Beta-integrals and finite orthogonal systems of Wilson polynomials
Neretin, Yu A
2002-08-31
The integral is calculated and the system of orthogonal polynomials with weight equal to the corresponding integrand is constructed. This weight decreases polynomially, therefore only finitely many of its moments converge. As a result the system of orthogonal polynomials is finite. Systems of orthogonal polynomials related to {sub 5}H{sub 5}-Dougall's formula and the Askey integral is also constructed. All the three systems consist of Wilson polynomials outside the domain of positiveness of the usual weight.
Quasi-kernel polynomials and convergence results for quasi-minimal residual iterations
NASA Technical Reports Server (NTRS)
Freund, Roland W.
1992-01-01
Recently, Freund and Nachtigal have proposed a novel polynominal-based iteration, the quasi-minimal residual algorithm (QMR), for solving general nonsingular non-Hermitian linear systems. Motivated by the QMR method, we have introduced the general concept of quasi-kernel polynomials, and we have shown that the QMR algorithm is based on a particular instance of quasi-kernel polynomials. In this paper, we continue our study of quasi-kernel polynomials. In particular, we derive bounds for the norms of quasi-kernel polynomials. These results are then applied to obtain convergence theorems both for the QMR method and for a transpose-free variant of QMR, the TFQMR algorithm.
The Rational Polynomial Coefficients Modification Using Digital Elevation Models
NASA Astrophysics Data System (ADS)
Alidoost, F.; Azizi, A.; Arefi, H.
2015-12-01
The high-resolution satellite imageries (HRSI) are as primary dataset for different applications such as DEM generation, 3D city mapping, change detection, monitoring, and deformation detection. The geo-location information of HRSI are stored in metadata called Rational Polynomial Coefficients (RPCs). There are many methods to improve and modify the RPCs in order to have a precise mapping. In this paper, an automatic approach is presented for the RPC modification using global Digital Elevation Models. The main steps of this approach are: relative digital elevation model generation, shift parameters calculation, sparse point cloud generation and shift correction, and rational polynomial fitting. Using some ground control points, the accuracy of the proposed method is evaluated based on statistical descriptors in which the results show that the geo-location accuracy of HRSI can be improved without using Ground Control Points (GCPs).
Extending a Property of Cubic Polynomials to Higher-Degree Polynomials
ERIC Educational Resources Information Center
Miller, David A.; Moseley, James
2012-01-01
In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…
Recognition of Arabic Sign Language Alphabet Using Polynomial Classifiers
NASA Astrophysics Data System (ADS)
Assaleh, Khaled; Al-Rousan, M.
2005-12-01
Building an accurate automatic sign language recognition system is of great importance in facilitating efficient communication with deaf people. In this paper, we propose the use of polynomial classifiers as a classification engine for the recognition of Arabic sign language (ArSL) alphabet. Polynomial classifiers have several advantages over other classifiers in that they do not require iterative training, and that they are highly computationally scalable with the number of classes. Based on polynomial classifiers, we have built an ArSL system and measured its performance using real ArSL data collected from deaf people. We show that the proposed system provides superior recognition results when compared with previously published results using ANFIS-based classification on the same dataset and feature extraction methodology. The comparison is shown in terms of the number of misclassified test patterns. The reduction in the rate of misclassified patterns was very significant. In particular, we have achieved a 36% reduction of misclassifications on the training data and 57% on the test data.
Time-dependent generalized polynomial chaos
Gerritsma, Marc; Steen, Jan-Bart van der; Vos, Peter; Karniadakis, George
2010-11-01
Generalized polynomial chaos (gPC) has non-uniform convergence and tends to break down for long-time integration. The reason is that the probability density distribution (PDF) of the solution evolves as a function of time. The set of orthogonal polynomials associated with the initial distribution will therefore not be optimal at later times, thus causing the reduced efficiency of the method for long-time integration. Adaptation of the set of orthogonal polynomials with respect to the changing PDF removes the error with respect to long-time integration. In this method new stochastic variables and orthogonal polynomials are constructed as time progresses. In the new stochastic variable the solution can be represented exactly by linear functions. This allows the method to use only low order polynomial approximations with high accuracy. The method is illustrated with a simple decay model for which an analytic solution is available and subsequently applied to the three mode Kraichnan-Orszag problem with favorable results.
Torus Knot Polynomials and Susy Wilson Loops
NASA Astrophysics Data System (ADS)
Giasemidis, Georgios; Tierz, Miguel
2014-12-01
We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.
Chebyshev Polynomials Are Not Always Optimal
NASA Technical Reports Server (NTRS)
Fischer, B.; Freund, E.
1989-01-01
The authors are concerned with the problem of finding among all polynomials of degree at most n and normalized to be 1 at c the one with minimal uniform norm on Epsilon. Here, Epsilon is a given ellipse with both foci on the real axis and c is a given real point not contained in Epsilon. Problems of this type arise in certain iterative matrix computations, and, in this context, it is generally believed and widely referenced that suitably normalized Chebyshev polynomials are optimal for such constrained approximation problems. In this note, the authors show that this is not true in general. Moreover, the authors derive sufficient conditions which guarantee that Chebyshev polynomials are optimal. Also, some numerical examples are presented.
Fitting parametrized polynomials with scattered surface data.
van Ruijven, L J; Beek, M; van Eijden, T M
1999-07-01
Currently used joint-surface models require the measurements to be structured according to a grid. With the currently available tracking devices a large quantity of unstructured surface points can be measured in a relatively short time. In this paper a method is presented to fit polynomial functions to three-dimensional unstructured data points. To test the method spherical, cylindrical, parabolic, hyperbolic, exponential, logarithmic, and sellar surfaces with different undulations were used. The resulting polynomials were compared with the original shapes. The results show that even complex joint surfaces can be modelled with polynomial functions. In addition, the influence of noise and the number of data points was also analyzed. From a surface (diam: 20 mm) which is measured with a precision of 0.2 mm a model can be constructed with a precision of 0.02 mm. PMID:10400359
Minimal residual method stronger than polynomial preconditioning
Faber, V.; Joubert, W.; Knill, E.
1994-12-31
Two popular methods for solving symmetric and nonsymmetric systems of equations are the minimal residual method, implemented by algorithms such as GMRES, and polynomial preconditioning methods. In this study results are given on the convergence rates of these methods for various classes of matrices. It is shown that for some matrices, such as normal matrices, the convergence rates for GMRES and for the optimal polynomial preconditioning are the same, and for other matrices such as the upper triangular Toeplitz matrices, it is at least assured that if one method converges then the other must converge. On the other hand, it is shown that matrices exist for which restarted GMRES always converges but any polynomial preconditioning of corresponding degree makes no progress toward the solution for some initial error. The implications of these results for these and other iterative methods are discussed.
Sun, Liang; Wang, Yan-Ping; Chen, Pei; Ren, Jie; Ji, Kai; Li, Qian; Li, Ping; Dai, Sheng-Jie; Leng, Ping
2011-01-01
In order to characterize the potential transcriptional regulation of core components of abscisic acid (ABA) signal transduction in tomato fruit development and drought stress, eight SlPYL (ABA receptor), seven SlPP2C (type 2C protein phosphatase), and eight SlSnRK2 (subfamily 2 of SNF1-related kinases) full-length cDNA sequences were isolated from the tomato nucleotide database of NCBI GenBank. All SlPYL, SlPP2C, and SlSnRK2 genes obtained are homologous to Arabidopsis AtPYL, AtPP2C, and AtSnRK2 genes, respectively. Based on phylogenetic analysis, SlPYLs and SlSnRK2s were clustered into three subfamilies/subclasses, and all SlPP2Cs belonged to PP2C group A. Within the SlPYL gene family, SlPYL1, SlPYL2, SlPYL3, and SlPYL6 were the major genes involved in the regulation of fruit development. Among them, SlPYL1 and SlPYL2 were expressed at high levels throughout the process of fruit development and ripening; SlPYL3 was strongly expressed at the immature green (IM) and mature green (MG) stages, while SlPYL6 was expressed strongly at the IM and red ripe (RR) stages. Within the SlPP2C gene family, the expression of SlPP2C, SlPP2C3, and SlPP2C4 increased after the MG stage; SlPP2C1 and SlPP2C5 peaked at the B3 stage, while SlPP2C2 and SlPP2C6 changed little during fruit development. Within the SlSnRK2 gene family, the expression of SlSnRK2.2, SlSnRK2.3, SlSnRK2.4, and SlSnRK2C was higher than that of other members during fruit development. Additionally, most SlPYL genes were down-regulated, while most SlPP2C and SlSnRK2 genes were up-regulated by dehydration in tomato leaf. PMID:21873532
Bispectrality of the Complementary Bannai-Ito Polynomials
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2013-03-01
A one-parameter family of operators that have the complementary Bannai-Ito (CBI) polynomials as eigenfunctions is obtained. The CBI polynomials are the kernel partners of the Bannai-Ito polynomials and also correspond to a q→"1 limit of the Askey-Wilson polynomials. The eigenvalue equations for the CBI polynomials are found to involve second order Dunkl shift operators with reflections and exhibit quadratic spectra. The algebra associated to the CBI polynomials is given and seen to be a deformation of the Askey-Wilson algebra with an involution. The relation between the CBI polynomials and the recently discovered dual "1 Hahn and para-Krawtchouk polynomials, as well as their relation with the symmetric Hahn polynomials, is also discussed.
On the derivatives of unimodular polynomials
NASA Astrophysics Data System (ADS)
Nevai, P.; Erdélyi, T.
2016-04-01
Let D be the open unit disk of the complex plane; its boundary, the unit circle of the complex plane, is denoted by \\partial D. Let \\mathscr P_n^c denote the set of all algebraic polynomials of degree at most n with complex coefficients. For λ ≥ 0, let {\\mathscr K}_n^λ \\stackrel{{def}}{=} \\biggl\\{P_n: P_n(z) = \\sumk=0^n{ak k^λ z^k}, ak \\in { C}, |a_k| = 1 \\biggr\\} \\subset {\\mathscr P}_n^c.The class \\mathscr K_n^0 is often called the collection of all (complex) unimodular polynomials of degree n. Given a sequence (\\varepsilon_n) of positive numbers tending to 0, we say that a sequence (P_n) of polynomials P_n\\in\\mathscr K_n^λ is \\{λ, (\\varepsilon_n)\\}-ultraflat if \\displaystyle (1-\\varepsilon_n)\\frac{nλ+1/2}{\\sqrt{2λ+1}}≤\\ve......a +1/2}}{\\sqrt{2λ +1}},\\qquad z \\in \\partial D,\\quad n\\in N_0.Although we do not know, in general, whether or not \\{λ, (\\varepsilon_n)\\}-ultraflat sequences of polynomials P_n\\in\\mathscr K_n^λ exist for each fixed λ>0, we make an effort to prove various interesting properties of them. These allow us to conclude that there are no sequences (P_n) of either conjugate, or plain, or skew reciprocal unimodular polynomials P_n\\in\\mathscr K_n^0 such that (Q_n) with Q_n(z)\\stackrel{{def}}{=} zP_n'(z)+1 is a \\{1,(\\varepsilon_n)\\}-ultraflat sequence of polynomials.Bibliography: 18 titles.
High degree interpolation polynomial in Newton form
NASA Technical Reports Server (NTRS)
Tal-Ezer, Hillel
1988-01-01
Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.
On the Waring problem for polynomial rings.
Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris
2012-04-10
In this note we discuss an analog of the classical Waring problem for C[x0,x1,...,x(n)]. Namely, we show that a general homogeneous polynomial p ∈ C[x0,x1,...,x(n)] of degree divisible by k≥2 can be represented as a sum of at most k(n) k-th powers of homogeneous polynomials in C[x0,x1,...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count. PMID:22460787
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Perturbations around the zeros of classical orthogonal polynomials
NASA Astrophysics Data System (ADS)
Sasaki, Ryu
2015-04-01
Starting from degree N solutions of a time dependent Schrödinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived. The matrix has remarkable Diophantine properties. Its eigenvalues are independent of the zeros. The corresponding eigenvectors provide the representations of the lower degree ( 0 , 1 , … , N - 1 ) polynomials in terms of the zeros of the degree N polynomial. The results are valid universally for all the classical orthogonal polynomials, including the Askey scheme of hypergeometric orthogonal polynomials and its q-analogues.
A transfectant RK13 cell line permissive to classical caprine scrapie prion propagation.
Dassanayake, Rohana P; Zhuang, Dongyue; Truscott, Thomas C; Madsen-Bouterse, Sally A; O'Rourke, Katherine I; Schneider, David A
2016-03-01
To assess scrapie infectivity associated with caprine-origin tissues, bioassay can be performed using kids, lambs or transgenic mice expressing caprine or ovine prion (PRNP) alleles, but the incubation periods are fairly long. Although several classical ovine scrapie prion permissive cell lines with the ability to detect brain-derived scrapie prion have been available, no classical caprine scrapie permissive cell line is currently available. Therefore, the aims of this study were to generate a rabbit kidney epithelial cell line (RK13) stably expressing caprine wild-type PRNP (cpRK13) and then to assess permissiveness of cpRK13 cells to classical caprine scrapie prion propagation. The cpRK13 and plasmid control RK13 (pcRK13) cells were incubated with brain-derived classical caprine scrapie inocula prepared from goats or ovinized transgenic mice (Tg338, express ovine VRQ allele) infected with caprine scrapie. Significant PrP(Sc) accumulation, which is indicative of scrapie prion propagation, was detected by TSE ELISA and immunohistochemistry in cpRK13 cells inoculated with classical caprine scrapie inocula. Western blot analysis revealed the typical proteinase K-resistant 3 PrP(res) isoforms in the caprine scrapie prion inoculated cpRK13 cell lysate. Importantly, PrP(Sc) accumulation was not detected in similarly inoculated pcRK13 cells, whether by TSE ELISA, immunohistochemistry, or western blot. These findings suggest that caprine scrapie prions can be propagated in cpRK13 cells, thus this cell line may be a useful tool for the assessment of classical caprine prions in the brain tissues of goats. PMID:27216989
Simultaneous explanation of the RK and R (D (*)) puzzles
NASA Astrophysics Data System (ADS)
Bhattacharya, Bhubanjyoti; Datta, Alakabha; London, David; Shivashankara, Shanmuka
2015-03-01
At present, there are several hints of lepton flavor non-universality. The LHCb Collaboration has measured RK ≡ B (B+ →K+μ+μ-) / B (B+ →K+e+e-), and the BaBar Collaboration has measured R (D (*)) ≡ B (B bar →D (*) +τ-νbarτ) / B (B bar →D (*) +ℓ-νbarℓ) (ℓ = e , μ). In all cases, the experimental results differ from the standard model predictions by 2- 3 σ. Recently, an explanation of the RK puzzle was proposed in which new physics (NP) generates a neutral-current operator involving only third-generation particles. Now, assuming the scale of NP is much larger than the weak scale, this NP operator must be made invariant under the full SU (3)C × SU (2)L × U(1)Y gauge group. In this Letter, we note that, when this is done, a new charged-current operator can appear, and this can explain the R (D (*)) puzzle. A more precise measurement of the double ratio R (D) / R (D*) can rule out this model.
Information-theoretic lengths of Jacobi polynomials
NASA Astrophysics Data System (ADS)
Guerrero, A.; Sánchez-Moreno, P.; Dehesa, J. S.
2010-07-01
The information-theoretic lengths of the Jacobi polynomials P(α, β)n(x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are investigated. They quantify the spreading of the polynomials along the orthogonality interval [- 1, 1] in a complementary but different way as the root-mean-square or standard deviation because, contrary to this measure, they do not refer to any specific point of the interval. The explicit expressions of the Fisher length are given. The Renyi lengths are found by the use of the combinatorial multivariable Bell polynomials in terms of the polynomial degree n and the parameters (α, β). The Shannon length, which cannot be exactly calculated because of its logarithmic functional form, is bounded from below by using sharp upper bounds to general densities on [- 1, +1] given in terms of various expectation values; moreover, its asymptotics is also pointed out. Finally, several computational issues relative to these three quantities are carefully analyzed.
Piecewise Polynomial Representations of Genomic Tracks
Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz
2012-01-01
Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/. PMID:23166601
Polynomials Generated by the Fibonacci Sequence
NASA Astrophysics Data System (ADS)
Garth, David; Mills, Donald; Mitchell, Patrick
2007-06-01
The Fibonacci sequence's initial terms are F_0=0 and F_1=1, with F_n=F_{n-1}+F_{n-2} for n>=2. We define the polynomial sequence p by setting p_0(x)=1 and p_{n}(x)=x*p_{n-1}(x)+F_{n+1} for n>=1, with p_{n}(x)= sum_{k=0}^{n} F_{k+1}x^{n-k}. We call p_n(x) the Fibonacci-coefficient polynomial (FCP) of order n. The FCP sequence is distinct from the well-known Fibonacci polynomial sequence. We answer several questions regarding these polynomials. Specifically, we show that each even-degree FCP has no real zeros, while each odd-degree FCP has a unique, and (for degree at least 3) irrational, real zero. Further, we show that this sequence of unique real zeros converges monotonically to the negative of the golden ratio. Using Rouche's theorem, we prove that the zeros of the FCP's approach the golden ratio in modulus. We also prove a general result that gives the Mahler measures of an infinite subsequence of the FCP sequence whose coefficients are reduced modulo an integer m>=2. We then apply this to the case that m=L_n, the nth Lucas number, showing that the Mahler measure of the subsequence is phi^{n-1}, where phi=(1+sqrt 5)/2.
On solvable Dirac equation with polynomial potentials
Stachowiak, Tomasz
2011-01-15
One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.
A recursive algorithm for Zernike polynomials
NASA Technical Reports Server (NTRS)
Davenport, J. W.
1982-01-01
The analysis of a function defined on a rotationally symmetric system, with either a circular or annular pupil is discussed. In order to numerically analyze such systems it is typical to expand the given function in terms of a class of orthogonal polynomials. Because of their particular properties, the Zernike polynomials are especially suited for numerical calculations. Developed is a recursive algorithm that can be used to generate the Zernike polynomials up to a given order. The algorithm is recursively defined over J where R(J,N) is the Zernike polynomial of degree N obtained by orthogonalizing the sequence R(J), R(J+2), ..., R(J+2N) over (epsilon, 1). The terms in the preceding row - the (J-1) row - up to the N+1 term is needed for generating the (J,N)th term. Thus, the algorith generates an upper left-triangular table. This algorithm was placed in the computer with the necessary support program also included.
Optimization of Cubic Polynomial Functions without Calculus
ERIC Educational Resources Information Center
Taylor, Ronald D., Jr.; Hansen, Ryan
2008-01-01
In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…
Piecewise polynomial representations of genomic tracks.
Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz
2012-01-01
Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/. PMID:23166601
Polynomial preconditioning for conjugate gradient methods
Ashby, S.F.
1987-12-01
The solution of a linear system of equations, Ax = b, arises in many scientific applications. If A is large and sparse, an iterative method is required. When A is hermitian positive definite (hpd), the conjugate gradient method of Hestenes and Stiefel is popular. When A is hermitian indefinite (hid), the conjugate residual method may be used. If A is ill-conditioned, these methods may converge slowly, in which case a preconditioner is needed. In this thesis we examine the use of polynomial preconditioning in CG methods for both hermitian positive definite and indefinite matrices. Such preconditioners are easy to employ and well-suited to vector and/or parallel architectures. We first show that any CG method is characterized by three matrices: an hpd inner product matrix B, a preconditioning matrix C, and the hermitian matrix A. The resulting method, CG(B,C,A), minimizes the B-norm of the error over a Krylov subspace. We next exploit the versatility of polynomial preconditioners to design several new CG methods. To obtain an optimum preconditioner, we solve a constrained minimax approximation problem. The preconditioning polynomial, C(lambda), is optimum in that it minimizes a bound on the condition number of the preconditioned matrix, p/sub m/(A). An adaptive procedure for dynamically determining the optimum preconditioner is also discussed. Finally, in a variety of numerical experiments, conducted on a Cray X-MP/48, we demonstrate the effectiveness of polynomial preconditioning. 66 ref., 19 figs., 39 tabs.
Polynomial Asymptotes of the Second Kind
ERIC Educational Resources Information Center
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
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.
The ratio monotonicity of the Boros-Moll polynomials
NASA Astrophysics Data System (ADS)
Chen, William Y. C.; Xia, Ernest X. W.
2009-12-01
In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are log-concave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a conjecture which is stronger than Moll's conjecture on the infty -log-concavity.
Herman's Condition and Siegel Disks of Bi-Critical Polynomials
NASA Astrophysics Data System (ADS)
Chéritat, Arnaud; Roesch, Pascale
2016-06-01
We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such polynomials, under a diophantine condition (called Herman's condition) on the rotation number, must have a critical point on their boundaries.
The New Polynomial Invariants of Knots and Links.
ERIC Educational Resources Information Center
Lickorish, W. B. R.; Millett, K. C.
1988-01-01
Knot theory has been inspirational to algebraic and geometric topology. The principal problem has been to ascertain whether two links are equivalent. New methods have been discovered which are effective and simple. Considered are background information; the oriented polynomial; the Jones polynomial; the semioriented polynomial; and calculations,…
The Gibbs Phenomenon for Series of Orthogonal Polynomials
ERIC Educational Resources Information Center
Fay, T. H.; Kloppers, P. Hendrik
2006-01-01
This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…
Inverse of polynomial matrices in the irreducible form
NASA Technical Reports Server (NTRS)
Chang, Fan R.; Shieh, Leang S.; Mcinnis, Bayliss C.
1987-01-01
An algorithm is developed for finding the inverse of polynomial matrices in the irreducible form. The computational method involves the use of the left (right) matrix division method and the determination of linearly dependent vectors of the remainders. The obtained transfer function matrix has no nontrivial common factor between the elements of the numerator polynomial matrix and the denominator polynomial.
An acoustical interpretation of the zeroes of ultraspherical polynomials
NASA Astrophysics Data System (ADS)
Le Vey, Georges
2016-06-01
In 1887, T.J. Stieltjes gave an electrostatical interpretation of the zeroes of Jacobi polynomials. This was extended later to Laguerre and Hermite polynomials by G. Szegö. An analogous interpretation is given here for ultraspherical polynomials in terms of piecewise cylindrical acoustical resonators. xml:lang="fr"
Global Monte Carlo Simulation with High Order Polynomial Expansions
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-12-13
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, possibly increasing the communication across a loosely coupled system and thereby improving convergence over the conventional fission bank approach used in most production Monte Carlo codes. The project examined a number of basis functions, including global Legendre polynomials as well as “local” piecewise polynomials such as finite element hat functions and higher order versions. The global FET showed an improvement in convergence over the conventional fission bank approach. The local FET methods showed some advantages versus global polynomials in handling geometries with discontinuous material properties. The conventional finite element hat functions had the disadvantage that the expansion coefficients could not be estimated directly but had to be obtained by solving a linear system whose matrix elements were estimated. An alternative fission matrix-based response matrix algorithm was formulated. Studies were made of two alternative applications of the FET, one based on the kernel density estimator and one based on Arnoldi’s method of minimized iterations. Preliminary results for both methods indicate improvements in fission source convergence. These developments indicate that the FET has promise for speeding up Monte Carlo fission source
Polynomial search and global modeling: Two algorithms for modeling chaos.
Mangiarotti, S; Coudret, R; Drapeau, L; Jarlan, L
2012-10-01
Global modeling aims to build mathematical models of concise description. Polynomial Model Search (PoMoS) and Global Modeling (GloMo) are two complementary algorithms (freely downloadable at the following address: http://www.cesbio.ups-tlse.fr/us/pomos_et_glomo.html) designed for the modeling of observed dynamical systems based on a small set of time series. Models considered in these algorithms are based on ordinary differential equations built on a polynomial formulation. More specifically, PoMoS aims at finding polynomial formulations from a given set of 1 to N time series, whereas GloMo is designed for single time series and aims to identify the parameters for a selected structure. GloMo also provides basic features to visualize integrated trajectories and to characterize their structure when it is simple enough: One allows for drawing the first return map for a chosen Poincaré section in the reconstructed space; another one computes the Lyapunov exponent along the trajectory. In the present paper, global modeling from single time series is considered. A description of the algorithms is given and three examples are provided. The first example is based on the three variables of the Rössler attractor. The second one comes from an experimental analysis of the copper electrodissolution in phosphoric acid for which a less parsimonious global model was obtained in a previous study. The third example is an exploratory case and concerns the cycle of rainfed wheat under semiarid climatic conditions as observed through a vegetation index derived from a spatial sensor. PMID:23214661
Possible quantum algorithms for the Bollobas-Riordan-Tutte polynomial of a ribbon graph
NASA Astrophysics Data System (ADS)
Vélez, Mario; Ospina, Juan
2008-04-01
Three possible quantum algorithms, for the computation of the Bollobás-Riordan-Tutte polynomial of a given ribbon graph, are presented and discussed. The first possible algorithm is based on the spanning quasi-trees expansion for generalized Tutte polynomials of generalized graphs and on a quantum version of the Binary Decision Diagram (BDD) for quasi-trees . The second possible algorithm is based on the relation between the Kauffman bracket and the Tutte polynomial; and with an application of the recently introduced Aharonov-Arad-Eban-Landau quantum algorithm. The third possible algorithm is based on the relation between the HOMFLY polynomial and the Tutte polynomial; and with an application of the Wocjan-Yard quantum algorithm. It is claimed that these possible algorithms may be more efficient that the best known classical algorithms. These three algorithms may have interesting applications in computer science at general or in computational biology and bio-informatics in particular. A line for future research based on the categorification project is mentioned.
New optimal polynomial theory for NN-scattering
Rijken, T A; Signell, P
1980-01-01
A new optimal polynomial theory for nucleon-nucleon scattering is presented. For the first time in nucleon-nucleon scattering, the derivative amplitudes originally introduced by Fubini, Furlan, and Rosetti are applied. Based on the properties of these amplitudes we introduce K-matrix functions which have suitable analyticity properties as functions of cos theta, where theta is the center of mass scattering angle. The K-matrix functions enable introduction of a new set of functions for which the optimal mapping techniques of Cutkosky, Deo and Ciulli can be applied. Results are shown for proton-proton phase shift analyses at 210 and 330 MeV.
Cho, Hsing-Yi; Wen, Tuan-Nan; Wang, Ying-Tsui; Shih, Ming-Che
2016-04-01
SNF1 RELATED PROTEIN KINASE 1 (SnRK1) is proposed to be a central integrator of the plant stress and energy starvation signalling pathways. We observed that the Arabidopsis SnRK1.1 dominant negative mutant (SnRK1.1 (K48M) ) had lower tolerance to submergence than the wild type, suggesting that SnRK1.1-dependent phosphorylation of target proteins is important in signalling pathways triggered by submergence. We conducted quantitative phosphoproteomics and found that the phosphorylation levels of 57 proteins increased and the levels of 27 proteins decreased in Col-0 within 0.5-3h of submergence. Among the 57 proteins with increased phosphorylation in Col-0, 38 did not show increased phosphorylation levels in SnRK1.1 (K48M) under submergence. These proteins are involved mainly in sugar and protein synthesis. In particular, the phosphorylation of MPK6, which is involved in regulating ROS responses under abiotic stresses, was disrupted in the SnRK1.1 (K48M) mutant. In addition, PTP1, a negative regulator of MPK6 activity that directly dephosphorylates MPK6, was also regulated by SnRK1.1. We also showed that energy conservation was disrupted in SnRK1.1 (K48M) , mpk6, and PTP1 (S7AS8A) under submergence. These results reveal insights into the function of SnRK1 and the downstream signalling factors related to submergence. PMID:27029354
Cho, Hsing-Yi; Wen, Tuan-Nan; Wang, Ying-Tsui; Shih, Ming-Che
2016-01-01
SNF1 RELATED PROTEIN KINASE 1 (SnRK1) is proposed to be a central integrator of the plant stress and energy starvation signalling pathways. We observed that the Arabidopsis SnRK1.1 dominant negative mutant (SnRK1.1 K48M) had lower tolerance to submergence than the wild type, suggesting that SnRK1.1-dependent phosphorylation of target proteins is important in signalling pathways triggered by submergence. We conducted quantitative phosphoproteomics and found that the phosphorylation levels of 57 proteins increased and the levels of 27 proteins decreased in Col-0 within 0.5–3h of submergence. Among the 57 proteins with increased phosphorylation in Col-0, 38 did not show increased phosphorylation levels in SnRK1.1 K48M under submergence. These proteins are involved mainly in sugar and protein synthesis. In particular, the phosphorylation of MPK6, which is involved in regulating ROS responses under abiotic stresses, was disrupted in the SnRK1.1 K48M mutant. In addition, PTP1, a negative regulator of MPK6 activity that directly dephosphorylates MPK6, was also regulated by SnRK1.1. We also showed that energy conservation was disrupted in SnRK1.1 K48M, mpk6, and PTP1 S7AS8A under submergence. These results reveal insights into the function of SnRK1 and the downstream signalling factors related to submergence. PMID:27029354
NASA Astrophysics Data System (ADS)
Sakarya, Ufuk; Hakkı Demirhan, İsmail; Seda Deveci, Hüsne; Teke, Mustafa; Demirkesen, Can; Küpçü, Ramazan; Feray Öztoprak, A.; Efendioğlu, Mehmet; Fehmi Şimşek, F.; Berke, Erdinç; Zübeyde Gürbüz, Sevgi
2016-06-01
TÜBİTAK UZAY has conducted a research study on the use of space-based satellite resources for several aspects of agriculture. Especially, there are two precision agriculture related projects: HASSAS (Widespread application of sustainable precision agriculture practices in Southeastern Anatolia Project Region (GAP) Project) and AKTAR (Smart Agriculture Feasibility Project). The HASSAS project aims to study development of precision agriculture practice in GAP region. Multi-spectral satellite imagery and aerial hyperspectral data along with ground measurements was collected to analyze data in an information system. AKTAR aims to develop models for irrigation, fertilization and spectral signatures of crops in Inner Anatolia. By the end of the project precision agriculture practices to control irrigation, fertilization, pesticide and estimation of crop yield will be developed. Analyzing the phenology of crops using NDVI is critical for the projects. For this reason, absolute radiometric calibration of the Red and NIR bands in space-based satellite sensors is an important issue. The Göktürk-2 satellite is an earth observation satellite which was designed and built in Turkey and was launched in 2012. The Göktürk-2 satellite sensor has a resolution 2.5 meters in panchromatic and 5 meters in R/G/B/NIR bands. The absolute radiometric calibration of the Göktürk-2 satellite sensor was performed via the ground-based measurements - spectra-radiometer, sun photometer, and meteorological station- in Tuz Gölü cal/val site in 2015. In this paper, the first ground-based absolute radiometric calibration results of the Göktürk-2 satellite sensor using Tuz Gölü is demonstrated. The absolute radiometric calibration results of this paper are compared with the published cross-calibration results of the Göktürk-2 satellite sensor utilizing Landsat 8 imagery. According to the experimental comparison results, the Göktürk-2 satellite sensor coefficients for red and NIR bands
Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies
Hampton, Jerrad; Doostan, Alireza
2015-01-01
Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ{sub 1}-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence on the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.
