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.
Polynomial driven time base and PN generator
NASA Technical Reports Server (NTRS)
Brokl, S. S.
1983-01-01
In support of the planetary radar upgrade new hardware was designed to increase resolution and take advantage of new technology. Included is a description of the Polynomial Driven Time Base and PN Generator which is used for range gate coding in the planetary radar system.
Polynomial optimization techniques for activity scheduling. Optimization based prototype scheduler
NASA Technical Reports Server (NTRS)
Reddy, Surender
1991-01-01
Polynomial optimization techniques for activity scheduling (optimization based prototype scheduler) are presented in the form of the viewgraphs. The following subject areas are covered: agenda; need and viability of polynomial time techniques for SNC (Space Network Control); an intrinsic characteristic of SN scheduling problem; expected characteristics of the schedule; optimization based scheduling approach; single resource algorithms; decomposition of multiple resource problems; prototype capabilities, characteristics, and test results; computational characteristics; some features of prototyped algorithms; and some related GSFC references.
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
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.
Parameter-based Fisher's information of orthogonal polynomials
NASA Astrophysics Data System (ADS)
Dehesa, J. S.; Olmos, B.; Yanez, R. J.
2008-04-01
The Fisher information of the classical orthogonal polynomials with respect to a parameter is introduced, its interest justified and its explicit expression for the Jacobi, Laguerre, Gegenbauer and Grosjean polynomials found.
Adaptive sparse polynomial chaos expansion based on least angle regression
NASA Astrophysics Data System (ADS)
Blatman, Géraud; Sudret, Bruno
2011-03-01
Polynomial chaos (PC) expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable (so-called polynomial chaos) basis. The number of terms to be computed grows dramatically with the size of the input random vector, which makes the computational cost of classical solution schemes (may it be intrusive (i.e. of Galerkin type) or non intrusive) unaffordable when the deterministic finite element model is expensive to evaluate. To address such problems, the paper describes a non intrusive method that builds a sparse PC expansion. First, an original strategy for truncating the PC expansions, based on hyperbolic index sets, is proposed. Then an adaptive algorithm based on least angle regression (LAR) is devised for automatically detecting the significant coefficients of the PC expansion. Beside the sparsity of the basis, the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon. The accuracy of the PC metamodel is checked using an estimate inspired by statistical learning theory, namely the corrected leave-one-out error. As a consequence, a rather small number of PC terms are eventually retained ( sparse representation), which may be obtained at a reduced computational cost compared to the classical "full" PC approximation. The convergence of the algorithm is shown on an analytical function. Then the method is illustrated on three stochastic finite element problems. The first model features 10 input random variables, whereas the two others involve an input random field, which is discretized into 38 and 30 - 500 random variables, respectively.
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
General polynomial factorization-based design of sparse periodic linear arrays.
Mitra, Sanjit K; Mondal, Kalyan; Tchobanou, Mikhail K; Dolecek, Gordana Jovanovic
2010-09-01
We have developed several methods of designing sparse periodic arrays based upon the polynomial factorization method. In these methods, transmit and receive aperture polynomials are selected such that their product results in a polynomial representing the desired combined transmit/receive (T/R) effective aperture function. A desired combined T/R effective aperture is simply an aperture with an appropriate width exhibiting a spectrum that corresponds to the desired two-way radiation pattern. At least one of the two aperture functions that constitute the combined T/R effective aperture function will be a sparse polynomial. A measure of sparsity of the designed array is defined in terms of the element reduction factor. We show that elements of a linear array can be reduced with varying degrees of beam mainlobe width to sidelobe reduction properties.
Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation
Li, Mingchu; Guo, Cheng; Choo, Kim-Kwang Raymond; Ren, Yizhi
2016-01-01
After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t′, n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely. PMID:27792784
A general U-block model-based design procedure for nonlinear polynomial control systems
NASA Astrophysics Data System (ADS)
Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua
2016-10-01
The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.
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
Security analysis of an encryption scheme based on nonpositional polynomial notations
NASA Astrophysics Data System (ADS)
Kapalova, Nursulu; Dyusenbayev, Dilmukhanbet
2016-01-01
The aim of the research was to conduct a cryptographic analysis of an encryption scheme developed on the basis of nonpositional polynomial notations to estimate the algorithm strength. Nonpositional polynomial notations (NPNs) are residue number systems (RNSs) based on irreducible polynomials over GF(2). To evaluate if the algorithms developed on the basis of NPNs are secure, mathematical models of cryptanalysis involving algebraic, linear and differential methods have been designed. The cryptanalysis is as follows. A system of nonlinear equations is obtained from a function transforming plaintext into ciphertext with a key. Next, a possibility of transition of the nonlinear system to a linear one is considered. The cryptanalysis was conducted for the cases with known: 1) ciphertext; 2) plaintext and the related ciphertext; 3) plaintext file format; and 4) ASCII-encoded plaintext.
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
Distance-based topological polynomials and indices of friendship graphs.
Gao, Wei; Farahani, Mohammad Reza; Imran, Muhammad; Rajesh Kanna, M R
2016-01-01
Drugs and chemical compounds are often modeled as graphs in which the each vertex of the graph expresses an atom of molecule and covalent bounds between atoms are represented by the edges between their corresponding vertices. The topological indicators defined over this molecular graph have been shown to be strongly correlated to various chemical properties of the compounds. In this article, by means of graph structure analysis, we determine several distance based topological indices of friendship graph [Formula: see text] which is widely appeared in various classes of new nanomaterials, drugs and chemical compounds. PMID:27652136
da Silva, M R; Brandão, N A A; Dorta, M L; Fátima, R D; Costa, D L; Costa, C H N; Oliveira, M A P
2015-06-01
Visceral leishmaniasis (VL) is a tropical neglected disease endemic in 98 countries and affects more than 58 000 individuals per year. Several serological tests are available for VL diagnosis, including an immunochromatographic (IC) test with the rK39 antigen and finger prick-collected blood, a rapid and low-invasive test. Here, we investigate the possibility to use saliva as a non-invasive source of biological material for the rK39 IC test. Blood samples from 84 patients with suspected VL were screened by the rK39 IC test, and 29 were confirmed as being infected by a positive rK39 IC test and the presence of amastigotes on smears slides or parasite DNA (detected using PCR-RFLP) from bone marrow aspirate. The rK39 IC test using saliva samples was positive for 17 of the 29 confirmed VL cases (58.6%). The amount of Leishmania-specific IgG or total IgG, as evaluated by an immunoenzymatic assay, was higher in the saliva of patients who had rK39 IC test positivity using saliva, whereas the amount of Leishmania-specific IgA or total IgA was similar to the healthy donors. These results suggest that saliva is not an appropriated material for diagnosing VL with this test.
Delles, Michael; Rengier, Fabian; Ley, Sebastian; von Tengg-Kobligk, Hendrik; Kauczor, Hans-Ulrich; Dillmann, Rüdiger; Unterhinninghofen, Roland
2011-01-01
In cardiovascular diagnostics, phase-contrast MRI is a valuable technique for measuring blood flow velocities and computing blood pressure values. Unfortunately, both velocity and pressure data typically suffer from the strong image noise of velocity-encoded MRI. In the past, separate approaches of regularization with physical a-priori knowledge and data representation with continuous functions have been proposed to overcome these drawbacks. In this article, we investigate polynomial regularization as an exemplary specification of combining these two techniques. We perform time-resolved three-dimensional velocity measurements and pressure gradient computations on MRI acquisitions of steady flow in a physical phantom. Results based on the higher quality temporal mean data are used as a reference. Thereby, we investigate the performance of our approach of polynomial regularization, which reduces the root mean squared errors to the reference data by 45% for velocities and 60% for pressure gradients.
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
Narimani, Mohammand; Lam, H K; Dilmaghani, R; Wolfe, Charles
2011-06-01
Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.
Polynomial-based approximate solutions to the Boussinesq equation near a well
NASA Astrophysics Data System (ADS)
Telyakovskiy, Aleksey S.; Kurita, Satoko; Allen, Myron B.
2016-10-01
This paper presents a method for constructing polynomial-based approximate solutions to the Boussinesq equation with cylindrical symmetry. This equation models water injection at a single well in an unconfined aquifer; as a sample problem we examine recharge of an initially empty aquifer. For certain injection regimes it is possible to introduce similarity variables, reducing the original problem to a boundary-value problem for an ordinary differential equation. The approximate solutions introduced here incorporate both a singular part to model the behavior near the well and a polynomial part to model the behavior in the far field. Although the nonlinearity of the problem prevents decoupling of the singular and polynomial parts, the paper presents an approach for calculating the solution based on its spatial moments. This approach yields closed-form expressions for the position of the wetting front and for the form of the phreatic surface. Comparison with a highly accurate numerical solution verifies the accuracy of the newly derived approximate solutions.
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.
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.
Novel image encryption scheme based on Chebyshev polynomial and Duffing map.
Stoyanov, Borislav; Kordov, Krasimir
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 10(113) key space and desirable level of security based on the good statistical results and theoretical arguments. PMID:25143970
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
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…
NASA Astrophysics Data System (ADS)
Liu, Jie; Sun, Xingsheng; Han, Xu; Jiang, Chao; Yu, Dejie
2015-05-01
Based on the Gegenbauer polynomial expansion theory and regularization method, an analytical method is proposed to identify dynamic loads acting on stochastic structures. Dynamic loads are expressed as functions of time and random parameters in time domain and the forward model of dynamic load identification is established through the discretized convolution integral of loads and the corresponding unit-pulse response functions of system. Random parameters are approximated through the random variables with λ-probability density function (PDFs) or their derivative PDFs. For this kind of random variables, Gegenbauer polynomial expansion is the unique correct choice to transform the problem of load identification for a stochastic structure into its equivalent deterministic system. Just via its equivalent deterministic system, the load identification problem of a stochastic structure can be solved by any available deterministic methods. With measured responses containing noise, the improved regularization operator is adopted to overcome the ill-posedness of load reconstruction and to obtain the stable and approximate solutions of certain inverse problems and the valid assessments of the statistics of identified loads. Numerical simulations demonstrate that with regard to stochastic structures, the identification and assessment of dynamic loads are achieved steadily and effectively by the presented method.
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.
Edee, K; Plumey, J P
2015-03-01
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution.
Edee, K; Plumey, J P
2015-03-01
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account boundary conditions and also to make the method more flexible in use. In the previous versions of MMGE, an undersized matrix relation is obtained by solving Maxwell's equations, and the boundary conditions complement this undersized system. In the current work, contrary to this previous version of the MMGE, boundary conditions are incorporated into the definition of a new basis of polynomial functions, which are adapted to the boundary value problem of interest. Results are successfully compared for both metallic and dielectric structures to those obtained from the modal method based on Fourier expansion (MMFE) and MMFE with adaptative spatial resolution. PMID:26366651
NASA Astrophysics Data System (ADS)
Saad, George; Ghanem, Roger
2009-04-01
Model-based predictions of flow in porous media are critically dependent on assumptions and hypotheses that are not always based on first principles and that cannot necessarily be justified on the basis of known prevalent physics. Constitutive models, for instance, fall under this category. While these predictive tools are usually calibrated using observational data, the scatter in the resulting parameters has typically been ignored. In this paper, this scatter is used to construct stochastic process models of the parameters which are then used as the cornerstone in a novel model validation methodology useful for ascertaining the confidence in model-based predictions. The uncertainties are first quantified by representing the unknown model parameters via their polynomial chaos decompositions. These are descriptions of stochastic processes in terms of their coordinates with respect to an orthogonal basis. This is followed by a filtering step to update these representations with measurements as they become available. In order to account for the non-Gaussian nature of model parameters and model errors, an adaptation of the ensemble Kalman filter is developed. Instead of propagating an ensemble of model states forward in time as is suggested within the framework of the ensemble Kalman filter, the proposed approach allows the propagation of a stochastic representation of unknown variables using their respective polynomial chaos decompositions. The model is propagated forward in time by solving the system of partial differential equations using a stochastic projection method. Whenever measurements are available, the proposed data assimilation technique is used to update the stochastic parameters of the numerical model. The proposed method is applied to a black oil reservoir simulation model where measurements are used to stochastically characterize the flow medium and to verify the model validity with specified confidence bounds. The updated model can then be employed to
Vega, Sonia; Abian, Olga; Velazquez-Campoy, Adrian
2015-04-01
Isothermal titration calorimetry (ITC) has become the gold-standard technique for studying binding processes due to its high precision and sensitivity, as well as its capability for the simultaneous determination of the association equilibrium constant, the binding enthalpy and the binding stoichiometry. The current widespread use of ITC for biological systems has been facilitated by technical advances and the availability of commercial calorimeters. However, the complexity of data analysis for non-standard models is one of the most significant drawbacks in ITC. Many models for studying macromolecular interactions can be found in the literature, but it looks like each biological system requires specific modeling and data analysis approaches. The aim of this article is to solve this lack of unity and provide a unified methodological framework for studying binding interactions by ITC that can be applied to any experimental system. The apparent complexity of this methodology, based on the binding polynomial, is overcome by its easy generalization to complex systems.
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
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
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
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.
Molinet, Félix Javier León; Ampuero, Julia Sonia; Costa, Rodrigo Diniz; Noronha, Elza Ferreira; Romero, Gustavo Adolfo Sierra
2013-05-01
The aim of this study was to evaluate the specificity of a rapid immunochromatographic test that was developed to detect antibodies against the rK39 antigen for the diagnosis of visceral leishmaniasis (VL). This evaluation was performed using sera from patients with a confirmed diagnosis of active cutaneous leishmaniasis. The sera from 272 patients with a confirmed diagnosis of localised cutaneous leishmaniasis (CL) who resided in an area endemic for Leishmania braziliensis in Brazil were obtained before the initiation of antileishmanial treatment. Kalazar Detect(r)(InBios, Seattle, WA) recombinant K39 antigen-based immunochromatographic strips were used according to the manufacturer's instructions. The test results were evaluated independently by two examiners in sequential order. The positive controls for the test included five serum samples from five patients with parasitologically confirmed diagnosis of VL caused by Leishmania infantum in Brazil. Overall, 100% of the samples obtained from patients with CL were negative, confirming the absence of a serological cross-reaction for individuals with cutaneous disease when these patients were evaluated using the rapid test. The lack of a cross-reaction in patients who were infected by parasites of the same genus highlights the specificity of the rK39 antigen for the diagnosis of VL in areas with the sympatric circulation of L. braziliensis and L. infantum.
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
Stabilisation of matrix polynomials
NASA Astrophysics Data System (ADS)
Galindo, R.
2015-10-01
A state feedback is proposed to analyse the stability of a matrix polynomial in closed loop. First, it is shown that a matrix polynomial is stable if and only if a state space realisation of a ladder form of certain transfer matrix is stable. Following the ideas of the Routh-Hurwitz stability procedure for scalar polynomials, certain continued-fraction expansions of polynomial matrices are carrying out by unimodular matrices to achieve the Euclid's division algorithm which leads to an extension of the well-known Routh-Hurwitz stability criteria but this time in terms of matrix coefficients. After that, stability of the closed-loop matrix polynomial is guaranteed based on a Corollary of a Lyapunov Theorem. The sufficient stability conditions are: (i) The matrices of one column of the presented array must be symmetric and positive definite and (ii) the matrices of the cascade realisation must satisfy a commutative condition. These stability conditions are also necessary for matrix polynomial of second order. The results are illustrated through examples.
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.
A model-based 3D phase unwrapping algorithm using Gegenbauer polynomials.
Langley, Jason; Zhao, Qun
2009-09-01
The application of a two-dimensional (2D) phase unwrapping algorithm to a three-dimensional (3D) phase map may result in an unwrapped phase map that is discontinuous in the direction normal to the unwrapped plane. This work investigates the problem of phase unwrapping for 3D phase maps. The phase map is modeled as a product of three one-dimensional Gegenbauer polynomials. The orthogonality of Gegenbauer polynomials and their derivatives on the interval [-1, 1] are exploited to calculate the expansion coefficients. The algorithm was implemented using two well-known Gegenbauer polynomials: Chebyshev polynomials of the first kind and Legendre polynomials. Both implementations of the phase unwrapping algorithm were tested on 3D datasets acquired from a magnetic resonance imaging (MRI) scanner. The first dataset was acquired from a homogeneous spherical phantom. The second dataset was acquired using the same spherical phantom but magnetic field inhomogeneities were introduced by an external coil placed adjacent to the phantom, which provided an additional burden to the phase unwrapping algorithm. Then Gaussian noise was added to generate a low signal-to-noise ratio dataset. The third dataset was acquired from the brain of a human volunteer. The results showed that Chebyshev implementation and the Legendre implementation of the phase unwrapping algorithm give similar results on the 3D datasets. Both implementations of the phase unwrapping algorithm compare well to PRELUDE 3D, 3D phase unwrapping software well recognized for functional MRI. PMID:19671967
A model-based 3D phase unwrapping algorithm using Gegenbauer polynomials
NASA Astrophysics Data System (ADS)
Langley, Jason; Zhao, Qun
2009-09-01
The application of a two-dimensional (2D) phase unwrapping algorithm to a three-dimensional (3D) phase map may result in an unwrapped phase map that is discontinuous in the direction normal to the unwrapped plane. This work investigates the problem of phase unwrapping for 3D phase maps. The phase map is modeled as a product of three one-dimensional Gegenbauer polynomials. The orthogonality of Gegenbauer polynomials and their derivatives on the interval [-1, 1] are exploited to calculate the expansion coefficients. The algorithm was implemented using two well-known Gegenbauer polynomials: Chebyshev polynomials of the first kind and Legendre polynomials. Both implementations of the phase unwrapping algorithm were tested on 3D datasets acquired from a magnetic resonance imaging (MRI) scanner. The first dataset was acquired from a homogeneous spherical phantom. The second dataset was acquired using the same spherical phantom but magnetic field inhomogeneities were introduced by an external coil placed adjacent to the phantom, which provided an additional burden to the phase unwrapping algorithm. Then Gaussian noise was added to generate a low signal-to-noise ratio dataset. The third dataset was acquired from the brain of a human volunteer. The results showed that Chebyshev implementation and the Legendre implementation of the phase unwrapping algorithm give similar results on the 3D datasets. Both implementations of the phase unwrapping algorithm compare well to PRELUDE 3D, 3D phase unwrapping software well recognized for functional MRI.
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 Astrophysics Data System (ADS)
Cooper, Guy A.; Peterson, Randolph S.; Gruber, Ralf; Cooper, W. Anthony; Graves, Jonathan P.
2009-11-01
An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials.footnotetextG. A. Cooper, J. P. Graves, W. A. Cooper, R. Gruber and R. S. Peterson, J. Comput. Phys. 228 (2009) 4911-4916. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code.footnotetextA. Cooper, Plasma Phys. Control. Fusion 34 (1992) 1011-1036. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.
Milgram, A
2011-02-21
This comment addresses critics on the claimed stability of solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem, proposed by Dubey al. (2010. A solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem using Boubaker polynomial expansion scheme. Journal of Theoretical Biology 264, 154-160). Critics are based on incompatibilities between the claimed asymptotic behavior and the presumed Malthusian growth of prey population in absence of predator.
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].
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
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, ?.
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].
Towards top-hat spatial shaping of ultrafast laser beam based on Zernike polynomials
NASA Astrophysics Data System (ADS)
Mauclair, Cyril; Faure, Nicolas; Houzet, Julien
2016-04-01
Femtosecond laser micro machining of surfaces knows a gain of interest as it demonstrates efficient and precise processing with reduced side effects around the irradiated zone, and also because of the remarkable costs reduction and reliability improvements of nowadays commercially available sources. Controlling the intensity distribution spatially can offer a supplementary degree of flexibility and precision in achieving user-defined ablation spatial profile, drilling, cutting of materials or in-volume laser-induced modifications. In this scope, the possibility to generate a top-hat intensity distribution by spatially shaping the beam wavefront is studied in this work. An optimization of Zernike polynomials coefficients is conducted to numerically determine an adequate phase mask that shapes the laser intensity distribution following a targeted top hat distribution in the processing plane, usually at the focal length of a converging lens. The efficiency of the method is numerically investigated in the optimization by evaluation of the root mean square error (RMS) between the top-hat target and the calculated laser distribution in the far field. We numerically verify that acceptable top-hat beam shaping of various size can be achieved with a sufficient number of Zernike polynomials, opening the way to phase mask calculations adapted to the wavefront modulator ability to reproduce Zernike polynomials.
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
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings.
Edee, Kofi
2011-10-01
A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauer's polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM.
Modal method based on subsectional Gegenbauer polynomial expansion for lamellar gratings.
Edee, Kofi
2011-10-01
A first approach of a modal method by Gegenbauer polynomial expansion (MMGE1) is presented for a plane wave diffraction by a lamellar grating. Modal methods are among the most popular methods that are used to solve the problem of lamellar gratings. They consist in describing the electromagnetic field in terms of eigenfunctions and eigenvalues of an operator. In the particular case of the Fourier modal method (FMM), the eigenfunctions are approximated by a finite Fourier sum, and this approximation can lead to a poor convergence of the FMM. The Wilbraham-Gibbs phenomenon may be one of the reasons for this poor convergence. Thus, it is interesting to investigate other basis functions that may represent the fields more accurately. The approach proposed in this paper consists in subdividing the pattern in homogeneous layers, according to the periodicity axis. The field is expanded, in each layer, on the basis of Gegenbauer's polynomials. Boundary conditions are rigorously written between adjacent layers; thus, an eigenvalue equation is obtained. The approach presented in this paper proves to describe the fields accurately. Finally, it is demonstrated that the results obtained with the MMGE1 are more accurate than several existing modal methods, such as the classical and the parametric FMM. PMID:21979505
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.
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.
NASA Astrophysics Data System (ADS)
Karkar, Sami; Cochelin, Bruno; Vergez, Christophe
2013-02-01
In this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of non-polynomial nonlinearities. This extension allows for the computation of branches of periodic solutions of a broader class of nonlinear dynamical systems. The principle remains to transform the original ODE system into an extended polynomial quadratic system for an easy application of the harmonic balance method (HBM). The transformation of non-polynomial terms is based on the differentiation of state variables with respect to the time variable, shifting the nonlinear non-polynomial nonlinearity to a time-independent initial condition equation, not concerned with the HBM. The continuation of the resulting algebraic system is here performed by the asymptotic numerical method (high order Taylor series representation of the solution branch) using a further differentiation of the non-polynomial algebraic equation with respect to the path parameter. A one dof vibro-impact system is used to illustrate how an exponential nonlinearity is handled, showing that the method works at very high order, 1000 in that case. Various kinds of nonlinear functions are also treated, and finally the nonlinear free pendulum is addressed, showing that very accurate periodic solutions can be computed with the proposed method.
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
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.
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.
Houck, T.; Anderson, D.; Giordano, G.
1996-04-11
A prototype rf power source based on the Relativistic Klystron Two-Beam Accelerator (RK-TBA) concept is being constructed at the Lawrence Berkeley National Laboratory to study physics, engineering, and costing issues. The prototype is described and compared to a full scale design appropriate for driving the Next Linear Collider (NLC). Specific details of the induction core tests and pulsed power system are presented. The 1-MeV, 1.2-kA induction gun currently under construction is also described in detail.
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)
RK-TBA studies at the RTA test facility
Lidia, S.; Anderson, D.; Eylon, S.; Henestroza, E.; Houck, T.; Reginato, L.; Vanecek, D.; Westenskow, G.; Yu, S.
1997-03-01
Construction of a prototype RF power source based on the RK-TBA concept, called the RTA, has commenced at the Lawrence Berkeley National Laboratory. This prototype will be used to study physics, engineering, and costing issues involved in the application of the RK-TBA concept to linear colliders. The status of the prototype is presented, specifically the 1-MV, 1.2-kA induction electron gun and the pulsed power system that are in assembly. The RTA program theoretical effort, in addition to supporting the development of the prototype, has been studying optimization parameters for the application of the RK-TBA concept to higher-energy linear colliders. An overview of this work is presented. {copyright} {ital 1997 American Institute of Physics.}
RK-TBA Studies at the RTA Test Facility
Lidia, S.; Anderson, D.; Eylon, S.; Reginato, L.; Vanecek, D.; Yu, S.; Henestroza, E.; Houck, T.; Westenskow, G.
1997-01-01
Construction of a prototype RF power source based on the RK-TBA concept, called the RTA, has commenced at the Lawrence Berkeley National Laboratory. This prototype will be used to study physics, engineering, and costing issues involved in the application of the RK-TBA concept to linear colliders. The status of the prototype is presented, specifically the 1-MV, 1.2-kA induction electron gun and the pulsed power system that are in assembly. The RTA program theoretical effort, in addition to supporting the development of the prototype, has been studying optimization parameters for the application of the RK-TBA concept to higher-energy linear colliders. An overview of this work is presented. 1 fig.
SABIO-RK--database for biochemical reaction kinetics.
Wittig, Ulrike; Kania, Renate; Golebiewski, Martin; Rey, Maja; Shi, Lei; Jong, Lenneke; Algaa, Enkhjargal; Weidemann, Andreas; Sauer-Danzwith, Heidrun; Mir, Saqib; Krebs, Olga; Bittkowski, Meik; Wetsch, Elina; Rojas, Isabel; Müller, Wolfgang
2012-01-01
SABIO-RK (http://sabio.h-its.org/) is a web-accessible database storing comprehensive information about biochemical reactions and their kinetic properties. SABIO-RK offers standardized data manually extracted from the literature and data directly submitted from lab experiments. The database content includes kinetic parameters in relation to biochemical reactions and their biological sources with no restriction on any particular set of organisms. Additionally, kinetic rate laws and corresponding equations as well as experimental conditions are represented. All the data are manually curated and annotated by biological experts, supported by automated consistency checks. SABIO-RK can be accessed via web-based user interfaces or automatically via web services that allow direct data access by other tools. Both interfaces support the export of the data together with its annotations in SBML (Systems Biology Markup Language), e.g. for import in modelling tools.
Valentín-Vargas, Alexis; Chorover, Jon; Maier, Raina M.
2013-01-01
The Standard-Based Polynomial Interpolation (SBPIn) method is a new simple three-step protocol proposed to address common gel-to-gel variations for the comparison of sample profiles across multiple DGGE gels. The advantages of this method include no requirement for additional software or modification of the standard DGGE protocol. PMID:23234884
Plain Polynomial Arithmetic on GPU
NASA Astrophysics Data System (ADS)
Anisul Haque, Sardar; Moreno Maza, Marc
2012-10-01
As for serial code on CPUs, parallel code on GPUs for dense polynomial arithmetic relies on a combination of asymptotically fast and plain algorithms. Those are employed for data of large and small size, respectively. Parallelizing both types of algorithms is required in order to achieve peak performances. In this paper, we show that the plain dense polynomial multiplication can be efficiently parallelized on GPUs. Remarkably, it outperforms (highly optimized) FFT-based multiplication up to degree 212 while on CPU the same threshold is usually at 26. We also report on a GPU implementation of the Euclidean Algorithm which is both work-efficient and runs in linear time for input polynomials up to degree 218 thus showing the performance of the GCD algorithm based on systolic arrays.
On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients
ERIC Educational Resources Information Center
Si, Do Tan
1977-01-01
Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)
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.
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 (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.
Dougherty, Geoff; Johnson, Michael J
2008-03-01
The clinical recognition of abnormal vascular tortuosity is important in the diagnosis of many diseases. Metrics based on three-dimensional (3D) curvature, using approximating polynomial spline-fitting to "data balls" centered along the mid-line of the vessel, minimize digitization errors and give tortuosity values largely independent of the resolution of the imaging system. We applied two of these metrics to a number of clinical vascular systems, using both 2D and 3D datasets. Using abdominal aortograms of low tortuosity, we established their validity by their strong correlation with the ranking of an expert panel of three vascular surgeons. The values of the Spearman rank correlation coefficient between our rankings, using a data ball radius of one-quarter of the local vessel radius, and the average ranking of the expert panel were 0.96 (with a 95% confidence interval of [0.91, 0.99]) for the mean curvature and 0.98 ([0.94, 0.99]) for the root-mean-square (RMS) curvature. These confidence intervals indicate that our automated analysis is producing rankings whose reliability is similar to that of a human expert, and is significantly better than that achieved with existing algorithms. The metrics provided good discrimination between vessels of different tortuosity for both 2D and 3D datasets, and produced values sufficiently discriminating to assess the relative utility of arteries for endoluminal repair of aneurysms. PMID:17419088
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
Ubiquity of Kostka Polynomials
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2001-04-01
We report about results revolving around Kostka-Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup, which we call Liskova semigroup. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among such polynomials we study rectangular q-Catalan numbers; generalized exponents polynomials; principal specializations of the internal product of Schur functions; generalized q-Gaussian polynomials; parabolic Kostant partition function and its q-analog certain generating functions on the set of transportation matrices. In each case we apply rigged configurations technique to obtain some interesting and new information about Kostka-Foulkes and parabolic Kostka polynomials, Kostant partition function, MacMahon, Gelfand-Tsetlin and Chan-Robbins polytopes. We describe certain connections between generalized saturation and Fulton's conjectures and parabolic Kostka polynomials; domino tableaux and rigged configurations. We study also some properties of l-restricted generalized exponents and the stable behaviour of certain Kostka-Foulkes polynomials.
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-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...
Edee, Kofi; Abboud, Mira; Granet, Gérard; Cornet, Jean Francois; Dauchet, Jéremi
2014-10-01
The work presented here focuses on the numerical modeling of cylindrical structure eigenmodes with an arbitrary cross section using Gegenbauer polynomials. The new eigenvalue equation leads to considerable reduction in computation time compared to the previous formulation. The main idea of this new formulation involves considering that the numerical scheme can be partially separated into two independent parts and the size of the eigenvalue matrix equation may be reduced by a factor of 2. We show that the ratio of the computation times between the first and current versions follows a linear relation with respect to the number of polynomials. PMID:25401241
Edee, Kofi; Abboud, Mira; Granet, Gérard; Cornet, Jean Francois; Gippius, Nikolay A
2014-04-01
We present a modal method for the computation of eigenmodes of cylindrical structures with arbitrary cross sections. These modes are found as eigenvectors of a matrix eigenvalue equation that is obtained by introducing a new coordinate system that takes into account the profile of the cross section. We show that the use of Hertz potentials is suitable for the derivation of this eigenvalue equation and that the modal method based on Gegenbauer expansion (MMGE) is an efficient tool for the numerical solution of this equation. Results are successfully compared for both perfectly conducting and dielectric structures. A complex coordinate version of the MMGE is introduced to solve the dielectric case. PMID:24695126
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…
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
Fast-Polynomial-Transform Program
NASA Technical Reports Server (NTRS)
Truong, T. K.; Hsu, I. S.; Chu, Y. F.
1987-01-01
Computer program uses fast-polynomial-transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional cyclic convolutions converted to one-dimensional convolutions in polynomial rings. Program decomposes cyclic polynomials into polynomial convolutions of same length. Only FPT's and fast Fourier transforms of same length required. Modular approach saves computional resources. Program written in C.
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.
Blatny, J M; Brautaset, T; Winther-Larsen, H C; Haugan, K; Valla, S
1997-01-01
The plasmid vectors described in this report are derived from the broad-host-range RK2 replicon and can be maintained in many gram-negative bacterial species. The complete nucleotide sequences of all of the cloning and expression vectors are known. Important characteristics of the cloning vectors are as follows: a size range of 4.8 to 7.1 kb, unique cloning sites, different antibiotic resistance markers for selection of plasmid-containing cells, oriT-mediated conjugative plasmid transfer, plasmid stabilization functions, and a means for a simple method for modification of plasmid copy number. Expression vectors were constructed by insertion of the inducible Pu or Pm promoter together with its regulatory gene xylR or xylS, respectively, from the TOL plasmid of Pseudomonas putida. One of these vectors was used in an analysis of the correlation between phosphoglucomutase activity and amylose accumulation in Escherichia coli. The experiments showed that amylose synthesis was only marginally affected by the level of basal expression from the Pm promoter of the Acetobacter xylinum phosphoglucomutase gene (celB). In contrast, amylose accumulation was strongly reduced when transcription from Pm was induced. CelB was also expressed with a very high induction ratio in Xanthomonas campestris. These experiments showed that the A. xylinum celB gene could not complement the role of the bifunctional X. campestris phosphoglucomutase-phosphomannomutase gene in xanthan biosynthesis. We believe that the vectors described here are useful for cloning experiments, gene expression, and physiological studies with a wide range of bacteria and presumably also for analysis of gene transfer in the environment. PMID:9023917
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.
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.