Polynomial Operators on Classes of Regular Languages
NASA Astrophysics Data System (ADS)
Klíma, Ondřej; Polák, Libor
We assign to each positive variety mathcal V and each natural number k the class of all (positive) Boolean combinations of the restricted polynomials, i.e. the languages of the form L_0a_1 L_1a_2dots a_ell L_ell, text{ where } ell≤ k, a 1,...,a ℓ are letters and L 0,...,L ℓ are languages from the variety mathcal V. For this polynomial operator we give a certain algebraic counterpart which works with identities satisfied by syntactic (ordered) monoids of languages considered. We also characterize the property that a variety of languages is generated by a finite number of languages. We apply our constructions to particular examples of varieties of languages which are crucial for a certain famous open problem concerning concatenation hierarchies.
Fast and practical parallel polynomial interpolation
Egecioglu, O.; Gallopoulos, E.; Koc, C.K.
1987-01-01
We present fast and practical parallel algorithms for the computation and evaluation of interpolating polynomials. The algorithms make use of fast parallel prefix techniques for the calculation of divided differences in the Newton representation of the interpolating polynomial. For n + 1 given input pairs the proposed interpolation algorithm requires 2 (log (n + 1)) + 2 parallel arithmetic steps and circuit size O(n/sup 2/). The algorithms are numerically stable and their floating-point implementation results in error accumulation similar to that of the widely used serial algorithms. This is in contrast to other fast serial and parallel interpolation algorithms which are subject to much larger roundoff. We demonstrate that in a distributed memory environment context, a cube connected system is very suitable for the algorithms' implementation, exhibiting very small communication cost. As further advantages we note that our techniques do not require equidistant points, preconditioning, or use of the Fast Fourier Transform. 21 refs., 4 figs.
Cabling procedure for the colored HOMFLY polynomials
NASA Astrophysics Data System (ADS)
Anokhina, A. S.; Morozov, A. A.
2014-02-01
We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We describe how it can be used and how the projectors and -matrices needed for this procedure can be found. The constructed matrix expressions for the projectors and -matrices in the fundamental representation allow calculating the HOMFLY polynomial in an arbitrary representation for an arbitrary knot. The computational algorithm can be used for the knots and links with ¦ Q¦ m ≤ 12, where m is the number of strands in a braid representation of the knot and ¦ Q¦ is the number of boxes in the Young diagram of the representation. We also discuss the justification of the cabling procedure from the group theory standpoint, deriving expressions for the fundamental -matrices and clarifying some conjectures formulated in previous papers.
The basic function scheme of polynomial type
WU, Wang-yi; Lin, Guang
2009-12-01
A new numerical method---Basic Function Method is proposed. This method can directly discrete differential operator on unstructured grids. By using the expansion of basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as basic function and applying the technique of flux splitting method and the combination of central and upwind schemes to suppress the non-physical fluctuation near the shock wave, the second-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical results of many typical examples for two dimensional inviscid compressible transonic and supersonic steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave. Especially, combining with the adaptive remeshing technique, the satisfactory results can be obtained by these schemes.
On computing factors of cyclotomic polynomials
NASA Astrophysics Data System (ADS)
Brent, Richard P.
1993-07-01
For odd square-free n > 1 the cyclotomic polynomial {Φ_n}(x) satisfies the identity of Gauss, 4{Φ_n}(x) = A_n^2 - {( - 1)^{(n - 1)/2}}nB_n^2. A similar identity of Aurifeuille, Le Lasseur, and Lucas is {Φ_n}({( - 1)^{(n - 1)/2}}x) = C_n^2 - nxD_n^2 or, in the case that n is even and square-free, ± {Φ_{n/2}}( - {x^2}) = C_n^2 - nxD_n^2. Here, {A_n}(x), ldots ,{D_n}(x) are polynomials with integer coefficients. We show how these coefficients can be computed by simple algorithms which require O({n^2}) arithmetic operations and work over the integers. We also give explicit formulae and generating functions for {A_n}(x), ldots ,{D_n}(x) , and illustrate the application to integer factorization with some numerical examples.
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Trigonometric Polynomials For Estimation Of Spectra
NASA Technical Reports Server (NTRS)
Greenhall, Charles A.
1990-01-01
Orthogonal sets of trigonometric polynomials used as suboptimal substitutes for discrete prolate-spheroidal "windows" of Thomson method of estimation of spectra. As used here, "windows" denotes weighting functions used in sampling time series to obtain their power spectra within specified frequency bands. Simplified windows designed to require less computation than do discrete prolate-spheroidal windows, albeit at price of some loss of accuracy.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Detecting Prime Numbers via Roots of Polynomials
ERIC Educational Resources Information Center
Dobbs, David E.
2012-01-01
It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…
Vortex knot cascade in polynomial skein relations
NASA Astrophysics Data System (ADS)
Ricca, Renzo L.
2016-06-01
The process of vortex cascade through continuous reduction of topological complexity by stepwise unlinking, that has been observed experimentally in the production of vortex knots (Kleckner & Irvine, 2013), is shown to be reproduced in the branching of the skein relations of knot polynomials (Liu & Ricca, 2015) used to identify topological complexity of vortex systems. This observation can be usefully exploited for predictions of energy-complexity estimates for fluid flows.
Detecting prime numbers via roots of polynomials
NASA Astrophysics Data System (ADS)
Dobbs, David E.
2012-04-01
It is proved that an integer n ≥ 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z n , the ring of integers modulo n, such that each element of Z n is a root of f. This classroom note could find use in any introductory course on abstract algebra or elementary number theory.
Eye aberration analysis with Zernike polynomials
NASA Astrophysics Data System (ADS)
Molebny, Vasyl V.; Chyzh, Igor H.; Sokurenko, Vyacheslav M.; Pallikaris, Ioannis G.; Naoumidis, Leonidas P.
1998-06-01
New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberration, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.
Nested Canalyzing, Unate Cascade, and Polynomial Functions.
Jarrah, Abdul Salam; Raposa, Blessilda; Laubenbacher, Reinhard
2007-09-15
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. In the same context, polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks. Finally, unate cascade functions have been studied in the design of logic circuits and binary decision diagrams. This paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions. Furthermore, it provides a description of nested canalyzing functions as a certain type of Boolean polynomial function. Using the polynomial framework one can show that the class of nested canalyzing functions, or, equivalently, the class of unate cascade functions, forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra. As a corollary of the functional equivalence derived here, a formula in the literature for the number of unate cascade functions provides such a formula for the number of nested canalyzing functions. PMID:18437250
Role of discriminantly separable polynomials in integrable dynamical systems
NASA Astrophysics Data System (ADS)
Dragović, Vladimir; Kukić, Katarina
2014-11-01
Discriminantly separable polynomials of degree two in each of the three variables are considered. Those polynomials are by definition polynomials which discriminants are factorized as the products of the polynomials in one variable. Motivating example for introducing such polynomials is the famous Kowalevski top. Motivated by the role of such polynomials in the Kowalevski top, we generalize Kowalevski's integration procedure on a whole class of systems basically obtained by replacing so called the Kowalevski's fundamental equation by some other instance of the discriminantly separable polynomial. We present also the role of the discriminantly separable polynomils in twowell-known examples: the case of Kirchhoff elasticae and the Sokolov's case of a rigid body in an ideal fluid.
Polynomials and Neural Networks for Gas Turbine Monitoring: a Comparative Study
NASA Astrophysics Data System (ADS)
Loboda, Igor; Feldshteyn, Yakov
2011-09-01
Gas turbine health monitoring includes the common stages of problem detection, fault identification, and prognostics. To extract useful diagnostic information from raw recorded data, these stages require a preliminary operation of computing differences between measurements and an engine baseline, which is a function of engine operating conditions. These deviations of measured values from the baseline data can be good indicators of engine health. However, their quality and the success of all diagnostic stages strongly depend on the adequacy of the baseline model employed and, in particular, on the mathematical techniques applied to create it. To create a baseline model, we have applied polynomials and the least squares method for computing the coefficients over a long period of time. Methods were proposed to enhance such a polynomial-based model. The resulting accuracy was sufficient for reliable monitoring of gas turbine deterioration effects. The polynomials previously investigated thus far are used in the present study as a standard for evaluating artificial neural networks, a very popular technique in gas turbine diagnostics. The focus of this comparative study is to verify whether the use of networks results in a better description of the engine baseline. Extensive field data for two different industrial gas turbines were used to compare these two techniques under various conditions. The deviations were computed for all available data, and the quality of the resulting deviation plots was compared visually. The mean error of the baseline model was used as an additional criterion for comparing the techniques. To find the best network configurations, many network variations were realised and compared with the polynomials. Although the neural networks studied were found to be close to the polynomials in accuracy, they did not exceed the polynomials in any variation. In this way, it seems that polynomials can be successfully used for engine monitoring, at least for
Long-time uncertainty propagation using generalized polynomial chaos and flow map composition
Luchtenburg, Dirk M.; 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 composition 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.
Molecular Mimicry Regulates ABA Signaling by SnRK2 Kinases and PP2C Phosphatases
Soon, Fen-Fen; Ng, Ley-Moy; Zhou, X. Edward; West, Graham M.; Kovach, Amanda; Tan, M.H. Eileen; Suino-Powell, Kelly M.; He, Yuanzheng; Xu, Yong; Chalmers, Michael J.; Brunzelle, Joseph S.; Zhang, Huiming; Yang, Huaiyu; Jiang, Hualiang; Li, Jun; Yong, Eu-Leong; Cutler, Sean; Zhu, Jian-Kang; Griffin, Patrick R.; Melcher, Karsten; Xu, H. Eric
2014-10-02
Abscisic acid (ABA) is an essential hormone for plants to survive environmental stresses. At the center of the ABA signaling network is a subfamily of type 2C protein phosphatases (PP2Cs), which form exclusive interactions with ABA receptors and subfamily 2 Snfl-related kinase (SnRK2s). Here, we report a SnRK2-PP2C complex structure, which reveals marked similarity in PP2C recognition by SnRK2 and ABA receptors. In the complex, the kinase activation loop docks into the active site of PP2C, while the conserved ABA-sensing tryptophan of PP2C inserts into the kinase catalytic cleft, thus mimicking receptor-PP2C interactions. These structural results provide a simple mechanism that directly couples ABA binding to SnRK2 kinase activation and highlight a new paradigm of kinase-phosphatase regulation through mutual packing of their catalytic sites.
Combining fractional polynomial model building with multiple imputation
Morris, Tim P.; White, Ian R.; Carpenter, James R.; Stanworth, Simon J.; Royston, Patrick
2016-01-01
Multivariable fractional polynomial (MFP) models are commonly used in medical research. The datasets in which MFP models are applied often contain covariates with missing values. To handle the missing values, we describe methods for combining multiple imputation with MFP modelling, considering in turn three issues: first, how to impute so that the imputation model does not favour certain fractional polynomial (FP) models over others; second, how to estimate the FP exponents in multiply imputed data; and third, how to choose between models of differing complexity. Two imputation methods are outlined for different settings. For model selection, methods based on Wald-type statistics and weighted likelihood-ratio tests are proposed and evaluated in simulation studies. The Wald-based method is very slightly better at estimating FP exponents. Type I error rates are very similar for both methods, although slightly less well controlled than analysis of complete records; however, there is potential for substantial gains in power over the analysis of complete records. We illustrate the two methods in a dataset from five trauma registries for which a prognostic model has previously been published, contrasting the selected models with that obtained by analysing the complete records only. PMID:26095614
Combining fractional polynomial model building with multiple imputation.
Morris, Tim P; White, Ian R; Carpenter, James R; Stanworth, Simon J; Royston, Patrick
2015-11-10
Multivariable fractional polynomial (MFP) models are commonly used in medical research. The datasets in which MFP models are applied often contain covariates with missing values. To handle the missing values, we describe methods for combining multiple imputation with MFP modelling, considering in turn three issues: first, how to impute so that the imputation model does not favour certain fractional polynomial (FP) models over others; second, how to estimate the FP exponents in multiply imputed data; and third, how to choose between models of differing complexity. Two imputation methods are outlined for different settings. For model selection, methods based on Wald-type statistics and weighted likelihood-ratio tests are proposed and evaluated in simulation studies. The Wald-based method is very slightly better at estimating FP exponents. Type I error rates are very similar for both methods, although slightly less well controlled than analysis of complete records; however, there is potential for substantial gains in power over the analysis of complete records. We illustrate the two methods in a dataset from five trauma registries for which a prognostic model has previously been published, contrasting the selected models with that obtained by analysing the complete records only. PMID:26095614
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.
Replacement of a Björk-Shiley Delrin Aortic Valve Still Functioning after 25 Years
Badak, M. Ismail; Ozkisacik, Erdem Ali; Boga, Mehmet; Gurcun, Ugur; Discigil, Berent
2004-01-01
We report the case of a patient who had undergone implantation of a Björk-Shiley Delrin valve in the aortic position 25 years earlier and who now presented with severe mitral stenosis. The patient underwent mitral valve replacement and aortic valve re-replacement. We review the justification for prophylactic replacement of Björk-Shiley Delrin heart valves. PMID:15562853
NASA Astrophysics Data System (ADS)
Petronilho, J.
2007-08-01
It is well-known that the classical orthogonal polynomials of Jacobi, Bessel, Laguerre and Hermite are solutions of a Sturm-Liouville problem of the type where [sigma] and [tau] are polynomials such that deg[sigma][less-than-or-equals, slant]2 and deg[tau]=1, and [lambda]n is a constant independent of x. Recently, based on the hypergeometric character of the solutions of this differential equation, W. Koepf and M. Masjed-Jamei [A generic formula for the values at the boundary points of monic classical orthogonal polynomials, J. Comput. Appl. Math. 191 (2006) 98-105] found a generic formula, only in terms of the coefficients of [sigma] and [tau], for the values of the classical orthogonal polynomials at the singular points of the above differential hypergeometric equation. In this paper, we generalize the mentioned result giving the analogous formulas for both the classical q-orthogonal polynomials (of the q-Hahn tableau) and the classical D[omega]-orthogonal polynomials. Both are special cases of the classical Hq,[omega]-orthogonal polynomials, which are solutions of the hypergeometric-type difference equation where Hq,[omega] is the difference operator introduced by Hahn, and [sigma], [tau] and [lambda]n being as above. Our approach is algebraic and it does not require hypergeometric functions.
Rk1, a ginsenoside, is a new blocker of vascular leakage acting through actin structure remodeling.
Maeng, Yong-Sun; Maharjan, Sony; Kim, Jeong-Hun; Park, Jeong-Hill; Suk Yu, Young; Kim, Young-Myoung; Kwon, Young-Guen
2013-01-01
Endothelial barrier integrity is essential for vascular homeostasis and increased vascular permeability and has been implicated in many pathological processes, including diabetic retinopathy. Here, we investigated the effect of Rk1, a ginsenoside extracted from sun ginseng, on regulation of endothelial barrier function. In human retinal endothelial cells, Rk1 strongly inhibited permeability induced by VEGF, advanced glycation end-product, thrombin, or histamine. Furthermore, Rk1 significantly reduced the vessel leakiness of retina in a diabetic mouse model. This anti-permeability activity of Rk1 is correlated with enhanced stability and positioning of tight junction proteins at the boundary between cells. Signaling experiments revealed that Rk1 induces phosphorylation of myosin light chain and cortactin, which are critical regulators for the formation of the cortical actin ring structure and endothelial barrier. These findings raise the possibility that ginsenoside Rk1 could be exploited as a novel prototype compound for the prevention of human diseases that are characterized by vascular leakage. PMID:23894330
Perturbing polynomials with all their roots on the unit circle
NASA Astrophysics Data System (ADS)
Mossinghoff, M. J.; Pinner, C. G.; Vaaler, J. D.
1998-10-01
Given a monic real polynomial with all its roots on the unit circle, we ask to what extent one can perturb its middle coefficient and still have a polynomial with all its roots on the unit circle. We show that the set of possible perturbations forms a closed interval of length at most 4, with 4 achieved only for polynomials of the form x(2n) + cx(n) + 1 with c in [-2, 2]. The problem can also be formulated in terms of perturbing the constant coefficient of a polynomial having all its roots in [-1, 1]. If we restrict to integer coefficients, then the polynomials in question are products of cyclotomics. We show that in this case there are no perturbations of length 3 that do not arise from a perturbation of length 4. We also investigate the connection between slightly perturbed products of cyclotomic polynomials and polynomials with small Mahler measure. We describe an algorithm for searching for polynomials with small Mahler measure by perturbing the middle coefficients of products of cyclotomic polynomials. We show that the complexity of this algorithm is O(C-root d), where d is the degree, and we report on the polynomials found by this algorithm through degree 64.
Momentum space orthogonal polynomial projection quantization
NASA Astrophysics Data System (ADS)
Handy, C. R.; Vrinceanu, D.; Marth, C. B.; Gupta, R.
2016-04-01
The orthogonal polynomial projection quantization (OPPQ) is an algebraic method for solving Schrödinger’s equation by representing the wave function as an expansion {{\\Psi }}(x)={\\displaystyle \\sum }n{{{Ω }}}n{P}n(x)R(x) in terms of polynomials {P}n(x) orthogonal with respect to a suitable reference function R(x), which decays asymptotically not faster than the bound state wave function. The expansion coefficients {{{Ω }}}n are obtained as linear combinations of power moments {μ }{{p}}=\\int {x}p{{\\Psi }}(x) {{d}}x. In turn, the {μ }{{p}}'s are generated by a linear recursion relation derived from Schrödinger’s equation from an initial set of low order moments. It can be readily argued that for square integrable wave functions representing physical states {{lim}}n\\to ∞ {{{Ω }}}n=0. Rapidly converging discrete energies are obtained by setting Ω coefficients to zero at arbitrarily high order. This paper introduces an extention of OPPQ in momentum space by using the representation {{Φ }}(k)={\\displaystyle \\sum }n{{{\\Xi }}}n{Q}n(k)T(k), where Q n (k) are polynomials orthogonal with respect to a suitable reference function T(k). The advantage of this new representation is that it can help solving problems for which there is no coordinate space moment equation. This is because the power moments in momentum space are the Taylor expansion coefficients, which are recursively calculated via Schrödinger’s equation. We show the convergence of this new method for the sextic anharmonic oscillator and an algebraic treatment of Gross-Pitaevskii nonlinear equation.
Wavelet approach to accelerator problems. 1: Polynomial dynamics
Fedorova, A.; Zeitlin, M.; Parsa, Z.
1997-05-01
This is the first part of a series of talks in which the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In the general case they have the solution as a multiresolution expansion in the base of compactly supported wavelet basis. The solution is parameterized by solutions of two reduced algebraical problems, one is nonlinear and the second is some linear problem, which is obtained from one of the next wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coefficients. In this paper the authors consider the problem of calculation of orbital motion in storage rings. The key point in the solution of this problem is the use of the methods of wavelet analysis, relatively novel set of mathematical methods, which gives one a possibility to work with well-localized bases in functional spaces and with the general type of operators (including pseudodifferential) in such bases.
Supersymmetric Casimir energy and the anomaly polynomial
NASA Astrophysics Data System (ADS)
Bobev, Nikolay; Bullimore, Mathew; Kim, Hee-Cheol
2015-09-01
We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology S 1 × S D-1 is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.
A polynomial f(R) inflation model
Huang, Qing-Guo
2014-02-01
Motivated by the ultraviolet complete theory of quantum gravity, for example the string theory, we investigate a polynomial f(R) inflation model in detail. We calculate the spectral index and tensor-to-scalar ratio in the f(R) inflation model with the form of f(R) = R + (R{sup 2})/6M{sup 2} + (λn)/2n (R{sup n})/(3M{sup 2}){sup n-1}. Compared to Planck 2013, we find that R{sup n} term should be exponentially suppressed, i.e. |λ{sub n}|∼<10{sup −2n+2.6}.
A polynomial f(R) inflation model
Huang, Qing-Guo
2014-02-19
Motivated by the ultraviolet complete theory of quantum gravity, for example the string theory, we investigate a polynomial f(R) inflation model in detail. We calculate the spectral index and tensor-to-scalar ratio in the f(R) inflation model with the form of f(R)=R+((R{sup 2})/(6M{sup 2}))+((λ{sub n})/(2n))((R{sup n})/((3M{sup 2}){sup n−1})). Compared to Planck 2013, we find that R{sup n} term should be exponentially suppressed, i.e. |λ{sub n}|≲10{sup −2n+2.6}.
A multiple-scale Pascal polynomial for 2D Stokes and inverse Cauchy-Stokes problems
NASA Astrophysics Data System (ADS)
Liu, Chein-Shan; Young, D. L.
2016-05-01
The polynomial expansion method is a useful tool for solving both the direct and inverse Stokes problems, which together with the pointwise collocation technique is easy to derive the algebraic equations for satisfying the Stokes differential equations and the specified boundary conditions. In this paper we propose two novel numerical algorithms, based on a third-first order system and a third-third order system, to solve the direct and the inverse Cauchy problems in Stokes flows by developing a multiple-scale Pascal polynomial method, of which the scales are determined a priori by the collocation points. To assess the performance through numerical experiments, we find that the multiple-scale Pascal polynomial expansion method (MSPEM) is accurate and stable against large noise.
Polynomial invariants for discrimination and classification of four-qubit entanglement
Viehmann, Oliver; Eltschka, Christopher; Siewert, Jens
2011-05-15
The number of entanglement classes in stochastic local operations and classical communication (SLOCC) classifications increases with the number of qubits and is already infinite for four qubits. Criteria for explicitly discriminating and classifying pure states of four and more qubits are highly desirable and therefore at the focus of intense theoretical research. We develop a general criterion for the discrimination of pure N-partite entangled states in terms of polynomial SL(d,C){sup xN} invariants. By means of this criterion, existing SLOCC classifications of four-qubit entanglement are reproduced. Based on this we propose a polynomial classification scheme in which entanglement types are identified through 'tangle patterns'. This scheme provides a practicable way to classify states of arbitrary multipartite systems. Moreover, the use of polynomials induces a corresponding quantification of the different types of entanglement.
Myers, N.J.
1994-12-31
The author gives a hybrid method for the iterative solution of linear systems of equations Ax = b, where the matrix (A) is nonsingular, sparse and nonsymmetric. As in a method developed by Starke and Varga the method begins with a number of steps of the Arnoldi method to produce some information on the location of the spectrum of A. This method then switches to an iterative method based on the Faber polynomials for an annular sector placed around these eigenvalue estimates. The Faber polynomials for an annular sector are used because, firstly an annular sector can easily be placed around any eigenvalue estimates bounded away from zero, and secondly the Faber polynomials are known analytically for an annular sector. Finally the author gives three numerical examples, two of which allow comparison with Starke and Varga`s results. The third is an example of a matrix for which many iterative methods would fall, but this method converges.
Lüchow, Arne; Sturm, Alexander; Schulte, Christoph; Haghighi Mood, Kaveh
2015-02-28
Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a few examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.
Polynomial solutions of the Monge-Ampère equation
Aminov, Yu A
2014-11-30
The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction of such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.
Lin, Chien-Ru; Lee, Kuo-Wei; Chen, Chih-Yu; Hong, Ya-Fang; Chen, Jyh-Long; Lu, Chung-An; Chen, Ku-Ting; Ho, Tuan-Hua David; Yu, Su-May
2014-02-01
In plants, source-sink communication plays a pivotal role in crop productivity, yet the underlying regulatory mechanisms are largely unknown. The SnRK1A protein kinase and transcription factor MYBS1 regulate the sugar starvation signaling pathway during seedling growth in cereals. Here, we identified plant-specific SnRK1A-interacting negative regulators (SKINs). SKINs antagonize the function of SnRK1A, and the highly conserved GKSKSF domain is essential for SKINs to function as repressors. Overexpression of SKINs inhibits the expression of MYBS1 and hydrolases essential for mobilization of nutrient reserves in the endosperm, leading to inhibition of seedling growth. The expression of SKINs is highly inducible by drought and moderately by various stresses, which is likely related to the abscisic acid (ABA)-mediated repression of SnRK1A under stress. Overexpression of SKINs enhances ABA sensitivity for inhibition of seedling growth. ABA promotes the interaction between SnRK1A and SKINs and shifts the localization of SKINs from the nucleus to the cytoplasm, where it binds SnRK1A and prevents SnRK1A and MYBS1 from entering the nucleus. Our findings demonstrate that SnRK1A plays a key role regulating source-sink communication during seedling growth. Under abiotic stress, SKINs antagonize the function of SnRK1A, which is likely a key factor restricting seedling vigor. PMID:24569770
NASA Astrophysics Data System (ADS)
Singh, Manjit; Gupta, R. K.
2016-08-01
Based on binary Bell polynomial approach, the bilinear equation and B a ¨cklund transformations for (3+1)-dimensional Jimbo-Miwa equation are obtained. By virtue of Cole-Hopf transformation, Lax system is constructed by direct linearization of coupled system of binary Bell polynomials. Furthermore, infinite conservation laws are obtained from two field condition in quick and natural way. Finally, a test function of extended three wave method is used to construct multisoliton solutions via bilinear equation.
NASA Astrophysics Data System (ADS)
Fan, Hong-Yi; Lou, Sen-Yue
2015-07-01
Based on the operator Hermite polynomials method (OHPM), we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications. As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials. Project supported by the National Natural Science Foundation of China (Grant No. 11175113).
Monogenic Generalized Hermite Polynomials and Associated Hermite-Bessel Functions
NASA Astrophysics Data System (ADS)
Cação, I.
2010-09-01
A large range of generalizations of the ordinary Hermite polynomials of one or several real or complex variables has been considered by several authors, using different methods. We construct monogenic generalizations of ordinary Hermite polynomials starting from a hypercomplex analogue to the real valued Lahiri exponential generating function. By using specific operational techniques, we derive some of their properties. As an application of the constructed polynomials, we define associated monogenic Hermite-Bessel functions.
Modeling of noise pollution and estimated human exposure around İstanbul Atatürk Airport in Turkey.
Ozkurt, Nesimi; Sari, Deniz; Akdag, Ali; Kutukoglu, Murat; Gurarslan, Aliye
2014-06-01
The level of aircraft noise exposure around İstanbul Atatürk Airport was calculated according to the European Noise Directive. These calculations were based on the actual flight data for each flight in the year 2011. The study area was selected to cover of 25km radius centered on the Aerodrome Reference Point of the airport. The geographical data around İstanbul Atatürk Airport was used to prepare elevation, residential building, auxiliary building, hospital and school layers in SoundPlan software. It was found that 1.2% of the land area of İstanbul City exceeds the threshold of 55dB(A) during daytime. However, when the exceedance of threshold of 65dB(A)is investigated, the affected area is found quite small (0.2% of land area of city). About 0.3% of the land area of İstanbul City has noise levels exceeding 55dB(A) during night-time. Our results show that about 4% of the resident population was exposed to 55dB(A) or higher noises during daytime in İstanbul. When applying the second threshhold criteria, nearly 1% of the population is exposed to noise levels greater than 65dB(A). At night-time, 1.3% of the population is exposed to 55dB(A) or higher noise levels. PMID:23998505
Black brane solutions governed by fluxbrane polynomials
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.
2014-12-01
A family of composite black brane solutions in the model with scalar fields and fields of forms is presented. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat 'internal' spaces. The solutions are governed by moduli functions Hs (s = 1 , … , m) obeying non-linear differential equations with certain boundary conditions imposed. These master equations are equivalent to Toda-like equations and depend upon the non-degenerate (m × m) matrix A. It was conjectured earlier that the functions Hs should be polynomials if A is a Cartan matrix for some semisimple finite-dimensional Lie algebra (of rank m). It is shown that the solutions to master equations may be found by using so-called fluxbrane polynomials which can be calculated (in principle) for any semisimple finite-dimensional Lie algebra. Examples of dilatonic charged black hole (0-brane) solutions related to Lie algebras A1, A2, C2 and G2 are considered.
Seizure prediction using polynomial SVM classification.
Zisheng Zhang; Parhi, Keshab K
2015-08-01
This paper presents a novel patient-specific algorithm for prediction of seizures in epileptic patients with low hardware complexity and low power consumption. In the proposed approach, we first compute the spectrogram of the input fragmented EEG signals from a few electrodes. Each fragmented data clip is ten minutes in duration. Band powers, relative spectral powers and ratios of spectral powers are extracted as features. The features are then subjected to electrode selection and feature selection using classification and regression tree. The baseline experiment uses all features from selected electrodes and these features are then subjected to a radial basis function kernel support vector machine (RBF-SVM) classifier. The proposed method further selects a small number features from the selected electrodes and train a polynomial support vector machine (SVM) classifier with degree of 2 on these features. Prediction performances are compared between the baseline experiment and the proposed method. The algorithm is tested using intra-cranial EEG (iEEG) from the American Epilepsy Society Seizure Prediction Challenge database. The baseline experiment using a large number of features and RBF-SVM achieves a 100% sensitivity and an average AUC of 0.9985, while the proposed algorithm using only a small number of features and polynomial SVM with degree of 2 can achieve a sensitivity of 100.0%, an average area under curve (AUC) of 0.9795. For both experiments, only 10% of the available training data are used for training. PMID:26737598
Generalization ability of fractional polynomial models.
Lei, Yunwen; Ding, Lixin; Ding, Yiming
2014-01-01
In this paper, the problem of learning the functional dependency between input and output variables from scattered data using fractional polynomial models (FPM) is investigated. The estimation error bounds are obtained by calculating the pseudo-dimension of FPM, which is shown to be equal to that of sparse polynomial models (SPM). A linear decay of the approximation error is obtained for a class of target functions which are dense in the space of continuous functions. We derive a structural risk analogous to the Schwartz Criterion and demonstrate theoretically that the model minimizing this structural risk can achieve a favorable balance between estimation and approximation errors. An empirical model selection comparison is also performed to justify the usage of this structural risk in selecting the optimal complexity index from the data. We show that the construction of FPM can be efficiently addressed by the variable projection method. Furthermore, our empirical study implies that FPM could attain better generalization performance when compared with SPM and cubic splines. PMID:24140985
On factorization of generalized Macdonald polynomials
NASA Astrophysics Data System (ADS)
Kononov, Ya.; Morozov, A.
2016-08-01
A remarkable feature of Schur functions—the common eigenfunctions of cut-and-join operators from W_∞ —is that they factorize at the peculiar two-parametric topological locus in the space of time variables, which is known as the hook formula for quantum dimensions of representations of U_q(SL_N) and which plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to generalized Macdonald polynomials (GMPs), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time variables, we discover a weak factorization—on a one- (rather than four-) parametric slice of the topological locus, which is already a very non-trivial property, calling for proof and better understanding.
Using Tutte polynomials to characterize sexual contact networks
NASA Astrophysics Data System (ADS)
Cadavid Muñoz, Juan José
2014-06-01
Tutte polynomials are used to characterize the dynamic and topology of the sexual contact networks, in which pathogens are transmitted as an epidemic. Tutte polynomials provide an algebraic characterization of the sexual contact networks and allow the projection of spread control strategies for sexual transmission diseases. With the usage of Tutte polynomials, it allows obtaining algebraic expressions for the basic reproductive number of different pathogenic agents. Computations are done using the computer algebra software Maple, and it's GraphTheory Package. The topological complexity of a contact network is represented by the algebraic complexity of the correspondent polynomial. The change in the topology of the contact network is represented as a change in the algebraic form of the associated polynomial. With the usage of the Tutte polynomials, the number of spanning trees for each contact network can be obtained. From the obtained results in the polynomial form, it can be said that Tutte polynomials are of great importance for designing and implementing control measures for slowing down the propagation of sexual transmitted pathologies. As a future research line, the analysis of weighted sexual contact networks using weighted Tutte polynomials is considered.
Quantum algorithms for virtual Jones polynomials via Thistlethwaite theorems
NASA Astrophysics Data System (ADS)
Vélez, Mario; Ospina, Juan
2010-04-01
Recently a quantum algorithm for the Jones polynomial of virtual links was proposed by Kauffman and Dye via the implementation of the virtual braid group in anyonic topological quantum computation when the virtual crossings are considered as generalized swap gates. Also recently, a mathematical method for the computation of the Jones polynomial of a given virtual link in terms of the relative Tuttle polynomial of its face (Tait) graph with some suitable variable substitutions was proposed by Diao and Hetyei. The method of Diao and Hetyei is offered as an alternative to the ribbon graph approach according to which the Tutte polynomial of a given virtual link is computed in terms of the Bollobás- Riordan polynomial of the corresponding ribbon graph. The method of Diao and Hetyei can be considered as an extension of the celebrated Thistlethwaite theorem according to which invariant polynomials for knots and links are derived from invariant polynomials for graphs. Starting from these ideas we propose a quantum algorithm for the Jones polynomial of a given virtual link in terms of the generalized Tutte polynomials by exploiting the Thistlethwaite theorem and the Kauffman algorithm . Our method is claimed as the quantum version of the Diao-Hetyei method. Possible supersymmetric implementations of our algortihm are discussed jointly with its formulations using topological quantum lambda calculus.
NASA Astrophysics Data System (ADS)
Afanas'ev, A. P.; Dzyuba, S. M.
2015-10-01
A method for constructing approximate analytic solutions of systems of ordinary differential equations with a polynomial right-hand side is proposed. The implementation of the method is based on the Picard method of successive approximations and a procedure of continuation of local solutions. As an application, the problem of constructing the minimal sets of the Lorenz system is considered.
CAD techniques applied to diesel engine design. Extension of the RK range. [Ruston diesels
Sinha, S.K.; Buckthorpe, D.E.
1980-01-01
Rustion Diesels Ltd. produce three ranges of engines, the AP range covering engine powers from 500 to 1400 bhp (350 to 1000 kW electrical), the RK range covering 1410 to 4200 bhp (1 to 3 MW electrical), and the AT range covering 1650 to 4950 bhp (1-2 to 3-5 MW electrical). The AT engine range is available at speeds up to 600 rev/min, whereas the AP and RK ranges cover engine speeds from 600 to 1000 rev/min. The design philosophy and extension of the RK range of engines are investigated. This is a 251 mm (ten inch) bore by 305mm (twelve inch) stroke engine and is available in 6-cylinder in-line form and 8-, 12-, and 16-cylinder vee form. The RK engine features a cast-iron crankcase and bedplate design with a forged alloy-steel crankshaft. Combustion-chamber components consist of a cast-iron cylinder head and liner, steel exhaust and inlet valves, and a single-piece aluminium piston. The durability and reliability of RK engines have been fully proven in service with over 30 years' experience in numerous applications for power generation, reaction, and marine propulsion.
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.
Experimental evaluation of chromatic dispersion estimation method using polynomial fitting
NASA Astrophysics Data System (ADS)
Jiang, Xin; Wang, Junyi; Pan, Zhongqi
2014-11-01
We experimentally validate a non-data-aided, modulation-format independent chromatic dispersion (CD) estimation method based on polynomial fitting algorithm in single-carrier coherent optical system with a 40 Gb/s polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) system. The non-data-aided CD estimation for arbitrary modulation formats is achieved by measuring the differential phase between frequency f±fs/2 (fs is the symbol rate) in digital coherent receivers. The estimation range for a 40 Gb/s PDM-QPSK signal can be up to 20,000 ps/nm with a measurement accuracy of ±200 ps/nm. The maximum CD measurement is 25,000 ps/nm with a measurement error of 2%.
Predicting Cutting Forces in Aluminum Using Polynomial Classifiers
NASA Astrophysics Data System (ADS)
Kadi, H. El; Deiab, I. M.; Khattab, A. A.
Due to increased calls for environmentally benign machining processes, there has been focus and interest in making processes more lean and agile to enhance efficiency, reduce emissions and increase profitability. One approach to achieving lean machining is to develop a virtual simulation environment that enables fast and reasonably accurate predictions of various machining scenarios. Polynomial Classifiers (PCs) are employed to develop a smart data base that can provide fast prediction of cutting forces resulting from various combinations of cutting parameters. With time, the force model can expand to include different materials, tools, fixtures and machines and would be consulted prior to starting any job. In this work, first, second and third order classifiers are used to predict the cutting coefficients that can be used to determine the cutting forces. Predictions obtained using PCs are compared to experimental results and are shown to be in good agreement.
Polynomial interior-point algorithms for horizontal linear complementarity problem
NASA Astrophysics Data System (ADS)
Wang, G. Q.; Bai, Y. Q.
2009-11-01
In this paper a class of polynomial interior-point algorithms for horizontal linear complementarity problem based on a new parametric kernel function, with parameters p[set membership, variant][0,1] and [sigma]>=1, are presented. The proposed parametric kernel function is not exponentially convex and also not strongly convex like the usual kernel functions, and has a finite value at the boundary of the feasible region. It is used both for determining the search directions and for measuring the distance between the given iterate and the [mu]-center for the algorithm. The currently best known iteration bounds for the algorithm with large- and small-update methods are derived, namely, and , respectively, which reduce the gap between the practical behavior of the algorithms and their theoretical performance results. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p,[sigma] and [theta].
Kinetic term anarchy for polynomial chaotic inflation
NASA Astrophysics Data System (ADS)
Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.
2014-09-01
We argue that there may arise a relatively flat inflaton potential over super-Planckian field values with an approximate shift symmetry, if the coefficients of the kinetic terms for many singlet scalars are subject to a certain random distribution. The inflation takes place along the flat direction with a super-Planckian length, whereas the other light directions can be stabilized by the Hubble-induced mass. The inflaton potential generically contains various shift-symmetry breaking terms, leading to a possibly large deviation of the predicted values of the spectral index and tensor-to-scalar ratio from those of the simple quadratic chaotic inflation. We revisit a polynomial chaotic inflation in supergravity as such.
Orthogonal polynomials for refinable linear functionals
NASA Astrophysics Data System (ADS)
Laurie, Dirk; de Villiers, Johan
2006-12-01
A refinable linear functional is one that can be expressed as a convex combination and defined by a finite number of mask coefficients of certain stretched and shifted replicas of itself. The notion generalizes an integral weighted by a refinable function. The key to calculating a Gaussian quadrature formula for such a functional is to find the three-term recursion coefficients for the polynomials orthogonal with respect to that functional. We show how to obtain the recursion coefficients by using only the mask coefficients, and without the aid of modified moments. Our result implies the existence of the corresponding refinable functional whenever the mask coefficients are nonnegative, even when the same mask does not define a refinable function. The algorithm requires O(n^2) rational operations and, thus, can in principle deliver exact results. Numerical evidence suggests that it is also effective in floating-point arithmetic.
Animating Nested Taylor Polynomials to Approximate a Function
ERIC Educational Resources Information Center
Mazzone, Eric F.; Piper, Bruce R.
2010-01-01
The way that Taylor polynomials approximate functions can be demonstrated by moving the center point while keeping the degree fixed. These animations are particularly nice when the Taylor polynomials do not intersect and form a nested family. We prove a result that shows when this nesting occurs. The animations can be shown in class or…
On P -orderings, rings of integer-valued polynomials, and ultrametric analysis
NASA Astrophysics Data System (ADS)
Bhargava, Manjul
2009-10-01
We introduce two new notions of `` P -ordering'' and use them to define a three-parameter generalization of the usual factorial function. We then apply these notions of P -orderings and factorials to some classical problems in two distinct areas, namely: 1) the study of integer-valued polynomials and 2) P -adic analysis. Specifically, we first use these notions of P -orderings and factorials to construct explicit Polya-style regular bases for two natural families of rings of integer-valued polynomials defined on an arbitrary subset of a Dedekind domain. Second, we classify ``smooth'' functions on an arbitrary compact subset S of a local field, by constructing explicit interpolation series (i.e., orthonormal bases) for the Banach space of functions on S satisfying any desired conditions of continuous differentiability or local analyticity. Our constructions thus extend Mahler's Theorem (classifying the functions that are continuous on {Z}_p ) to a very general setting. In particular, our constructions prove that, for any epsilon>0 , the functions in any of the above Banach spaces can be epsilon -approximated by polynomials (with respect to their respective Banach norms). Thus we obtain the non-Archimedean analogues of the classical polynomial approximation theorems in real and complex analysis proven by Weierstrass, de la Vallee-Poussin, and Bernstein. Our proofs are effective.
Properties of the zeros of generalized basic hypergeometric polynomials
NASA Astrophysics Data System (ADS)
Bihun, Oksana; Calogero, Francesco
2015-11-01
We define the generalized basic hypergeometric polynomial of degree N in terms of the generalized basic hypergeometric function, by choosing one of its parameters to allow the termination of the series after a finite number of summands. In this paper, we obtain a set of nonlinear algebraic equations satisfied by the N zeros of the polynomial. Moreover, we obtain an N × N matrix M defined in terms of the zeros of the polynomial, which, in turn, depend on the parameters of the polynomial. The eigenvalues of this remarkable matrix M are given by neat expressions that depend only on some of the parameters of the polynomial; that is, the matrix M is isospectral. Moreover, in case the parameters that appear in the expressions for the eigenvalues of M are rational, the matrix M has rational eigenvalues, a Diophantine property.
Robust stability of diamond families of polynomials with complex coefficients
NASA Technical Reports Server (NTRS)
Xu, Zhong Ling
1993-01-01
Like the interval model of Kharitonov, the diamond model proves to be an alternative powerful device for taking into account the variation of parameters in prescribed ranges. The robust stability of some kinds of diamond polynomial families with complex coefficients are discussed. By exploiting the geometric characterizations of their value sets, we show that, for the family of polynomials with complex coefficients and both their real and imaginary parts lying in a diamond, the stability of eight specially selected extreme point polynomials is necessary as well as sufficient for the stability of the whole family. For the so-called simplex family of polynomials, four extreme point and four exposed edge polynomials of this family need to be checked for the stability of the entire family. The relations between the stability of various diamonds are also discussed.
Approximating smooth functions using algebraic-trigonometric polynomials
NASA Astrophysics Data System (ADS)
Sharapudinov, Idris I.
2011-01-01
The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p_n(t)+\\tau_m(t), where p_n(t) is an algebraic polynomial of degree n and \\tau_m(t)=a_0+\\sum_{k=1}^ma_k\\cos k\\pi t+b_k\\sin k\\pi t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W^r_\\infty(M) and an upper bound for similar approximations in the class W^r_p(M) with \\frac43 are found. The proof of these estimates uses mixed series in Legendre polynomials which the author has introduced and investigated previously. Bibliography: 13 titles.
Polynomial harmonic GMDH learning networks for time series modeling.
Nikolaev, Nikolay Y; Iba, Hitoshi
2003-12-01
This paper presents a constructive approach to neural network modeling of polynomial harmonic functions. This is an approach to growing higher-order networks like these build by the multilayer GMDH algorithm using activation polynomials. Two contributions for enhancement of the neural network learning are offered: (1) extending the expressive power of the network representation with another compositional scheme for combining polynomial terms and harmonics obtained analytically from the data; (2) space improving the higher-order network performance with a backpropagation algorithm for further gradient descent learning of the weights, initialized by least squares fitting during the growing phase. Empirical results show that the polynomial harmonic version phGMDH outperforms the previous GMDH, a Neurofuzzy GMDH and traditional MLP neural networks on time series modeling tasks. Applying next backpropagation training helps to achieve superior polynomial network performances. PMID:14622880
Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians
NASA Astrophysics Data System (ADS)
Ndayiragije, F.; Van Assche, W.
2013-12-01
Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind.
Nam, Bora; Li, Ganwu; Zheng, Ying; Zhang, Jianqiang; Shuck, Kathleen M.; Timoney, Peter J.
2015-01-01
A high-passage rabbit kidney RK-13 cell line (HP-RK-13[KY], originally derived from the ATCC CCL-37 cell line) used in certain laboratories worldwide is contaminated with noncytopathic bovine viral diarrhea virus (ncpBVDV). On complete genome sequence analysis, the virus strain was found to belong to BVDV group 1b. PMID:26430037
Ng, Ley-Moy; Soon, Fen-Fen; Zhou, X. Edward; West, Graham M.; Kovach, Amanda; Suino-Powell, Kelly M.; Chalmers, Michael J.; Li, Jun; Yong, Eu-Leong; Zhu, Jian-Kang; Griffin, Patrick R.; Melcher, Karsten; Xu, H. Eric
2014-10-02
Abscisic acid (ABA) is an essential hormone that controls plant growth, development, and responses to abiotic stresses. Central for ABA signaling is the ABA-mediated autoactivation of three monomeric Snf1-related kinases (SnRK2.2, -2.3, and -2.6). In the absence of ABA, SnRK2s are kept in an inactive state by forming physical complexes with type 2C protein phosphatases (PP2Cs). Upon relief of this inhibition, SnRK2 kinases can autoactivate through unknown mechanisms. Here, we report the crystal structures of full-length Arabidopsis thaliana SnRK2.3 and SnRK2.6 at 1.9- and 2.3-{angstrom} resolution, respectively. The structures, in combination with biochemical studies, reveal a two-step mechanism of intramolecular kinase activation that resembles the intermolecular activation of cyclin-dependent kinases. First, release of inhibition by PP2C allows the SnRK2s to become partially active because of an intramolecular stabilization of the catalytic domain by a conserved helix in the kinase regulatory domain. This stabilization enables SnRK2s to gain full activity by activation loop autophosphorylation. Autophosphorylation is more efficient in SnRK2.6, which has higher stability than SnRK2.3 and has well-structured activation loop phosphate acceptor sites that are positioned next to the catalytic site. Together, these data provide a structural framework that links ABA-mediated release of PP2C inhibition to activation of SnRK2 kinases.
Conformal Laplace superintegrable systems in 2D: polynomial invariant subspaces
NASA Astrophysics Data System (ADS)
Escobar-Ruiz, M. A.; Miller, Willard, Jr.
2016-07-01
2nd-order conformal superintegrable systems in n dimensions are Laplace equations on a manifold with an added scalar potential and 2n-1 independent 2nd order conformal symmetry operators. They encode all the information about Helmholtz (eigenvalue) superintegrable systems in an efficient manner: there is a 1-1 correspondence between Laplace superintegrable systems and Stäckel equivalence classes of Helmholtz superintegrable systems. In this paper we focus on superintegrable systems in two-dimensions, n = 2, where there are 44 Helmholtz systems, corresponding to 12 Laplace systems. For each Laplace equation we determine the possible two-variate polynomial subspaces that are invariant under the action of the Laplace operator, thus leading to families of polynomial eigenfunctions. We also study the behavior of the polynomial invariant subspaces under a Stäckel transform. The principal new results are the details of the polynomial variables and the conditions on parameters of the potential corresponding to polynomial solutions. The hidden gl 3-algebraic structure is exhibited for the exact and quasi-exact systems. For physically meaningful solutions, the orthogonality properties and normalizability of the polynomials are presented as well. Finally, for all Helmholtz superintegrable solvable systems we give a unified construction of one-dimensional (1D) and two-dimensional (2D) quasi-exactly solvable potentials possessing polynomial solutions, and a construction of new 2D PT-symmetric potentials is established.
NASA Astrophysics Data System (ADS)
Ozcan, O.; Bookhagen, B.; Musaoglu, N.
2012-07-01
meteorological time series. For all images, geometric corrections including digital elevation information and Tasseled Cap transformations were carried out to attain changes in surface reflectance and denoting disturbance of Landsat reflectance data. Consequently, thematic maps of the affected areas were created by using appropriate visualization and classification techniques in conjunction with geographical information system. The resulting dataset was used in a linear trend analysis to characterize spatiotemporal patterns of vegetation-cover development. Analysis has been conducted in ecological units that have been determined by climate and land cover/use. Based on the results of the trend analysis and the primary factor analysis, selected parts of South-eastern Anatolia region are analyzed. The results showed that approximately 368 km2 of agricultural fields have been affected because of inundation due to the Atatürk Dam Lake. However, irrigated agricultural fields have been increased by 56.3% of the total area (1552 km2 of 2756km2) on Harran Plain within the period of 1984 - 2011. This study presents an effective method for time-series analysis that can be used to regularly monitor irrigated fields in the Southeastern Anatolia region.
Generalized Freud's equation and level densities with polynomial potential
NASA Astrophysics Data System (ADS)
Boobna, Akshat; Ghosh, Saugata
2013-08-01
We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.
Ladder operators and recursion relations for the associated Bessel polynomials
NASA Astrophysics Data System (ADS)
Fakhri, H.; Chenaghlou, A.
2006-10-01
Introducing the associated Bessel polynomials in terms of two non-negative integers, and under an integrability condition we simultaneously factorize their corresponding differential equation into a product of the ladder operators by four different ways as shape invariance symmetry equations. This procedure gives four different pairs of recursion relations on the associated Bessel polynomials. In spite of description of Bessel and Laguerre polynomials in terms of each other, we show that the associated Bessel differential equation is factorized in four different ways whereas for Laguerre one we have three different ways.
Symmetrized quartic polynomial oscillators and their partial exact solvability
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2016-04-01
Sextic polynomial oscillator is probably the best known quantum system which is partially exactly alias quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states ψ (x) at certain couplings and energies. In contrast, the apparently simpler and phenomenologically more important quartic polynomial oscillator is not QES. A resolution of the paradox is proposed: The one-dimensional Schrödinger equation is shown QES after the analyticity-violating symmetrization V (x) = A | x | + Bx2 + C | x|3 +x4 of the quartic polynomial potential.
SO(N) restricted Schur polynomials
Kemp, Garreth
2015-02-15
We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d-1 dimensions and type II string theory defined on an AdS space in d-dimensions) dual in the form of type IIB string theory with AdS{sub 5}×RP{sup 5} geometry. With the aim of studying excited giant graviton dynamics, we construct an orthogonal basis for this sector of the gauge theory in this work. First, we demonstrate that the counting of states, as given by the partition function, and the counting of restricted Schur polynomials match by restricting to a particular class of Young diagram labels. We then give an explicit construction of these gauge invariant operators and evaluate their two-point function exactly. This paves the way to studying the spectral problem of these operators and their D-brane duals.
Polynomial method for PLL controller optimization.
Wang, Ta-Chung; Lall, Sanjay; Chiou, Tsung-Yu
2011-01-01
The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach. PMID:22163973
Transfer matrix computation of critical polynomials for two-dimensional Potts models
Jacobsen, Jesper Lykke; Scullard, Christian R.
2013-02-04
We showed, In our previous work, that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial PB(q, v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic two-dimensional lattice. It depends on a finite subgraph B, called the basis, and the manner in which B is tiled to construct the lattice. The real roots v = eK — 1 of PB(q, v) either give the exact critical points for the lattice, or provide approximations that, in principle, can be made arbitrarily accurate by increasing the size ofmore » B in an appropriate way. In earlier work, PB(q, v) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give a probabilistic definition of PB(q, v), which facilitates its computation, using the transfer matrix, on much larger B than was previously possible.We present results for the critical polynomial on the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162, and 243 edges, compared to the limit of 36 edges with contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. The critical temperatures vc obtained for ferromagnetic (v > 0) Potts models are at least as precise as the best available results from Monte Carlo simulations or series expansions. For instance, with q = 3 we obtain vc(4, 82) = 3.742 489 (4), vc(kagome) = 1.876 459 7 (2), and vc(3, 122) = 5.033 078 49 (4), the precision being comparable or superior to the best simulation results. More generally, we trace the critical manifolds in the real (q, v) plane and discuss the intricate structure of the phase diagram in the antiferromagnetic (v < 0) region.« less
Vector-Valued Polynomials and a Matrix Weight Function with B2-Action
NASA Astrophysics Data System (ADS)
Dunkl, Charles F.
2013-01-01
The structure of orthogonal polynomials on {R}^{2} with the weight function \\vert x_{1}^{2}-x_{2}^{2}\\vert ^{2k_{0}}\\vert x_{1}x_{2}\\vert ^{2k_{1}}e^{-( x_{1}^{2}+x_{2}^{2}) /2} is based on the Dunkl operators of type B_{2}. This refers to the full symmetry group of the square, generated by reflections in the lines x_{1}=0 and x_{1}-x_{2}=0. The weight function is integrable if k_{0},k_{1},k_{0} +k_{1}>-1/2. Dunkl operators can be defined for polynomials taking values in a module of the associated reflection group, that is, a vector space on which the group has an irreducible representation. The unique 2-dimensional representation of the group B_{2} is used here. The specific operators for this group and an analysis of the inner products on the harmonic vector-valued polynomials are presented in this paper. An orthogonal basis for the harmonic polynomials is constructed, and is used to define an exponential-type kernel. In contrast to the ordinary scalar case the inner product structure is positive only when ( k_{0},k_{1}) satisfy - 1/2 < k_{0}± k_{1} < 1/2. For vector polynomials (f_{i}) _{i=1}^{2}, ( g_{i}) _{i=1}^{2} the inner product has the form iint_{{R}^{2}}f(x) K(x) g(x) ^{T}e^{-( x_{1}^{2}+x_{2}^{2}) /2}dx_{1}dx_{2} where the matrix function K(x) has to satisfy various transformation and boundary conditions. The matrix K is expressed in terms of hypergeometric functions.
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy
NASA Astrophysics Data System (ADS)
Flyer, Natasha; Fornberg, Bengt; Bayona, Victor; Barnett, Gregory A.
2016-09-01
Radial basis function-generated finite difference (RBF-FD) approximations generalize classical grid-based finite differences (FD) from lattice-based to scattered node layouts. This greatly increases the geometric flexibility of the discretizations and makes it easier to carry out local refinement in critical areas. Many different types of radial functions have been considered in this RBF-FD context. In this study, we find that (i) polyharmonic splines (PHS) in conjunction with supplementary polynomials provide a very simple way to defeat stagnation (also known as saturation) error and (ii) give particularly good accuracy for the tasks of interpolation and derivative approximations without the hassle of determining a shape parameter. In follow-up studies, we will focus on how to best use these hybrid RBF polynomial bases for FD approximations in the contexts of solving elliptic and hyperbolic type PDEs.
NASA Astrophysics Data System (ADS)
Dianat, Rouhollah; Kasaei, Shohreh
2009-11-01
A new and efficient method for incorporating the spatiality into difference-based change detection (CD) algorithms is introduced in this paper. It uses the spatial derivatives of image pixels to extract spatial relations among them. Based on this methodology, the performances of two famous difference-based CD methods, conventional polynomial regression (CPR) and multivariate alteration detection (MAD), are improved and called modified polynomial regression (MPR) and spatial multivariate alteration detection (SMAD), respectively. Various quantitative and qualitative evaluations have shown the superiority of MPR over CPR and SMAD over MAD. Also, the superiority of SMAD over all mentioned CD algorithms is shown. Moreover, it has been proved that both proposed methods enjoy the affine invariance property.
Draft Genome Sequence of Ustilago trichophora RK089, a Promising Malic Acid Producer
Zambanini, Thiemo; Buescher, Joerg M.; Meurer, Guido; Blank, Lars M.
2016-01-01
The basidiomycetous smut fungus Ustilago trichophora RK089 produces malate from glycerol. De novo genome sequencing revealed a 20.7-Mbp genome (301 gap-closed contigs, 246 scaffolds). A comparison to the genome of Ustilago maydis 521 revealed all essential genes for malate production from glycerol contributing to metabolic engineering for improving malate production. PMID:27469969
Draft Genome Sequence of Ustilago trichophora RK089, a Promising Malic Acid Producer.
Zambanini, Thiemo; Buescher, Joerg M; Meurer, Guido; Wierckx, Nick; Blank, Lars M
2016-01-01
The basidiomycetous smut fungus Ustilago trichophora RK089 produces malate from glycerol. De novo genome sequencing revealed a 20.7-Mbp genome (301 gap-closed contigs, 246 scaffolds). A comparison to the genome of Ustilago maydis 521 revealed all essential genes for malate production from glycerol contributing to metabolic engineering for improving malate production. PMID:27469969
SMiRK: an Automated Pipeline for miRNA Analysis
Milholland, Brandon; Gombar, Saurabh; Suh, Yousin
2015-01-01
Background Micro RNAs (miRNAs), important regulators of cell function, can be interrogated by high-throughput sequencing in a rapid and cost-effective manner. However, the tremendous amount of data generated by such methods is not easily analyzed. In order to extract meaningful information and draw biological conclusions from miRNA data, many challenges in quality control, alignment, normalization, and analysis must be overcome. Typically, these would only be possible with the dedicated efforts of a specialized computational biologist for a sustained period of time. Results Here, we present SMiRK, an automated pipeline that allows such tasks to be completed with minimal time and without dedicated bioinformatics personnel. SMiRK’s flexibility also allows experienced users to exert more control, if they wish. We describe how SMiRK automatically normalizes the data, removes low-information miRNAs, and produces heatmaps of the processed data. We give details on SMiRK’s implementation and use cases for novice and advanced users. As a demonstration of its capabilities, SMiRK was used to rapidly and automatically analyze a dataset taken from the literature. Conclusion SMiRK is a useful and efficient tool that can be used by investigators at multiple skill levels. Those who lack bioinformatics training can use it to easily and automatically analyze their data, while those with experience will find it beneficial to not need to write tools from scratch. PMID:26613105
Nietzsche, Madlen; Schießl, Ingrid; Börnke, Frederik
2014-01-01
In plants, SNF1-related kinase (SnRK1) responds to the availability of carbohydrates as well as to environmental stresses by down-regulating ATP consuming biosynthetic processes, while stimulating energy-generating catabolic reactions through gene expression and post-transcriptional regulation. The functional SnRK1 complex is a heterotrimer where the catalytic α subunit associates with a regulatory β subunit and an activating γ subunit. Several different metabolites as well as the hormone abscisic acid (ABA) have been shown to modulate SnRK1 activity in a cell- and stimulus-type specific manner. It has been proposed that tissue- or stimulus-specific expression of adapter proteins mediating SnRK1 regulation can at least partly explain the differences observed in SnRK1 signaling. By using yeast two-hybrid and in planta bi-molecular fluorescence complementation assays we were able to demonstrate that proteins containing the domain of unknown function (DUF) 581 could interact with both isoforms of the SnRK1α subunit (AKIN10/11) of Arabidopsis. A structure/function analysis suggests that the DUF581 is a generic SnRK1 interaction module and co-expression with DUF581 proteins in plant cells leads to reallocation of the kinase to specific regions within the nucleus. Yeast two-hybrid analyses suggest that SnRK1 and DUF581 proteins share common interaction partners inside the nucleus. The analysis of available microarray data implies that expression of the 19 members of the DUF581 encoding gene family in Arabidopsis is differentially regulated by hormones and environmental cues, indicating specialized functions of individual family members. We hypothesize that DUF581 proteins could act as mediators conferring tissue- and stimulus-type specific differences in SnRK1 regulation. PMID:24600465
SnRK1 Phosphorylation of AL2 Delays Cabbage Leaf Curl Virus Infection in Arabidopsis
Shen, Wei; Dallas, Mary Beth; Goshe, Michael B.