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.…
NASA Astrophysics Data System (ADS)
Srivastava, H. M.; Lin, Shy-Der; Liu, Shuoh-Jung; Lu, Han-Chun
2012-03-01
Motivated essentially by their potential for applications in the mathematical, physical, and statistical sciences, the object of this paper is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing the main results presented here, the corresponding integral representations are derived for familiar simpler classes of hypergeometric polynomials such as (for example) the Lagrange polynomials, Shively's pseudo-Laguerre polynomials, and generalized Bessel polynomials. Each of the integral representations derived in this paper may be also viewed as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.
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
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…
NASA Astrophysics Data System (ADS)
Kuipers, J.
2012-06-01
New features of the symbolic algebra package Form 4 are discussed. Most importantly, these features include polynomial factorization and polynomial gcd computation. Examples of their use are shown. One of them is an exact version of Mincer which gives answers in terms of rational polynomials and 5 master integrals.
On Hermite Matrix Polynomials of Two Variables
NASA Astrophysics Data System (ADS)
Kahmmash, Ghazi S.
This study deals with the two-variable Hermite matrix polynomials, some relevant matrix functions appear interims of the two-variable Hermite matrix polynomials the relationships with Hermite matrix polynomials of one variable, Chepyshev matrix polynomials of the second kind have been obtained and expansion of the. Gegenbauer matrix polynomials as series of Hermite matrix polynomials.
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.
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.
Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers
NASA Technical Reports Server (NTRS)
Wong, Yau Shu; Jiang, Hong
1987-01-01
Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.
Chardin, Camille; Girin, Thomas; Roudier, François; Meyer, Christian; Krapp, Anne
2014-10-01
The plant specific RWP-RK family of transcription factors, initially identified in legumes and Chlamydomonas, are found in all vascular plants, green algae, and slime molds. These proteins possess a characteristic RWP-RK motif, which mediates DNA binding. Based on phylogenetic and domain analyses, we classified the RWP-RK proteins of six different species in two subfamilies: the NIN-like proteins (NLPs), which carry an additional PB1 domain at their C-terminus, and the RWP-RK domain proteins (RKDs), which are divided into three subgroups. Although, the functional analysis of this family is still in its infancy, several RWP-RK proteins have a key role in regulating responses to nitrogen availability. The nodulation-specific NIN proteins are involved in nodule organogenesis and rhizobial infection under nitrogen starvation conditions. Arabidopsis NLP7 in particular is a major player in the primary nitrate response. Several RKDs act as transcription factors involved in egg cell specification and differentiation or gametogenesis in algae, the latter modulated by nitrogen availability. Further studies are required to extend the general picture of the functional role of these exciting transcription factors.
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.
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.
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
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
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…
Inverse polynomial reconstruction method in DCT domain
NASA Astrophysics Data System (ADS)
Dadkhahi, Hamid; Gotchev, Atanas; Egiazarian, Karen
2012-12-01
The discrete cosine transform (DCT) offers superior energy compaction properties for a large class of functions and has been employed as a standard tool in many signal and image processing applications. However, it suffers from spurious behavior in the vicinity of edge discontinuities in piecewise smooth signals. To leverage the sparse representation provided by the DCT, in this article, we derive a framework for the inverse polynomial reconstruction in the DCT expansion. It yields the expansion of a piecewise smooth signal in terms of polynomial coefficients, obtained from the DCT representation of the same signal. Taking advantage of this framework, we show that it is feasible to recover piecewise smooth signals from a relatively small number of DCT coefficients with high accuracy. Furthermore, automatic methods based on minimum description length principle and cross-validation are devised to select the polynomial orders, as a requirement of the inverse polynomial reconstruction method in practical applications. The developed framework can considerably enhance the performance of the DCT in sparse representation of piecewise smooth signals. Numerical results show that denoising and image approximation algorithms based on the proposed framework indicate significant improvements over wavelet counterparts for this class of signals.
The number of polynomial solutions of polynomial Riccati equations
NASA Astrophysics Data System (ADS)
Gasull, Armengol; Torregrosa, Joan; Zhang, Xiang
2016-11-01
Consider real or complex polynomial Riccati differential equations a (x) y ˙ =b0 (x) +b1 (x) y +b2 (x)y2 with all the involved functions being polynomials of degree at most η. We prove that the maximum number of polynomial solutions is η + 1 (resp. 2) when η ≥ 1 (resp. η = 0) and that these bounds are sharp. For real trigonometric polynomial Riccati differential equations with all the functions being trigonometric polynomials of degree at most η ≥ 1 we prove a similar result. In this case, the maximum number of trigonometric polynomial solutions is 2η (resp. 3) when η ≥ 2 (resp. η = 1) and, again, these bounds are sharp. Although the proof of both results has the same starting point, the classical result that asserts that the cross ratio of four different solutions of a Riccati differential equation is constant, the trigonometric case is much more involved. The main reason is that the ring of trigonometric polynomials is not a unique factorization domain.
NASA Astrophysics Data System (ADS)
Murariu, Gabriel; Condurache-Bota, Simona
2013-01-01
The Kramers-Kronig transforms (KK) constitute a powerful tool to validate experimental data. The present study is implemented for Bi2O3 thin films deposited by thermal vacuum evaporation at different temperatures of the glass substrates. Since the extraordinary properties of this fabric allow us to consider particular analytical approach as it was previously shown, the reflectance properties of Bi2O3 as a function of temperature could be studied. The novelty of this article is the studying of a global effective analytical representation, based on polynomial functions, in order to obtain a general model that includes temperature dependence of the optical properties, using the Kramers-Kronig transformation type. In the mathematical expressions, were included mix combined term in order to avoid the effects of Runge phenomenon. As a case study was chosen Bi2O3 — a substance less studied in literature. In the last part are the presented and commented the results obtained for a series of eight studied models.
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.
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.
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.
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.
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.
Extension of vector-valued integral polynomials
NASA Astrophysics Data System (ADS)
Carando, Daniel; Lassalle, Silvia
2005-07-01
We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they are extendible to X-valued polynomials. The Aron-Berner extension of an integral polynomial is also studied. A canonical integral representation is given for domains not containing l1.
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
Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware
NASA Astrophysics Data System (ADS)
Repka, Marek
2016-01-01
Modular reduction in extended finite fields and polynomial rings is presented, which once implemented works for any random reduction polynomial without changes of the hardware. It is possible to reduce polynomials of whatever degree. Based on the principal defined, two example RTL architectures are designed, and some useful features are noted furthermore. The first architecture is sequential and reduce whatever degree polynomials, taking 2 cycles per term. The second one is Parallel and designed for reduction of polynomials of 2(t -1) degree at most, taking 1 cycle for the whole reduction.
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
Difference oscillator in terms of the Meixner polynomials
NASA Astrophysics Data System (ADS)
Atakishiyev, Natig M.; Jafarov, Elchin I.; Nagiyev, Shakir M.; Wolf, Kurt B.
1998-07-01
We discuss a difference model of the linear harmonic oscillator based on the Meixner polynomials. As limit and special cases, it contains difference oscillator models in terms of the Kravchuk and Charlier polynomials, as well as the wavefunctions of the linear harmonic oscillator in quantum mechanics. We show that the dynamical group is SU(1,1) and construct explicitly the corresponding coherent state. The reproducing kernel for the wavefunctions of the Meixner model is also found.
Bell Polynomial Approach to Associated Camassa-Holm Equation
NASA Astrophysics Data System (ADS)
Luo, Lin; Xie, Xiaoqiang
2013-02-01
Based on the theory of Bell polynomials, the bilinear form is obtained for the associated Camassa-Holm equation, and the bilinear Bäcklund transformations and Lax pair are derived by virtue of the Bell polynomial technology. At the same time, an infinite number of conservation laws of associated Camassa-Holm equation are constructed, and conserved densities and fluxes are given with explicit recursion formulae.
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.
The bivariate Rogers Szegö polynomials
NASA Astrophysics Data System (ADS)
Chen, William Y. C.; Saad, Husam L.; Sun, Lisa H.
2007-06-01
We present an operator approach to deriving Mehler's formula and the Rogers formula for the bivariate Rogers-Szegö polynomials hn(x, y|q). The proof of Mehler's formula can be considered as a new approach to the nonsymmetric Poisson kernel formula for the continuous big q-Hermite polynomials Hn(x; a|q) due to Askey, Rahman and Suslov. Mehler's formula for hn(x, y|q) involves a 3phi2 sum and the Rogers formula involves a 2phi1 sum. The proofs of these results are based on parameter augmentation with respect to the q-exponential operator and the homogeneous q-shift operator in two variables. By extending recent results on the Rogers-Szegö polynomials hn(x|q) due to Hou, Lascoux and Mu, we obtain another Rogers-type formula for hn(x, y|q). Finally, we give a change of base formula for Hn(x; a|q) which can be used to evaluate some integrals by using the Askey-Wilson integral.
Clustering properties, Jack polynomials and unitary conformal field theories
NASA Astrophysics Data System (ADS)
Estienne, Benoit; Regnault, Nicolas; Santachiara, Raoul
2010-01-01
Recently, Jack polynomials have been proposed as natural generalizations of Z Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A. These theories can be considered as non-unitary solutions of a more general series of CFTs with Z symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.
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.
The multivariate Hahn polynomials and the singular oscillator
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc
2014-11-01
Karlin and McGregor's d-variable Hahn polynomials are shown to arise in the (d+1)-dimensional singular oscillator model as the overlap coefficients between bases associated with the separation of variables in Cartesian and hyperspherical coordinates. These polynomials in d discrete variables depend on d+1 real parameters and are orthogonal with respect to the multidimensional hypergeometric distribution. The focus is put on the d = 2 case for which the connection with the three-dimensional singular oscillator is used to derive the main properties of the polynomials: forward/backward shift operators, orthogonality relation, generating function, recurrence relations, bispectrality (difference equations) and explicit expression in terms of the univariate Hahn polynomials. The extension of these results to an arbitrary number of variables is presented at the end of the paper.
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
Polynomial Beam Element Analysis Module
Ning, S. Andrew
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.
Damped harmonics and polynomial phase signals
NASA Astrophysics Data System (ADS)
Zhou, Guotong; Giannakis, Georgios B.
1994-10-01
The concern here is of retrieving damped harmonics and polynomial phase signals in the presence of additive noise. The damping function is not limited to the exponential model, and in certain cases, the additive noise does not have to be white. Three classes of algorithms are presented, namely DFT based, Kumaresan-Tufts type extensions, and subspace variants including the MUSIC algorithm. Preference should be based on the available data length and frequency separations. In addition, retrieval of self coupled damped harmonics, which may be present when nonlinearities exist in physical systems, is investigated. Simulation examples illustrate main points of the paper.
Tables of properties of airfoil polynomials
NASA Technical Reports Server (NTRS)
Desmarais, Robert N.; Bland, Samuel R.
1995-01-01
This monograph provides an extensive list of formulas for airfoil polynomials. These polynomials provide convenient expansion functions for the description of the downwash and pressure distributions of linear theory for airfoils in both steady and unsteady subsonic flow.
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
Wang, Yan; Cordewener, Jan H G; America, Antoine H P; Shan, Weixing; Bouwmeester, Klaas; Govers, Francine
2015-09-01
L-type lectin receptor kinases (LecRK) are potential immune receptors. Here, we characterized two closely-related Arabidopsis LecRK, LecRK-IX.1 and LecRK-IX.2, of which T-DNA insertion mutants showed compromised resistance to Phytophthora brassicae and Phytophthora capsici, with double mutants showing additive susceptibility. Overexpression of LecRK-IX.1 or LecRK-IX.2 in Arabidopsis and transient expression in Nicotiana benthamiana increased Phytophthora resistance but also induced cell death. Phytophthora resistance required both the lectin domain and kinase activity, but for cell death, the lectin domain was not needed. Silencing of the two closely related mitogen-activated protein kinase genes NbSIPK and NbNTF4 in N. benthamiana completely abolished LecRK-IX.1-induced cell death but not Phytophthora resistance. Liquid chromatography-mass spectrometry analysis of protein complexes coimmunoprecipitated in planta with LecRK-IX.1 or LecRK-IX.2 as bait, resulted in the identification of the N. benthamiana ABC transporter NbPDR1 as a potential interactor of both LecRK. The closest homolog of NbPDR1 in Arabidopsis is ABCG40, and coimmunoprecipitation experiments showed that ABCG40 associates with LecRK-IX.1 and LecRK-IX.2 in planta. Similar to the LecRK mutants, ABCG40 mutants showed compromised Phytophthora resistance. This study shows that LecRK-IX.1 and LecRK-IX.2 are Phytophthora resistance components that function independent of each other and independent of the cell-death phenotype. They both interact with the same ABC transporter, suggesting that they exploit similar signal transduction pathways.
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.
A risk assessment and control model for the failing Björk-Shiley convexo-concave heart valve.
Koornneef, F; van Gaalen, G L; de Mol, B A
1996-01-01
For risk assessment and control of the failing Björk-Shiley convexo-concave heart valve, we present a life cycle-based complex system model and a risk intensity assessment model, allowing consistent analysis of this complex medical problem and identification of all pertinent aspects of product-related risks to patients.
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.
Stability margins for Hurwitz polynomials
NASA Technical Reports Server (NTRS)
Chapellat, Herve; Bhattacharyya, S. P.; Keel, L. H.
1988-01-01
The authors treat the robust stability issue using the characteristic polynomial, for two different cases: first in coefficient space with respect to perturbations in the coefficient of the characteristic polynomial; and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l-(squared) stability margin for both the monic and nonmonic cases. Following this, a method is given to find the l(infinity) margin, and the method is extended to reveal much larger stability regions. In parameter space the authors consider all single-input (multi-output) or single-output (multi-input) systems with a fixed controller and a plant described by a set of transfer functions which are ratios of polynomials with variable coefficients. A procedure is presented to calculate the radius of the largest stability ball in the space of these variable parameters. The calculation serves as a stability margin for the control system. The formulas that result are quasi-closed-form expressions for the stability margin and are computationally efficient.
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.
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.
Factorization of Polynomials and GCD Computations for Finding Universal Denominators
NASA Astrophysics Data System (ADS)
Abramov, S. A.; Gheffar, A.; Khmelnov, D. E.
We discuss the algorithms which, given a linear difference equation with rational function coefficients over a field k of characteristic 0, compute a polynomial U(x) ∈ k[x] (a universal denominator) such that the denominator of each of rational solutions (if exist) of the given equation divides U(x). We consider two types of such algorithms. One of them is based on constructing a set of irreducible polynomials that are candidates for divisors of denominators of rational solutions, and on finding a bound for the exponent of each of these candidates (the full factorization of polynomials is used). The second one is related to earlier algorithms for finding universal denominators, where the computation of gcd was used instead of the full factorization. The algorithms are applicable to scalar equations of arbitrary orders as well as to systems of first-order equations.
Karunakaran, Ponniah; Blatny, Janet Martha; Ertesvåg, Helga; Valla, Svein
1998-01-01
TrfA is the only plasmid-encoded protein required for initiation of replication of the broad-host-range plasmid RK2. Here we describe the isolation of four trfA mutants temperature sensitive for replication in Pseudomonas aeruginosa. One of the mutations led to substitution of arginine 247 with cysteine. This mutant has been previously described to be temperature sensitive for replication, but poorly functional, in Escherichia coli. The remaining three mutants were identical, and each of them carried two mutations, one leading to substitution of arginine 163 with cysteine (mutation 163C) and the other a codon-neutral mutation changing the codon for glycine 235 from GGC to GGU (mutation 235). Neither of the two mutations caused a temperature-sensitive phenotype alone in P. aeruginosa, and the effect of the neutral mutation was caused by its ability to strongly reduce the trfA expression level. The double mutant and mutant 163C could not be stably maintained in E. coli, but mutant 235 could be established and, surprisingly, displayed a temperature-sensitive phenotype in this host. Mutation 235 strongly reduced the trfA expression level also in E. coli. The glycine 85 codon in trfA mRNA is GGU, and a change of this to GGC did not significantly affect expression. In addition, we found that wild-type trfA was expressed at much lower levels in E. coli than in P. aeruginosa, indicating that this level is a key parameter in the determination of the temperature-sensitive phenotypes in different species. The E. coli lacZ gene was translationally fused at the 3′ end and internally in trfA, in both cases leading to elimination of the effect of mutation 235 on expression. We therefore propose that this mutation acts through an effect on mRNA structure or stability. PMID:9683473
Discrete Tchebycheff orthonormal polynomials and applications
NASA Technical Reports Server (NTRS)
Lear, W. M.
1980-01-01
Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.
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.
Relative risk regression models with inverse polynomials.
Ning, Yang; Woodward, Mark
2013-08-30
The proportional hazards model assumes that the log hazard ratio is a linear function of parameters. In the current paper, we model the log relative risk as an inverse polynomial, which is particularly suitable for modeling bounded and asymmetric functions. The parameters estimated by maximizing the partial likelihood are consistent and asymptotically normal. The advantages of the inverse polynomial model over the ordinary polynomial model and the fractional polynomial model for fitting various asymmetric log relative risk functions are shown by simulation. The utility of the method is further supported by analyzing two real data sets, addressing the specific question of the location of the minimum risk threshold.
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
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.
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
Genus expansion of HOMFLY polynomials
NASA Astrophysics Data System (ADS)
Mironov, A. D.; Morozov, A. Yu.; Sleptsov, A. V.
2013-11-01
In the planar limit of the' t Hooft expansion, the Wilson-loop vacuum average in the three-dimensional Chern-Simons theory (in other words, the HOMFLY polynomial) depends very simply on the representation (Young diagram), HR(A|q)|q=1 = (σ1(A)|R|. As a result, the (knot-dependent) Ooguri-Vafa partition function becomes a trivial τ -function of the Kadomtsev-Petviashvili hierarchy. We study higher-genus corrections to this formula for HR in the form of an expansion in powers of z = q - q-1. The expansion coefficients are expressed in terms of the eigenvalues of cut-and-join operators, i.e., symmetric group characters. Moreover, the z-expansion is naturally written in a product form. The representation in terms of cut-and-join operators relates to the Hurwitz theory and its sophisticated integrability. The obtained relations describe the form of the genus expansion for the HOMFLY polynomials, which for the corresponding matrix model is usually given using Virasoro-like constraints and the topological recursion. The genus expansion differs from the better-studied weak-coupling expansion at a finite number N of colors, which is described in terms of Vassiliev invariants and the Kontsevich integral.
Polynomial Transformations For Discrete-Time Linear Systems
NASA Technical Reports Server (NTRS)
Baram, Yoram
1991-01-01
Transformations based on polynomial matrices of finite degree developed for use in computing functions for compensation, inversion, and approximation of discrete-time, multivariable, linear systems. Method derived from z-transform transfer-function form of matrices. Applicable to cascade-compensation problems in design of control systems.
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
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
Image distortion analysis using polynomial series expansion.
Baggenstoss, Paul M
2004-11-01
In this paper, we derive a technique for analysis of local distortions which affect data in real-world applications. In the paper, we focus on image data, specifically handwritten characters. Given a reference image and a distorted copy of it, the method is able to efficiently determine the rotations, translations, scaling, and any other distortions that have been applied. Because the method is robust, it is also able to estimate distortions for two unrelated images, thus determining the distortions that would be required to cause the two images to resemble each other. The approach is based on a polynomial series expansion using matrix powers of linear transformation matrices. The technique has applications in pattern recognition in the presence of distortions. PMID:15521492
Fitting Polynomial Equations to Curves and Surfaces
NASA Technical Reports Server (NTRS)
Arbuckle, P. D.; Sliwa, S. M.; Tiffany, S. H.
1986-01-01
FIT is computer program for interactively determining least-squares polynomial equations that fit user-supplied data. Finds leastsquares fits for functions of two independent variables. Interactive graphical and editing capabilities in FIT enables user to control polynomial equations to be fitted to data arising from most practical applications. FIT written in FORTRAN and COMPASS.
Fostering Connections between Classes of Polynomial Functions.
ERIC Educational Resources Information Center
Buck, Judy Curran
The typical path of instruction in high school algebra courses for the study of polynomial functions has been from linear functions, to quadratic functions, to polynomial functions of degree greater than two. This paper reports results of clinical interviews with an Algebra II student. The interviews were used to probe into the student's…
Polynomial interpretation of multipole vectors
NASA Astrophysics Data System (ADS)
Katz, Gabriel; Weeks, Jeff
2004-09-01
Copi, Huterer, Starkman, and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year Wilkinson microwave anisotropy probe (WMAP) quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article, the language of polynomials provides a new and independent derivation of the multipole vector concept. Bézout’s theorem supports an elementary proof that the multipole vectors exist and are unique (up to rescaling). The constructive nature of the proof leads to a fast, practical algorithm for computing multipole vectors. We illustrate the algorithm by finding exact solutions for some simple toy examples and numerical solutions for the first-year WMAP quadrupole and octopole. We then apply our algorithm to Monte Carlo skies to independently reconfirm the estimate that the WMAP quadrupole and octopole planes align at the 99.9% level.
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.
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.
The Arabidopsis CDPK-SnRK superfamily of protein kinases.
Hrabak, Estelle M; Chan, Catherine W M; Gribskov, Michael; Harper, Jeffrey F; Choi, Jung H; Halford, Nigel; Kudla, Jorg; Luan, Sheng; Nimmo, Hugh G; Sussman, Michael R; Thomas, Martine; Walker-Simmons, Kay; Zhu, Jian-Kang; Harmon, Alice C
2003-06-01
The CDPK-SnRK superfamily consists of seven types of serine-threonine protein kinases: calcium-dependent protein kinase (CDPKs), CDPK-related kinases (CRKs), phosphoenolpyruvate carboxylase kinases (PPCKs), PEP carboxylase kinase-related kinases (PEPRKs), calmodulin-dependent protein kinases (CaMKs), calcium and calmodulin-dependent protein kinases (CCaMKs), and SnRKs. Within this superfamily, individual isoforms and subfamilies contain distinct regulatory domains, subcellular targeting information, and substrate specificities. Our analysis of the Arabidopsis genome identified 34 CDPKs, eight CRKs, two PPCKs, two PEPRKs, and 38 SnRKs. No definitive examples were found for a CCaMK similar to those previously identified in lily (Lilium longiflorum) and tobacco (Nicotiana tabacum) or for a CaMK similar to those in animals or yeast. CDPKs are present in plants and a specific subgroup of protists, but CRKs, PPCKs, PEPRKs, and two of the SnRK subgroups have been found only in plants. CDPKs and at least one SnRK have been implicated in decoding calcium signals in Arabidopsis. Analysis of intron placements supports the hypothesis that CDPKs, CRKs, PPCKs and PEPRKs have a common evolutionary origin; however there are no conserved intron positions between these kinases and the SnRK subgroup. CDPKs and SnRKs are found on all five Arabidopsis chromosomes. The presence of closely related kinases in regions of the genome known to have arisen by genome duplication indicates that these kinases probably arose by divergence from common ancestors. The PlantsP database provides a resource of continuously updated information on protein kinases from Arabidopsis and other plants.
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
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.
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. PMID:27433494
Polynomial time blackbox identity testers for depth-3 circuits : the field doesn't matter.
Seshadhri, Comandur; Saxena, Nitin
2010-11-01
Let C be a depth-3 circuit with n variables, degree d and top fanin k (called {Sigma}{Pi}{Sigma}(k, d, n) circuits) over base field F. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. Klivans & Spielman (STOC 2001) observed that the problem is open even when k is a constant. This case has been subjected to a serious study over the past few years, starting from the work of Dvir & Shpilka (STOC 2005). We give the first polynomial time blackbox algorithm for this problem. Our algorithm runs in time poly(n)d{sup k}, regardless of the base field. The only field for which polynomial time algorithms were previously known is F = Q (Kayal & Saraf, FOCS 2009, and Saxena & Seshadhri, FOCS 2010). This is the first blackbox algorithm for depth-3 circuits that does not use the rank based approaches of Karnin & Shpilka (CCC 2008). We prove an important tool for the study of depth-3 identities. We design a blackbox polynomial time transformation that reduces the number of variables in a {Sigma}{Pi}{Sigma}(k, d, n) circuit to k variables, but preserves the identity structure. Polynomial identity testing (PIT) is a major open problem in theoretical computer science. The input is an arithmetic circuit that computes a polynomial p(x{sub 1}, x{sub 2},..., x{sub n}) over a base field F. We wish to check if p is the zero polynomial, or in other words, is identically zero. We may be provided with an explicit circuit, or may only have blackbox access. In the latter case, we can only evaluate the polynomial p at various domain points. The main goal is to devise a deterministic blackbox polynomial time algorithm for PIT.
Sequences of versatile, broad-host-range vectors of the RK2 family.
Scott, H. N.; Laible, P. D.; Hanson, D. K.; Biosciences Division
2003-07-01
Plasmid pRK404-a smaller derivative of RK2-is a tetracycline-resistant broad-host-range vector that carries a multiple cloning site and the lacZ(alpha) peptide that enables blue/white selection for cloned inserts in Escherichia coli. We present herein the complete and annotated sequence of pRK404 and three related vectors-pRK437, pRK442, and pRK442(H). These derivatives have proven to be valuable tools for genetic manipulation in Gram-negative bacteria. The knowledge of their complete sequences will facilitate efficient future engineering of them and will enhance their general applicability to the design of genetic systems for use in organisms for which new genomic sequence data are becoming available.
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.)
Gaussian quadrature for multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Coussement, Jonathan; van Assche, Walter
2005-06-01
We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.
Harmonic polynomials, hyperspherical harmonics, and atomic spectra
NASA Astrophysics Data System (ADS)
Avery, John Scales
2010-01-01
The properties of monomials, homogeneous polynomials and harmonic polynomials in d-dimensional spaces are discussed. The properties are shown to lead to formulas for the canonical decomposition of homogeneous polynomials and formulas for harmonic projection. Many important properties of spherical harmonics, Gegenbauer polynomials and hyperspherical harmonics follow from these formulas. Harmonic projection also provides alternative ways of treating angular momentum and generalised angular momentum. Several powerful theorems for angular integration and hyperangular integration can be derived in this way. These purely mathematical considerations have important physical applications because hyperspherical harmonics are related to Coulomb Sturmians through the Fock projection, and because both Sturmians and generalised Sturmians have shown themselves to be extremely useful in the quantum theory of atoms and molecules.
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.
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…
Positive maps, positive polynomials and entanglement witnesses
NASA Astrophysics Data System (ADS)
Skowronek, Łukasz; Życzkowski, Karol
2009-08-01
We link the study of positive quantum maps, block positive operators and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic forms that are not sums of squares. Although the general problem of describing the set of positive maps remains open, in some particular cases we solve the corresponding polynomial inequalities and obtain explicit conditions for positivity.
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.
Diffusion tensor image registration using polynomial expansion
NASA Astrophysics Data System (ADS)
Wang, Yuanjun; Chen, Zengai; Nie, Shengdong; Westin, Carl-Fredrik
2013-09-01
In this paper, we present a deformable registration framework for the diffusion tensor image (DTI) using polynomial expansion. The use of polynomial expansion in image registration has previously been shown to be beneficial due to fast convergence and high accuracy. However, earlier work was developed only for 3D scalar medical image registration. In this work, it is shown how polynomial expansion can be applied to DTI registration. A new measurement is proposed for DTI registration evaluation, which seems to be robust and sensitive in evaluating the result of DTI registration. We present the algorithms for DTI registration using polynomial expansion by the fractional anisotropy image, and an explicit tensor reorientation strategy is inherent to the registration process. Analytic transforms with high accuracy are derived from polynomial expansion and used for transforming the tensor's orientation. Three measurements for DTI registration evaluation are presented and compared in experimental results. The experiments for algorithm validation are designed from simple affine deformation to nonlinear deformation cases, and the algorithms using polynomial expansion give a good performance in both cases. Inter-subject DTI registration results are presented showing the utility of the proposed method.
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.
Tensor calculus in polar coordinates using Jacobi polynomials
NASA Astrophysics Data System (ADS)
Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.
2016-11-01
Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.
On multiple orthogonal polynomials for discrete Meixner measures
Sorokin, Vladimir N
2010-12-07
The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.
Smallest zeros of some types of orthogonal polynomials: asymptotics
NASA Astrophysics Data System (ADS)
Moreno-Balcazar, Juan Jose
2005-07-01
We establish Mehler-Heine-type formulas for orthogonal polynomials related to rational modifications of Hermite weight on the real line and for Hermite-Sobolev orthogonal polynomials. These formulas give us the asymptotic behaviour of the smallest zeros of the corresponding orthogonal polynomials. Furthermore, we solve a conjecture posed in a previous paper about the asymptotics of the smallest zeros of the Hermite-Sobolev polynomials as well as an open problem concerning the asymptotics of these Sobolev orthogonal polynomials.
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.
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).
[Solving resolution of diffraction gratings using coefficients of Zernike polynomials].
Yu, Hai-li; Qi, Xiang-dong; Bayanheshig; Tang, Yu-guo
2012-01-01
It is hard and costly to test resolution directly, because the focal length of testing equipment could be nearly ten meters. Solving resolution by diffraction wavefront aberration indirectly is an effective solution to this problem. A normalization model of solving resolution using fitting coefficients of Zernike polynomials was established based on the spectral imaging theory of Fourier optics. The relationship between resolution and wavefront aberration of diffraction gratings was illustrated by this model. Finally, a new method of testing resolution using fitting coefficients of Zernike polynomials was proposed. According to this method, the resolution of a grating is tested by ZYGO interferometer indirectly. Compared with direct method, results indicate that the error of indirect method is less than 4.22%, and this method could be an effective way to avoid the difficulty of direct method to solve resolution. Meanwhile, this method can be used in ZYGO interferometer to solve resolution by wavefront testing easily.
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.
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
Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan
2012-01-01
Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.
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.
Fast beampattern evaluation by polynomial rooting
NASA Astrophysics Data System (ADS)
Häcker, P.; Uhlich, S.; Yang, B.
2011-07-01
Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.
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.
Enhancing sparsity of Hermite polynomial expansions by iterative rotations
NASA Astrophysics Data System (ADS)
Yang, Xiu; Lei, Huan; Baker, Nathan A.; Lin, Guang
2016-02-01
Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation-based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional (O (100)) problems.
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.
Classroom Aids for Mathematics, Volume 1: Polynomials.
ERIC Educational Resources Information Center
Holden, Herbert L.
The goal of this pamphlet is to provide instructors of various scientific disciplines with mathematically accurate graphs of elementary polynomial functions. The figures in this pamphlet are intended to provide suitable material for the preparation of classroom handouts and overhead transparencies. In addition, sample sets of exercises are…
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…
An integral relation for tensor polynomials
NASA Astrophysics Data System (ADS)
Vshivtseva, P. A.; Denisov, V. I.; Denisova, I. P.
2011-02-01
We prove two lemmas and one theorem that allow integrating the product of an arbitrary number of unit vectors and the Legendre polynomials over a sphere of arbitrary radius. Such integral tensor products appear in solving inhomogeneous Helmholtz equations whose right-hand side is proportional to the product of a nonfixed number of unit vectors.
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.
Benchmarking a reduced multivariate polynomial pattern classifier.
Toh, Kar-Ann; Tran, Quoc-Long; Srinivasan, Dipti
2004-06-01
A novel method using a reduced multivariate polynomial model has been developed for biometric decision fusion where simplicity and ease of use could be a concern. However, much to our surprise, the reduced model was found to have good classification accuracy for several commonly used data sets from the Web. In this paper, we extend the single output model to a multiple outputs model to handle multiple class problems. The method is particularly suitable for problems with small number of features and large number of examples. Basic component of this polynomial model boils down to construction of new pattern features which are sums of the original features and combination of these new and original features using power and product terms. A linear regularized least-squares predictor is then built using these constructed features. The number of constructed feature terms varies linearly with the order of the polynomial, instead of having a power law in the case of full multivariate polynomials. The method is simple as it amounts to only a few lines of Matlab code. We perform extensive experiments on this reduced model using 42 data sets. Our results compared remarkably well with best reported results of several commonly used algorithms from the literature. Both the classification accuracy and efficiency aspects are reported for this reduced model.
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…
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/.
Pitch contour stylization using an optimal piecewise polynomial approximation
Ghosh, Prasanta Kumar; Narayanan, Shrikanth S.
2014-01-01
We propose a dynamic programming (DP) based piecewise polynomial approximation of discrete data such that the L2 norm of the approximation error is minimized. We apply this technique for the stylization of speech pitch contour. Objective evaluation verifies that the DP based technique indeed yields minimum mean square error (MSE) compared to other approximation methods. Subjective evaluation reveals that the quality of the synthesized speech using stylized pitch contour obtained by the DP method is almost identical to that of the original speech. PMID:24453471
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.
On a Family of Multivariate Modified Humbert Polynomials
Aktaş, Rabia; Erkuş-Duman, Esra
2013-01-01
This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. PMID:23935411
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
From sequences to polynomials and back, via operator orderings
NASA Astrophysics Data System (ADS)
Amdeberhan, Tewodros; De Angelis, Valerio; Dixit, Atul; Moll, Victor H.; Vignat, Christophe
2013-12-01
Bender and Dunne ["Polynomials and operator orderings," J. Math. Phys. 29, 1727-1731 (1988)] showed that linear combinations of words qkpnqn-k, where p and q are subject to the relation qp - pq = ı, may be expressed as a polynomial in the symbol z = 1/2(qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.