2014-01-01
ABSTRACT Geminivirus AL2/C2 proteins play key roles in establishing infection and causing disease in their plant hosts. They are involved in viral gene expression, counter host defenses by suppressing transcriptional gene silencing, and interfere with the host signaling involved in pathogen resistance. We report here that begomovirus and curtovirus AL2/C2 proteins interact strongly with host geminivirus Rep-interacting kinases (GRIKs), which are upstream activating kinases of the protein kinase SnRK1, a global regulator of energy and nutrient levels in plants. We used an in vitro kinase system to show that GRIK-activated SnRK1 phosphorylates recombinant AL2/C2 proteins from several begomoviruses and to map the SnRK1 phosphorylation site to serine-109 in the AL2 proteins of two New World begomoviruses: Cabbage Leaf Curl Virus (CaLCuV) and Tomato mottle virus. A CaLCuV AL2 S109D phosphomimic mutation did not alter viral DNA levels in protoplast replication assays. In contrast, the phosphomimic mutant was delayed for symptom development and viral DNA accumulation during infection of Arabidopsis thaliana, demonstrating that SnRK1 contributes to host defenses against CaLCuV. Our observation that serine-109 is not conserved in all AL2/C2 proteins that are SnRK1 substrates in vitro suggested that phosphorylation of viral proteins by plant kinases contributes to the evolution of geminivirus-host interactions. IMPORTANCE Geminiviruses are single-stranded DNA viruses that cause serious diseases in many crops. Dicot-infecting geminiviruses carry genes that encode multifunctional AL2/C2 proteins that are essential for infection. However, it is not clear how AL2/C2 proteins are regulated. Here, we show that the host protein kinase SnRK1, a central regulator of energy balance and nutrient metabolism in plants, phosphorylates serine-109 in AL2 proteins of three subgroups of New World begomoviruses, resulting in a delay in viral DNA accumulation and symptom appearance. Our results
miRNAs mediate SnRK1-dependent energy signaling in Arabidopsis
Confraria, Ana; Martinho, Cláudia; Elias, Alexandre; Rubio-Somoza, Ignacio; Baena-González, Elena
2013-01-01
The SnRK1 protein kinase, the plant ortholog of mammalian AMPK and yeast Snf1, is activated by the energy depletion caused by adverse environmental conditions. Upon activation, SnRK1 triggers extensive transcriptional changes to restore homeostasis and promote stress tolerance and survival partly through the inhibition of anabolism and the activation of catabolism. Despite the identification of a few bZIP transcription factors as downstream effectors, the mechanisms underlying gene regulation, and in particular gene repression by SnRK1, remain mostly unknown. microRNAs (miRNAs) are 20–24 nt RNAs that regulate gene expression post-transcriptionally by driving the cleavage and/or translation attenuation of complementary mRNA targets. In addition to their role in plant development, mounting evidence implicates miRNAs in the response to environmental stress. Given the involvement of miRNAs in stress responses and the fact that some of the SnRK1-regulated genes are miRNA targets, we postulated that miRNAs drive part of the transcriptional reprogramming triggered by SnRK1. By comparing the transcriptional response to energy deprivation between WT and dcl1-9, a mutant deficient in miRNA biogenesis, we identified 831 starvation genes misregulated in the dcl1-9 mutant, out of which 155 are validated or predicted miRNA targets. Functional clustering analysis revealed that the main cellular processes potentially co-regulated by SnRK1 and miRNAs are translation and organelle function and uncover TCP transcription factors as one of the most highly enriched functional clusters. TCP repression during energy deprivation was impaired in miR319 knockdown (MIM319) plants, demonstrating the involvement of miR319 in the stress-dependent regulation of TCPs. Altogether, our data indicates that miRNAs are components of the SnRK1 signaling cascade contributing to the regulation of specific mRNA targets and possibly tuning down particular cellular processes during the stress response
Symmetric polynomials in information theory: Entropy and subentropy
Jozsa, Richard; Mitchison, Graeme
2015-06-15
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.
Orthogonal sets of data windows constructed from trigonometric polynomials
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
1989-01-01
Suboptimal, easily computable substitutes for the discrete prolate-spheroidal windows used by Thomson for spectral estimation are given. Trigonometric coefficients and energy leakages of the window polynomials are tabulated.
Quantization of gauge fields, graph polynomials and graph homology
Kreimer, Dirk; Sars, Matthias; Suijlekom, Walter D. van
2013-09-15
We review quantization of gauge fields using algebraic properties of 3-regular graphs. We derive the Feynman integrand at n loops for a non-abelian gauge theory quantized in a covariant gauge from scalar integrands for connected 3-regular graphs, obtained from the two Symanzik polynomials. The transition to the full gauge theory amplitude is obtained by the use of a third, new, graph polynomial, the corolla polynomial. This implies effectively a covariant quantization without ghosts, where all the relevant signs of the ghost sector are incorporated in a double complex furnished by the corolla polynomial–we call it cycle homology–and by graph homology. -- Highlights: •We derive gauge theory Feynman from scalar field theory with 3-valent vertices. •We clarify the role of graph homology and cycle homology. •We use parametric renormalization and the new corolla polynomial.
Cubic Polynomials with Rational Roots and Critical Points
ERIC Educational Resources Information Center
Gupta, Shiv K.; Szymanski, Waclaw
2010-01-01
If you want your students to graph a cubic polynomial, it is best to give them one with rational roots and critical points. In this paper, we describe completely all such cubics and explain how to generate them.
Polynomial Extensions of the Weyl C*-Algebra
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Dhahri, Ameur
2015-09-01
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) nontrivial central extension of the Heisenberg algebra, which can be concretely realized as sub-Lie algebras of the polynomial algebra generated by the creation and annihilation operators in the Schrödinger representation. The simplest nontrivial of these extensions (the quadratic one) is isomorphic to the Galilei algebra, widely studied in quantum physics. By exponentiation of this representation we construct the corresponding polynomial analogue of the Weyl C*-algebra and compute the polynomial Weyl relations. From this we deduce the explicit form of the composition law of the associated nonlinear extensions of the 1-dimensional Heisenberg group. The above results are used to calculate a simple explicit form of the vacuum characteristic functions of the nonlinear field operators of the Galilei algebra, as well as of their moments. The corresponding measures turn out to be an interpolation family between Gaussian and Meixner, in particular Gamma.
Polynomial modeling of analog-to-digital converters
Solomon, O.M. Jr.
1994-01-01
Analog-to-digital converters are frequently modeled as a linear polynomial plus a random process. The parameters of the linear polynomial are the familiar gain and offset of the analog-to-digital converter. The output of the random process is uniformly distributed on plus or minus the least significant bit of the analog-to-digital converter. In this paper, the transfer function of an analog-to-digital converter is modeled as a nonlinear polynomial plus a random process. This model can explain the generation of harmonics by the analog-to-digital converter, but the simpler linear model cannot. The parameters of the nonlinear polynomial are estimated from the response to the analog-to-digital converter to a sine wave. The model parameters are used to estimate the nonlinear part of the transfer function of the analog-to-digital converter.
Detergent-like activity and alpha-helical structure of warnericin RK, an anti-Legionella peptide.
Verdon, Julien; Falge, Mirjam; Maier, Elke; Bruhn, Heike; Steinert, Michael; Faber, Cornelius; Benz, Roland; Héchard, Yann
2009-10-01
Warnericin RK is the first antimicrobial peptide known to be active against Legionella pneumophila, a pathogen bacterium that is responsible for severe pneumonia. Strikingly, this peptide displays a very narrow range of antimicrobial activity, almost limited to the Legionella genus, and a hemolytic activity. A similar activity has been described for delta-lysin, a well-known hemolytic peptide of Staphylococci that has not been described as antimicrobial. In this study we aimed to understand the mode of action of warnericin RK and to explain its particular target specificity. We found that warnericin RK permeabilizes artificial membranes in a voltage-independent manner. Osmotic protection experiments on erythrocytes showed that warnericin RK does not form well-defined pores, suggesting a detergent-like mode of action, as previously described for delta-lysin at high concentrations. Warnericin RK also permeabilized Legionella cells, and these cells displayed a high sensitivity to detergents. Depending on the detergent used, Legionella was from 10- to 1000-fold more sensitive than the other bacteria tested. Finally, the structure of warnericin RK was investigated by means of circular dichroism and NMR spectroscopy. The peptide adopted an amphiphilic alpha-helical structure, consistent with the proposed mode of action. We conclude that the specificity of warnericin RK toward Legionella results from both the detergent-like mode of action of the peptide and the high sensitivity of these bacteria to detergents. PMID:19804724
Detergent-Like Activity and α-Helical Structure of Warnericin RK, an Anti-Legionella Peptide
Verdon, Julien; Falge, Mirjam; Maier, Elke; Bruhn, Heike; Steinert, Michael; Faber, Cornelius; Benz, Roland; Héchard, Yann
2009-01-01
Abstract Warnericin RK is the first antimicrobial peptide known to be active against Legionella pneumophila, a pathogen bacterium that is responsible for severe pneumonia. Strikingly, this peptide displays a very narrow range of antimicrobial activity, almost limited to the Legionella genus, and a hemolytic activity. A similar activity has been described for δ-lysin, a well-known hemolytic peptide of Staphylococci that has not been described as antimicrobial. In this study we aimed to understand the mode of action of warnericin RK and to explain its particular target specificity. We found that warnericin RK permeabilizes artificial membranes in a voltage-independent manner. Osmotic protection experiments on erythrocytes showed that warnericin RK does not form well-defined pores, suggesting a detergent-like mode of action, as previously described for δ-lysin at high concentrations. Warnericin RK also permeabilized Legionella cells, and these cells displayed a high sensitivity to detergents. Depending on the detergent used, Legionella was from 10- to 1000-fold more sensitive than the other bacteria tested. Finally, the structure of warnericin RK was investigated by means of circular dichroism and NMR spectroscopy. The peptide adopted an amphiphilic α-helical structure, consistent with the proposed mode of action. We conclude that the specificity of warnericin RK toward Legionella results from both the detergent-like mode of action of the peptide and the high sensitivity of these bacteria to detergents. PMID:19804724
Performance comparison of polynomial representations for optimizing optical freeform systems
NASA Astrophysics Data System (ADS)
Brömel, A.; Gross, H.; Ochse, D.; Lippmann, U.; Ma, C.; Zhong, Y.; Oleszko, M.
2015-09-01
Optical systems can benefit strongly from freeform surfaces, however the choice of the right representation isn`t an easy one. Classical representations like X-Y-polynomials, as well as Zernike-polynomials are often used for such systems, but should have some disadvantage regarding their orthogonality, resulting in worse convergence and reduced quality in final results compared to newer representations like the Q-polynomials by Forbes. Additionally the supported aperture is a circle, which can be a huge drawback in case of optical systems with rectangular aperture. In this case other representations like Chebyshev-or Legendre-polynomials come into focus. There are a larger number of possibilities; however the experience with these newer representations is rather limited. Therefore in this work the focus is on investigating the performance of four widely used representations in optimizing two ambitious systems with very different properties: Three-Mirror-Anastigmat and an anamorphic System. The chosen surface descriptions offer support for circular or rectangular aperture, as well as different grades of departure from rotational symmetry. The basic shapes are for example a conic or best-fit-sphere and the polynomial set is non-, spatial or slope-orthogonal. These surface representations were chosen to evaluate the impact of these aspects on the performance optimization of the two example systems. Freeform descriptions investigated here were XY-polynomials, Zernike in Fringe representation, Q-polynomials by Forbes, as well as 2-dimensional Chebyshev-polynomials. As a result recommendations for the right choice of freeform surface representations for practical issues in the optimization of optical systems can be given.
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.
Higher order derivatives of R-Jacobi polynomials
NASA Astrophysics Data System (ADS)
Das, Sourav; Swaminathan, A.
2016-06-01
In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.
Constructing Polynomial Spectral Models for Stars
NASA Astrophysics Data System (ADS)
Rix, Hans-Walter; Ting, Yuan-Sen; Conroy, Charlie; Hogg, David W.
2016-08-01
Stellar spectra depend on the stellar parameters and on dozens of photospheric elemental abundances. Simultaneous fitting of these { N } ˜ 10–40 model labels to observed spectra has been deemed unfeasible because the number of ab initio spectral model grid calculations scales exponentially with { N }. We suggest instead the construction of a polynomial spectral model (PSM) of order { O } for the model flux at each wavelength. Building this approximation requires a minimum of only ≤ft(≥nfrac{}{}{0em}{}{{ N }+{ O }}{{ O }}\\right) calculations: e.g., a quadratic spectral model ({ O }=2) to fit { N }=20 labels simultaneously can be constructed from as few as 231 ab initio spectral model calculations; in practice, a somewhat larger number (˜300–1000) of randomly chosen models lead to a better performing PSM. Such a PSM can be a good approximation only over a portion of label space, which will vary case-by-case. Yet, taking the APOGEE survey as an example, a single quadratic PSM provides a remarkably good approximation to the exact ab initio spectral models across much of this survey: for random labels within that survey the PSM approximates the flux to within 10‑3 and recovers the abundances to within ˜0.02 dex rms of the exact models. This enormous speed-up enables the simultaneous many-label fitting of spectra with computationally expensive ab initio models for stellar spectra, such as non-LTE models. A PSM also enables the simultaneous fitting of observational parameters, such as the spectrum’s continuum or line-spread function.
Traversa, Fabio Lorenzo; Ramella, Chiara; Bonani, Fabrizio; Di Ventra, Massimiliano
2015-01-01
Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently proven mathematically that memcomputing machines have the same computational power of nondeterministic Turing machines. Therefore, they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size. The reason for this computational power stems from properties inspired by the brain and shared by any universal memcomputing machine, in particular intrinsic parallelism and information overhead, namely, the capability of compressing information in the collective state of the memprocessor network. We show an experimental demonstration of an actual memcomputing architecture that solves the NP-complete version of the subset sum problem in only one step and is composed of a number of memprocessors that scales linearly with the size of the problem. We have fabricated this architecture using standard microelectronic technology so that it can be easily realized in any laboratory setting. Although the particular machine presented here is eventually limited by noise—and will thus require error-correcting codes to scale to an arbitrary number of memprocessors—it represents the first proof of concept of a machine capable of working with the collective state of interacting memory cells, unlike the present-day single-state machines built using the von Neumann architecture. PMID:26601208
Traversa, Fabio Lorenzo; Ramella, Chiara; Bonani, Fabrizio; Di Ventra, Massimiliano
2015-07-01
Memcomputing is a novel non-Turing paradigm of computation that uses interacting memory cells (memprocessors for short) to store and process information on the same physical platform. It was recently proven mathematically that memcomputing machines have the same computational power of nondeterministic Turing machines. Therefore, they can solve NP-complete problems in polynomial time and, using the appropriate architecture, with resources that only grow polynomially with the input size. The reason for this computational power stems from properties inspired by the brain and shared by any universal memcomputing machine, in particular intrinsic parallelism and information overhead, namely, the capability of compressing information in the collective state of the memprocessor network. We show an experimental demonstration of an actual memcomputing architecture that solves the NP-complete version of the subset sum problem in only one step and is composed of a number of memprocessors that scales linearly with the size of the problem. We have fabricated this architecture using standard microelectronic technology so that it can be easily realized in any laboratory setting. Although the particular machine presented here is eventually limited by noise-and will thus require error-correcting codes to scale to an arbitrary number of memprocessors-it represents the first proof of concept of a machine capable of working with the collective state of interacting memory cells, unlike the present-day single-state machines built using the von Neumann architecture. PMID:26601208
Universal Racah matrices and adjoint knot polynomials: Arborescent knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.
2016-04-01
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.
Factorization of colored knot polynomials at roots of unity
NASA Astrophysics Data System (ADS)
Kononov, Ya.; Morozov, A.
2015-07-01
HOMFLY polynomials are the Wilson-loop averages in Chern-Simons theory and depend on four variables: the closed line (knot) in 3d space-time, representation R of the gauge group SU (N) and exponentiated coupling constant q. From analysis of a big variety of different knots we conclude that at q, which is a 2m-th root of unity, q2m = 1, HOMFLY polynomials in symmetric representations [ r ] satisfy recursion identity: Hr+m =Hr ṡHm for any A =qN, which is a generalization of the property Hr = H1r for special polynomials at m = 1. We conjecture a further generalization to arbitrary representation R, which, however, is checked only for torus knots. Next, Kashaev polynomial, which arises from HR at q2 = e 2 πi / | R |, turns equal to the special polynomial with A substituted by A| R |, provided R is a single-hook representations (including arbitrary symmetric) - what provides a q - A dual to the similar property of Alexander polynomial. All this implies non-trivial relations for the coefficients of the differential expansions, which are believed to provide reasonable coordinates in the space of knots - existence of such universal relations means that these variables are still not unconstrained.
Complex Exceptional Orthogonal Polynomials and Quasi-invariance
NASA Astrophysics Data System (ADS)
Haese-Hill, William A.; Hallnäs, Martin A.; Veselov, Alexander P.
2016-05-01
Consider the Wronskians of the classical Hermite polynomials H_{λ, l}(x):=Wr(H_l(x),H_{k_1}(x),ldots,H_{k_n}(x)), quad l in Z_{≥0}{setminus} {k_1,ldots,k_n}, where {k_i=λ_i+n-i, i=1,ldots, n} and {λ=(λ_1, ldots, λ_n)} is a partition. Gómez-Ullate et al. showed that for a special class of partitions the corresponding polynomials are orthogonal and dense among all polynomials with respect to a certain inner product, but in contrast to the usual case have some degrees missing (so-called exceptional orthogonal polynomials). We generalise their results to all partitions by considering complex contours of integration and non-positive Hermitian products. The corresponding polynomials are orthogonal and dense in a finite-codimensional subspace of {C[x]} satisfying certain quasi-invariance conditions. A Laurent version of exceptional orthogonal polynomials, related to monodromy-free trigonometric Schrödinger operators, is also presented.
NASA Technical Reports Server (NTRS)
Belcastro, Christine M.
1998-01-01
Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.
Hou Xi; Wu Fan; Yang Li; Wu Shibin; Chen Qiang
2006-05-20
We propose a more accurate and efficient reconstruction method used in testing large aspheric surfaces with annular subaperture interferometry. By the introduction of the Zernike annular polynomials that are orthogonal over the annular region, the method proposed here eliminates the coupling problem in the earlier reconstruction algorithm based on Zernike circle polynomials. Because of the complexity of recurrence definition of Zernike annular polynomials, a general symbol representation of that in a computing program is established. The program implementation for the method is provided in detail. The performance of the reconstruction algorithm is evaluated in some pertinent cases, such as different random noise levels, different subaperture configurations, and misalignments.
NASA Astrophysics Data System (ADS)
Bihun, Oksana; Calogero, Francesco
2016-07-01
The notion of generations of monic polynomials such that the coefficients of each polynomial of the next generation coincide with the zeros of a polynomial of the current generation is introduced, and its relevance to the identification of endless sequences of new solvable many-body problems "of goldfish type" is demonstrated.
Stochastic Polynomial Dynamic Models of the Yeast Cell Cycle
NASA Astrophysics Data System (ADS)
Mitra, Indranil; Dimitrova, Elena; Jarrah, Abdul S.
2010-03-01
In the last decade a new holistic approach for tackling biological problems, systems biology, which takes into account the study of the interactions between the components of a biological system to predict function and behavior has emerged. The reverse-engineering of biochemical networks from experimental data have increasingly become important in systems biology. Based on Boolean networks, we propose a time-discrete stochastic framework for the reverse engineering of the yeast cell cycle regulatory network from experimental data. With a suitable choice of state set, we have used powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. Stochasticity is introduced by choosing at each update step a random coordinate function for each variable, chosen from a probability space of update functions. The algorithm is based on a combinatorial structure known as the Gr"obner fans of a polynomial ideal which identifies the underlying network structure and dynamics. The model depicts a correct dynamics of the yeast cell cycle network and reproduces the time sequence of expression patterns along the biological cell cycle. Our findings indicate that the methodolgy has high chance of success when applied to large and complex systems to determine the dynamical properties of corresponding networks.
NASA Astrophysics Data System (ADS)
Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E.
2016-03-01
We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wave function. In between, we interpolate using a single parameter. The effective Hamiltonian is non-Hermitian and this polynomial similarity transformation theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit, whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction strengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
Bayes Node Energy Polynomial Distribution to Improve Routing in Wireless Sensor Network.
Palanisamy, Thirumoorthy; Krishnasamy, Karthikeyan N
2015-01-01
Wireless Sensor Network monitor and control the physical world via large number of small, low-priced sensor nodes. Existing method on Wireless Sensor Network (WSN) presented sensed data communication through continuous data collection resulting in higher delay and energy consumption. To conquer the routing issue and reduce energy drain rate, Bayes Node Energy and Polynomial Distribution (BNEPD) technique is introduced with energy aware routing in the wireless sensor network. The Bayes Node Energy Distribution initially distributes the sensor nodes that detect an object of similar event (i.e., temperature, pressure, flow) into specific regions with the application of Bayes rule. The object detection of similar events is accomplished based on the bayes probabilities and is sent to the sink node resulting in minimizing the energy consumption. Next, the Polynomial Regression Function is applied to the target object of similar events considered for different sensors are combined. They are based on the minimum and maximum value of object events and are transferred to the sink node. Finally, the Poly Distribute algorithm effectively distributes the sensor nodes. The energy efficient routing path for each sensor nodes are created by data aggregation at the sink based on polynomial regression function which reduces the energy drain rate with minimum communication overhead. Experimental performance is evaluated using Dodgers Loop Sensor Data Set from UCI repository. Simulation results show that the proposed distribution algorithm significantly reduce the node energy drain rate and ensure fairness among different users reducing the communication overhead. PMID:26426701
Bayes Node Energy Polynomial Distribution to Improve Routing in Wireless Sensor Network
Palanisamy, Thirumoorthy; Krishnasamy, Karthikeyan N.
2015-01-01
Wireless Sensor Network monitor and control the physical world via large number of small, low-priced sensor nodes. Existing method on Wireless Sensor Network (WSN) presented sensed data communication through continuous data collection resulting in higher delay and energy consumption. To conquer the routing issue and reduce energy drain rate, Bayes Node Energy and Polynomial Distribution (BNEPD) technique is introduced with energy aware routing in the wireless sensor network. The Bayes Node Energy Distribution initially distributes the sensor nodes that detect an object of similar event (i.e., temperature, pressure, flow) into specific regions with the application of Bayes rule. The object detection of similar events is accomplished based on the bayes probabilities and is sent to the sink node resulting in minimizing the energy consumption. Next, the Polynomial Regression Function is applied to the target object of similar events considered for different sensors are combined. They are based on the minimum and maximum value of object events and are transferred to the sink node. Finally, the Poly Distribute algorithm effectively distributes the sensor nodes. The energy efficient routing path for each sensor nodes are created by data aggregation at the sink based on polynomial regression function which reduces the energy drain rate with minimum communication overhead. Experimental performance is evaluated using Dodgers Loop Sensor Data Set from UCI repository. Simulation results show that the proposed distribution algorithm significantly reduce the node energy drain rate and ensure fairness among different users reducing the communication overhead. PMID:26426701
Verdon, Julien; Labanowski, Jérome; Sahr, Tobias; Ferreira, Thierry; Lacombe, Christian; Buchrieser, Carmen; Berjeaud, Jean-Marc; Héchard, Yann
2011-04-01
Warnericin RK is an antimicrobial peptide, produced by a Staphyloccocus warneri strain, described to be specifically active against Legionella, the pathogenic bacteria responsible for Legionnaires' disease. Warnericin RK is an amphiphilic alpha-helical peptide, which possesses a detergent-like mode of action. Two others peptides, δ-hemolysin I and II, produced by the same S. warneri strain, are highly similar to S. aureus δ-hemolysin and also display anti-Legionella activity. It has been recently reported that S. aureus δ-hemolysin activity on vesicles is likewise related to phospholipid acyl-chain structure, such as chain length and saturation. As staphylococcal δ-hemolysins were highly similar, we thus hypothesized that fatty acid composition of Legionella's membrane might influence the sensitivity of the bacteria to warnericin RK. Relationship between sensitivity to the peptide and fatty acid composition was then followed in various conditions. Cells in stationary phase, which were already described as less resistant than cells in exponential phase, displayed higher amounts of branched-chain fatty acids (BCFA) and short chain fatty acids. An adapted strain, able to grow at a concentration 33 fold higher than minimal inhibitory concentration of the wild type (i.e. 1μM), was isolated after repeated transfers of L. pneumophila in the presence of increased concentrations of warnericin RK. The amount of BCFA was significantly higher in the adapted strain than in the wild type strain. Also, a transcriptomic analysis of the wild type and adapted strains showed that two genes involved in fatty acid biosynthesis were repressed in the adapted strain. These genes encode enzymes involved in desaturation and elongation of fatty acids respectively. Their repression was in agreement with the decrease of unsaturated fatty acids and fatty acid chain length in the adapted strain. Conclusively, our results indicate that the increase of BCFA and the decrease of fatty acid
NASA Astrophysics Data System (ADS)
Li, Jun; Jiang, Bin; Guo, Hua
2013-11-01
A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.
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.
NASA Astrophysics Data System (ADS)
Wang, Shuai; Yang, Ping; Dong, Lizhi; Xu, Bing; Ao, Mingwu
2015-02-01
Walsh functions have been modified and utilized as binary-aberration-mode basis which are especially suitable for representing discrete wavefronts. However, when wavefront sensing techniques based on binary-aberration-mode detection trying to reconstruct common wavefronts with continuous forms, the Modified Walsh functions are incompetent. The limited space resolution of Modified Walsh functions will leave substantial residual wavefronts. In order to sidestep the space-resolution problem of binary-aberration modes, it's necessary to transform the Modified-Walsh-function expansion coefficients of wavefront to Zernike-polynomial coefficients and use Zernike polynomials to represent the wavefront to be reconstructed. For this reason, a transformation method for wavefront expansion coefficients of the two aberration modes is proposed. The principle of the transformation is the linear of wavefront expansion and the method of least squares. The numerical simulation demonstrates that the coefficient transformation with the transformation matrix is reliable and accurate.
A Generalized Estimate of the SLR B Polynomial Ripples for RF Pulse Generation.
Raddi; Klose
1998-06-01
The nonlinearity of the parameter relations for the Shinnar-Le Roux RF pulse design algorithm has induced to performa classification based on the features of the slice profile dueto the RF pulse. In the present paper a generalization ofthe relation between the ripple amplitudes of the SLR B polynomial and those of the slice profile is given. It allows generation of RF pulses with better slice profiles and slightly reduced energy, avoiding any a priori classification. The effect of our estimation has been shown by generating several pulses by generalized estimation of B polynomial ripples. In addition, their behavior has been compared to that of analogous pulses generated by means of the classification just mentioned. Copyright 1998 Academic Press. PMID:9632551
Li, Jun; Jiang, Bin; Guo, Hua
2013-11-28
A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.
NASA Astrophysics Data System (ADS)
Saliba, J.; Lugan, P.; Savona, V.
2013-04-01
An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al (2010 Phys. Rev. A 81 053603). The kernel polynomial scheme is also used to study the disorder-induced condensate depletion in the two-dimensional geometry. Our approach paves the way for an analysis of coherence properties of Bose gases across the superfluid-insulator transition in two and three dimensions.
Dynamic Harmony Search with Polynomial Mutation Algorithm for Valve-Point Economic Load Dispatch
Karthikeyan, M.; Sree Ranga Raja, T.
2015-01-01
Economic load dispatch (ELD) problem is an important issue in the operation and control of modern control system. The ELD problem is complex and nonlinear with equality and inequality constraints which makes it hard to be efficiently solved. This paper presents a new modification of harmony search (HS) algorithm named as dynamic harmony search with polynomial mutation (DHSPM) algorithm to solve ORPD problem. In DHSPM algorithm the key parameters of HS algorithm like harmony memory considering rate (HMCR) and pitch adjusting rate (PAR) are changed dynamically and there is no need to predefine these parameters. Additionally polynomial mutation is inserted in the updating step of HS algorithm to favor exploration and exploitation of the search space. The DHSPM algorithm is tested with three power system cases consisting of 3, 13, and 40 thermal units. The computational results show that the DHSPM algorithm is more effective in finding better solutions than other computational intelligence based methods. PMID:26491710
Numerical Polynomial Homotopy Continuation Method and String Vacua
Mehta, Dhagash
2011-01-01
Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less
Deflectometry for optics evaluation: free form segments of polynomial mirror
NASA Astrophysics Data System (ADS)
Sironi, Giorgia; Canestrari, Rodolfo; Pareschi, Giovanni; Pelliciari, Carlo
2014-07-01
Deflectometry is a well-known method for astronomical mirror metrology. This paper describes the method we developed for the characterization of free-form concave mirrors. Our technique is based on the synergy between deflectometry and ray-tracing. The deflectometrical test is performed by illuminating the reflecting surface with a known light pattern in a Ronchi - like configuration and retrieving the slope errors by the observed rays deflection. The ray-tracing code allows us to measure the slopes and to evaluate the mirror optical performance. This technique has two main advantages: it is fast and it is applicable on-site, as an intermediate step in the manufacturing process, preventing that out-of-specification mirrors may proceed towards further production steps. Thus, we obtain a considerable time and cost reduction. As an example, we describe the results obtained measuring the primary mirror segments of the Cherenkov prototypal telescope manufactured by the Italian National Institute for Astrophysics in the context of the ASTRI Project. This specific case is challenging because the segmentation of the polynomial primary mirror lead to individual mirrors with deviations from the spherical optical design up to a few millimeters.