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.
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
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.
A polynomial texture extraction with application in dynamic texture classification
NASA Astrophysics Data System (ADS)
El Moubtahij, R.; Augereau, B.; Fernandez-Maloigne, C.; Tairi, H.
2015-04-01
Geometry and texture image decomposition is an important paradigm in image processing. Following to Yves Meyer works based on Total Variation (VT), the decomposition model has known a renewed interest. In this paper, we propose an algorithm which decomposes color image into geometry and texture component by projecting the image in a bivariate polynomial basis and considering the geometry component as the partial reconstruction and the texture component as the remaining part. The experimental results show the adequacy of using our method as a texture extraction tool. Furthermore, we integrate it into a dynamic texture classification process.
Periods of relativistic oscillators with even polynomial potentials
NASA Astrophysics Data System (ADS)
Solon, Mikhail P.; Esguerra, J. P. H.
2008-10-01
The authors modify a non-perturbative variational approach based on the Principle of Minimal Sensitivity to calculate the periods of relativistic oscillators with even polynomial potentials. The optimization of the variational parameter is adapted by introducing additional free parameters whose values are set using the ultrarelativistic limit of the period as a boundary condition. Compact general approximations for the potentials x/2+x2/m2m, ∑n=1mx2n/2n and x2m/2m prove to be accurate over the whole solution domain and even for large values of m.
Optimal approximation of harmonic growth clusters by orthogonal polynomials
Teodorescu, Razvan
2008-01-01
Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.
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.
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.
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.
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.
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
2013-01-01
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. PMID:22116026
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.
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.
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.
Generalized polynomials, operational identities and their applications
NASA Astrophysics Data System (ADS)
Dattoli, G.
2000-06-01
It is shown that an appropriate combination of methods, relevant to generalized operational calculus and to special functions, can be a very useful tool to treat a large body of problems both in physics and mathematics. We discuss operational methods associated with multivariable Hermite, Laguerre, Legendre, and other polynomials to derive a wealth of identities useful in quantum mechanics, electromagnetism, optics, etc., or to derive new identities between special functions as, e.g., Mehler- or mixed-type generating functions.
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…
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.
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.
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.
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
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.
The Corolla Polynomial for Spontaneously Broken Gauge Theories
NASA Astrophysics Data System (ADS)
Prinz, David
2016-09-01
In Kreimer and Yeats (Electr. J. Comb. 41-41, 2013), Kreimer et al. (Annals Phys. 336, 180-222, 2013) and Sars (2015) the Corolla Polynomial C ({Γ }) in C [a_{h1}, ldots , a_{h_{ \\vert {Γ }^{[1/2]} \\vert }}] was introduced as a graph polynomial in half-edge variables {ah}_{h in {Γ }^{[1/2]}} over a 3-regular scalar quantum field theory (QFT) Feynman graph Γ. It allows for a covariant quantization of pure Yang-Mills theory without the need for introducing ghost fields, clarifies the relation between quantum gauge theory and scalar QFT with cubic interaction and translates back the problem of renormalizing quantum gauge theory to the problem of renormalizing scalar QFT with cubic interaction (which is super renormalizable in 4 dimensions of spacetime). Furthermore, it is, as we believe, useful for computer calculations. In Prinz (2015) on which this paper is based the formulation of Kreimer and Yeats (Electr. J. Comb. 41-41, 2013), Kreimer et al. (Annals Phys. 336, 180-222, 2013) and Sars (2015) gets slightly altered in a fashion specialized in the case of the Feynman gauge. It is then formulated as a graph polynomial C ({Γ } ) in C [a_{h_{1 ± }}, ldots , a_{h_{ \\vert {Γ }^{[1/2]} \\vert } {h}_{± }}, b_{h1}, ldots , b_{h_{ \\vert {Γ }^{[1/2]} \\vert }}] in three different types of half-edge variables {a_{h+} , a_{h-} , bh}_{h in {Γ }^{[1/2]}} . This formulation is also suitable for the generalization to the case of spontaneously broken gauge theories (in particular all bosons from the Standard Model), as was first worked out in Prinz (2015) and gets reviewed here.
Meneses, Domingos De Sousa; Rousseau, Benoit; Echegut, Patrick; Matzen, Guy
2007-06-01
A new expression of dielectric function model based on piecewise polynomials is introduced. Its association with spline and more recent shape preserving interpolation algorithms allows easy reproduction of every kind of experimental spectra and thus retrieval of all the linear optical functions of a material. Based on a pure mathematical framework, the expression of the model is always applicable and does not necessitate any knowledge of the microscopic mechanisms of absorption responsible for the optical response. The potential of piecewise polynomial dielectric functions is shown through synthetic examples and the analysis of experimental spectra.
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.
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.
Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan
2012-01-01
Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz.
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.
Blasina, A; Kittell, B L; Toukdarian, A E; Helinski, D R
1996-01-01
The broad host range plasmid RK2 replicates and regulates its copy number in a wide range of Gram-negative bacteria. The plasmid-encoded trans-acting replication protein TrfA and the origin of replication oriV are sufficient for controlled replication of the plasmid in all Gram-negative bacteria tested. The TrfA protein binds specifically to direct repeat sequences (iterons) at the origin of replication. A replication control model, designated handcuffing or coupling, has been proposed whereby the formation of coupled TrfA-oriV complexes between plasmid molecules results in hindrance of origin activity and, consequently, a shut-down of plasmid replication under conditions of higher than normal copy number. Therefore, according to this model, the coupling activity of an initiation protein is essential for copy number control and a copy-up initiation protein mutant should have reduced ability to form coupled complexes. To test this model for plasmid RK2, two previously characterized copy-up TrfA mutations, trfA-254D and trfA-267L, were combined and the resulting copy-up double mutant TFrfA protein TrfA-254D/267L was characterized. Despite initiating runaway (uncontrolled) replication in vivo, the copy-up double-mutant TrfA protein exhibited replication kinetics similar to the wild-type protein in vitro. Purified TrfA-254D, TrfA-267L, and TrfA-254D/267L proteins were then examined for binding to the iterons and for coupling activity using an in vitro ligase-catalyzed multimerization assay. It was found that both single and double TrfA mutant proteins exhibited substantially reduced (single mutants) or barely detectable (double mutant) levels of coupling activity while not being diminished in their capacity to bind to the origin of replication. These observations provide direct evidence in support of the coupling model of replication control. Images Fig. 1 Fig. 2 Fig. 4 PMID:8622975
High order overlay modeling and APC simulation with Zernike-Legendre polynomials
NASA Astrophysics Data System (ADS)
Ju, JawWuk; Kim, MinGyu; Lee, JuHan; Sherwin, Stuart; Hoo, George; Choi, DongSub; Lee, Dohwa; Jeon, Sanghuck; Lee, Kangsan; Tien, David; Pierson, Bill; Robinson, John C.; Levy, Ady; Smith, Mark D.
2015-03-01
Feedback control of overlay errors to the scanner is a well-established technique in semiconductor manufacturing [1]. Typically, overlay errors are measured, and then modeled by least-squares fitting to an overlay model. Overlay models are typically Cartesian polynomial functions of position within the wafer (Xw, Yw), and of position within the field (Xf, Yf). The coefficients from the data fit can then be fed back to the scanner to reduce overlay errors in future wafer exposures, usually via a historically weighted moving average. In this study, rather than using the standard Cartesian formulation, we examine overlay models using Zernike polynomials to represent the wafer-level terms, and Legendre polynomials to represent the field-level terms. Zernike and Legendre polynomials can be selected to have the same fitting capability as standard polynomials (e.g., second order in X and Y, or third order in X and Y). However, Zernike polynomials have the additional property of being orthogonal over the unit disk, which makes them appropriate for the wafer-level model, and Legendre polynomials are orthogonal over the unit square, which makes them appropriate for the field-level model. We show several benefits of Zernike/Legendre-based models in this investigation in an Advanced Process Control (APC) simulation using highly-sampled fab data. First, the orthogonality property leads to less interaction between the terms, which makes the lot-to-lot variation in the fitted coefficients smaller than when standard polynomials are used. Second, the fitting process itself is less coupled - fitting to a lower-order model, and then fitting the residuals to a higher order model gives very similar results as fitting all of the terms at once. This property makes fitting techniques such as dual pass or cascading [2] unnecessary, and greatly simplifies the options available for the model recipe. The Zernike/Legendre basis gives overlay performance (mean plus 3 sigma of the residuals
Direct discriminant locality preserving projection with Hammerstein polynomial expansion.
Chen, Xi; Zhang, Jiashu; Li, Defang
2012-12-01
Discriminant locality preserving projection (DLPP) is a linear approach that encodes discriminant information into the objective of locality preserving projection and improves its classification ability. To enhance the nonlinear description ability of DLPP, we can optimize the objective function of DLPP in reproducing kernel Hilbert space to form a kernel-based discriminant locality preserving projection (KDLPP). However, KDLPP suffers the following problems: 1) larger computational burden; 2) no explicit mapping functions in KDLPP, which results in more computational burden when projecting a new sample into the low-dimensional subspace; and 3) KDLPP cannot obtain optimal discriminant vectors, which exceedingly optimize the objective of DLPP. To overcome the weaknesses of KDLPP, in this paper, a direct discriminant locality preserving projection with Hammerstein polynomial expansion (HPDDLPP) is proposed. The proposed HPDDLPP directly implements the objective of DLPP in high-dimensional second-order Hammerstein polynomial space without matrix inverse, which extracts the optimal discriminant vectors for DLPP without larger computational burden. Compared with some other related classical methods, experimental results for face and palmprint recognition problems indicate the effectiveness of the proposed HPDDLPP.
Maximum of the Characteristic Polynomial of Random Unitary Matrices
NASA Astrophysics Data System (ADS)
Arguin, Louis-Pierre; Belius, David; Bourgade, Paul
2016-09-01
It was recently conjectured by Fyodorov, Hiary and Keating that the maximum of the characteristic polynomial on the unit circle of a {N× N} random unitary matrix sampled from the Haar measure grows like {CN/(log N)^{3/4}} for some random variable C. In this paper, we verify the leading order of this conjecture, that is, we prove that with high probability the maximum lies in the range {[N^{1 - ɛ},N^{1 + ɛ}]} , for arbitrarily small ɛ. The method is based on identifying an approximate branching random walk in the Fourier decomposition of the characteristic polynomial, and uses techniques developed to describe the extremes of branching random walks and of other log-correlated random fields. A key technical input is the asymptotic analysis of Toeplitz determinants with dimension-dependent symbols. The original argument for these asymptotics followed the general idea that the statistical mechanics of 1/f-noise random energy models is governed by a freezing transition. We also prove the conjectured freezing of the free energy for random unitary matrices.
A Riemann-Hilbert approach to the Akhiezer polynomials.
Chen, Yang; Its, Alexander R
2008-03-28
In this paper, we study those polynomials, orthogonal with respect to a particular weight, over the union of disjoint intervals, first introduced by N. I. Akhiezer, via a reformulation as a matrix factorization or Riemann-Hilbert problem. This approach complements the method proposed in a previous paper, which involves the construction of a certain meromorphic function on a hyperelliptic Riemann surface. The method described here is based on the general Riemann-Hilbert scheme of the theory of integrable systems and will enable us to derive, in a very straightforward way, the relevant system of Fuchsian differential equations for the polynomials and the associated system of the Schlesinger deformation equations for certain quantities involving the corresponding recurrence coefficients. Both of these equations were obtained earlier by A. Magnus. In our approach, however, we are able to go beyond Magnus' results by actually solving the equations in terms of the Riemanni Theta-functions. We also show that the related Hankel determinant can be interpreted as the relevant tau-function.
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.
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.
A Polynomial-Time Algorithm for Optimizing over N-Fold 4-Block Decomposable Integer Programs
NASA Astrophysics Data System (ADS)
Hemmecke, Raymond; Köppe, Matthias; Weismantel, Robert
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions.
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.
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.
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.
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 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}.
On global non-oscillation of linear ordinary differential equations with polynomial coefficients
NASA Astrophysics Data System (ADS)
Novikov, Dmitry; Shapiro, Boris
2016-10-01
Based on a new explicit upper bound for the number of zeros of exponential polynomials in a horizontal strip, we obtain a uniform upper bound for the number of zeros of solutions to an ordinary differential equation near its Fuchsian singular point, provided that any two distinct characteristic exponents at this point have distinct real parts. The latter result implies that a Fuchsian differential equation with polynomial coefficients is globally non-oscillating in CP1 if and only if every its singular point satisfies the above condition.
Polynomial solutions of the Monge-Ampère equation
NASA Astrophysics Data System (ADS)
Aminov, Yu A.
2014-11-01
The question of the existence of polynomial solutions to the Monge-Ampère equation zxxzyy-zxy^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.
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.
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.
Conventional modeling of the multilayer perceptron using polynomial basis functions.
Chen, M S; Manry, M T
1993-01-01
A technique for modeling the multilayer perceptron (MLP) neural network, in which input and hidden units are represented by polynomial basis functions (PBFs), is presented. The MLP output is expressed as a linear combination of the PBFs and can therefore be expressed as a polynomial function of its inputs. Thus, the MLP is isomorphic to conventional polynomial discriminant classifiers or Volterra filters. The modeling technique was successfully applied to several trained MLP networks.
Conventional modeling of the multilayer perceptron using polynomial basis functions
NASA Technical Reports Server (NTRS)
Chen, Mu-Song; Manry, Michael T.
1993-01-01
A technique for modeling the multilayer perceptron (MLP) neural network, in which input and hidden units are represented by polynomial basis functions (PBFs), is presented. The MLP output is expressed as a linear combination of the PBFs and can therefore be expressed as a polynomial function of its inputs. Thus, the MLP is isomorphic to conventional polynomial discriminant classifiers or Volterra filters. The modeling technique was successfully applied to several trained MLP networks.
Hong, X; Harris, C J
2000-01-01
This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bézier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bézier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bézier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bézier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.
Structure relations for monic orthogonal polynomials in two discrete variables
NASA Astrophysics Data System (ADS)
Rodal, J.; Area, I.; Godoy, E.
2008-04-01
In this paper, extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given, by using an appropriate vector-matrix notation. Three-term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type. Structure relations, difference representations as well as lowering and raising operators are obtained. Finally, expressions for all matrix coefficients appearing in these finite-type relations are explicitly presented for a finite set of Hahn and Kravchuk orthogonal polynomials.
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.
From sequences to polynomials and back, via operator orderings
Amdeberhan, Tewodros Dixit, Atul Moll, Victor H.; De Angelis, Valerio; Vignat, Christophe
2013-12-15
Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.
d-Orthogonality of Humbert and Jacobi type polynomials
NASA Astrophysics Data System (ADS)
Lamiri, I.; Ouni, A.
2008-05-01
In this paper, we treat three questions related to the d-orthogonality of the Humbert polynomials. The first one consists to determinate the explicit expression of the d-dimensional functional vector for which the d-orthogonality holds. The second one is the investigation of the components of Humbert polynomial sequence. That allows us to introduce, as far as we know, new d-orthogonal polynomials generalizing the classical Jacobi ones. The third one consists to solve a characterization problem related to a generalized hypergeometric representation of the Humbert polynomials.
Multi-indexed Jacobi polynomials and Maya diagrams
NASA Astrophysics Data System (ADS)
Takemura, Kouichi
2014-11-01
Multi-indexed Jacobi polynomials are defined by the Wronskian of four types of eigenfunctions of the Pöschl-Teller Hamiltonian. We give a correspondence between multi-indexed Jacobi polynomials and pairs of Maya diagrams, and we show that any multi-indexed Jacobi polynomial is essentially equal to some multi-indexed Jacobi polynomial of two types of eigenfunction. As an application, we show a Wronskian-type formula of some special eigenstates of the deformed Pöschl-Teller Hamiltonian.
Tutte Polynomial of Pseudofractal Scale-Free Web
NASA Astrophysics Data System (ADS)
Peng, Junhao; Xiong, Jian; Xu, Guoai
2015-06-01
The Tutte polynomial of a graph is a 2-variable polynomial which is quite important in both Combinatorics and Statistical physics. It contains various numerical invariants and polynomial invariants, such as the number of spanning trees, the number of spanning forests, the number of acyclic orientations, the reliability polynomial, chromatic polynomial and flow polynomial. In this paper, we study and obtain a recursive formula for the Tutte polynomial of pseudofractal scale-free web (PSFW), and thus logarithmic complexity algorithm to calculate the Tutte polynomial of the PSFW is obtained, although it is NP-hard for general graph. By solving the recurrence relations derived from the Tutte polynomial, the rigorous solution for the number of spanning trees of the PSFW is obtained. Therefore, an alternative approach to determine explicitly the number of spanning trees of the PSFW is given. Furthermore, we analyze the all-terminal reliability of the PSFW and compare the results with those of the Sierpinski gasket which has the same number of nodes and edges as the PSFW. In contrast with the well-known conclusion that inhomogeneous networks (e.g., scale-free networks) are more robust than homogeneous networks (i.e., networks in which each node has approximately the same number of links) with respect to random deletion of nodes, the Sierpinski gasket (which is a homogeneous network), as our results show, is more robust than the PSFW (which is an inhomogeneous network) with respect to random edge failures.
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.
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.
Regression Analysis Of Zernike Polynomials Part II
NASA Astrophysics Data System (ADS)
Grey, Louis D.
1989-01-01
In an earlier paper entitled "Regression Analysis of Zernike Polynomials, Proceedings of SPIE, Vol. 18, pp. 392-398, the least squares fitting process of Zernike polynomials was examined from the point of view of linear statistical regression theory. Among the topics discussed were measures for determining how good the fit was, tests for the underlying assumptions of normality and constant variance, the treatment of outliers, the analysis of residuals and the computation of confidence intervals for the coefficients. The present paper is a continuation of the earlier paper and concerns applications of relatively new advances in certain areas of statistical theory made possible by the advent of the high speed computer. Among these are: 1. Jackknife - A technique for improving the accuracy of any statistical estimate. 2. Bootstrap - Increasing the accuracy of an estimate by generating new samples of data from some given set. 3. Cross-validation - The division of a data set into two halves, the first half of which is used to fit the model and the second half to see how well the fitted model predicts the data. The exposition is mainly by examples.
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
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.
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.
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.
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 the coefficients of differentiated expansions of ultraspherical polynomials
NASA Technical Reports Server (NTRS)
Karageorghis, Andreas; Phillips, Timothy N.
1989-01-01
A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.
Old and new results about relativistic Hermite polynomials
NASA Astrophysics Data System (ADS)
Vignat, C.
2011-09-01
We provide new proofs of already known results as well as new results about the family of relativistic Hermite polynomials. We use essentially probabilistic tools such as moment representations, pioneered by Ismail et al., but also subordination, that allows to explicit links between Gegenbauer, usual Hermite, and relativistic Hermite polynomials.
A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE
NASA Technical Reports Server (NTRS)
Truong, T. K.
1994-01-01
This program utilizes a fast polynomial transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional convolution has many applications, particularly in image processing. Two-dimensional cyclic convolutions can be converted to a one-dimensional convolution in a polynomial ring. Traditional FPT methods decompose the one-dimensional cyclic polynomial into polynomial convolutions of different lengths. This program will decompose a cyclic polynomial into polynomial convolutions of the same length. Thus, only FPTs and Fast Fourier Transforms of the same length are required. This modular approach can save computational resources. To further enhance its appeal, the program is written in the transportable 'C' language. The steps in the algorithm are: 1) formulate the modulus reduction equations, 2) calculate the polynomial transforms, 3) multiply the transforms using a generalized fast Fourier transformation, 4) compute the inverse polynomial transforms, and 5) reconstruct the final matrices using the Chinese remainder theorem. Input to this program is comprised of the row and column dimensions and the initial two matrices. The matrices are printed out at all steps, ending with the final reconstruction. This program is written in 'C' for batch execution and has been implemented on the IBM PC series of computers under DOS with a central memory requirement of approximately 18K of 8 bit bytes. This program was developed in 1986.
TMD PDFs in the Laguerre polynomial basis
NASA Astrophysics Data System (ADS)
Vladimirov, A. A.
2014-08-01
We suggest the modified matching procedure for TMD PDF to the integrated PDF aimed to increase the amount of perturbative information in the TMD PDF expression. The procedure consists in the selection and usage of the non-minimal operator basis, which restricts the expansion to desired general behavior. The implication of OPE allows to systematic account of the higher order corrections. In the case of TMD PDF we assume the Gaussian behavior, which suggests Laguerre polynomial basis as the best for the convergence of OPE. We present the leading and next-to-leading expression of TMD PDF in this basis. The obtained perturbative expression for the TMD PDF is valid in the wide region of b T (we estimate this region as b T ≲ 2 - 3 GeV-1 depending on x).
Approximate protein structural alignment in polynomial time.
Kolodny, Rachel; Linial, Nathan
2004-08-17
Alignment of protein structures is a fundamental task in computational molecular biology. Good structural alignments can help detect distant evolutionary relationships that are hard or impossible to discern from protein sequences alone. Here, we study the structural alignment problem as a family of optimization problems and develop an approximate polynomial-time algorithm to solve them. For a commonly used scoring function, the algorithm runs in O(n(10)/epsilon(6)) time, for globular protein of length n, and it detects alignments that score within an additive error of epsilon from all optima. Thus, we prove that this task is computationally feasible, although the method that we introduce is too slow to be a useful everyday tool. We argue that such approximate solutions are, in fact, of greater interest than exact ones because of the noisy nature of experimentally determined protein coordinates. The measurement of similarity between a pair of protein structures used by our algorithm involves the Euclidean distance between the structures (appropriately rigidly transformed). We show that an alternative approach, which relies on internal distance matrices, must incorporate sophisticated geometric ingredients if it is to guarantee optimality and run in polynomial time. We use these observations to visualize the scoring function for several real instances of the problem. Our investigations yield insights on the computational complexity of protein alignment under various scoring functions. These insights can be used in the design of scoring functions for which the optimum can be approximated efficiently and perhaps in the development of efficient algorithms for the multiple structural alignment problem. PMID:15304646
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.
Approximating smooth functions using algebraic-trigonometric polynomials
Sharapudinov, Idris I
2011-01-14
The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p{sub n}(t)+{tau}{sub m}(t), where p{sub n}(t) is an algebraic polynomial of degree n and {tau}{sub m}(t)=a{sub 0}+{Sigma}{sub k=1}{sup m}a{sub k} cos k{pi}t + b{sub k} sin k{pi}t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W{sup r}{sub {infinity}(}M) and an upper bound for similar approximations in the class W{sup r}{sub p}(M) with 4/3
polynomials which the author has introduced and investigated previously. Bibliography: 13 titles.
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.
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.
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.
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
2011-01-01
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-Å 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. PMID:22160701
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.
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.
RK2 plasmid dynamics in Caulobacter crescentus cells--two modes of DNA replication initiation.
Wegrzyn, Katarzyna; Witosinska, Monika; Schweiger, Pawel; Bury, Katarzyna; Jenal, Urs; Konieczny, Igor
2013-06-01
Undisturbed plasmid dynamics is required for the stable maintenance of plasmid DNA in bacterial cells. In this work, we analysed subcellular localization, DNA synthesis and nucleoprotein complex formation of plasmid RK2 during the cell cycle of Caulobacter crescentus. Our microscopic observations showed asymmetrical distribution of plasmid RK2 foci between the two compartments of Caulobacter predivisional cells, resulting in asymmetrical allocation of plasmids to progeny cells. Moreover, using a quantitative PCR (qPCR) method, we estimated that multiple plasmid particles form a single fluorescent focus and that the number of plasmids per focus is approximately equal in both swarmer and predivisional Caulobacter cells. Analysis of the dynamics of TrfA-oriV complex formation during the Caulobacter cell cycle revealed that TrfA binds oriV primarily during the G1 phase, however, plasmid DNA synthesis occurs during the S and G2 phases of the Caulobacter cell cycle. Both in vitro and in vivo analysis of RK2 replication initiation in C. crescentus cells demonstrated that it is independent of the Caulobacter DnaA protein in the presence of the longer version of TrfA protein, TrfA-44. However, in vivo stability tests of plasmid RK2 derivatives suggested that a DnaA-dependent mode of plasmid replication initiation is also possible.
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
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
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
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
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.
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
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.
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.
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
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.
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.
Genome-wide identification and expression profiling of the SnRK2 gene family in Malus prunifolia.
Shao, Yun; Qin, Yuan; Zou, Yangjun; Ma, Fengwang
2014-11-15
Sucrose non-fermenting-1-related protein kinase 2 (SnRK2) constitutes a small plant-specific serine/threonine kinase family with essential roles in the abscisic acid (ABA) signal pathway and in responses to osmotic stress. Although a genome-wide analysis of this family has been conducted in some species, little is known about SnRK2 genes in apple (Malus domestica). We identified 14 putative sequences encoding 12 deduced SnRK2 proteins within the apple genome. Gene chromosomal location and synteny analysis of the apple SnRK2 genes indicated that tandem and segmental duplications have likely contributed to the expansion and evolution of these genes. All 12 full-length coding sequences were confirmed by cloning from Malus prunifolia. The gene structure and motif compositions of the apple SnRK2 genes were analyzed. Phylogenetic analysis showed that MpSnRK2s could be classified into four groups. Profiling of these genes presented differential patterns of expression in various tissues. Under stress conditions, transcript levels for some family members were up-regulated in the leaves in response to drought, salinity, or ABA treatments. This suggested their possible roles in plant response to abiotic stress. Our findings provide essential information about SnRK2 genes in apple and will contribute to further functional dissection of this gene family.
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.
Nunes, Cátia; O'Hara, Liam E; Primavesi, Lucia F; Delatte, Thierry L; Schluepmann, Henriette; Somsen, Govert W; Silva, Anabela B; Fevereiro, Pedro S; Wingler, Astrid; Paul, Matthew J
2013-07-01
Trehalose 6-P (T6P) is a sugar signal in plants that inhibits SNF1-related protein kinase, SnRK1, thereby altering gene expression and promoting growth processes. This provides a model for the regulation of growth by sugar. However, it is not known how this model operates under sink-limited conditions when tissue sugar content is uncoupled from growth. To test the physiological importance of this model, T6P, SnRK1 activities, sugars, gene expression, and growth were measured in Arabidopsis (Arabidopsis thaliana) seedlings after transfer to cold or zero nitrogen compared with sugar feeding under optimal conditions. Maximum in vitro activities of SnRK1 changed little, but T6P accumulated up to 55-fold, correlating with tissue Suc content in all treatments. SnRK1-induced and -repressed marker gene expression strongly related to T6P above and below a threshold of 0.3 to 0.5 nmol T6P g(-1) fresh weight close to the dissociation constant (4 µm) of the T6P/ SnRK1 complex. This occurred irrespective of the growth response to Suc. This implies that T6P is not a growth signal per se, but through SnRK1, T6P primes gene expression for growth in response to Suc accumulation under sink-limited conditions. To test this hypothesis, plants with genetically decreased T6P content and SnRK1 overexpression were transferred from cold to warm to analyze the role of T6P/SnRK1 in relief of growth restriction. Compared with the wild type, these plants were impaired in immediate growth recovery. It is concluded that the T6P/SnRK1 signaling pathway responds to Suc induced by sink restriction that enables growth recovery following relief of limitations such as low temperature.
Discrete Darboux transformation for discrete polynomials of hypergeometric type
NASA Astrophysics Data System (ADS)
Bangerezako, Gaspard
1998-03-01
The Darboux transformation, well known in second-order differential operator theory, is applied to the difference equations satisfied by the discrete hypergeometric polynomials (Charlier, Meixner-Kravchuk, Hahn).
Kernel polynomial approximations for densities of states and spectral functions
Silver, R.N.; Voter, A.F.; Kress, J.D.; Roeder, H.
1996-03-01
Chebyshev polynomial approximations are an efficient and numerically stable way to calculate properties of the very large Hamiltonians important in computational condensed matter physics. The present paper derives an optimal kernal polynomial which enforces positivity of density of states and spectral estimates, achieves the best energy resolution, and preserves normalization. This kernel polynomial method (KPM) is demonstrated for electronic structure and dynamic magnetic susceptibility calculations. For tight binding Hamiltonians of Si, we show how to achieve high precision and rapid convergence of the cohesive energy and vacancy formation energy by careful attention to the order of approximation. For disordered XXZ-magnets, we show that the KPM provides a simpler and more reliable procedure for calculating spectral functions than Lanczos recursion methods. Polynomial approximations to Fermi projection operators are also proposed. 26 refs., 10 figs.
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.
Hermite polynomials and representations of the unitary group
NASA Astrophysics Data System (ADS)
Strasburger, A.; Dziewa-Dawidczyk, D.
2015-04-01
Spaces of homogeneous complex polynomials in D variables form carrier spaces for representations of the unitary group U(D). These representations are well understood and their connections with certain families of classical orthogonal polynomials (Gegenbauer, Jacobi, and other) are widely studied. However, there is another realization for the action of the unitary group U(D) on polynomials, not necessarily homogeneous, in which Hermite polynomials in D variables play an important role. This action is related to the metaplectic (oscillator) representation, and was studied some time ago by one of the present authors (A. S.) and, independently, by A. Wünsche for D = 2. In this note we want to concentrate on the latter realization and describe its properties in a more comprehensible way.
An operator approach to the Al-Salam-Carlitz polynomials
NASA Astrophysics Data System (ADS)
Chen, William Y. C.; Saad, Husam L.; Sun, Lisa H.
2010-04-01
We present an operator approach to Rogers-type formulas and Mehler's formula for the Al-Salam-Carlitz polynomials Un(x,y,a;q). By using the q-exponential operator, we obtain a Rogers-type formula, which leads to a linearization formula. With the aid of a bivariate augmentation operator, we get a simple derivation of Mehler's formula due to Al-Salam and Carlitz ["Some orthogonal q-polynomials," Math. Nachr. 30, 47 (1965)]. By means of the Cauchy companion augmentation operator, we obtain an equivalent form of Mehler's formula. We also give several identities on the generating functions for products of the Al-Salam-Carlitz polynomials, which are extensions of the formulas for the Rogers-Szegö polynomials.
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.
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.
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.
Quantum random walk polynomial and quantum random walk measure
NASA Astrophysics Data System (ADS)
Kang, Yuanbao; Wang, Caishi
2014-05-01
In the paper, we introduce a quantum random walk polynomial (QRWP) that can be defined as a polynomial , which is orthogonal with respect to a quantum random walk measure (QRWM) on , such that the parameters are in the recurrence relations and satisfy . We firstly obtain some results of QRWP and QRWM, in which case the correspondence between measures and orthogonal polynomial sequences is one-to-one. It shows that any measure with respect to which a quantum random walk polynomial sequence is orthogonal is a quantum random walk measure. We next collect some properties of QRWM; moreover, we extend Karlin and McGregor's representation formula for the transition probabilities of a quantum random walk (QRW) in the interacting Fock space, which is a parallel result with the CGMV method. Using these findings, we finally obtain some applications for QRWM, which are of interest in the study of quantum random walk, highlighting the role played by QRWP and QRWM.
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.
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.
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
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.
Efficient source mask optimization with Zernike polynomial functions for source representation.
Wu, Xiaofei; Liu, Shiyuan; Li, Jia; Lam, Edmund Y
2014-02-24
In 22nm optical lithography and beyond, source mask optimization (SMO) becomes vital for the continuation of advanced ArF technology node development. The pixel-based method permits a large solution space, but involves a time-consuming optimization procedure because of the large number of pixel variables. In this paper, we introduce the Zernike polynomials as basis functions to represent the source patterns, and propose an improved SMO algorithm with this representation. The source patterns are decomposed into the weighted superposition of some well-chosen Zernike polynomial functions, and the number of variables decreases significantly. We compare the computation efficiency and optimization performance between the proposed method and the conventional pixel-based algorithm. Simulation results demonstrate that the former can obtain substantial speedup of source optimization while improving the pattern fidelity at the same time.
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.
Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions.
Wu, Yu-Qiang; Liu, Zhen-Guo
2015-09-01
This paper addresses the problem of output feedback stabilization for a class of time-delay nonholonomic systems. One distinct characteristic or difficulty of this paper is that time-delay exists in polynomial nonlinear growing conditions. Based on input-state-scaling technique, homogeneous domination approach and Lyapunov-Krasovskii theorem, a new output feedback control law which guarantees all the system states converge to the origin is designed. Examples are provided to demonstrate the validness of the proposed approach.