3D Model Segmentation and Representation with Implicit Polynomials
NASA Astrophysics Data System (ADS)
Zheng, Bo; Takamatsu, Jun; Ikeuchi, Katsushi
When large-scale and complex 3D objects are obtained by range finders, it is often necessary to represent them by algebraic surfaces for such purposes as data compression, multi-resolution, noise elimination, and 3D recognition. Representing the 3D data with algebraic surfaces of an implicit polynomial (IP) has proved to offer the advantages that IP representation is capable of encoding geometric properties easily with desired smoothness, few parameters, algebraic/geometric invariants, and robustness to noise and missing data. Unfortunately, generating a high-degree IP surface for a whole complex 3D shape is impossible because of high computational cost and numerical instability. In this paper we propose a 3D segmentation method based on a cut-and-merge approach. Two cutting procedures adopt low-degree IPs to divide and fit the surface segments simultaneously, while avoiding generating high-curved segments. A merging procedure merges the similar adjacent segments to avoid over-segmentation. To prove the effectiveness of this segmentation method, we open up some new vistas for 3D applications such as 3D matching, recognition, and registration.
Zhang, Yan; Sahinidis, Nikolaos V
2013-04-06
In this paper, surrogate models are iteratively built using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the values of the uncertain parameters into the closed-form polynomial functions. Based on the results of MC simulation, the uncertainties of injecting CO{sub 2} underground are quantified for a saline aquifer. Moreover, based on the PCE model, we formulate an optimization problem to determine the optimal CO{sub 2} injection rate so as to maximize the gas saturation (residual trapping) during injection, and thereby minimize the chance of leakage.
Shao, Yan-Lin Faltinsen, Odd M.
2014-10-01
We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods, e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.
Zhang, Hongying; Mao, Xinguo; Jing, Ruilian; Chang, Xiaoping; Xie, Huimin
2011-01-01
Sucrose non-fermenting-1-related protein kinase 2 (SnRK2) plays a key role in the plant stress signalling transduction pathway via phosphorylation. Here, a SnRK2 member of common wheat, TaSnRK2.7, was cloned and characterized. Southern blot analysis suggested that the common wheat genome contains three copies of TaSnRK2.7. Subcellular localization showed the presence of TaSnRK2.7 in the cell membrane, cytoplasm, and nucleus. Expression patterns revealed that TaSnRK2.7 is expressed strongly in roots, and responds to polyethylene glycol, NaCl, and cold stress, but not to abscisic acid (ABA) application, suggesting that TaSnRK2.7 might participate in non-ABA-dependent signal transduction pathways. TaSnRK2.7 was transferred to Arabidopsis under the control of the CaMV-35S promoter. Function analysis showed that TaSnRK2.7 is involved in carbohydrate metabolism, decreasing osmotic potential, enhancing photosystem II activity, and promoting root growth. Its overexpression results in enhanced tolerance to multi-abiotic stress. Therefore, TaSnRK2.7 is a multifunctional regulatory factor in plants, and has the potential to be utilized in transgenic breeding to improve abiotic stress tolerance in crop plants. PMID:21030389
NASA Astrophysics Data System (ADS)
Isah, Abdulnasir; Chang, Phang
2016-06-01
In this article we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of non-linear systems of fractional order differential equations (NSFDEs). The operational matrix of fractional derivative derived through wavelet-polynomial transformation are used together with the collocation method to turn the NSFDEs to a system of non-linear algebraic equations. Illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe
2013-01-01
This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.
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.
Asymptotic formulae for the zeros of orthogonal polynomials
Badkov, V M
2012-09-30
Let p{sub n}(t) be an algebraic polynomial that is orthonormal with weight p(t) on the interval [-1, 1]. When p(t) is a perturbation (in certain limits) of the Chebyshev weight of the first kind, the zeros of the polynomial p{sub n}( cos {tau}) and the differences between pairs of (not necessarily consecutive) zeros are shown to satisfy asymptotic formulae as n{yields}{infinity}, which hold uniformly with respect to the indices of the zeros. Similar results are also obtained for perturbations of the Chebyshev weight of the second kind. First, some preliminary results on the asymptotic behaviour of the difference between two zeros of an orthogonal trigonometric polynomial, which are needed, are established. Bibliography: 15 titles.
Euler polynomials and identities for non-commutative operators
NASA Astrophysics Data System (ADS)
De Angelis, Valerio; Vignat, Christophe
2015-12-01
Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.
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.
Nuclear-magnetic-resonance quantum calculations of the Jones polynomial
Marx, Raimund; Spoerl, Andreas; Pomplun, Nikolas; Schulte-Herbrueggen, Thomas; Glaser, Steffen J.; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Myers, John M.
2010-03-15
The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation, however, involves many known experimental challenges. Here we present experimental results for a small-scale approximate evaluation of the Jones polynomial by nuclear magnetic resonance (NMR); in addition, we show how to escape from the limitations of NMR approaches that employ pseudopure states. Specifically, we use two spin-1/2 nuclei of natural abundance chloroform and apply a sequence of unitary transforms representing the trefoil knot, the figure-eight knot, and the Borromean rings. After measuring the nuclear spin state of the molecule in each case, we are able to estimate the value of the Jones polynomial for each of the knots.
Mechanisms of regulation of SNF1/AMPK/SnRK1 protein kinases
Crozet, Pierre; Margalha, Leonor; Confraria, Ana; Rodrigues, Américo; Martinho, Cláudia; Adamo, Mattia; Elias, Carlos A.; Baena-González, Elena
2014-01-01
The SNF1 (sucrose non-fermenting 1)-related protein kinases 1 (SnRKs1) are the plant orthologs of the budding yeast SNF1 and mammalian AMPK (AMP-activated protein kinase). These evolutionarily conserved kinases are metabolic sensors that undergo activation in response to declining energy levels. Upon activation, SNF1/AMPK/SnRK1 kinases trigger a vast transcriptional and metabolic reprograming that restores energy homeostasis and promotes tolerance to adverse conditions, partly through an induction of catabolic processes and a general repression of anabolism. These kinases typically function as a heterotrimeric complex composed of two regulatory subunits, β and γ, and an α-catalytic subunit, which requires phosphorylation of a conserved activation loop residue for activity. Additionally, SNF1/AMPK/SnRK1 kinases are controlled by multiple mechanisms that have an impact on kinase activity, stability, and/or subcellular localization. Here we will review current knowledge on the regulation of SNF1/AMPK/SnRK1 by upstream components, post-translational modifications, various metabolites, hormones, and others, in an attempt to highlight both the commonalities of these essential eukaryotic kinases and the divergences that have evolved to cope with the particularities of each one of these systems. PMID:24904600
Mechanisms of regulation of SNF1/AMPK/SnRK1 protein kinases.
Crozet, Pierre; Margalha, Leonor; Confraria, Ana; Rodrigues, Américo; Martinho, Cláudia; Adamo, Mattia; Elias, Carlos A; Baena-González, Elena
2014-01-01
The SNF1 (sucrose non-fermenting 1)-related protein kinases 1 (SnRKs1) are the plant orthologs of the budding yeast SNF1 and mammalian AMPK (AMP-activated protein kinase). These evolutionarily conserved kinases are metabolic sensors that undergo activation in response to declining energy levels. Upon activation, SNF1/AMPK/SnRK1 kinases trigger a vast transcriptional and metabolic reprograming that restores energy homeostasis and promotes tolerance to adverse conditions, partly through an induction of catabolic processes and a general repression of anabolism. These kinases typically function as a heterotrimeric complex composed of two regulatory subunits, β and γ, and an α-catalytic subunit, which requires phosphorylation of a conserved activation loop residue for activity. Additionally, SNF1/AMPK/SnRK1 kinases are controlled by multiple mechanisms that have an impact on kinase activity, stability, and/or subcellular localization. Here we will review current knowledge on the regulation of SNF1/AMPK/SnRK1 by upstream components, post-translational modifications, various metabolites, hormones, and others, in an attempt to highlight both the commonalities of these essential eukaryotic kinases and the divergences that have evolved to cope with the particularities of each one of these systems. PMID:24904600
Zaunders, John; Jing, Junmei; Leipold, Michael; Maecker, Holden; Kelleher, Anthony D; Koch, Inge
2016-01-01
Many methods have been described for automated clustering analysis of complex flow cytometry data, but so far the goal to efficiently estimate multivariate densities and their modes for a moderate number of dimensions and potentially millions of data points has not been attained. We have devised a novel approach to describing modes using second order polynomial histogram estimators (SOPHE). The method divides the data into multivariate bins and determines the shape of the data in each bin based on second order polynomials, which is an efficient computation. These calculations yield local maxima and allow joining of adjacent bins to identify clusters. The use of second order polynomials also optimally uses wide bins, such that in most cases each parameter (dimension) need only be divided into 4-8 bins, again reducing computational load. We have validated this method using defined mixtures of up to 17 fluorescent beads in 16 dimensions, correctly identifying all populations in data files of 100,000 beads in <10 s, on a standard laptop. The method also correctly clustered granulocytes, lymphocytes, including standard T, B, and NK cell subsets, and monocytes in 9-color stained peripheral blood, within seconds. SOPHE successfully clustered up to 36 subsets of memory CD4 T cells using differentiation and trafficking markers, in 14-color flow analysis, and up to 65 subpopulations of PBMC in 33-dimensional CyTOF data, showing its usefulness in discovery research. SOPHE has the potential to greatly increase efficiency of analysing complex mixtures of cells in higher dimensions. PMID:26097104
Simulation of stochastic systems via polynomial chaos expansions and convex optimization
NASA Astrophysics Data System (ADS)
Fagiano, Lorenzo; Khammash, Mustafa
2012-09-01
Polynomial chaos expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and nontrivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allows to take into account the specific features of polynomial chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated in the approach by means of convex constraints. We show the effectiveness of the proposed technique in three applications in diverse fields, including the analysis of a nonlinear electric circuit, a chaotic model of organizational behavior, and finally a chemical oscillator.
A quasi-static polynomial nodal method for nuclear reactor analysis
Gehin, J.C.
1992-09-01
Modern nodal methods are currently available which can accurately and efficiently solve the static and transient neutron diffusion equations. Most of the methods, however, are limited to two energy groups for practical application. The objective of this research is the development of a static and transient, multidimensional nodal method which allows more than two energy groups and uses a non-linear iterative method for efficient solution of the nodal equations. For both the static and transient methods, finite-difference equations which are corrected by the use of discontinuity factors are derived. The discontinuity factors are computed from a polynomial nodal method using a non-linear iteration technique. The polynomial nodal method is based upon a quartic approximation and utilizes a quadratic transverse-leakage approximation. The solution of the time-dependent equations is performed by the use of a quasi-static method in which the node-averaged fluxes are factored into shape and amplitude functions. The application of the quasi-static polynomial method to several benchmark problems demonstrates that the accuracy is consistent with that of other nodal methods. The use of the quasi-static method is shown to substantially reduce the computation time over the traditional fully-implicit time-integration method. Problems involving thermal-hydraulic feedback are accurately, and efficiently, solved by performing several reactivity/thermal-hydraulic updates per shape calculation.
Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion
NASA Astrophysics Data System (ADS)
Perkó, Zoltán; van der Voort, Sebastian R.; van de Water, Steven; Hartman, Charlotte M. H.; Hoogeman, Mischa; Lathouwers, Danny
2016-06-01
The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications.
Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion.
Perkó, Zoltán; van der Voort, Sebastian R; van de Water, Steven; Hartman, Charlotte M H; Hoogeman, Mischa; Lathouwers, Danny
2016-06-21
The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications. PMID:27227661
Mapping Landslides in Lunar Impact Craters Using Chebyshev Polynomials and Dem's
NASA Astrophysics Data System (ADS)
Yordanov, V.; Scaioni, M.; Brunetti, M. T.; Melis, M. T.; Zinzi, A.; Giommi, P.
2016-06-01
Geological slope failure processes have been observed on the Moon surface for decades, nevertheless a detailed and exhaustive lunar landslide inventory has not been produced yet. For a preliminary survey, WAC images and DEM maps from LROC at 100 m/pixels have been exploited in combination with the criteria applied by Brunetti et al. (2015) to detect the landslides. These criteria are based on the visual analysis of optical images to recognize mass wasting features. In the literature, Chebyshev polynomials have been applied to interpolate crater cross-sections in order to obtain a parametric characterization useful for classification into different morphological shapes. Here a new implementation of Chebyshev polynomial approximation is proposed, taking into account some statistical testing of the results obtained during Least-squares estimation. The presence of landslides in lunar craters is then investigated by analyzing the absolute values off odd coefficients of estimated Chebyshev polynomials. A case study on the Cassini A crater has demonstrated the key-points of the proposed methodology and outlined the required future development to carry out.
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.
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.
Improvement on the polynomial modeling of digital camera colorimetric characterization
NASA Astrophysics Data System (ADS)
Huang, Xiaoqiao; Yu, Hongfei; Shi, Junsheng; Tai, Yonghang
2014-11-01
The digital camera has become a requisite for people's life, also essential in imaging applications, and it is important to get more accurate colors with digital camera. The colorimetric characterization of digital camera is the basis of image copy and color management process. One of the traditional methods for deriving a colorimetric mapping between camera RGB signals and the tristimulus values CIEXYZ is to use polynomial modeling with 3×11 polynomial transfer matrices. In this paper, an improved polynomial modeling is presented, in which the normalized luminance replaces the camera inherent RGB values in the traditional polynomial modeling. The improved modeling can be described by a two stage model. The first stage, relationship between the camera RGB values and normalized luminance with six gray patches in the X-rite ColorChecker 24-color card was described as "Gamma", camera RGB values were converted into normalized luminance using Gamma. The second stage, the traditional polynomial modeling was improved to the colorimetric mapping between normalized luminance and the CIEXYZ. Meanwhile, this method was used under daylight lighting environment, the users can not measure the CIEXYZ of the color target char using professional instruments, but they can accomplish the task of the colorimetric characterization of digital camera. The experimental results show that: (1) the proposed method for the colorimetric characterization of digital camera performs better than traditional polynomial modeling; (2) it's a feasible approach to handle the color characteristics using this method under daylight environment without professional instruments, the result can satisfy for request of simple application.
Connection preserving deformations and q-semi-classical orthogonal polynomials
NASA Astrophysics Data System (ADS)
Ormerod, Christopher M.; Witte, N. S.; Forrester, Peter J.
2011-09-01
We present a framework for the study of q-difference equations satisfied by q-semi-classical orthogonal systems. As an example, we identify the q-difference equation satisfied by a deformed version of the little q-Jacobi polynomials as a gauge transformation of a special case of the associated linear problem for q-PVI. We obtain a parametrization of the associated linear problem in terms of orthogonal polynomial variables and find the relation between this parametrization and that of Jimbo and Sakai.
Discrete-time ? filtering for nonlinear polynomial systems
NASA Astrophysics Data System (ADS)
Basin, M. V.; Hernandez-Gonzalez, M.
2016-07-01
This paper presents a suboptimal ? filtering problem solution for a class of discrete-time nonlinear polynomial systems over linear observations. The solution is obtained splitting the whole problem into finding a-priori and a-posteriori equations for state estimates and gain matrices. The closed-form filtering equations for the state estimate and gain matrix are obtained in case of a third-degree polynomial system. Numerical simulations are carried out to show effectiveness of the proposed filter. The obtained filter is compared to the extended Kalman-like ? filter.
Hermite polynomial excited squeezed vacuum as quantum optical vortex states
NASA Astrophysics Data System (ADS)
Li, Ya-Zhou; Jia, Fang; Zhang, Hao-Liang; Huang, Jie-Hui; Hu, Li-Yun
2015-11-01
We introduce theoretically a kind of Hermite polynomial excited squeezed vacuum by extending the wave-packet states with a vortex structure to a general case. Its normalised factor is found to be the Legendre polynomial and the condition converting the general case to a special one is achieved. Then we consider its statistical properties according to the photon number distribution and the Wigner function. As an application, we investigate the performance of the teleportation of the coherent state. It is shown that these parameters in the generalised state can modulate all the above properties including the vortex structure.
A novel computational approach to approximate fuzzy interpolation polynomials.
Jafarian, Ahmad; Jafari, Raheleh; Mohamed Al Qurashi, Maysaa; Baleanu, Dumitru
2016-01-01
This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form [Formula: see text] where [Formula: see text] is crisp number (for [Formula: see text], which interpolates the fuzzy data [Formula: see text]. Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient. PMID:27625982
Integrability and Transition Coefficients Related to Jack Polynomials
NASA Astrophysics Data System (ADS)
Liu, Zhi-Sheng; Xu, Ying-Ying; Yu, Ming
2014-05-01
Integrability plays a central role in solving many body problems in physics. The explicit construction of the Jack polynomials is an essential ingredient in solving the Calogero—Sutherland model, which is a one-dimensional integrable system. Starting from a special class of the Jack polynomials associated to the hook Young diagram, we find a systematic way in the explicit construction of the transition coefficients in the power-sum basis, which is closely related to a set of mutually commuting operators, i.e. the conserved charges.
Multi-mode entangled states represented as Grassmannian polynomials
NASA Astrophysics Data System (ADS)
Maleki, Y.
2016-06-01
We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map the Hilbert space of the finite-dimensional multi-mode states to the space of some Grassmannian polynomial functions. These Grassmannian polynomials form a well-defined space in the framework of Grassmann variables; namely Grassmannian representative space. Therefore, a quantum state can be uniquely defined and determined by an element of Grassmannian representative space. Furthermore, the Grassmannian representatives of some maximally entangled states are considered, and it is shown that there is a tight connection between the entanglement of the states and their Grassmannian representatives.
Polynomial approximation of Poincare maps for Hamiltonian system
NASA Technical Reports Server (NTRS)
Froeschle, Claude; Petit, Jean-Marc
1992-01-01
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Two-variable orthogonal polynomials of big q-Jacobi type
NASA Astrophysics Data System (ADS)
Lewanowicz, Stanislaw; Wozny, Pawel
2010-01-01
A four-parameter family of orthogonal polynomials in two discrete variables is defined for a weight function of basic hypergeometric type. The polynomials, which are expressed in terms of univariate big q-Jacobi polynomials, form an extension of Dunkl's bivariate (little) q-Jacobi polynomials [C.F. Dunkl, Orthogonal polynomials in two variables of q-Hahn and q-Jacobi type, SIAM J. Algebr. Discrete Methods 1 (1980) 137-151]. We prove orthogonality property of the new polynomials, and show that they satisfy a three-term relation in a vector-matrix notation, as well as a second-order partial q-difference equation.
Kauffman knot polynomials in classical abelian Chern-Simons field theory
Liu Xin
2010-12-15
Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant t{sup I(L)} is constructed for a link L, where I is the abelian Chern-Simons action and t a formal constant. For oriented knotted vortex lines, t{sup I} satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, t{sup I} satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.
The rK39 strip test is non-predictor of clinical status for kala-azar
Singh, Dharmendra P; Sundar, Shyam; Mohapatra, Tribhuban M
2009-01-01
Background The rK39 strip test is reported to be simple, sensitive, specific, non-invasive and economical test. Since this method is supposed to be patient friendly, it may easily be accepted for sero-epidemiological surveys. An attempt was made to evaluate the role of rK39 strip test in pre and post treatment phases of Kala azar, as a diagnostic and prognostic marker, in addition to other laboratory investigations, in order to evaluate its role in sero-epidemiological surveys. Findings A total of 210 cases were selected for the study. One hundred clinically and parasitologically confirmed cases were corroborated with other hematological profiles. The formol-gel test was included along with well matched control group comprising of normal endemic controls (50), non-endemic normals (20) and other febrile cases (40). All groups were tested by rK39 strip test. Fifty Kala azar cases were followed up after completion of successful treatment. They were subjected to rK39 strip test after 0, 90 and 180 days of completion of successful treatment. The rK39 showed sensitivity, specificity, PPV, NPV, and diagnostic accuracy of 98% (95% CI 91.7-100), 100%, 100%, 90% (95% CI 66-100) and 98% (95% CI 92.6-100) respectively. All the 50 cured followed up cases showed positive result by rK39 strip test even after 180 days of completion of successful treatment. Conclusion The test seems an ideal qualitative test for the diagnosis of kala-azar. But for sero-epidemiological studies the test may be used with other parameters. Alternatively a quantitative ELISA using rK39 antigen may be used. PMID:19772616
Computer Algebra Systems and Theorems on Real Roots of Polynomials
ERIC Educational Resources Information Center
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
Verification of bifurcation diagrams for polynomial-like equations
NASA Astrophysics Data System (ADS)
Korman, Philip; Li, Yi; Ouyang, Tiancheng
2008-03-01
The results of our recent paper [P. Korman, Y. Li, T. Ouyang, Computing the location and the direction of bifurcation, Math. Res. Lett. 12 (2005) 933-944] appear to be sufficient to justify computer-generated bifurcation diagram for any autonomous two-point Dirichlet problem. Here we apply our results to polynomial-like nonlinearities.
Computing Tutte polynomials of contact networks in classrooms
NASA Astrophysics Data System (ADS)
Hincapié, Doracelly; Ospina, Juan
2013-05-01
Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network
Computational Technique for Teaching Mathematics (CTTM): Visualizing the Polynomial's Resultant
ERIC Educational Resources Information Center
Alves, Francisco Regis Vieira
2015-01-01
We find several applications of the Dynamic System Geogebra--DSG related predominantly to the basic mathematical concepts at the context of the learning and teaching in Brasil. However, all these works were developed in the basic level of Mathematics. On the other hand, we discuss and explore, with DSG's help, some applications of the polynomial's…
Chemical Equilibrium and Polynomial Equations: Beware of Roots.
ERIC Educational Resources Information Center
Smith, William R.; Missen, Ronald W.
1989-01-01
Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…
Variational Iteration Method for Delay Differential Equations Using He's Polynomials
NASA Astrophysics Data System (ADS)
Mohyud-Din, Syed Tauseef; Yildirim, Ahmet
2010-12-01
January 21, 2010 In this paper, we apply the variational iteration method using He's polynomials (VIMHP) for solving delay differential equations which are otherwise too difficult to solve. These equations arise very frequently in signal processing, digital images, physics, and applied sciences. Numerical results reveal the complete reliability and efficiency of the proposed combination.
The Coulomb problem on a 3-sphere and Heun polynomials
NASA Astrophysics Data System (ADS)
Bellucci, Stefano; Yeghikyan, Vahagn
2013-08-01
The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials.
The Coulomb problem on a 3-sphere and Heun polynomials
Bellucci, Stefano; Yeghikyan, Vahagn
2013-08-15
The paper studies the quantum mechanical Coulomb problem on a 3-sphere. We present a special parametrization of the ellipto-spheroidal coordinate system suitable for the separation of variables. After quantization we get the explicit form of the spectrum and present an algebraic equation for the eigenvalues of the Runge-Lentz vector. We also present the wave functions expressed via Heun polynomials.
Can a polynomial interpolation improve on the Kaplan Yorke dimension?
NASA Astrophysics Data System (ADS)
Richter, Hendrik
2008-06-01
The Kaplan-Yorke dimension can be derived using a linear interpolation between an h-dimensional Lyapunov exponent λ>0 and an h+1-dimensional Lyapunov exponent λ<0. In this Letter, we use a polynomial interpolation to obtain generalized Lyapunov dimensions and study the relationships among them for higher-dimensional systems.
Spatial image polynomial decomposition with application to video classification
NASA Astrophysics Data System (ADS)
El Moubtahij, Redouane; Augereau, Bertrand; Tairi, Hamid; Fernandez-Maloigne, Christine
2015-11-01
This paper addresses the use of orthogonal polynomial basis transform in video classification due to its multiple advantages, especially for multiscale and multiresolution analysis similar to the wavelet transform. In our approach, we benefit from these advantages to reduce the resolution of the video by using a multiscale/multiresolution decomposition to define a new algorithm that decomposes a color image into geometry and texture component by projecting the image on a bivariate polynomial basis and considering the geometry component as the partial reconstruction and the texture component as the remaining part, and finally to model the features (like motion and texture) extracted from reduced image sequences by projecting them into a bivariate polynomial basis in order to construct a hybrid polynomial motion texture video descriptor. To evaluate our approach, we consider two visual recognition tasks, namely the classification of dynamic textures and recognition of human actions. The experimental section shows that the proposed approach achieves a perfect recognition rate in the Weizmann database and highest accuracy in the Dyntex++ database compared to existing methods.
XXZ-type Bethe ansatz equations and quasi-polynomials
NASA Astrophysics Data System (ADS)
Li, Jian Rong; Tarasov, Vitaly
2013-01-01
We study solutions of the Bethe ansatz equation for the XXZ-type integrable model associated with the Lie algebra fraktur sfraktur lN. We give a correspondence between solutions of the Bethe ansatz equations and collections of quasi-polynomials. This extends the results of E. Mukhin and A. Varchenko for the XXX-type model and the trigonometric Gaudin model.
The complexity of class polynomial computation via floating point approximations
NASA Astrophysics Data System (ADS)
Enge, Andreas
2009-06-01
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the presented approaches uses a technique devised by Dupont to evaluate modular functions by Newton iterations on an expression involving the arithmetic-geometric mean. Under the heuristic assumption, justified by experiments, that the correctness of the result is not perturbed by rounding errors, the algorithm runs in time O left( sqrt {\\vert D\\vert} log^3 \\vert D\\vert M left( sq... ...arepsilon} \\vert D\\vert right) subseteq O left( h^{2 + \\varepsilon} right) for any \\varepsilon > 0 , where D is the CM discriminant, h is the degree of the class polynomial and M (n) is the time needed to multiply two n -bit numbers. Up to logarithmic factors, this running time matches the size of the constructed polynomials. The estimate also relies on a new result concerning the complexity of enumerating the class group of an imaginary quadratic order and on a rigorously proven upper bound for the height of class polynomials.
Effects of Polynomial Trends on Detrending Moving Average Analysis
NASA Astrophysics Data System (ADS)
Shao, Ying-Hui; Gu, Gao-Feng; Jiang, Zhi-Qiang; Zhou, Wei-Xing
2015-07-01
The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.
New Bernstein type inequalities for polynomials on ellipses
NASA Technical Reports Server (NTRS)
Freund, Roland; Fischer, Bernd
1990-01-01
New and sharp estimates are derived for the growth in the complex plane of polynomials known to have a curved majorant on a given ellipse. These so-called Bernstein type inequalities are closely connected with certain constrained Chebyshev approximation problems on ellipses. Also presented are some new results for approximation problems of this type.
Billiard systems with polynomial integrals of third and fourth degree
NASA Astrophysics Data System (ADS)
Kozlova, Tatiana
2001-03-01
The problem of the existence of polynomial-in-momenta first integrals for dynamical billiard systems is considered. Examples of billiards with irreducible integrals of third and fourth degree are constructed with the help of the integrable problems of Goryachev-Chaplygin and Kovalevsky from rigid body dynamics.
Solutions of differential equations in a Bernstein polynomial basis
NASA Astrophysics Data System (ADS)
Idrees Bhatti, M.; Bracken, P.
2007-08-01
An algorithm for approximating solutions to differential equations in a modified new Bernstein polynomial basis is introduced. The algorithm expands the desired solution in terms of a set of continuous polynomials over a closed interval and then makes use of the Galerkin method to determine the expansion coefficients to construct a solution. Matrix formulation is used throughout the entire procedure. However, accuracy and efficiency are dependent on the size of the set of Bernstein polynomials and the procedure is much simpler compared to the piecewise B spline method for solving differential equations. A recursive definition of the Bernstein polynomials and their derivatives are also presented. The current procedure is implemented to solve three linear equations and one nonlinear equation, and excellent agreement is found between the exact and approximate solutions. In addition, the algorithm improves the accuracy and efficiency of the traditional methods for solving differential equations that rely on much more complicated numerical techniques. This procedure has great potential to be implemented in more complex systems where there are no exact solutions available except approximations.
Finding All Coefficients of a Polynomial with One Calculation.
ERIC Educational Resources Information Center
Satianov, Pavel
2003-01-01
The values of a polynomial with integer coefficients can be computed using a graphing calculator, but it is impossible to see the formula itself. Suggests finding this formula from numerical data and describes the unusual way to solve this problem with one calculation only. (Author/NB)
Chebyshev moment problems: Maximum entropy and kernel polynomial methods
Silver, R.N.; Roeder, H.; Voter, A.F.; Kress, J.D.
1995-12-31
Two Chebyshev recursion methods are presented for calculations with very large sparse Hamiltonians, the kernel polynomial method (KPM) and the maximum entropy method (MEM). They are applicable to physical properties involving large numbers of eigenstates such as densities of states, spectral functions, thermodynamics, total energies for Monte Carlo simulations and forces for tight binding molecular dynamics. this paper emphasizes efficient algorithms.
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.
On Polynomials of Prescribed Height in Finite Fields
NASA Astrophysics Data System (ADS)
Shparlinskiĭ, I. E.
1989-02-01
This paper deals with the set \\mathfrak{M}(B) of monic polynomials of degree n with integral coefficients belonging to a given n-dimensional cube B with side h. An asymptotic formula is obtained for the number of polynomials in \\mathfrak{M}(B) having a specific type of decomposition into irreducible factors modulo some prime p, and an asymptotic formula for the number of primitive polynomials modulo p in \\mathfrak{M}(B), which translates when n=1 into known results of I. M. Vinogradov on the distribution of primitive roots. These asymptotic formulas are nontrivial when h\\geq p^{n/(n+1)+\\varepsilon} for any \\varepsilon>0.Moreover, an asymptotic formula is obtained for the average value of the number of divisors modulo p of polynomials in \\mathfrak{M}(B), a result that is nontrivial when h\\geq\\max(p^{1-2/n}\\ln p,\\,p^{1/2}\\ln p).Bibliography: 11 titles.
Modelling Childhood Growth Using Fractional Polynomials and Linear Splines
Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.
2014-01-01
Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651
Segmented Polynomial Models in Quasi-Experimental Research.
ERIC Educational Resources Information Center
Wasik, John L.
1981-01-01
The use of segmented polynomial models is explained. Examples of design matrices of dummy variables are given for the least squares analyses of time series and discontinuity quasi-experimental research designs. Linear combinations of dummy variable vectors appear to provide tests of effects in the two quasi-experimental designs. (Author/BW)
FEDOROVA,A.; ZEITLIN,M.; PARSA,Z.
2000-03-31
In this paper the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to a variational approach in the general case they have the solution as a multiresolution (multiscales) expansion on the base of compactly supported wavelet basis. They give an extension of their results to the cases of periodic orbital particle motion and arbitrary variable coefficients. Then they consider more flexible variational method which is based on a biorthogonal wavelet approach. Also they consider a different variational approach, which is applied to each scale.
Multimodal fusion of polynomial classifiers for automatic person recgonition
NASA Astrophysics Data System (ADS)
Broun, Charles C.; Zhang, Xiaozheng
2001-03-01
With the prevalence of the information age, privacy and personalization are forefront in today's society. As such, biometrics are viewed as essential components of current evolving technological systems. Consumers demand unobtrusive and non-invasive approaches. In our previous work, we have demonstrated a speaker verification system that meets these criteria. However, there are additional constraints for fielded systems. The required recognition transactions are often performed in adverse environments and across diverse populations, necessitating robust solutions. There are two significant problem areas in current generation speaker verification systems. The first is the difficulty in acquiring clean audio signals in all environments without encumbering the user with a head- mounted close-talking microphone. Second, unimodal biometric systems do not work with a significant percentage of the population. To combat these issues, multimodal techniques are being investigated to improve system robustness to environmental conditions, as well as improve overall accuracy across the population. We propose a multi modal approach that builds on our current state-of-the-art speaker verification technology. In order to maintain the transparent nature of the speech interface, we focus on optical sensing technology to provide the additional modality-giving us an audio-visual person recognition system. For the audio domain, we use our existing speaker verification system. For the visual domain, we focus on lip motion. This is chosen, rather than static face or iris recognition, because it provides dynamic information about the individual. In addition, the lip dynamics can aid speech recognition to provide liveness testing. The visual processing method makes use of both color and edge information, combined within Markov random field MRF framework, to localize the lips. Geometric features are extracted and input to a polynomial classifier for the person recognition process. A late
Efficient modeling of photonic crystals with local Hermite polynomials
NASA Astrophysics Data System (ADS)
Boucher, C. R.; Li, Zehao; Albrecht, J. D.; Ram-Mohan, L. R.
2014-04-01
Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.
Efficient modeling of photonic crystals with local Hermite polynomials
Boucher, C. R.; Li, Zehao; Albrecht, J. D.; Ram-Mohan, L. R.
2014-04-21
Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.
Transfer matrix computation of critical polynomials for two-dimensional Potts models
Jacobsen, Jesper Lykke; Scullard, Christian R.
2013-02-04
We showed, In our previous work, that critical manifolds of the q-state Potts model can be studied by means of a graph polynomial P_{B}(q, v), henceforth referred to as the critical polynomial. This polynomial may be defined on any periodic two-dimensional lattice. It depends on a finite subgraph B, called the basis, and the manner in which B is tiled to construct the lattice. The real roots v = e^{K} — 1 of P_{B}(q, v) either give the exact critical points for the lattice, or provide approximations that, in principle, can be made arbitrarily accurate by increasing the size of B in an appropriate way. In earlier work, P_{B}(q, v) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give a probabilistic definition of P_{B}(q, v), which facilitates its computation, using the transfer matrix, on much larger B than was previously possible.We present results for the critical polynomial on the (4, 8^{2}), kagome, and (3, 12^{2}) lattices for bases of up to respectively 96, 162, and 243 edges, compared to the limit of 36 edges with contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. The critical temperatures v_{c }obtained for ferromagnetic (v > 0) Potts models are at least as precise as the best available results from Monte Carlo simulations or series expansions. For instance, with q = 3 we obtain v_{c}(4, 8^{2}) = 3.742 489 (4), v_{c}(kagome) = 1.876 459 7 (2), and v_{c}(3, 12^{2}) = 5.033 078 49 (4), the precision being comparable or superior to the best simulation results. More generally, we trace the critical manifolds in the real (q, v) plane and discuss the intricate structure of the phase diagram in the antiferromagnetic (v < 0) region.
NASA Astrophysics Data System (ADS)
Calogero, Francesco; Yi, Ge
2013-06-01
By investigating the behavior of two solvable isochronous N-body problems in the immediate vicinity of their equilibria, functional equations satisfied by the para-Jacobi polynomial {pN (0, 1; γ; x )} and by the Jacobi polynomial {PN^{(-N-1,-N-1 )} (x )} (or, equivalently, by the Gegenbauer polynomial {CN^{-N-1/2}( x ) }) are identified, as well as Diophantine properties of the zeros and coefficients of these polynomials.
Rodriguez-Cardenas, Yalil Augusto; Arriola-Guillen, Luis Ernesto; Flores-Mir, Carlos
2014-01-01
OBJECTIVE: The objective of this study was to evaluate the Björk and Jabarak cephalometric analysis generated from cone-beam computed tomography (CBCT) synthesized lateral cephalograms in adults with different sagittal skeletal patterns. METHODS: The sample consisted of 46 CBCT synthesized cephalograms obtained from patients between 16 and 40 years old. A Björk and Jarabak cephalometric analysis among different sagittal skeletal classes was performed. Analysis of variance (ANOVA), multiple range test of Tukey, Kruskal-Wallis test, and independent t-test were used as appropriate. RESULTS: In comparison to the standard values: Skeletal Class III had increased gonial and superior gonial angles (P < 0.001). This trend was also evident when sex was considered. For Class I males, the sella angle was decreased (P = 0.041), articular angle increased (P = 0.027) and gonial angle decreased (P = 0.002); whereas for Class III males, the gonial angle was increased (P = 0.012). For Class I females, the articular angle was increased (P = 0.029) and the gonial angle decreased (P = 0.004). Björk's sum and Björk and Jabarak polygon sum showed no significant differences. The facial biotype presented in the three sagittal classes was mainly hypodivergent and neutral. CONCLUSIONS: In this sample, skeletal Class III malocclusion was strongly differentiated from the other sagittal classes, specifically in the mandible, as calculated through Björk and Jarabak analysis. PMID:25628079
Huang, Zhinan; Tang, Jun; Duan, Weike; Wang, Zhen; Song, Xiaoming; Hou, Xilin
2015-01-01
The sucrose non-fermenting 1-related protein kinase 2 (SnRK2) family members are plant-specific serine/threonine kinases that are involved in the plant response to abiotic stress and abscisic acid (ABA)-dependent plant development. Further understanding of the evolutionary history and expression characteristics of these genes will help to elucidate the mechanisms of the stress tolerance in Pak-choi, an important green leafy vegetable in China. Thus, we investigated the evolutionary patterns, footprints and conservation of SnRK2 genes in selected plants and later cloned and analyzed SnRK2 genes in Pak-choi. We found that this gene family was preferentially retained in Brassicas after the Brassica-Arabidopsis thaliana split. Next, we cloned and sequenced 13 SnRK2 from both cDNA and DNA libraries of stress-induced Pak-choi, which were under conditions of ABA, salinity, cold, heat, and osmotic treatments. Most of the BcSnRK2s have eight exons and could be divided into three groups. The subcellular localization predictions suggested that the putative BcSnRK2 proteins were enriched in the nucleus. The results of an analysis of the expression patterns of the BcSnRK2 genes showed that BcSnRK2 group III genes were robustly induced by ABA treatments. Most of the BcSnRK2 genes were activated by low temperature, and the BcSnRK2.6 genes responded to both ABA and low temperature. In fact, most of the BcSnRK2 genes showed positive or negative regulation under ABA and low temperature treatments, suggesting that they may be global regulators that function at the intersection of multiple signaling pathways to play important roles in Pak-choi stress responses. PMID:26557127
Huang, Zhinan; Tang, Jun; Duan, Weike; Wang, Zhen; Song, Xiaoming; Hou, Xilin
2015-01-01
The sucrose non-fermenting 1-related protein kinase 2 (SnRK2) family members are plant-specific serine/threonine kinases that are involved in the plant response to abiotic stress and abscisic acid (ABA)-dependent plant development. Further understanding of the evolutionary history and expression characteristics of these genes will help to elucidate the mechanisms of the stress tolerance in Pak-choi, an important green leafy vegetable in China. Thus, we investigated the evolutionary patterns, footprints and conservation of SnRK2 genes in selected plants and later cloned and analyzed SnRK2 genes in Pak-choi. We found that this gene family was preferentially retained in Brassicas after the Brassica-Arabidopsis thaliana split. Next, we cloned and sequenced 13 SnRK2 from both cDNA and DNA libraries of stress-induced Pak-choi, which were under conditions of ABA, salinity, cold, heat, and osmotic treatments. Most of the BcSnRK2s have eight exons and could be divided into three groups. The subcellular localization predictions suggested that the putative BcSnRK2 proteins were enriched in the nucleus. The results of an analysis of the expression patterns of the BcSnRK2 genes showed that BcSnRK2 group III genes were robustly induced by ABA treatments. Most of the BcSnRK2 genes were activated by low temperature, and the BcSnRK2.6 genes responded to both ABA and low temperature. In fact, most of the BcSnRK2 genes showed positive or negative regulation under ABA and low temperature treatments, suggesting that they may be global regulators that function at the intersection of multiple signaling pathways to play important roles in Pak-choi stress responses. PMID:26557127
Yoo, Mi-Jeong; Ma, Tianyi; Zhu, Ning; Liu, Lihong; Harmon, Alice C; Wang, Qiaomei; Chen, Sixue
2016-05-01
Sucrose non-fermenting-1-related protein kinase 2 (SnRK2) proteins constitute a small plant-specific serine/threonine kinase family involved in abscisic acid (ABA) signaling and plant responses to biotic and abiotic stresses. Although SnRK2s have been well-studied in Arabidopsis thaliana, little is known about SnRK2s in Brassica napus. Here we identified 30 putative sequences encoding 10 SnRK2 proteins in the B. napus genome and the expression profiles of a subset of 14 SnRK2 genes in guard cells of B. napus. In agreement with its polyploid origin, B. napus maintains both homeologs from its diploid parents. The results of quantitative real-time PCR (qRT-PCR) and reanalysis of RNA-Seq data showed that certain BnSnRK2 genes were commonly expressed in leaf tissues in different varieties of B. napus. In particular, qRT-PCR results showed that 12 of the 14 BnSnRK2s responded to drought stress in leaves and in ABA-treated guard cells. Among them, BnSnRK2.4 and BnSnRK2.6 were of interest because of their robust responsiveness to ABA treatment and drought stress. Notably, BnSnRK2 genes exhibited up-regulation of different homeologs, particularly in response to abiotic stress. The homeolog expression bias in BnSnRK2 genes suggests that parental origin of genes might be responsible for efficient regulation of stress responses in polyploids. This work has laid a foundation for future functional characterization of the different BnSnKR2 homeologs in B. napus and its parents, especially their functions in guard cell signaling and stress responses. PMID:26898295
From Chebyshev to Bernstein: A Tour of Polynomials Small and Large
ERIC Educational Resources Information Center
Boelkins, Matthew; Miller, Jennifer; Vugteveen, Benjamin
2006-01-01
Consider the family of monic polynomials of degree n having zeros at -1 and +1 and all their other real zeros in between these two values. This article explores the size of these polynomials using the supremum of the absolute value on [-1, 1], showing that scaled Chebyshev and Bernstein polynomials give the extremes.
A note on the zeros of Freud-Sobolev orthogonal polynomials
NASA Astrophysics Data System (ADS)
Moreno-Balcazar, Juan J.
2007-10-01
We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.
Design and Use of a Learning Object for Finding Complex Polynomial Roots
ERIC Educational Resources Information Center
Benitez, Julio; Gimenez, Marcos H.; Hueso, Jose L.; Martinez, Eulalia; Riera, Jaime
2013-01-01
Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…
Calabi-Yau three-folds:. Poincaré polynomials and fractals
NASA Astrophysics Data System (ADS)
Ashmore, Anthony; He, Yang-Hui
2013-10-01
We study the Poincaré polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the wellknown investigation into the distribution of the Euler characteristic and Hodge numbers. We find interesting fractal behaviour in the roots of these polynomials, in relation to the existence of isometries, distribution versus typicality, and mirror symmetry.
Test report : Raytheon / KTech RK30 energy storage system.
Rose, David Martin; Schenkman, Benjamin L.; Borneo, Daniel R.
2013-10-01
The Department of Energy Office of Electricity (DOE/OE), Sandia National Laboratories (SNL) and the Base Camp Integration Lab (BCIL) partnered together to incorporate an energy storage system into a microgrid configured Forward Operating Base to reduce the fossil fuel consumption and to ultimately save lives. Energy storage vendors will be sending their systems to SNL Energy Storage Test Pad (ESTP) for functional testing and then to the BCIL for performance evaluation. The technologies that will be tested are electro-chemical energy storage systems comprising of lead acid, lithium-ion or zinc-bromide. Raytheon/KTech has developed an energy storage system that utilizes zinc-bromide flow batteries to save fuel on a military microgrid. This report contains the testing results and some limited analysis of performance of the Raytheon/KTech Zinc-Bromide Energy Storage System.
Matrix-valued polynomials in Lanczos type methods
Simoncini, V.; Gallopoulos, E.
1994-12-31
It is well known that convergence properties of iterative methods can be derived by studying the behavior of the residual polynomial over a suitable domain of the complex plane. Block Krylov subspace methods for the solution of linear systems A[x{sub 1},{hor_ellipsis}, x{sub s}] = [b{sub 1},{hor_ellipsis}, b{sub s}] lead to the generation of residual polynomials {phi}{sub m} {element_of} {bar P}{sub m,s} where {bar P}{sub m,s} is the subset of matrix-valued polynomials of maximum degree m and size s such that {phi}{sub m}(0) = I{sub s}, R{sub m} := B - AX{sub m} = {phi}{sub m}(A) {circ} R{sub 0}, where {phi}{sub m}(A) {circ} R{sub 0} := R{sub 0} - A{summation}{sub j=0}{sup m-1} A{sup j}R{sub 0}{xi}{sub j}, {xi}{sub j} {element_of} R{sup sxs}. An effective method has to balance adequate approximation with economical computation of iterates defined by the polynomial. Matrix valued polynomials can be used to improve the performance of block methods. Another approach is to solve for a single right-hand side at a time and use the generated information in order to update the approximations of the remaining systems. In light of this, a more general scheme is as follows: A subset of residuals (seeds) is selected and a block short term recurrence method is used to compute approximate solutions for the corresponding systems. At the same time the generated matrix valued polynomial is implicitly applied to the remaining residuals. Subsequently a new set of seeds is selected and the process is continued as above, till convergence of all right-hand sides. The use of a quasi-minimization technique ensures a smooth convergence behavior for all systems. In this talk the authors discuss the implementation of this class of algorithms and formulate strategies for the selection of parameters involved in the computation. Experiments and comparisons with other methods will be presented.
Bifurcation of critical periods of polynomial systems
NASA Astrophysics Data System (ADS)
Ferčec, Brigita; Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
2015-10-01
We describe a general approach to studying bifurcations of critical periods based on a complexification of the system and algorithms of computational algebra. Using this approach we obtain upper bounds on the number of critical periods of several families of cubic systems. In some cases we overcome the problem of nonradicality of a relevant ideal by moving it to a subalgebra generated by invariants of a group of linear transformations.
A comparison of polynomial approximations and artificial neural nets as response surfaces
NASA Technical Reports Server (NTRS)
Carpenter, William C.; Barthelemy, Jean-Francois M.
1992-01-01
Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net, and the number of designs needed to train an approximation is discussed.
A numerical experiment related to Zolotarev polynomials for weighted sup-norm
NASA Astrophysics Data System (ADS)
Sklyarov, V. P.
2011-10-01
The behavior of the graph of the function Z n ( t) = ∥ Z n '(·, t)∥/∥ Z n (·, t)∥ is discussed in the case where the functions Z n ( x, t) are the Zolotarev polynomials and the norm is a weighted sup norm. Based on calculations performed for various weights, it is conjectured that the characteristic jump in Z n ( t) in the case of the Laguerre weight on a semiaxis is caused by the fact that the weight function is not symmetric about the midpoint of the interval.
How the Jones polynomial give rise to physical states of quantum general relativity
Bruegmann, B. ); Gambini, R. ); Pullin, J. )
1993-01-01
Solutions to both the diffeomorphism and the hamiltonian constraint of quantum gravity have been found in the loop representation, which is based on Ashtekar's new variables. While the diffeomorphism constraint is easily solved by considering loop functionals which are knot invariants, there remains the puzzle why several of the known knot invariants are also solutions to the hamiltonian constraint. We show how the Jones polynomial gives rise to an infinite set of solutions to all the constraints of quantum gravity thereby illuminating the structure of the space of solutions and suggesting the existence of a deep connection between quantum gravity and knot theory at a dynamical level.
NASA Technical Reports Server (NTRS)
Tennyson, R. C.; Nanyaro, A. P.; Wharram, G. E.
1980-01-01
A comparative failure analysis is presented based on the application of quadratic and cubic forms of the tensor polynomial lamina strength criterion to various composite structural configurations in a plane stress state. Failure loads have been predicted for off-angle laminates under simple loading conditions and for symmetric-balanced laminates subject to varying degrees of biaxial tension, including configurations subject to multimode failures. Some experimental data are also provided to support these calculations. From these results, the necessity of employing a cubic strength criterion to accurately predict the failure of composite laminae is demonstrated.
Real-Time Curvature Defect Detection on Outer Surfaces Using Best-Fit Polynomial Interpolation
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
Fast Chebyshev-polynomial method for simulating the time evolution of linear dynamical systems.
Loh, Y L; Taraskin, S N; Elliott, S R
2001-05-01
We present a fast method for simulating the time evolution of any linear dynamical system possessing eigenmodes. This method does not require an explicit calculation of the eigenvectors and eigenfrequencies, and is based on a Chebyshev polynomial expansion of the formal operator matrix solution in the eigenfrequency domain. It does not suffer from the limitations of ordinary time-integration methods, and can be made accurate to almost machine precision. Among its possible applications are harmonic classical mechanical systems, quantum diffusion, and stochastic transport theory. An example of its use is given for the problem of vibrational wave-packet propagation in a disordered lattice. PMID:11415044
NASA Astrophysics Data System (ADS)
Wang, Feng; Chen, XueQin; Tsourdos, Antonios; White, Brian A.; Wu, YunHua
2011-06-01
A nonlinear relative position control algorithm is designed for spacecraft precise formation flying. Taking into account the effect of J2 gravitational perturbations and atmospheric drag, the relative motion dynamic equation of the formation flying is developed in a quasi-linear parameter-varying (QLPV) form without approximation. Base on this QLPV model, polynomial eigenstructure assignment (PEA) is applied to design the controller. The resulting PEA controller is a function of system state and parameters, and produces a closed-loop system with invariant performance over a wide range of conditions. Numerical simulation results show that the performance can fulfill precise formation flying requirements.
NASA Technical Reports Server (NTRS)
Tennyson, R. C.
1975-01-01
The experimental measures and techniques are described which are used to obtain the strength tensor components, including cubic terms. Based on a considerable number of biaxial pressure tests together with specimens subjected to a constant torque and internal pressure, a modified form of the plane stress tensor polynomial failure equation was obtained that was capable of predicting ultimate strength results well. Preliminary data were obtained to determine the effect of varying post cure times and ambient temperatures (-80 F to 250 F) on the change in two tensor strength terms, F sub 2 and F sub 22. Other laminate configurations yield corresponding variations for the remaining strength parameters.
ERIC Educational Resources Information Center
Rushton, J. Philippe
2004-01-01
First, I describe why intelligence (Spearman's "g") can only be fully understood through "r-K" theory, which places it into an evolutionary framework along with brain size, longevity, maturation speed, and several other life-history traits. The "r-K" formulation explains why IQ predicts longevity and also why the gap in mortality rates between…
White matter structure assessment from reduced HARDI data using low-rank polynomial approximations.
Gur, Yaniv; Jiao, Fangxiang; Zhu, Stella Xinghua; Johnson, Chris R
2012-10-01
Assessing white matter fiber orientations directly from DWI measurements in single-shell HARDI has many advantages. One of these advantages is the ability to model multiple fibers using fewer parameters than are required to describe an ODF and, thus, reduce the number of DW samples needed for the reconstruction. However, fitting a model directly to the data using Gaussian mixture, for instance, is known as an initialization-dependent unstable process. This paper presents a novel direct fitting technique for single-shell HARDI that enjoys the advantages of direct fitting without sacrificing the accuracy and stability even when the number of gradient directions is relatively low. This technique is based on a spherical deconvolution technique and decomposition of a homogeneous polynomial into a sum of powers of linear forms, known as a symmetric tensor decomposition. The fiber-ODF (fODF), which is described by a homogeneous polynomial, is approximated here by a discrete sum of even-order linear-forms that are directly related to rank-1 tensors and represent single-fibers. This polynomial approximation is convolved to a single-fiber response function, and the result is optimized against the DWI measurements to assess the fiber orientations and the volume fractions directly. This formulation is accompanied by a robust iterative alternating numerical scheme which is based on the Levenberg-Marquardt technique. Using simulated data and in vivo, human brain data we show that the proposed algorithm is stable, accurate and can model complex fiber structures using only 12 gradient directions. PMID:24818174
Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction
NASA Technical Reports Server (NTRS)
Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent
1993-01-01
The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.
Peng, Chen; Rothenburg, Stefan; Hersperger, Adam R.
2015-01-01
As a group, poxviruses have been shown to infect a wide variety of animal species. However, there is individual variability in the range of species able to be productively infected. In this study, we observed that ectromelia virus (ECTV) does not replicate efficiently in cultured rabbit RK13 cells. Conversely, vaccinia virus (VACV) replicates well in these cells. Upon infection of RK13 cells, the replication cycle of ECTV is abortive in nature, resulting in a greatly reduced ability to spread among cells in culture. We observed ample levels of early gene expression but reduced detection of virus factories and severely blunted production of enveloped virus at the cell surface. This work focused on two important host range genes, named E3L and K3L, in VACV. Both VACV and ECTV express a functional protein product from the E3L gene, but only VACV contains an intact K3L gene. To better understand the discrepancy in replication capacity of these viruses, we examined the ability of ECTV to replicate in wild-type RK13 cells compared to cells that constitutively express E3 and K3 from VACV. The role these proteins play in the ability of VACV to replicate in RK13 cells was also analyzed to determine their individual contribution to viral replication and PKR activation. Since E3L and K3L are two relevant host range genes, we hypothesized that expression of one or both of them may have a positive impact on the ability of ECTV to replicate in RK13 cells. Using various methods to assess virus growth, we did not detect any significant differences with respect to the replication of ECTV between wild-type RK13 compared to versions of this cell line that stably expressed VACV E3 alone or in combination with K3. Therefore, there remain unanswered questions related to the factors that limit the host range of ECTV. PMID:25734776
Hand, Erin S; Haller, Sherry L; Peng, Chen; Rothenburg, Stefan; Hersperger, Adam R
2015-01-01
As a group, poxviruses have been shown to infect a wide variety of animal species. However, there is individual variability in the range of species able to be productively infected. In this study, we observed that ectromelia virus (ECTV) does not replicate efficiently in cultured rabbit RK13 cells. Conversely, vaccinia virus (VACV) replicates well in these cells. Upon infection of RK13 cells, the replication cycle of ECTV is abortive in nature, resulting in a greatly reduced ability to spread among cells in culture. We observed ample levels of early gene expression but reduced detection of virus factories and severely blunted production of enveloped virus at the cell surface. This work focused on two important host range genes, named E3L and K3L, in VACV. Both VACV and ECTV express a functional protein product from the E3L gene, but only VACV contains an intact K3L gene. To better understand the discrepancy in replication capacity of these viruses, we examined the ability of ECTV to replicate in wild-type RK13 cells compared to cells that constitutively express E3 and K3 from VACV. The role these proteins play in the ability of VACV to replicate in RK13 cells was also analyzed to determine their individual contribution to viral replication and PKR activation. Since E3L and K3L are two relevant host range genes, we hypothesized that expression of one or both of them may have a positive impact on the ability of ECTV to replicate in RK13 cells. Using various methods to assess virus growth, we did not detect any significant differences with respect to the replication of ECTV between wild-type RK13 compared to versions of this cell line that stably expressed VACV E3 alone or in combination with K3. Therefore, there remain unanswered questions related to the factors that limit the host range of ECTV. PMID:25734776
Laguerre-Polynomial-Weighted Two-Mode Squeezed State
NASA Astrophysics Data System (ADS)
He, Rui; Fan, Hong-Yi; Song, Jun; Zhou, Jun
2016-07-01
We propose a new optical field named Laguerre-polynomial-weighted two-mode squeezed state. We find that such a state can be generated by passing the l-photon excited two-mode squeezed vacuum state C l a † l S 2|00> through an single-mode amplitude damping channel. Physically, this paper actually is concerned what happens when both excitation and damping of photons co-exist for a two-mode squeezed state, e.g., dessipation of photon-added two-mode squeezed vacuum state. We employ the summation method within ordered product of operators and a new generating function formula about two-variable Hermite polynomials to proceed our discussion.
Using the network reliability polynomial to characterize and design networks
EUBANK, STEPHEN; YOUSSEF, MINA; KHORRAMZADEH, YASAMIN
2015-01-01
We consider methods for solving certain network characterization and design problems that arise in network epidemiology. We argue that the network reliability polynomial introduced by Moore and Shannon is a useful framework in which to reason about these problems. Specifically, we show how efficient estimation of the polynomial permits characterizing and distinguishing very large networks in ways that are are dynamically relevant. Furthermore, a generalization of flows and cuts to structures that determine the reliability suggests a new measure of edge or vertex centrality that we call criticality. We describe how criticality is related to the more common notion of betweenness and illustrate its application to targeting interventions to control outbreaks of infectious disease. Although our applications are to infectious disease outbreaks, the methods we develop are applicable to many other diffusive dynamical systems over complex networks. PMID:26085930
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.
Weighted discrete least-squares polynomial approximation using randomized quadratures
NASA Astrophysics Data System (ADS)
Zhou, Tao; Narayan, Akil; Xiu, Dongbin
2015-10-01
We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results.
Wick polynomials and time-evolution of cumulants
NASA Astrophysics Data System (ADS)
Lukkarinen, Jani; Marcozzi, Matteo
2016-08-01
We show how Wick polynomials of random variables can be defined combinatorially as the unique choice, which removes all "internal contractions" from the related cumulant expansions, also in a non-Gaussian case. We discuss how an expansion in terms of the Wick polynomials can be used for derivation of a hierarchy of equations for the time-evolution of cumulants. These methods are then applied to simplify the formal derivation of the Boltzmann-Peierls equation in the kinetic scaling limit of the discrete nonlinear Schödinger equation (DNLS) with suitable random initial data. We also present a reformulation of the standard perturbation expansion using cumulants, which could simplify the problem of a rigorous derivation of the Boltzmann-Peierls equation by separating the analysis of the solutions to the Boltzmann-Peierls equation from the analysis of the corrections. This latter scheme is general and not tied to the DNLS evolution equations.
Experimental approximation of the Jones polynomial with one quantum bit.
Passante, G; Moussa, O; Ryan, C A; Laflamme, R
2009-12-18
We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time. PMID:20366244
Better Polynomial Algorithms on Graphs of Bounded Rank-Width
NASA Astrophysics Data System (ADS)
Ganian, Robert; Hliněný, Petr
Although there exist many polynomial algorithms for NP-hard problems running on a bounded clique-width expression of the input graph, there exists only little comparable work on such algorithms for rank-width. We believe that one reason for this is the somewhat obscure and hard-to-grasp nature of rank-decompositions. Nevertheless, strong arguments for using the rank-width parameter have been given by recent formalisms independently developed by Courcelle and Kanté, by the authors, and by Bui-Xuan et al. This article focuses on designing formally clean and understandable "pseudopolynomial" (XP) algorithms solving "hard" problems (non-FPT) on graphs of bounded rank-width. Those include computing the chromatic number and polynomial or testing the Hamiltonicity of a graph and are extendable to many other problems.
Correlations of RMT characteristic polynomials and integrability: Hermitean matrices
NASA Astrophysics Data System (ADS)
Osipov, Vladimir Al.; Kanzieper, Eugene
2010-10-01
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of τ functions, we (i) identify a zoo of hierarchical relations satisfied by τ functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasis is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.
Correlations of RMT characteristic polynomials and integrability: Hermitean matrices
Osipov, Vladimir Al.; Kanzieper, Eugene
2010-10-15
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of {tau} functions, we (i) identify a zoo of hierarchical relations satisfied by {tau} functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasis is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.
A robust regularization algorithm for polynomial networks for machine learning
NASA Astrophysics Data System (ADS)
Jaenisch, Holger M.; Handley, James W.