Polynomial-style region incremental multisecret image sharing
NASA Astrophysics Data System (ADS)
Wang, Ran-Zan; Lin, Yung-Yi
2011-03-01
This paper proposes a polynomial-style region incremental multisecret image sharing (PBRIMSIS), for sharing multiple secrets in an image among n participants. The method enables the dealer to distribute the content of an image S to multiple regions, where each region is associated with a certain level of secrecy. In the proposed n-level PBRIMSIS scheme, input image S is encoded to n+1 shadow images that exhibit the following features: a. each shadow image cannot reveal any region in S, b. any t (2 <= t <= n + 1) shadow images can be used to reveal these regions associated with up to t - 1 secret levels, and c. S can be completely reconstructed when all of the n+1 shadow images are available. A discrete cosine transform-based PBRIMSIS with a smaller shadow image scheme is designed to improve the transmission and storage of the generated shadow images. The property of incremental disclosure to the region-based secrets in an image is applicable to image sharing in diverse applications that require the sharing of multiple secrets with different secrecy priorities, such as in cooperative working or in military secrets.
Sánchez-López, Rosana; Jáuregui, David; Nava, Noreide; Alvarado-Affantranger, Xóchitl; Montiel, Jesús; Santana, Olivia; Sanchez, Federico; Quinto, Carmen
2011-12-01
The symbiotic interaction of legumes and rhizobia results in the formation of nitrogen-fixing nodules. Nodulation depends on the finely coordinated expression of a battery of genes involved in the infection and the organogenesis processes. After Nod factor perception, symbiosis receptor kinase (SymRK) receptor triggers a signal transduction cascade essential for nodulation leading to cortical cell divisions, infection thread (IT) formation and final release of rhizobia to the intracellular space, forming the symbiosome. Herein, the participation of SymRK receptor during the nodule organogenesis in Phaseolus vulgaris is addressed. Our findings indicate that besides its expression in the nodule epidermis, in IT, and in uninfected cells of the infection zone, PvSymRK immunolocalizes in the root and nodule vascular system. On the other hand, knockdown expression of PvSymRK led to the formation of scarce and defective nodules, which presented alterations in both IT/symbiosome formation and vascular system.
Dyer, Kimberly D.; Drummond, Rebecca A.; Rice, Tyler A.; Percopo, Caroline M.; Brenner, Todd A.; Barisas, Derek A. G.; Karpe, Kendal A.; Moore, Martin L.
2015-01-01
ABSTRACT Pneumonia virus of mice (PVM) is a natural rodent pathogen that replicates in bronchial epithelial cells and reproduces many clinical and pathological features of the more severe forms of disease associated with human respiratory syncytial virus. In order to track virus-target cell interactions during acute infection in vivo, we developed rK2-PVM, bacterial artificial chromosome-based recombinant PVM strain J3666 that incorporates the fluorescent tag monomeric Katushka 2 (mKATE2). The rK2-PVM pathogen promotes lethal infection in BALB/c mice and elicits characteristic cytokine production and leukocyte recruitment to the lung parenchyma. Using recombinant virus, we demonstrate for the first time PVM infection of both dendritic cells (DCs; CD11c+ major histocompatibility complex class II+) and alveolar macrophages (AMs; CD11c+ sialic acid-binding immunoglobulin-like lectin F+) in vivo and likewise detect mKATE2+ DCs in mediastinal lymph nodes from infected mice. AMs support both active virus replication and production of infectious virions. Furthermore, we report that priming of the respiratory tract with immunobiotic Lactobacillus plantarum, a regimen that results in protection against the lethal inflammatory sequelae of acute respiratory virus infection, resulted in differential recruitment of neutrophils, DCs, and lymphocytes to the lungs in response to rK2-PVM and a reduction from ∼40% to <10% mKATE2+ AMs in association with a 2-log drop in the release of infectious virions. In contrast, AMs from L. plantarum-primed mice challenged with virus ex vivo exhibited no differential susceptibility to rK2-PVM. Although the mechanisms underlying Lactobacillus-mediated viral suppression remain to be fully elucidated, this study provides insight into the cellular basis of this response. IMPORTANCE Pneumonia virus of mice (PVM) is a natural mouse pathogen that serves as a model for severe human respiratory syncytial virus disease. We have developed a fully
Alkhaldi, Weaam; Iskander, D Robert; Zoubir, Abdelhak M
2010-10-01
Corneal-height data are typically measured with videokeratoscopes and modeled using a set of orthogonal Zernike polynomials. We address the estimation of the number of Zernike polynomials, which is formalized as a model-order selection problem in linear regression. Classical information-theoretic criteria tend to overestimate the corneal surface due to the weakness of their penalty functions, while bootstrap-based techniques tend to underestimate the surface or require extensive processing. In this paper, we propose to use the efficient detection criterion (EDC), which has the same general form of information-theoretic-based criteria, as an alternative to estimating the optimal number of Zernike polynomials. We first show, via simulations, that the EDC outperforms a large number of information-theoretic criteria and resampling-based techniques. We then illustrate that using the EDC for real corneas results in models that are in closer agreement with clinical expectations and provides means for distinguishing normal corneal surfaces from astigmatic and keratoconic surfaces.
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
Wang, Pengcheng; Xue, Liang; Batelli, Giorgia; Lee, Shinyoung; Hou, Yueh-Ju; Van Oosten, Michael J; Zhang, Huiming; Tao, W Andy; Zhu, Jian-Kang
2013-07-01
Sucrose nonfermenting 1 (SNF1)-related protein kinase 2s (SnRK2s) are central components of abscisic acid (ABA) signaling pathways. The snrk2.2/2.3/2.6 triple-mutant plants are nearly completely insensitive to ABA, suggesting that most of the molecular actions of ABA are triggered by the SnRK2s-mediated phosphorylation of substrate proteins. Only a few substrate proteins of the SnRK2s are known. To identify additional substrate proteins of the SnRK2s and provide insight into the molecular actions of ABA, we used quantitative phosphoproteomics to compare the global changes in phosphopeptides in WT and snrk2.2/2.3/2.6 triple mutant seedlings in response to ABA treatment. Among the 5,386 unique phosphorylated peptides identified in this study, we found that ABA can increase the phosphorylation of 166 peptides and decrease the phosphorylation of 117 peptides in WT seedlings. In the snrk2.2/2.3/2.6 triple mutant, 84 of the 166 peptides, representing 58 proteins, could not be phosphorylated, or phosphorylation was not increased under ABA treatment. In vitro kinase assays suggest that most of the 58 proteins can serve as substrates of the SnRK2s. The SnRK2 substrates include proteins involved in flowering time regulation, RNA and DNA binding, miRNA and epigenetic regulation, signal transduction, chloroplast function, and many other cellular processes. Consistent with the SnRK2 phosphorylation of flowering time regulators, the snrk2.2/2.3/2.6 triple mutant flowered significantly earlier than WT. These results shed new light on the role of the SnRK2 protein kinases and on the downstream effectors of ABA action, and improve our understanding of plant responses to adverse environments.
Wang, Pengcheng; Xue, Liang; Batelli, Giorgia; Lee, Shinyoung; Hou, Yueh-Ju; Van Oosten, Michael J.; Zhang, Huiming; Tao, W. Andy; Zhu, Jian-Kang
2013-01-01
Sucrose nonfermenting 1 (SNF1)-related protein kinase 2s (SnRK2s) are central components of abscisic acid (ABA) signaling pathways. The snrk2.2/2.3/2.6 triple-mutant plants are nearly completely insensitive to ABA, suggesting that most of the molecular actions of ABA are triggered by the SnRK2s-mediated phosphorylation of substrate proteins. Only a few substrate proteins of the SnRK2s are known. To identify additional substrate proteins of the SnRK2s and provide insight into the molecular actions of ABA, we used quantitative phosphoproteomics to compare the global changes in phosphopeptides in WT and snrk2.2/2.3/2.6 triple mutant seedlings in response to ABA treatment. Among the 5,386 unique phosphorylated peptides identified in this study, we found that ABA can increase the phosphorylation of 166 peptides and decrease the phosphorylation of 117 peptides in WT seedlings. In the snrk2.2/2.3/2.6 triple mutant, 84 of the 166 peptides, representing 58 proteins, could not be phosphorylated, or phosphorylation was not increased under ABA treatment. In vitro kinase assays suggest that most of the 58 proteins can serve as substrates of the SnRK2s. The SnRK2 substrates include proteins involved in flowering time regulation, RNA and DNA binding, miRNA and epigenetic regulation, signal transduction, chloroplast function, and many other cellular processes. Consistent with the SnRK2 phosphorylation of flowering time regulators, the snrk2.2/2.3/2.6 triple mutant flowered significantly earlier than WT. These results shed new light on the role of the SnRK2 protein kinases and on the downstream effectors of ABA action, and improve our understanding of plant responses to adverse environments. PMID:23776212
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
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.
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.
Ding, A. Adam; Wu, Hulin
2015-01-01
We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093
NASA Astrophysics Data System (ADS)
Boreskov, K. G.; Turbiner, A. V.; López Vieyra, J. C.; García, M. A. G.
It is shown that the E8 trigonometric Olshanetsky-Perelomov Hamiltonian, when written in terms of the fundamental trigonometric invariants, is in algebraic form, i.e. it has polynomial coefficients, and preserves two infinite flags of polynomial spaces marked by the Weyl (co)-vector and E8 highest root (both in the basis of simple roots) as characteristic vectors. The explicit form of the Hamiltonian in new variables has been obtained both by direct calculation and by means of the orbit function technique. It is shown the triangularity of the Hamiltonian in the bases of orbit functions and of algebraic monomials ordered through Weyl heights. Examples of first eigenfunctions are presented.
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
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.
Cho, Young-Hee; Hong, Jung-Woo; Kim, Eun-Chul; Yoo, Sang-Dong
2012-04-01
Sucrose-nonfermentation1-related protein kinase1 (SnRK1) is an evolutionarily conserved energy sensor protein that regulates gene expression in response to energy depletion in plants. Efforts to elucidate the functions and mechanisms of this protein kinase are hampered, however, by inherent growth defects of snrk1-null mutant plants. To overcome these limitations and study SnRK1 functions in vivo, we applied a method combining transient expression in leaf mesophyll protoplasts and stable expression in transgenic plants. We found that both rice (Oryza sativa) and Arabidopsis (Arabidopsis thaliana) SnRK1 activities critically influence stress-inducible gene expression and the induction of stress tolerance. Genetic, molecular, and chromatin immunoprecipitation analyses further revealed that the nuclear SnRK1 modulated target gene transcription in a submergence-dependent manner. From early seedling development through late senescence, SnRK1 activities appeared to modulate developmental processes in the plants. Our findings offer insight into the regulatory functions of plant SnRK1 in stress-responsive gene regulation and in plant growth and development throughout the life cycle.
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.
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.
Polynomial chaos theory for performance evaluation of ATR systems
NASA Astrophysics Data System (ADS)
DeVore, Michael D.; Bateman, Alec J.
2010-04-01
The development of a more unified theory of automatic target recognition (ATR) has received considerable attention over the last several years from individual researchers, working groups, and workshops. One of the major benefits expected to accrue from such a theory is an ability to analytically derive performance metrics that accurately predict real-world behavior. Numerous sources of uncertainty affect the actual performance of an ATR system, so direct calculation has been limited in practice to a few special cases because of the practical difficulties of manipulating arbitrary probability distributions over high dimensional spaces. This paper introduces an alternative approach for evaluating ATR performance based on a generalization of NorbertWiener's polynomial chaos theory. Through this theory, random quantities are expressed not in terms of joint distribution functions but as convergent orthogonal series over a shared random basis. This form can be used to represent any finite-variance distribution and can greatly simplify the propagation of uncertainties through complex systems and algorithms. The paper presents an overview of the relevant theory and, as an example application, a discussion of how it can be applied to model the distribution of position errors from target tracking algorithms.
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
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.
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
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.
Limitations of polynomial chaos in Bayesian parameter estimation
NASA Astrophysics Data System (ADS)
Lu, F.; Morzfeld, M.; Tu, X.; Chorin, A. J.
2014-12-01
In many science or engineering problems one needs to estimate parameters in a model on the basis of noisy data. In a Bayesian approach, prior information and the likelihood of the model and data are combined to yield a posterior that describes the parameters. The posterior can be represented by Monte Carlo sampling, which requires repeated evaluation of the posterior, which in turn requires repeated evaluation of the model. This is expensive if the model is complex or if the dimension of the parameters is high. Polynomial chaos expansions (PCE) have been used to reduce the computational cost by providing an approximate representation of the model based on the prior and, hence, creating a surrogate posterior. This surrogate posterior can be evaluated inexpensively and without solving the model. Here we investigate the accuracy of the surrogate posterior and PCE-based samplers. We show, by analysis of the small noise setting, that the surrogate posterior can be very different from the posterior when the data contains significant information beyond what is assumed in the prior. In this case, the PCE-based parameter estimates are inaccurate. The accuracy can be improved by adaptively increasing the order of the PCE, but the cost may increase too fast for this to be efficient. We illustrate the theory with an example from subsurface hydrodynamics in which we estimate the permeability on the basis of noisy pressure measurements. Our numerical results confirm what we found in theory and indicate that an advanced MC sampler which uses data to generate effective samples can be be more efficient than a PCE-based sampler.
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.
Automatic differentiation for Fourier series and the radii polynomial approach
NASA Astrophysics Data System (ADS)
Lessard, Jean-Philippe; Mireles James, J. D.; Ransford, Julian
2016-11-01
In this work we develop a computer-assisted technique for proving existence of periodic solutions of nonlinear differential equations with non-polynomial nonlinearities. We exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system. We compute a numerical Fourier expansion of the periodic orbit for the augmented system, and prove the existence of a true solution nearby using an a-posteriori validation scheme (the radii polynomial approach). The problems considered here are given in terms of locally analytic vector fields (i.e. the field is analytic in a neighborhood of the periodic orbit) hence the computer-assisted proofs are formulated in a Banach space of sequences satisfying a geometric decay condition. In order to illustrate the use and utility of these ideas we implement a number of computer-assisted existence proofs for periodic orbits of the Planar Circular Restricted Three-Body Problem (PCRTBP).
Asymptotic formulae for the zeros of orthogonal polynomials
NASA Astrophysics Data System (ADS)
Badkov, V. M.
2012-09-01
Let p_n(t) be an algebraic polynomial that is orthonormal with weight p(t) on the interval \\lbrack -1, 1 \\rbrack . When p(t) is a perturbation (in certain limits) of the Chebyshev weight of the first kind, the zeros of the polynomial p_n(\\cos\\tau) and the differences between pairs of (not necessarily consecutive) zeros are shown to satisfy asymptotic formulae as n\\to\\infty, 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.
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.
Two-dimensional correlation spectroscopy (2DCOS) analysis of polynomials
NASA Astrophysics Data System (ADS)
Noda, Isao
2016-11-01
2DCOS analysis of dynamic spectra, which can be approximated in the form of a polynomial function by the least squares curve fitting method, is carried out. Curve fitting provides a practical way of condensing a large spectral dataset in terms of a small number of fitting parameters and filtering out noise and superfluous spectral intensity variations from the raw spectra. Pertinent features of the findings are illustrated by using a simple simulated spectral data subjected to curve fitting with polynomials. Closed-form analytical expressions for 2D correlation spectra are obtained from the polynomial functions used for the curve fitting and their Hilbert transform counterpart. Such analytical expressions provide useful insight into the inner working of 2DCOS analysis, especially the role of slope and curvature of spectral intensity variations, in determining the signs of cross peaks used in the interpretation of 2D spectra.
Dental maturity in South France: A comparison between Demirjian's method and polynomial functions.
Chaillet, Nils; Demirjian, Arto
2004-09-01
The dental maturity of 1031 healthy southern French subjects aged between 2 and 18 years was studied with dental panoramic tomograms. Demirjian's method based on seven and eight teeth has been used to determine maturity scores as a function of age and polynomial functions to determine age as a function of score. We give gender-specific tables of maturity scores and development graphs for each method. The goal of these methods is different because of the nature of the predictions. The percentiles give the dental maturity compared to a standard for a specific age, and polynomial functions give an age prediction with a confidence interval for age. The variations in dental maturity are specific to each population. Thus, the aim of this study is to give the dental maturity standards for southern French children and to compare both the efficiency and applicability of each method in several fields such as forensic sciences or dental health for the clinicians. The addition of the third molar increased the reliability and the capacity of prediction up to 18 years. The polynomial functions showed the best reliability (1.3% of misclassified) and the percentile methods the best accuracy (more or less 1.2 years, on average, between 2 and 18 years of age).