2011-06-01
We present an improvement to the fundamental Group Method of Data Handling (GMDH) Data Modeling algorithm that overcomes the parameter sensitivity to novel cases presented to derived networks. We achieve this result by regularization of the output and using a genetic weighting that selects intermediate models that do not exhibit divergence. The result is the derivation of multi-nested polynomial networks following the Kolmogorov-Gabor polynomial that are robust to mean estimators as well as novel exemplars for input. The full details of the algorithm are presented. We also introduce a new method for approximating GMDH in a single regression model using F, H, and G terms that automatically exports the answers as ordinary differential equations. The MathCAD 15 source code for all algorithms and results are provided.
Orthogonal polynomial interpretation of Δ-Toda equations
NASA Astrophysics Data System (ADS)
Area, I.; Branquinho, A.; Foulquié Moreno, A.; Godoy, E.
2015-10-01
In this paper a discretization of Toda equations is analyzed. The correspondence between these Δ-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. It is shown that the spectral measure of these operators evolve in t like {(1+x)}1-t {{d}}μ (x) where {{d}}μ is a given positive Borel measure. The Lax pair for the Δ-Toda equations is derived and characterized in terms of linear functionals, where orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ appear in a natural way. In order to illustrate the results of the paper we work out two examples of Δ-Toda equations related with Jacobi and Laguerre orthogonal polynomials.
Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
NASA Astrophysics Data System (ADS)
Odake, Satoru; Sasaki, Ryu
2011-08-01
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional Laguerre and Jacobi polynomials of types I and II constructed by the present authors. The totality of the integer indices of the new polynomials are finite and they correspond to the degrees of the 'virtual state wavefunctions' which are 'deleted' by the generalisation of Crum-Adler theorem. Each polynomial has another integer n which counts the nodes.
Stochastic Integration of Renewable Energy Technologies Based on Polynomial Expa
Energy Science and Technology Software Center (ESTSC)
2009-12-31
The software can be used to determine how different intermittent renewable energy technologies interact when supplying an electrical load to a building. By taking defined capacity factors for various time periods and the rated power for different technologies, the software calculates the percentage of the time the power system involving multiple technologies is in a certain state, i.e. the possible combinations and the percent of time each occurs. The user is able to determine howmore » much power would be purchased from a utility and how much would be returned.« less
Astronomical applications of grazing incidence telescopes with polynomial surfaces
NASA Technical Reports Server (NTRS)
Cash, W.; Shealy, D. L.; Underwood, J. H.
1979-01-01
The report has examined the claim that grazing incidence telescopes having surfaces described by generalized equations have image characteristics superior to those of the paraboloid-hyperboloid and Wolter-Schwarzschild configurations. With emphasis on specific applications in solar and cosmic X-ray/EUV astronomy, raytracing has shown that in many cases there is no advantage in the polynomial design, and in those cases where advantages are theoretically to be expected, the advantages are outweighed by practical considerations.
Fibonacci chain polynomials: Identities from self-similarity
NASA Technical Reports Server (NTRS)
Lang, Wolfdieter
1995-01-01
Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbor interaction and two kinds of atoms (mass-ratio r) arranged according to the self-similar binary Fibonacci sequence ABAABABA..., which is obtained by repeated substitution of A yields AB and B yields A. The implications of the self-similarity of this sequence for the associated orthogonal polynomial systems which govern these Fibonacci chains with fixed mass-ratio r are studied.
Polynomial Solutions of Nth Order Non-Homogeneous Differential Equations
ERIC Educational Resources Information Center
Levine, Lawrence E.; Maleh, Ray
2002-01-01
It was shown by Costa and Levine that the homogeneous differential equation (1-x[superscript N])y([superscript N]) + A[subscript N-1]x[superscript N-1)y([superscript N-1]) + A[subscript N-2]x[superscript N-2])y([superscript N-2]) + ... + A[subscript 1]xy[prime] + A[subscript 0]y = 0 has a finite polynomial solution if and only if [for…
A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models
NASA Technical Reports Server (NTRS)
Giunta, Anthony A.; Watson, Layne T.
1998-01-01
Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.
Information entropy of Gegenbauer polynomials and Gaussian quadrature
NASA Astrophysics Data System (ADS)
Sánchez-Ruiz, Jorge
2003-05-01
In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.
Zernike olivary polynomials for applications with olivary pupils.
Zheng, Yi; Sun, Shanshan; Li, Ying
2016-04-20
Orthonormal polynomials have been extensively applied in optical image systems. One important optical pupil, which is widely processed in lateral shearing interferometers (LSI) and subaperture stitch tests (SST), is the overlap region of two circular wavefronts that are displaced from each other. We call it an olivary pupil. In this paper, the normalized process of an olivary pupil in a unit circle is first presented. Then, using a nonrecursive matrix method, Zernike olivary polynomials (ZOPs) are obtained. Previously, Zernike elliptical polynomials (ZEPs) have been considered as an approximation over an olivary pupil. We compare ZOPs with their ZEPs counterparts. Results show that they share the same components but are in different proportions. For some low-order aberrations such as defocus, coma, and spherical, the differences are considerable and may lead to deviations. Using a least-squares method to fit coefficient curves, we present a power-series expansion form for the first 15 ZOPs, which can be used conveniently with less than 0.1% error. The applications of ZOP are demonstrated in wavefront decomposition, LSI interferogram reconstruction, and SST overlap domain evaluation. PMID:27140076
Hierarchical polynomial network approach to automated target recognition
NASA Astrophysics Data System (ADS)
Kim, Richard Y.; Drake, Keith C.; Kim, Tony Y.
1994-02-01
A hierarchical recognition methodology using abductive networks at several levels of object recognition is presented. Abductive networks--an innovative numeric modeling technology using networks of polynomial nodes--results from nearly three decades of application research and development in areas including statistical modeling, uncertainty management, genetic algorithms, and traditional neural networks. The systems uses pixel-registered multisensor target imagery provided by the Tri-Service Laser Radar sensor. Several levels of recognition are performed using detection, classification, and identification, each providing more detailed object information. Advanced feature extraction algorithms are applied at each recognition level for target characterization. Abductive polynomial networks process feature information and situational data at each recognition level, providing input for the next level of processing. An expert system coordinates the activities of individual recognition modules and enables employment of heuristic knowledge to overcome the limitations provided by a purely numeric processing approach. The approach can potentially overcome limitations of current systems such as catastrophic degradation during unanticipated operating conditions while meeting strict processing requirements. These benefits result from implementation of robust feature extraction algorithms that do not take explicit advantage of peculiar characteristics of the sensor imagery, and the compact, real-time processing capability provided by abductive polynomial networks.
Kostant polynomials and the cohomology ring for G/B
Billey, Sara C.
1997-01-01
The Schubert calculus for G/B can be completely determined by a certain matrix related to the Kostant polynomials introduced in section 5 of Bernstein, Gelfand, and Gelfand [Bernstein, I., Gelfand, I. & Gelfand, S. (1973) Russ. Math. Surv. 28, 1–26]. The polynomials are defined by vanishing properties on the orbit of a regular point under the action of the Weyl group. For each element w in the Weyl group the polynomials also have nonzero values on the orbit points corresponding to elements which are larger in the Bruhat order than w. The main theorem given here is an explicit formula for these values. The matrix of orbit values can be used to determine the cup product for the cohomology ring for G/B, using only linear algebra or as described by Lascoux and Schützenberger [Lascoux, A. & Schützenberger, M.-P. (1982) C. R. Seances Acad. Sci. Ser. A 294, 447–450]. Complete proofs of all the theorems will appear in a forthcoming paper. PMID:11038536
Kostant polynomials and the cohomology ring for G/B.
Billey, S C
1997-01-01
The Schubert calculus for G/B can be completely determined by a certain matrix related to the Kostant polynomials introduced in section 5 of Bernstein, Gelfand, and Gelfand [Bernstein, I., Gelfand, I. & Gelfand, S. (1973) Russ. Math. Surv. 28, 1-26]. The polynomials are defined by vanishing properties on the orbit of a regular point under the action of the Weyl group. For each element w in the Weyl group the polynomials also have nonzero values on the orbit points corresponding to elements which are larger in the Bruhat order than w. The main theorem given here is an explicit formula for these values. The matrix of orbit values can be used to determine the cup product for the cohomology ring for G/B, using only linear algebra or as described by Lascoux and Schützenberger [Lascoux, A. & Schützenberger, M.-P. (1982) C. R. Seances Acad. Sci. Ser. A 294, 447-450]. Complete proofs of all the theorems will appear in a forthcoming paper. PMID:11038536
Equations on knot polynomials and 3d/5d duality
Mironov, A.; Morozov, A.
2012-09-24
We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. The shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.
NASA Astrophysics Data System (ADS)
Marquette, Ian
2015-04-01
Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works.
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
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
NASA Astrophysics Data System (ADS)
Ahangar-Asr, A.; Faramarzi, A.; Mottaghifard, N.; Javadi, A. A.
2011-11-01
This paper presents a new approach, based on evolutionary polynomial regression (EPR), for prediction of permeability ( K), maximum dry density (MDD), and optimum moisture content (OMC) as functions of some physical properties of soil. EPR is a data-driven method based on evolutionary computing aimed to search for polynomial structures representing a system. In this technique, a combination of the genetic algorithm (GA) and the least-squares method is used to find feasible structures and the appropriate parameters of those structures. EPR models are developed based on results from a series of classification, compaction, and permeability tests from the literature. The tests included standard Proctor tests, constant head permeability tests, and falling head permeability tests conducted on soils made of four components, bentonite, limestone dust, sand, and gravel, mixed in different proportions. The results of the EPR model predictions are compared with those of a neural network model, a correlation equation from the literature, and the experimental data. Comparison of the results shows that the proposed models are highly accurate and robust in predicting permeability and compaction characteristics of soils. Results from sensitivity analysis indicate that the models trained from experimental data have been able to capture many physical relationships between soil parameters. The proposed models are also able to represent the degree to which individual contributing parameters affect the maximum dry density, optimum moisture content, and permeability.
Mao, Xinguo; Zhang, Hongying; Tian, Shanjun; Chang, Xiaoping; Jing, Ruilian
2010-03-01
Osmotic stresses such as drought, salinity, and cold are major environmental factors that limit agricultural productivity worldwide. Protein phosphorylation/dephosphorylation are major signalling events induced by osmotic stress in higher plants. Sucrose non-fermenting 1-related protein kinase2 family members play essential roles in response to hyperosmotic stresses in Arabidopsis, rice, and maize. In this study, the function of TaSnRK2.4 in drought, salt, and freezing stresses in Arabidopsis was characterized. A translational fusion protein of TaSnRK2.4 with green fluorescent protein showed subcellular localization in the cell membrane, cytoplasm, and nucleus. To examine the role of TaSnRK2.4 under various environmental stresses, transgenic Arabidopsis plants overexpressing wheat TaSnRK2.4 under control of the cauliflower mosaic virus 35S promoter were generated. Overexpression of TaSnRK2.4 resulted in delayed seedling establishment, longer primary roots, and higher yield under normal growing conditions. Transgenic Arabidopsis overexpressing TaSnRK2.4 had enhanced tolerance to drought, salt, and freezing stresses, which were simultaneously supported by physiological results, including decreased rate of water loss, enhanced higher relative water content, strengthened cell membrane stability, improved photosynthesis potential, and significantly increased osmotic potential. The results show that TaSnRK2.4 is involved in the regulation of enhanced osmotic potential, growth, and development under both normal and stress conditions, and imply that TaSnRK2.4 is a multifunctional regulatory factor in Arabidopsis. Since the overexpression of TaSnRK2.4 can significantly strengthen tolerance to drought, salt, and freezing stresses and does not retard the growth of transgenic Arabidopsis plants under well-watered conditions, TaSnRK2.4 could be utilized in transgenic breeding to improve abiotic stresses in crops. PMID:20022921
Mao, Xinguo; Zhang, Hongying; Tian, Shanjun; Chang, Xiaoping; Jing, Ruilian
2010-01-01
Osmotic stresses such as drought, salinity, and cold are major environmental factors that limit agricultural productivity worldwide. Protein phosphorylation/dephosphorylation are major signalling events induced by osmotic stress in higher plants. Sucrose non-fermenting 1-related protein kinase2 family members play essential roles in response to hyperosmotic stresses in Arabidopsis, rice, and maize. In this study, the function of TaSnRK2.4 in drought, salt, and freezing stresses in Arabidopsis was characterized. A translational fusion protein of TaSnRK2.4 with green fluorescent protein showed subcellular localization in the cell membrane, cytoplasm, and nucleus. To examine the role of TaSnRK2.4 under various environmental stresses, transgenic Arabidopsis plants overexpressing wheat TaSnRK2.4 under control of the cauliflower mosaic virus 35S promoter were generated. Overexpression of TaSnRK2.4 resulted in delayed seedling establishment, longer primary roots, and higher yield under normal growing conditions. Transgenic Arabidopsis overexpressing TaSnRK2.4 had enhanced tolerance to drought, salt, and freezing stresses, which were simultaneously supported by physiological results, including decreased rate of water loss, enhanced higher relative water content, strengthened cell membrane stability, improved photosynthesis potential, and significantly increased osmotic potential. The results show that TaSnRK2.4 is involved in the regulation of enhanced osmotic potential, growth, and development under both normal and stress conditions, and imply that TaSnRK2.4 is a multifunctional regulatory factor in Arabidopsis. Since the overexpression of TaSnRK2.4 can significantly strengthen tolerance to drought, salt, and freezing stresses and does not retard the growth of transgenic Arabidopsis plants under well-watered conditions, TaSnRK2.4 could be utilized in transgenic breeding to improve abiotic stresses in crops. PMID:20022921
The SnRK1 Energy Sensor in Plant Biotic Interactions.
Hulsmans, Sander; Rodriguez, Marianela; De Coninck, Barbara; Rolland, Filip
2016-08-01
Our understanding of plant biotic interactions has grown significantly in recent years with the identification of the mechanisms involved in innate immunity, hormone signaling, and secondary metabolism. The impact of such interactions on primary metabolism and the role of metabolic signals in the response of the plants, however, remain far less explored. The SnRK1 (SNF1-related kinase 1) kinases act as metabolic sensors, integrating very diverse stress conditions, and are key in maintaining energy homeostasis for growth and survival. Consistently, an important role is emerging for these kinases as regulators of biotic stress responses triggered by viral, bacterial, fungal, and oomycete infections as well as by herbivory. While this identifies SnRK1 as a promising target for directed modification or selection for more quantitative and sustainable resistance, its central function also increases the chances of unwanted side effects on growth and fitness, stressing the need for identification and in-depth characterization of the mechanisms and target processes involved. VIDEO ABSTRACT. PMID:27156455
Dhiman, Alisha; Bhatnagar, Sonika; Kulshreshtha, Parul; Bhatnagar, Rakesh
2014-01-01
Two-component signal transduction systems (TCS), consisting of a sensor histidine protein kinase and its cognate response regulator, are an important mode of environmental sensing in bacteria. Additionally, they have been found to regulate virulence determinants in several pathogens. Bacillus anthracis, the causative agent of anthrax and a bioterrorism agent, harbours 41 pairs of TCS. However, their role in its pathogenicity has remained largely unexplored. Here, we show that WalRK of B. anthracis forms a functional TCS which exhibits some species-specific functions. Biochemical studies showed that domain variants of WalK, the histidine kinase, exhibit classical properties of autophosphorylation and phosphotransfer to its cognate response regulator WalR. Interestingly, these domain variants also show phosphatase activity towards phosphorylated WalR, thereby making WalK a bifunctional histidine kinase/phosphatase. An in silico regulon determination approach, using a consensus binding sequence from Bacillus subtilis, provided a list of 30 genes that could form a putative WalR regulon in B. anthracis. Further, electrophoretic mobility shift assay was used to show direct binding of purified WalR to the upstream regions of three putative regulon candidates, an S-layer protein EA1, a cell division ABC transporter FtsE and a sporulation histidine kinase KinB3. Our work lends insight into the species-specific functions and mode of action of B. anthracis WalRK. PMID:24490131
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169
Flocke, N
2009-08-14
In this paper it is shown that shifted Jacobi polynomials G(n)(p,q,x) can be used in connection with the Gaussian quadrature modified moment technique to greatly enhance the accuracy of evaluation of Rys roots and weights used in Gaussian integral evaluation in quantum chemistry. A general four-term inhomogeneous recurrence relation is derived for the shifted Jacobi polynomial modified moments over the Rys weight function e(-Tx)/square root x. It is shown that for q=1/2 this general four-term inhomogeneous recurrence relation reduces to a three-term p-dependent inhomogeneous recurrence relation. Adjusting p to proper values depending on the Rys exponential parameter T, the method is capable of delivering highly accurate results for large number of roots and weights in the most difficult to treat intermediate T range. Examples are shown, and detailed formulas together with practical suggestions for their efficient implementation are also provided. PMID:19691378
NASA Astrophysics Data System (ADS)
Flocke, N.
2009-08-01
In this paper it is shown that shifted Jacobi polynomials Gn(p,q,x) can be used in connection with the Gaussian quadrature modified moment technique to greatly enhance the accuracy of evaluation of Rys roots and weights used in Gaussian integral evaluation in quantum chemistry. A general four-term inhomogeneous recurrence relation is derived for the shifted Jacobi polynomial modified moments over the Rys weight function e-Tx/√x . It is shown that for q =1/2 this general four-term inhomogeneous recurrence relation reduces to a three-term p-dependent inhomogeneous recurrence relation. Adjusting p to proper values depending on the Rys exponential parameter T, the method is capable of delivering highly accurate results for large number of roots and weights in the most difficult to treat intermediate T range. Examples are shown, and detailed formulas together with practical suggestions for their efficient implementation are also provided.
Ye, Lei; Youk, Ada O; Sereika, Susan M; Anderson, Stewart J; Burke, Lora E
2016-09-10
Parametric mixed-effects models are useful in longitudinal data analysis when the sampling frequencies of a response variable and the associated covariates are the same. We propose a three-step estimation procedure using local polynomial smoothing and demonstrate with data where the variables to be assessed are repeatedly sampled with different frequencies within the same time frame. We first insert pseudo data for the less frequently sampled variable based on the observed measurements to create a new dataset. Then standard simple linear regressions are fitted at each time point to obtain raw estimates of the association between dependent and independent variables. Last, local polynomial smoothing is applied to smooth the raw estimates. Rather than use a kernel function to assign weights, only analytical weights that reflect the importance of each raw estimate are used. The standard errors of the raw estimates and the distance between the pseudo data and the observed data are considered as the measure of the importance of the raw estimates. We applied the proposed method to a weight loss clinical trial, and it efficiently estimated the correlation between the inconsistently sampled longitudinal data. Our approach was also evaluated via simulations. The results showed that the proposed method works better when the residual variances of the standard linear regressions are small and the within-subjects correlations are high. Also, using analytic weights instead of kernel function during local polynomial smoothing is important when raw estimates have extreme values, or the association between the dependent and independent variable is nonlinear. Copyright © 2016 John Wiley & Sons, Ltd. PMID:27122363
NASA Astrophysics Data System (ADS)
Huang, Bin; Wang, Ji; Du, Jianke; Guo, Yan; Ma, Tingfeng; Yi, Lijun
2016-06-01
The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work, the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method (FEM). The convergent stresses have good agreements with those results obtained by three dimensional (3D) FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.
NASA Astrophysics Data System (ADS)
Porta, G.; Tamellini, L.; Lever, V.; Riva, M.
2014-12-01
We present an inverse modeling procedure for the estimation of model parameters of sedimentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophysical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likelihood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quantified through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approximations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored.
NASA Astrophysics Data System (ADS)
Bazargan, Hamid; Christie, Mike; Elsheikh, Ahmed H.; Ahmadi, Mohammad
2015-12-01
Markov Chain Monte Carlo (MCMC) methods are often used to probe the posterior probability distribution in inverse problems. This allows for computation of estimates of uncertain system responses conditioned on given observational data by means of approximate integration. However, MCMC methods suffer from the computational complexities in the case of expensive models as in the case of subsurface flow models. Hence, it is of great interest to develop alterative efficient methods utilizing emulators, that are cheap to evaluate, in order to replace the full physics simulator. In the current work, we develop a technique based on sparse response surfaces to represent the flow response within a subsurface reservoir and thus enable efficient exploration of the posterior probability density function and the conditional expectations given the data. Polynomial Chaos Expansion (PCE) is a powerful tool to quantify uncertainty in dynamical systems when there is probabilistic uncertainty in the system parameters. In the context of subsurface flow model, it has been shown to be more accurate and efficient compared with traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution when the order of the PCE is increased can be proved for the random variables with finite variances. However, the major drawback of PCE is related to the curse of dimensionality as the number of terms to be estimated grows drastically with the number of the input random variables. This renders the computational cost of classical PCE schemes unaffordable for reservoir simulation purposes when the deterministic finite element model is expensive to evaluate. To address this issue, we propose the reduced-terms polynomial chaos representation which uses an impact factor to only retain the most relevant terms of the PCE decomposition. Accordingly, the reduced-terms polynomial chaos proxy can be used as the pseudo
NASA Astrophysics Data System (ADS)
Pagnacco, E.; de Cursi, E. Souza; Sampaio, R.
2016-04-01
This study concerns the computation of frequency responses of linear stochastic mechanical systems through a modal analysis. A new strategy, based on transposing standards deterministic deflated and subspace inverse power methods into stochastic framework, is introduced via polynomial chaos representation. Applicability and effectiveness of the proposed schemes is demonstrated through three simple application examples and one realistic application example. It is shown that null and repeated-eigenvalue situations are addressed successfully.
SnRK1-triggered switch of bZIP63 dimerization mediates the low-energy response in plants
Mair, Andrea; Pedrotti, Lorenzo; Wurzinger, Bernhard; Anrather, Dorothea; Simeunovic, Andrea; Weiste, Christoph; Valerio, Concetta; Dietrich, Katrin; Kirchler, Tobias; Nägele, Thomas; Vicente Carbajosa, Jesús; Hanson, Johannes; Baena-González, Elena; Chaban, Christina; Weckwerth, Wolfram; Dröge-Laser, Wolfgang; Teige, Markus
2015-01-01
Metabolic adjustment to changing environmental conditions, particularly balancing of growth and defense responses, is crucial for all organisms to survive. The evolutionary conserved AMPK/Snf1/SnRK1 kinases are well-known metabolic master regulators in the low-energy response in animals, yeast and plants. They act at two different levels: by modulating the activity of key metabolic enzymes, and by massive transcriptional reprogramming. While the first part is well established, the latter function is only partially understood in animals and not at all in plants. Here we identified the Arabidopsis transcription factor bZIP63 as key regulator of the starvation response and direct target of the SnRK1 kinase. Phosphorylation of bZIP63 by SnRK1 changed its dimerization preference, thereby affecting target gene expression and ultimately primary metabolism. A bzip63 knock-out mutant exhibited starvation-related phenotypes, which could be functionally complemented by wild type bZIP63, but not by a version harboring point mutations in the identified SnRK1 target sites. DOI: http://dx.doi.org/10.7554/eLife.05828.001 PMID:26263501
Cotter, Paul D.; Guinane, Caitriona M.; Hill, Colin
2002-01-01
The Listeria monocytogenes two-component signal transduction system, LisRK, initially identified in strain LO28, plays a significant role in the virulence potential of this important food-borne pathogen. Here, it is shown that, in addition to its major contribution in responding to ethanol, pH, and hydrogen peroxide stresses, LisRK is involved in the ability of the cell to tolerate important antimicrobials used in food and in medicine, e.g., the lantibiotic nisin and the cephalosporin family of antibiotics. A ΔlisK mutant (lacking the LisK histidine kinase sensor component) displays significantly enhanced resistance to the lantibiotic nisin, a greatly enhanced sensitivity to the cephalosporins, and a large reduction in the expression of three genes thought to encode a penicillin-binding protein, another histidine kinase (other than LisK), and a protein of unknown function. Confirmation of the role of LisRK was obtained when the response regulator, LisR, was overexpressed using both constitutive and inducible (nisin-controlled expression) systems. Under these conditions we observed a reversion of the ΔlisK mutant to wild-type growth kinetics in the presence of nisin. It was also found that overexpression of LisR complemented the reduced expression of two of the aforementioned genes. These results demonstrate the important role of LisRK in the response of L. monocytogenes to a number of antimicrobial agents. PMID:12183229
NASA Astrophysics Data System (ADS)
Hubert-Ferrari, Aurélia; El-Ouahabi, Meriam; Garcia-Moreno, David; Avsar, Ulas; Altinok, Sevgi; Schmidt, Sabine; Cagatay, Namik
2016-04-01
Delta contains a sedimentary record primarily indicative of water level changes, but particularly sensitive to earthquake shaking, which results generally in soft-sediment-deformation structures. The Kürk Delta adjacent to a major strike-slip fault displays this type of deformation (Hempton and Dewey, 1983) as well as other types of earthquake fingerprints that are specifically investigated. This lacustrine delta stands at the south-western extremity of the Hazar Lake and is bound by the East Anatolian Fault (EAF), which generated earthquakes of magnitude 7 in eastern Turkey. Water level changes and earthquake shaking affecting the Kurk Delta have been reevaluated combining geophysical data (seismic-reflection profiles and side-scan sonar), remote sensing images, historical data, onland outcrops and offshore coring. The history of water level changes provides a temporal framework regarding the sedimentological record. In addition to the commonly soft-sediment-deformation previously documented, the onland outcrops reveal a record of deformation (faults and clastic dykes) linked to large earthquake-induced liquefactions. The recurrent liquefaction structures can be used to obtain a paleoseismological record. Five event horizons were identified that could be linked to historical earthquakes occurring in the last 1000 years along the EAF. Sedimentary cores sampling the most recent subaqueous sedimentation revealed the occurrence of another type of earthquake fingerprint. Based on radionuclide dating (137Cs and 210Pb), two major sedimentary events were attributed to the 1874-1875 earthquake sequence along the EAF. Their sedimentological characteristics were inferred based X-ray imagery, XRD, LOI, grain-size distribution, geophysical measurements. The events are interpreted to be hyperpycnal deposits linked to post-seismic sediment reworking of earthquake-triggered landslides. A time constraint regarding this sediment remobilization process could be achieved thanks to
NASA Astrophysics Data System (ADS)
Porter, Edward K.
2006-10-01
We introduce a new method for modelling the gravitational wave flux function of a test-mass particle inspiralling into an intermediate mass Schwarzschild black hole which is based on Chebyshev polynomials of the first kind. It is believed that these intermediate mass ratio inspiral events (IMRI) are expected to be seen in both the ground- and space-based detectors. Starting with the post-Newtonian expansion from black hole perturbation theory, we introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a model with faster convergence than either post-Newtonian- or Padé-based methods. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. We find that at the last stable orbit, the error between the Chebyshev approximation and a numerically calculated flux is reduced, <1.8%, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general >0.99, and smaller errors, <1/10%, in the estimation of the chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the intermediate test-mass case, the new Chebyshev template is superior to both PN and Padé approximant templates, especially at lower orders of approximation.
Dixon resultant's solution of systems of geodetic polynomial equations
NASA Astrophysics Data System (ADS)
Paláncz, Béla; Zaletnyik, Piroska; Awange, Joseph L.; Grafarend, Erik W.
2008-08-01
The Dixon resultant is proposed as an alternative to Gröbner basis or multipolynomial resultant approaches for solving systems of polynomial equations inherent in geodesy. Its smallness in size, high density (ratio on the number of nonzero elements to the number of all elements), speed, and robustness (insensitive to combinatorial sequence and monomial order, e.g., Gröbner basis) makes it extremely attractive compared to its competitors. Using 3D-intersection and conformal C 7 datum transformation problems, we compare its performance to those of the Sturmfels’s resultant and Gröbner basis. For the 3D-intersection problem, Sturmfels’s resultant needed 0.578 s to solve a 6 × 6 resultant matrix whose density was 0.639, the Dixon resultant on the other hand took 0.266 s to solve a 4 × 4 resultant matrix whose density was 0.870. For the conformal C 7 datum transformation problem, the Dixon resultant took 2.25 s to compute a quartic polynomial in scale parameter whereas the computaton of the Gröbner basis fails. Using relative coordinates to compute the quartic polynomial in scale parameter, the Gröbner basis needed 0.484 s, while the Dixon resultant took 0.016 s. This highlights the robustness of the Dixon resultant (i.e., the capability to use both absolute and relative coordinates with any order of variables) as opposed to Gröbner basis, which only worked well with relative coordinates, and was sensitive to the combinatorial sequence and order of variables. Geodetic users uncomfortable with lengthy expressions of Gröbner basis or multipolynomial resultants, and who aspire to optimize on the attractive features of Dixon resultant, may find it useful.
Modeling Source Water TOC Using Hydroclimate Variables and Local Polynomial Regression.
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. PMID:26998784
Senadheera, D. B.; Cordova, M.; Ayala, E. A.; Chávez de Paz, L. E.; Singh, K.; Downey, J. S.; Svensäter, G.; Goodman, S. D.
2012-01-01
The VicRK two-component signaling system modulates biofilm formation, genetic competence, and stress tolerance in Streptococcus mutans. We show here that the VicRK modulates bacteriocin production and cell viability, in part by direct modulation of competence-stimulating peptide (CSP) production in S. mutans. Global transcriptome and real-time transcriptional analysis of the VicK-deficient mutant (SmuvicK) revealed significant modulation of several bacteriocin-related loci, including nlmAB, nlmC, and nlmD (P < 0.001), suggesting a role for the VicRK in producing mutacins IV, V, and VI. Bacteriocin overlay assays revealed an altered ability of the vic mutants to kill related species. Since a well-conserved VicR binding site (TGTWAH-N5-TGTWAH) was identified within the comC coding region, we confirmed VicR binding to this sequence using DNA footprinting. Overexpression of the vic operon caused growth-phase-dependent repression of comC, comDE, and comX. In the vic mutants, transcription of nlmC/cipB encoding mutacin V, previously linked to CSP-dependent cell lysis, as well as expression of its putative immunity factor encoded by immB, were significantly affected relative to the wild type (P < 0.05). In contrast to previous reports that proposed a hyper-resistant phenotype for the VicK mutant in cell viability, the release of extracellular genomic DNA was significantly enhanced in SmuvicK (P < 0.05), likely as a result of increased autolysis compared with the parent. The drastic influence of VicRK on cell viability was also demonstrated using vic mutant biofilms. Taken together, we have identified a novel regulatory link between the VicRK and ComDE systems to modulate bacteriocin production and cell viability of S. mutans. PMID:22228735
Radchuk, Ruslana; Emery, R J Neil; Weier, Diana; Vigeolas, Helene; Geigenberger, Peter; Lunn, John E; Feil, Regina; Weschke, Winfriede; Weber, Hans
2010-01-01
Seed development passes through developmental phases such as cell division, differentiation and maturation: each have specific metabolic demands. The ubiquitous sucrose non-fermenting-like kinase (SnRK1) coordinates and adjusts physiological and metabolic demands with growth. In protoplast assays sucrose deprivation and hormone supplementation, such as with auxin and abscisic acid (ABA), stimulate SnRK1-promoter activity. This indicates regulation by nutrients: hormonal crosstalk under conditions of nutrient demand and cell proliferation. SnRK1-repressed pea (Pisum sativum) embryos show lower cytokinin levels and deregulation of cotyledonary establishment and growth, together with downregulated gene expression related to cell proliferation, meristem maintenance and differentiation, leaf formation, and polarity. This suggests that at early stages of seed development SnRK1 regulates coordinated cotyledon emergence and growth via cytokinin-mediated auxin transport and/or distribution. Decreased ABA levels and reduced gene expression, involved in ABA-mediated seed maturation and response to sugars, indicate that SnRK1 is required for ABA synthesis and/or signal transduction at an early stage. Metabolic profiling of SnRK1-repressed embryos revealed lower levels of most organic and amino acids. In contrast, levels of sugars and glycolytic intermediates were higher or unchanged, indicating decreased carbon partitioning into subsequent pathways such as the tricarbonic acid cycle and amino acid biosynthesis. It is hypothesized that SnRK1 mediates the responses to sugar signals required for early cotyledon establishment and patterning. As a result, later maturation and storage activity are strongly impaired. Changes observed in SnRK1-repressed pea seeds provide a framework for how SnRK1 communicates nutrient and hormonal signals from auxins, cytokinins and ABA to control metabolism and development. PMID:19845880
Nukarinen, Ella; Nägele, Thomas; Pedrotti, Lorenzo; Wurzinger, Bernhard; Mair, Andrea; Landgraf, Ramona; Börnke, Frederik; Hanson, Johannes; Teige, Markus; Baena-Gonzalez, Elena; Dröge-Laser, Wolfgang; Weckwerth, Wolfram
2016-01-01
Since years, research on SnRK1, the major cellular energy sensor in plants, has tried to define its role in energy signalling. However, these attempts were notoriously hampered by the lethality of a complete knockout of SnRK1. Therefore, we generated an inducible amiRNA::SnRK1α2 in a snrk1α1 knock out background (snrk1α1/α2) to abolish SnRK1 activity to understand major systemic functions of SnRK1 signalling under energy deprivation triggered by extended night treatment. We analysed the in vivo phosphoproteome, proteome and metabolome and found that activation of SnRK1 is essential for repression of high energy demanding cell processes such as protein synthesis. The most abundant effect was the constitutively high phosphorylation of ribosomal protein S6 (RPS6) in the snrk1α1/α2 mutant. RPS6 is a major target of TOR signalling and its phosphorylation correlates with translation. Further evidence for an antagonistic SnRK1 and TOR crosstalk comparable to the animal system was demonstrated by the in vivo interaction of SnRK1α1 and RAPTOR1B in the cytosol and by phosphorylation of RAPTOR1B by SnRK1α1 in kinase assays. Moreover, changed levels of phosphorylation states of several chloroplastic proteins in the snrk1α1/α2 mutant indicated an unexpected link to regulation of photosynthesis, the main energy source in plants. PMID:27545962
Nukarinen, Ella; Nägele, Thomas; Pedrotti, Lorenzo; Wurzinger, Bernhard; Mair, Andrea; Landgraf, Ramona; Börnke, Frederik; Hanson, Johannes; Teige, Markus; Baena-Gonzalez, Elena; Dröge-Laser, Wolfgang; Weckwerth, Wolfram
2016-01-01
Since years, research on SnRK1, the major cellular energy sensor in plants, has tried to define its role in energy signalling. However, these attempts were notoriously hampered by the lethality of a complete knockout of SnRK1. Therefore, we generated an inducible amiRNA::SnRK1α2 in a snrk1α1 knock out background (snrk1α1/α2) to abolish SnRK1 activity to understand major systemic functions of SnRK1 signalling under energy deprivation triggered by extended night treatment. We analysed the in vivo phosphoproteome, proteome and metabolome and found that activation of SnRK1 is essential for repression of high energy demanding cell processes such as protein synthesis. The most abundant effect was the constitutively high phosphorylation of ribosomal protein S6 (RPS6) in the snrk1α1/α2 mutant. RPS6 is a major target of TOR signalling and its phosphorylation correlates with translation. Further evidence for an antagonistic SnRK1 and TOR crosstalk comparable to the animal system was demonstrated by the in vivo interaction of SnRK1α1 and RAPTOR1B in the cytosol and by phosphorylation of RAPTOR1B by SnRK1α1 in kinase assays. Moreover, changed levels of phosphorylation states of several chloroplastic proteins in the snrk1α1/α2 mutant indicated an unexpected link to regulation of photosynthesis, the main energy source in plants. PMID:27545962
Recurrence relations of the multi-indexed orthogonal polynomials. III
NASA Astrophysics Data System (ADS)
Odake, Satoru
2016-02-01
In Paper II, we presented conjectures of the recurrence relations with constant coefficients for the multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types. In this paper we present a proof for the Laguerre and Jacobi cases. Their bispectral properties are also discussed, which gives a method to obtain the coefficients of the recurrence relations explicitly. This paper extends to the Laguerre and Jacobi cases the bispectral techniques recently introduced by Gómez-Ullate et al. [J. Approx. Theory 204, 1 (2016); e-print arXiv:1506.03651 [math.CA
Polynomials for evaluation of two-center overlap integrals
NASA Astrophysics Data System (ADS)
Petrov, Dimitar
2016-05-01
Expressions of products AkBk, where Ak and Bk are incomplete gamma functions, are given for evaluation of two-center overlap integrals (TCOIs) over unnormalized Slater-type orbitals (STOs). The polynomials of AkBk have been derived after the method proposed by Lofthus and pertain to two-center bonds of σ, π, δ, and φ axial symmetries. The functions of AkBk have been arranged in pairs of s, p, d, and f STOs with principal quantum numbers between 1 and 5. The contributions of these functions to various TCOIs have been evaluated and discussed. The formulae are applicable as input matrices for computations of TCOIs.
Stieltjes-type polynomials on the unit circle
NASA Astrophysics Data System (ADS)
de La Calle Ysern, B.; Lagomasino, G. Lopez; Reichel, L.
2009-06-01
Stieltjes-type polynomials corresponding to measures supported on the unit circle mathbb{T} are introduced and their asymptotic properties away from mathbb{T} are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Caratheodory function. In turn, this is used to give an estimate of the rate of convergence of certain quadrature formulae that resemble the Gauss-Kronrod rule, provided that the integrand is analytic in a neighborhood of mathbb{T} .
Efficient implementation of minimal polynomial and reduced rank extrapolation methods
NASA Technical Reports Server (NTRS)
Sidi, Avram
1990-01-01
The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.
The BQP-hardness of approximating the Jones polynomial
NASA Astrophysics Data System (ADS)
Aharonov, Dorit; Arad, Itai
2011-03-01
A celebrated important result due to Freedman et al (2002 Commun. Math. Phys. 227 605-22) states that providing additive approximations of the Jones polynomial at the kth root of unity, for constant k=5 and k>=7, is BQP-hard. Together with the algorithmic results of Aharonov et al (2005) and Freedman et al (2002 Commun. Math. Phys. 227 587-603), this gives perhaps the most natural BQP-complete problem known today and motivates further study of the topic. In this paper, we focus on the universality proof; we extend the result of Freedman et al (2002) to ks that grow polynomially with the number of strands and crossings in the link, thus extending the BQP-hardness of Jones polynomial approximations to all values to which the AJL algorithm applies (Aharonov et al 2005), proving that for all those values, the problems are BQP-complete. As a side benefit, we derive a fairly elementary proof of the Freedman et al density result, without referring to advanced results from Lie algebra representation theory, making this important result accessible to a wider audience in the computer science research community. We make use of two general lemmas we prove, the bridge lemma and the decoupling lemma, which provide tools for establishing the density of subgroups in SU(n). Those tools seem to be of independent interest in more general contexts of proving the quantum universality. Our result also implies a completely classical statement, that the multiplicative approximations of the Jones polynomial, at exactly the same values, are #P-hard, via a recent result due to Kuperberg (2009 arXiv:0908.0512). Since the first publication of those results in their preliminary form (Aharonov and Arad 2006 arXiv:quant-ph/0605181), the methods we present here have been used in several other contexts (Aharonov and Arad 2007 arXiv:quant-ph/0702008; Peter and Stephen 2008 Quantum Inf. Comput. 8 681). The present paper is an improved and extended version of the results presented by Aharonov and Arad
Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles
NASA Astrophysics Data System (ADS)
Breuer, Jonathan; Duits, Maurice
2016-03-01
We prove that the fluctuations of mesoscopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green's function for the associated Jacobi matrices.As a particular consequencewe obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.
Polynomial distance classifier correlation filter for pattern recognition.
Alkanhal, Mohamed; Vijaya Kumar, B V K
2003-08-10
We introduce what is to our knowledge a new nonlinear shift-invariant classifier called the polynomial distance classifier correlation filter (PDCCF). The underlying theory extends the original linear distance classifier correlation filter [Appl. Opt. 35, 3127 (1996)] to include nonlinear functions of the input pattern. This new filter provides a framework (for combining different classification filters) that takes advantage of the individual filter strengths. In this new filter design, all filters are optimized jointly. We demonstrate the advantage of the new PDCCF method using simulated and real multi-class synthetic aperture radar images. PMID:13678355
Multipartite-to-bipartite entanglement transformations and polynomial identity testing
Chitambar, Eric; Duan Runyao; Shi Yaoyun
2010-05-15
We consider the problem of deciding if some multiparty entangled pure state can be converted, with a nonzero success probability, into a given bipartite pure state shared between two specified parties through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to our question. As a result, a given transformation is possible if and only if it is generically attainable by a simple randomized protocol.
NASA Astrophysics Data System (ADS)
Zhang, Tian-Tian; Ma, Pan-Li; Xu, Mei-Juan; Zhang, Xing-Yong; Tian, Shou-Fu
2015-05-01
In this paper, a (3+1)-dimensional generalized variable-coefficients Kadomtsev-Petviashvili (gvcKP) equation is proposed, which describes many nonlinear phenomena in fluid dynamics and plasma physics. By a very natural way, the integrable constraint conditions on the variable coefficients are presented to investigate the integrabilities of the gvcKP equation. Based on the generalized Bell's polynomials, we succinctly obtain its bilinear representations, bilinear Bäcklund transformation and Lax pair, respectively. Furthermore, by virtue of the binary Bell polynomial form, the infinite conservation laws of the equation are found with explicit recursion formulas as well by using its Lax equations via algebraic and differential manipulation. In addition, by using the Hirota bilinear method, its N-soliton solutions are also obtained.
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.
NASA Astrophysics Data System (ADS)
Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.
2008-10-01
We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.
Vignat, C.; Lamberti, P. W.
2009-10-15
Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
A new generalization of Apostol type Hermite-Genocchi polynomials and its applications.
Araci, Serkan; Khan, Waseem A; Acikgoz, Mehmet; Özel, Cenap; Kumam, Poom
2016-01-01
By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite-Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679-695, 2015a) and Hermite-Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite-Genocchi polynomials defined in this paper. PMID:27386309
Longitudinal impedance measurement of an RK-TBA induction accelerating gap
Eylon, S.; Henestroza, E.; Kim, J.-S.; Houck, T.L.; Westenskow, G.A.; Yu, S.S.
1997-05-01
Induction accelerating gap designs are being studied for Relativistic Klystron Two-Beam Accelerator (RK-TBA) applications. The accelerating gap has to satisfy the following major requirements: hold-off of the applied accelerating voltage pulse, low transverse impedance to limit beam breakup, low longitudinal impedance at the beam-modulation frequency to minimize power loss. Various gap geometries, materials and novel insulating techniques were explored to optimize the gap design. We report on the experimental effort to evaluate the rf properties of the accelerating gaps in a simple pillbox cavity structure. The experimental cavity setup was designed using the AMOS, MAFIA and URMEL numerical codes. Longitudinal impedance measurements above beam-tube cut-off frequency using a single-wire measuring system are presented.
Detecting broken struts of a Björk-Shiley heart valve using ultrasound: a feasibility study.
van Neer, P L M J; Bouakaz, A; Vlaanderen, E; de Hart, J; van de Vosse, F N; van der Steen, A F W; de Jong, N
2006-04-01
The Björk-Shiley (BScc) mechanical heart valve has extensively been used in surgery from 1979 to 1986. There is, compared with equivalent valve types, increased occurrence of unexpected mechanical failure of the outlet strut of the valve, with a high incidence of mortality, when it occurs. Many approaches have been attempted to noninvasively determine BScc valve integrity. None of the approaches resulted in adequate assessment, mostly due to a lack of either sensitivity or specificity demonstrated in in vitro and/or in vivo studies. In our study we analyze leg movement of the BScc valves outlet strut during the cardiac cycle with ultrasound. For a broken strut, the movement of both legs will be significantly different, whereas the difference will be negligible for an intact strut. BScc valves were mounted in the mitral position in an in vitro pulse duplicator system. A focused single-element transducer was used to direct ultrasound on a leg of the outlet strut. Correlation-based time delay estimation was used to estimate differences in time of flight of the outlet strut echoes to determine outlet strut leg movement. The movement of an intact valve and a valve with a single-leg fracture with both ends grating against each other (SLF), the most difficult fracture to diagnose, has been studied. The results showed no significant difference in movement between both legs of the outlet strut of the intact BScc valve (amplitude of movement 9.2 microm +/- 0.1 microm). Whereas for the defective valve, the amplitude of movement of the broken leg of the SLF valve was 12 microm +/- 1.6 microm vs. 8.6 microm +/- 0.1 microm for the intact leg. In conclusion, the proposed method has shown to be feasible in vitro and has potentials for in vivo detection of BScc valve outlet strut fracture. PMID:16616597
Discrete-time ℋ∞ control for nonlinear polynomial systems
NASA Astrophysics Data System (ADS)
Hernandez-Gonzalez, M.; Basin, M. V.
2015-02-01
This paper presents a solution of the suboptimal ? regulator problem for a class of discrete-time nonlinear polynomial systems. The solution is obtained by reducing the ? control problem to the corresponding ? one. A general solution has been obtained for a polynomial of an arbitrary order; then, finite-dimensional regulator equations are derived explicitly for a second-order polynomial. Numerical simulations have been carried out to show effectiveness of the proposed method.
Anomalies in non-polynomial closed string field theory
NASA Astrophysics Data System (ADS)
Kaku, Michio
1990-11-01
The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.
Notes on the Polynomial Identities in Random Overlap Structures
NASA Astrophysics Data System (ADS)
Sollich, Peter; Barra, Adriano
2012-04-01
In these notes we review first in some detail the concept of random overlap structure (ROSt) applied to fully connected and diluted spin glasses. We then sketch how to write down the general term of the expansion of the energy part from the Boltzmann ROSt (for the Sherrington-Kirkpatrick model) and the corresponding term from the RaMOSt, which is the diluted extension suitable for the Viana-Bray model. From the ROSt energy term, a set of polynomial identities (often known as Aizenman-Contucci or AC relations) is shown to hold rigorously at every order because of a recursive structure of these polynomials that we prove. We show also, however, that this set is smaller than the full set of AC identities that is already known. Furthermore, when investigating the RaMOSt energy for the diluted counterpart, at higher orders, combinations of such AC identities appear, ultimately suggesting a crucial role for the entropy in generating these constraints in spin glasses.
Crossover ensembles of random matrices and skew-orthogonal polynomials
Kumar, Santosh; Pandey, Akhilesh
2011-08-15
Highlights: > We study crossover ensembles of Jacobi family of random matrices. > We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. > We use the method of skew-orthogonal polynomials and quaternion determinants. > We prove universality of spectral correlations in crossover ensembles. > We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we give details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.
Explicit energy expansion for general odd-degree polynomial potentials
NASA Astrophysics Data System (ADS)
Nanayakkara, Asiri; Mathanaranjan, Thilagarajah
2013-11-01
In this paper we derive an almost explicit analytic formula for asymptotic eigenenergy expansion of arbitrary odd-degree polynomial potentials of the form V (x) = (ix)2N+1 + β1x2N + β2x2N-1 + ··· + β2Nx, where β‧k are real or complex for 1 ⩽ k ⩽ 2N. The formula can be used to find semiclassical analytic expressions for eigenenergies up to any order, very efficiently. Each term of the expansion is given explicitly as a multinomial of the parameters β1,β2… and β2N of the potential. Unlike in the even-degree polynomial case, the highest-order term in the potential is pure imaginary and hence the system is non-Hermitian. Therefore all the integrations have been carried out along a contour enclosing two complex branch points, which lies within a wedge in the complex plane. With the help of some examples we demonstrate the accuracy of the method for both real and complex eigenspectra.
Colored HOMFLY polynomials of knots presented as double fat diagrams
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar
2015-07-01
Many knots and links in S 3 can be drawn as gluing of three manifolds with one or more four-punctured S 2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four -strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants which cannot be distinguished by [21] representation. The difference between the [21]-colored HOMFLY of two mutants seems to have a general form, with A-dependence completely defined by the old conjecture due to Morton and Cromwell. In particular, we check it for an entire multi-parametric family of mutant knots evaluated using evolution method.
Predicting physical time series using dynamic ridge polynomial neural networks.
Al-Jumeily, Dhiya; Ghazali, Rozaida; Hussain, Abir
2014-01-01
Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques. PMID:25157950
Predicting Physical Time Series Using Dynamic Ridge Polynomial Neural Networks
Al-Jumeily, Dhiya; Ghazali, Rozaida; Hussain, Abir
2014-01-01
Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques. PMID:25157950
Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights
NASA Astrophysics Data System (ADS)
Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.
2009-12-01
We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Miki, Hiroshi; Vinet, Luc; Zhedanov, Alexei
2014-01-01
The multivariate Meixner polynomials are shown to arise as matrix elements of unitary representations of the SO(d, 1) group on oscillator states. These polynomials depend on d discrete variables and are orthogonal with respect to the negative multinomial distribution. The emphasis is put on the bivariate case for which the SO(2, 1) connection is used to derive the main properties of the polynomials: orthogonality relation, raising/lowering relations, generating function, recurrence relations and difference equations as well as explicit expressions in terms of standard (univariate) Krawtchouk and Meixner polynomials. It is explained how these results generalize directly to d variables.
INVITED ARTICLE: The second Painlevé equation, its hierarchy and associated special polynomials
NASA Astrophysics Data System (ADS)
Clarkson, Peter A.; Mansfield, Elizabeth L.
2003-05-01
In this paper we are concerned with hierarchies of rational solutions and associated polynomials for the second Painlevé equation (PII) and the equations in the PII hierarchy which is derived from the modified Korteweg-de Vries hierarchy. These rational solutions of PII are expressible as the logarithmic derivative of special polynomials, the Yablonskii-Vorob'ev polynomials. The structure of the roots of these Yablonskii-Vorob'ev polynomials is studied and it is shown that these have a highly regular triangular structure. Further, the properties of the Yablonskii-Vorob'ev polynomials are compared and contrasted with those of classical orthogonal polynomials. We derive the special polynomials for the second and third equations of the PII hierarchy and give a representation of the associated rational solutions in the form of determinants through Schur functions. Additionally the analogous special polynomials associated with rational solutions and representation in the form of determinants are conjectured for higher equations in the PII hierarchy. The roots of these special polynomials associated with rational solutions for the equations of the PII hierarchy also have a highly regular structure.
On the zeros of d-symmetric d-orthogonal polynomials
NASA Astrophysics Data System (ADS)
Ben Romdhane, N.
2008-08-01
In this paper, we give some properties of the zeros of d-symmetric d-orthogonal polynomials and we localize these zeros on (d+1) rays emanating from the origin. We apply the obtained results to some known polynomials. In particular, we partially solve the conjecture about the zeros of the Humbert polynomials stated by Milovanovic and Dordevic [G.V. Milovanovic, G.B. Dordevic, On some properties of Humbert's polynomials, II, Ser. Math. Inform. 6 (1991) 23-30]. A study of the eigenvalues of a particular banded Hessenberg matrix is done.
Development of error criteria for adaptive multi-element polynomial chaos approaches
NASA Astrophysics Data System (ADS)
Chouvion, B.; Sarrouy, E.
2016-01-01
This paper presents and compares different methodologies to create an adaptive stochastic space partitioning in polynomial chaos applications which use a multi-element approach. To implement adaptive partitioning, Wan and Karniadakis first developed a criterion based on the relative error in local variance. We propose here two different error criteria: one based on the residual error and the other on the local variance discontinuity created by partitioning. The methods are applied to classical differential equations with long-term integration difficulties, including the Kraichnan-Orszag three-mode problem, and to simple linear and nonlinear mechanical systems whose stochastic dynamic responses are investigated. The efficiency and robustness of the approaches are investigated by comparison with Monte-Carlo simulations. For the different examples considered, they show significantly better convergence characteristics than the original error criterion used.
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.
NASA Astrophysics Data System (ADS)
Chen, Zhixiang; Fu, Bin
This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.
Veeken, Hans; Ritmeijer, Koert; Seaman, Jill; Davidson, Robert
2003-02-01
We compared an rK39 dipstick rapid test (Amrad ICT, Australia) with a direct agglutination test (DAT) and splenic aspirate for the diagnosis of kala-azar in 77 patients. The study was carried out under field conditions in an endemic area of north-east Sudan. The sensitivity of the rK39 test compared with splenic aspiration was 92% (46/50), the specificity 59% (16/27), and the positive predictive value 81% (46/57). Compared with the diagnostic protocol used by Médecins sans Frontières, the sensitivity of the rK39 test was 93% (50/54), the specificity 70% (16/23), and the positive predictive value 88% (50/57). Compared with splenic aspirates, the sensitivity of a DAT with a titre > or =1:400 was 100% (50/50), but its specificity only 55% (15/27) and the positive predictive value was 80% (50/62). Using a DAT titre > or =1:6400, the sensitivity was 84% (42/50), the specificity 85% (23/27) and the positive predictive value 91% (42/46). All four patients with DAT titre > or =1:6400 but negative splenic aspirate were also rK39 positive; we consider these are probably 'true' cases of kala-azar, i.e. false negative aspirates, rather than false DAT and rK39 seropositives. There were no false negative DATs (DAT titre < or =1:400 and aspirate positive), but there were four false negative rK39 tests (rK39 negative and aspirate positive). The rK39 dipstick is a good screening test for kala-azar; but further development is required before it can replace the DAT as a diagnostic test in endemic areas of the Sudan. PMID:12581443
A model of flexion-extension movement in hip joint using polynomial interpolation
NASA Astrophysics Data System (ADS)
Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan
2013-10-01
The study proposes a mathematical model of flexion-extension movement in hip joint based on Lagrange polynomial interpolation. In order to develop and validate the proposed model the angle of flexion-extension (F-E) in hip joint was analyzed. The two main reasons of this option rely on the importance of the hip joint in human locomotion and the fact that flexion-extension movement is developed in most of the human joints. The mathematical model of joint movement allows developing a more detailed kinematic analysis of the joint movements. The raw data representing the variation of the flexion-extension angle in hip joint was achieved by experimental kinematic analysis of a lot of ten young healthy subjects.
Typical Orbits of Quadratic Polynomials with a Neutral Fixed Point: Brjuno Type
NASA Astrophysics Data System (ADS)
Cheraghi, Davoud
2013-09-01
We describe the topological behavior of typical orbits of complex quadratic polynomials {P_{α}(z) = e^{2 π α {i}} z + z2}, with α of high return type. Here we prove that for such Brjuno values of α the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then we show that the limit set of the orbit of a typical point in the Julia set of P α is equal to the closure of the critical orbit. Our method is based on the near parabolic renormalization of Inou-Shishikura, and a uniform optimal estimate on the derivative of the Fatou coordinate that we prove here.
Benson, Kathleen F; Chada, Kiran
2002-01-01
Chromosomal rearrangements provide an important resource for molecular characterization of mutations in the mouse. In(10)17Rk mice contain a paracentric inversion of approximately 50 Mb on chromosome 10. Homozygous In(10)17Rk mice exhibit a pygmy phenotype, suggesting that the distal inversion breakpoint is within the pygmy locus. The pygmy mutation, originally isolated in 1944, is an autosomal recessive trait causing a dwarf phenotype in homozygous mice and has been mapped to the distal region of chromosome 10. The pygmy phenotype has subsequently been shown to result from disruption of the Hmgi-c gene. To identify the In(10)17Rk distal inversion breakpoint, In(10)17Rk DNA was subjected to RFLP analysis with single copy sequences derived from the wild-type pygmy locus. This analysis localized the In(10)17Rk distal inversion breakpoint to intron 3 of Hmgi-c and further study determined that a fusion transcript between novel 5' sequence and exons 4 and 5 of Hmgi-c is created. We employed 5' RACE to isolate the 5' end of the fusion transcript and this sequence was localized to the proximal end of chromosome 10 between markers Cni-rs2 and Mtap7. Northern blot analysis of individual tissues of wild-type mice determined that the gene at the In(10)17Rk proximal inversion breakpoint is a novel muscle-specific gene and its disruption does not lead to a readily observable phenotype. PMID:11805063
Chappuis, François; Rijal, Suman; Soto, Alonso; Menten, Joris; Boelaert, Marleen
2006-01-01
Objective To compare the performance of the direct agglutination test and rK39 dipstick for the diagnosis of visceral leishmaniasis. Data sources Medline, citation tracking, January 1986 to December 2004. Selection criteria Original studies evaluating the direct agglutination test or the rK39 dipstick with clinical visceral leishmaniasis as target condition; adequate reference classification; and absolute numbers of true positive, true negative, false positive, and false negative observations available or derivable from the data presented. Results 30 studies evaluating the direct agglutination test and 13 studies evaluating the rK39 dipstick met the inclusion criteria. The combined sensitivity estimates of the direct agglutination test and the rK39 dipstick were 94.8% (95% confidence interval 92.7% to 96.4%) and 93.9% (87.7% to 97.1%), respectively. Sensitivity seemed higher and more homogenous in the studies carried out in South Asia. Specificity estimates were influenced by the type of controls. In phase III studies carried out on patients with clinically suspected disease, the estimated specificity of the direct agglutination test was 85.9% (72.3% to 93.4%) and of the rK39 dipstick was 90.6% (66.8% to 97.9%). Conclusion The diagnostic performance of the direct agglutination test and the rK39 dipstick for visceral leishmaniasis is good to excellent and seem comparable. PMID:16882683
On ambiguity in knot polynomials for virtual knots
NASA Astrophysics Data System (ADS)
Morozov, A.; Morozov, And.; Popolitov, A.
2016-06-01
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual q and A =qN. These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conveniently observed in the hypercube formalism: then they substitute q-dimensions of certain fat graphs, which are not constrained by recursion and can be chosen arbitrarily. The number of these new topological invariants seems to grow fast with the number of non-virtual crossings: 0, 1, 1, 5, 15, 91, 784, 9160, ... This number can be decreased by imposing the factorization requirement for composites, in addition to topological invariance - still freedom remains. None of these new parameters, however, appears in HOMFLY for Kishino unknot, which thus remains unseparated from the ordinary unknots even by this enriched set of knot invariants.
Galois quantum systems, irreducible polynomials and Riemann surfaces
Vourdas, A.
2006-09-15
Finite quantum systems in which the position and momentum take values in the Galois field GF(p{sup l}), are studied. Ideas from the subject of field extension are transferred in the context of quantum mechanics. The Frobenius automorphisms in Galois fields lead naturally to the 'Frobenius formalism' in a quantum context. The Hilbert space splits into 'Frobenius subspaces' which are labeled with the irreducible polynomials associated with the y{sup p{sup l-y}}. The Frobenius maps transform unitarily the states of a Galois quantum system and leave fixed all states in some of its Galois subsystems (where the position and momentum take values in subfields of GF(p{sup l})). An analytic representation of these systems in the l-sheeted complex plane shows deeper links between Galois theory and Riemann surfaces.
Sphere-cone-polynomial special window with good aberration characteristic
NASA Astrophysics Data System (ADS)
Wang, Chao; Zhang, Xin; Qu, He-Meng; Wang, Ling-Jie; Wang, Yu
2013-07-01
Optical windows with external surfaces shaped to satisfy operational environment needs are known as special windows. A novel special window, a sphere-cone-polynomial (SCP) window, is proposed. The formulas of this window shape are given. An SCP MgF2 window with a fineness ratio of 1.33 is designed as an example. The field-of-regard (FOR) angle is ±75°. From the window system simulation results obtained with the calculated fluid dynamics (CFD) and optical design software, we find that compared to the conventional window forms, the SCP shape can not only introduce relatively less drag in the airflow, but also have the minimal effect on imaging. So the SCP window optical system can achieve a high image quality across a super wide FOR without adding extra aberration correctors. The tolerance analysis results show that the optical performance can be maintained with a reasonable fabricating tolerance to manufacturing errors.