NASA Astrophysics Data System (ADS)
Fukuchi, Tsugio
2014-06-01
The finite difference method (FDM) based on Cartesian coordinate systems can be applied to numerical analyses over any complex domain. A complex domain is usually taken to mean that the geometry of an immersed body in a fluid is complex; here, it means simply an analytical domain of arbitrary configuration. In such an approach, we do not need to treat the outer and inner boundaries differently in numerical calculations; both are treated in the same way. Using a method that adopts algebraic polynomial interpolations in the calculation around near-wall elements, all the calculations over irregular domains reduce to those over regular domains. Discretization of the space differential in the FDM is usually derived using the Taylor series expansion; however, if we use the polynomial interpolation systematically, exceptional advantages are gained in deriving high-order differences. In using the polynomial interpolations, we can numerically solve the Poisson equation freely over any complex domain. Only a particular type of partial differential equation, Poisson's equations, is treated; however, the arguments put forward have wider generality in numerical calculations using the FDM.
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.
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.
Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system
NASA Astrophysics Data System (ADS)
Sarrouy, E.; Dessombz, O.; Sinou, J.-J.
2013-02-01
This paper proposes numerical developments based on polynomial chaos (PC) expansions to process stochastic eigenvalue problems efficiently. These developments are applied to the problem of linear stability calculations for a simplified brake system: the stability of a finite element model of a brake is investigated when its friction coefficient or the contact stiffness are modeled as random parameters. Getting rid of the statistical point of view of the PC method but keeping the principle of a polynomial decomposition of eigenvalues and eigenvectors, the stochastic space is decomposed into several elements to realize a low degree piecewise polynomial approximation of these quantities. An approach relying on continuation principles is compared to the classical dichotomy method to build the partition. Moreover, a criterion for testing accuracy of the decomposition over each cell of the partition without requiring evaluation of exact eigenmodes is proposed and implemented. Several random distributions are tested, including a uniform-like law for description of friction coefficient variation. Results are compared to Monte Carlo simulations so as to determine the method accuracy and efficiency. Some general rules relative to the influence of the friction coefficient or the contact stiffness are also inferred from these calculations.
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.
Carneiro, Vânia M T; Trivella, Daniela B B; Scorsato, Valéria; Beraldo, Viviane L; Dias, Mariana P; Sobreira, Tiago J P; Aparicio, Ricardo; Pilli, Ronaldo A
2015-06-01
RK-682 (1) is a natural product known to selectively inhibit protein tyrosine phosphatases (PTPases) and is used commercially as a positive control for phosphatase inhibition in in vitro assays. Protein phosphatases are involved in several human diseases including diabetes, cancer and inflammation, and are considered important targets for pharmaceutical development. Here we report the synthesis of racemic RK-682 (rac-1) and a focused set of compounds, including racemic analogues of 1, dihydropyranones and C-acylated Meldrum's acid derivatives, the later obtained in one synthetic step from commercially available starting material. We further characterized the behavior of some representative compounds in aqueous solution and evaluated their in vitro PTPase binding and inhibition. Our data reveal that rac-1 and some derivatives are able to form large aggregates in solution, in which the aggregation capacity is dependent on the acyl side chain size. However, compound aggregation per se is not able to promote PTPase inhibition. Our data disclose a novel family of PTPase inhibitors (C-acylated Meldrum's acid derivatives) and that rac-1 and derivatives with an exposed latent negatively charged substructure (e.g.: the tetronic acid core of 1) can bind to the PTPase binding site, as well promiscuously to protein surfaces. The combined capacity of compounds to bind to proteins together with their intrinsic capacity to aggregate in solution seems essential to promote enzyme aggregation and thus, its inhibition. We also observed that divalent cations, such as magnesium frequently used in enzyme buffer solutions, can deplete the inhibitory activity of rac-1, thus influencing the enzyme inhibition experiment. Overall, these data help to characterize the mechanism of PTPase inhibition by rac-1 and derivatives, revealing that enzyme inhibition is not solely dependent on compound binding to the PTPase catalytic site as generally accepted in the literature. In addition, our
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
On the dimensions of oscillator algebras induced by orthogonal polynomials
NASA Astrophysics Data System (ADS)
Honnouvo, G.; Thirulogasanthar, K.
2014-09-01
There is a generalized oscillator algebra associated with every class of orthogonal polynomials lbrace Ψ _n(x)rbrace _{n = 0}^{infty }, on the real line, satisfying a three term recurrence relation xΨn(x) = bnΨn+1(x) + bn-1Ψn-1(x), Ψ0(x) = 1, b-1 = 0. This note presents necessary and sufficient conditions on bn for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator algebras associated with Hermite, Legendre, and Gegenbauer polynomials. Some remarks on the dimensions of oscillator algebras associated with multi-boson systems are also presented.
Multi-mode entangled states represented as Grassmannian polynomials
NASA Astrophysics Data System (ADS)
Maleki, Y.
2016-09-01
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.
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.
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.
Paraxial and nonparaxial polynomial beams and the analytic approach to propagation.
Dennis, Mark R; Götte, Jörg B; King, Robert P; Morgan, Michael A; Alonso, Miguel A
2011-11-15
We construct solutions of the paraxial and Helmholtz equations that are polynomials in their spatial variables. These are derived explicitly by using the angular spectrum method and generating functions. Paraxial polynomials have the form of homogeneous Hermite and Laguerre polynomials in Cartesian and cylindrical coordinates, respectively, analogous to heat polynomials for the diffusion equation. Nonparaxial polynomials are found by substituting monomials in the propagation variable z with reverse Bessel polynomials. These explicit analytic forms give insight into the mathematical structure of paraxially and nonparaxially propagating beams, especially in regard to the divergence of nonparaxial analogs to familiar paraxial beams.
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…
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.
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
NASA Technical Reports Server (NTRS)
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
On computing closed forms for summations. [polynomials and rational functions
NASA Technical Reports Server (NTRS)
Moenck, R.
1977-01-01
The problem of finding closed forms for a summation involving polynomials and rational functions is considered. A method closely related to Hermite's method for integration of rational functions derived. The method expresses the sum of a rational function as a rational function part and a transcendental part involving derivatives of the gamma function.
Connection coefficients between orthogonal polynomials and the canonical sequence
NASA Astrophysics Data System (ADS)
Maroni, P.; Da Rocha, Z.
2008-03-01
We deal with the problem of obtaining closed formulas for the connection coefficients between orthogonal polynomials and the canonical sequence. We use a recurrence relation fulfilled by these coefficients and symbolic computation with the Mathematica language. We treat the cases of Gegenbauer, Jacobi and a new semi-classical sequence.
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
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.
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…
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.
Optimal control for stochastic systems with polynomial chaos
NASA Astrophysics Data System (ADS)
Gallagher, David James
Assuring robustness of control system performance against model uncertainty is a significant component of control design. Current methods for developing a robust controller, however, are typically either too conservative or too computationally expensive. This thesis uses generalized polynomial chaos alongside finite-horizon optimal control as a new method of robust control design for a stochastic system. Since the equations for the mean and variance of the response can be expressed in terms of coefficients from a polynomial chaos expansion, optimizing a polynomial chaos expansion can be used to optimize the mean and variance, thus providing robust responses in a stochastic system. This thesis first provides a review of the concepts and literature then the rationale as well as the derivation of the proposed robust control method. Three examples are given to show the effectiveness of the new control method and are discussed. In particular, the final example demonstrates the applicability of using polynomial chaos to provide robust control for a stochastic soft landing problem.
Polynomial modal analysis of lamellar diffraction gratings in conical mounting.
Randriamihaja, Manjakavola Honore; Granet, Gérard; Edee, Kofi; Raniriharinosy, Karyl
2016-09-01
An efficient numerical modal method for modeling a lamellar grating in conical mounting is presented. Within each region of the grating, the electromagnetic field is expanded onto Legendre polynomials, which allows us to enforce in an exact manner the boundary conditions that determine the eigensolutions. Our code is successfully validated by comparison with results obtained with the analytical modal method.
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.
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)
A transform involving Chebyshev polynomials and its inversion formula
NASA Astrophysics Data System (ADS)
Ciaurri, Oscar; Navas, Luis M.; Varona, Juan L.
2006-11-01
We define a functional analytic transform involving the Chebyshev polynomials Tn(x), with an inversion formula in which the Mobius function [mu](n) appears. If with Re(s)>1, then given a bounded function from [-1,1] into , or from into itself, the following inversion formula holds: if and only if Some other similar results are given.
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.
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.
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.
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.
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.
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.
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
Various amenability properties of the L1-algebra of polynomial hypergroups and applications
NASA Astrophysics Data System (ADS)
Lasser, R.
2009-12-01
We investigate amenability, weak amenability and [alpha]t-amenability of the L1-algebra of polynomial hypergroups, and derive from these properties some applications for the corresponding orthogonal polynomials.
Method reduces computer time for smoothing functions and derivatives through ninth order polynomials
NASA Technical Reports Server (NTRS)
Glauz, R. D.; Wilgus, C. A.
1969-01-01
Analysis presented is an efficient technique to adjust previously calculated orthogonal polynomial coefficients for an odd number of equally spaced data points. The adjusting technique derivation is for a ninth order polynomial. It reduces computer time for smoothing functions.
A Numerical and Graphical Approach to Taylor Polynomials Using an Electronic Spreadsheet.
ERIC Educational Resources Information Center
Timmons, Todd
1991-01-01
Described is an instructional method that makes use of an electronic spreadsheet for the numerical and graphical introduction of the fundamentals of Taylor polynomials. Included is a demonstration spreadsheet using the expansion polynomial to evaluate the cosine function. (JJK)
Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree - 3
NASA Astrophysics Data System (ADS)
Llibre, Jaume; Mahdi, Adam; Valls, Claudia
2011-12-01
In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=-2,-1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree -3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.
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.
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.
Haemolysis with Björk-Shiley and Starr-Edwards prosthetic heart valves: a comparative study
Slater, S. D.; Sallam, I. A.; Bain, W. H.; Turner, M. A.; Lawrie, T. D. V.
1974-01-01
Slater, S. D., Sallam, I. A., Bain, W. H., Turner, M. A., and Lawrie, T. D. V. (1974).Thorax, 29, 624-632. Haemolysis with Björk-Shiley and Starr-Edwards prosthetic heart valves: a comparative study. A comparison was made of the haemolytic complications in 85 patients with two different types of Starr-Edwards cloth-covered ball and cage prosthesis with those in 44 patients with the Björk-Shiley tilting disc valve. Intravascular haemolysis, as detected by the presence of haemosiderinuria, occurred significantly less often with the Björk-Shiley than with the Starr-Edwards valve, the overall incidence with aortic, mitral or multiple replacements being 31%, 15%, and 20% for Björk-Shiley and 94%, 92%, and 88% for Starr-Edwards valves respectively. There was no significant difference in the frequency of haemolysis between each of the two types of Starr-Edwards prosthesis studied at either the aortic (2300 versus 2310 model) or mitral (6300 versus 6310) site. Haemolytic anaemia developed in only one patient with a Björk-Shiley valve but was common though usually mild with Starr-Edwards prostheses, particularly aortic valve replacements with the 2300 model and in aortic plus mitral (± tricuspid) replacements. The greater severity of haemolysis produced by Starr-Edwards valves, again especially of the latter types, was further demonstrated by higher serum lactate dehydrogenase and 24-hour urinary iron levels. It is concluded that the Björk-Shiley tilting disc valve represents a significant advance in the amelioration of the haemolytic complications of prosthetic valves. PMID:4450173
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…
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.
López Fontán, J L; Costa, J; Ruso, J M; Prieto, G; Sarmiento, F
2004-02-01
The application of a statistical method, the local polynomial regression method, (LPRM), based on a nonparametric estimation of the regression function to determine the critical micelle concentration (cmc) is presented. The method is extremely flexible because it does not impose any parametric model on the subjacent structure of the data but rather allows the data to speak for themselves. Good concordance of cmc values with those obtained by other methods was found for systems in which the variation of a measured physical property with concentration showed an abrupt change. When this variation was slow, discrepancies between the values obtained by LPRM and others methods were found.
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.
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.
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.
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
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
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
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
Huberts, W; Donders, W P; Delhaas, T; van de Vosse, F N
2014-12-01
Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space. PMID:25377937
Structure, function, and regulation of the kilB locus of promiscuous plasmid RK2.
Thomson, V J; Jovanovic, O S; Pohlman, R F; Chang, C H; Figurski, D H
1993-01-01
The kil-kor regulon of the self-transmissible, broad-host-range plasmid RK2 is a unique network with eight coregulated operons. Among the genes encoded by the kil-kor regulon are trfA, which encodes the replication initiator, and several kil loci (kilA, kilB, kilC, and kilE), each of which is lethal to the host cell in the absence of appropriate negative regulatory elements encoded by the korA, korB, korC, and korE determinants. We have proposed that the functions of the kil loci are related to RK2 maintenance or host range. Here, we report the nucleotide sequence of a 2.44-kb region that includes the lethal kilB determinant. We identified the first three genes of the kilB operon (designated klbA, klbB, and klbC), and we determined by deletion analysis that the host-lethal phenotype requires klbB. The predicted amino acid sequence of the 34,995-Da klbA product reveals a potential ATP-binding fold. The klbB product is predicted to be a membrane protein with a molecular mass of 15,012 Da with homology to the RK2 KlaC membrane protein encoded by the kilA operon. The amino acid sequence of the 12,085-Da klbC product contains a perfect match to the leucine zipper motif common to eukaryotic regulatory proteins. Primer extension analysis revealed unambiguously that transcription of the kilB operon begins 46 nucleotides upstream of klbA. No transcription was initiated from the sequence previously presumed by other investigators to be the kilB promoter. The abundance of kilB transcripts is reduced in the presence of KorB, consistent with the prediction that KorB acts at the level of transcription. A degenerate KorB-binding site that contains a perfect half-palindrome overlaps the kilB promoter, but this site is insufficient for regulation by KorB. The region containing a KorB-binding site located 183 bp upstream of the transcriptional start is required for regulation by KorB, indicating that KorB acts at a distance to regulate transcription of kilB. Our studies with the
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.
Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction
NASA Astrophysics Data System (ADS)
Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent
1993-12-01
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.
On limit relations between some families of bivariate hypergeometric orthogonal polynomials
NASA Astrophysics Data System (ADS)
Area, I.; Godoy, E.
2013-01-01
In this paper we deal with limit relations between bivariate hypergeometric polynomials. We analyze the limit relation from trinomial distribution to bivariate Gaussian distribution, obtaining the limit transition from the second-order partial difference equation satisfied by bivariate hypergeometric Kravchuk polynomials to the second-order partial differential equation verified by bivariate hypergeometric Hermite polynomials. As a consequence the limit relation between both families of orthogonal polynomials is established. A similar analysis between bivariate Hahn and bivariate Appell orthogonal polynomials is also presented.
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
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.
Constructive feedforward neural networks using hermite polynomial activation functions.
Ma, Liying; Khorasani, K
2005-07-01
In this paper, a constructive one-hidden-layer network is introduced where each hidden unit employs a polynomial function for its activation function that is different from other units. Specifically, both a structure level as well as a function level adaptation methodologies are utilized in constructing the network. The functional level adaptation scheme ensures that the "growing" or constructive network has different activation functions for each neuron such that the network may be able to capture the underlying input-output map more effectively. The activation functions considered consist of orthonormal Hermite polynomials. It is shown through extensive simulations that the proposed network yields improved performance when compared to networks having identical sigmoidal activation functions.
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.
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.
HOMFLY polynomials in representation [3, 1] for 3-strand braids
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A.
2016-09-01
This paper is a new step in the project of systematic description of colored knot polynomials started in [1]. In this paper, we managed to explicitly find the inclusive Racah matrix, i.e. the whole set of mixing matrices in channels R ⊗3 -→ Q with all possible Q, for R = [3 , 1]. The calculation is made possible by the use of a newly-developed efficient highest-weight method, still it remains tedious. The result allows one to evaluate and investigate [3 , 1]-colored polynomials for arbitrary 3-strand knots, and this confirms many previous conjectures on various factorizations, universality, and differential expansions. We consider in some detail the next-to-twist-knots three-strand family ( n, -1 | 1 , -1) and deduce its colored HOMFLY. Also confirmed and clarified is the eigenvalue hypothesis for the Racah matrices, which promises to provide a shortcut to generic formulas for arbitrary representations.
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.
The partially closed Griffith crack. [under polynomial loads
NASA Technical Reports Server (NTRS)
Thresher, R. W.; Smith, F. W.
1973-01-01
A solution is presented for a Griffith crack subjected to an arbitrary polynomial loading function which causes one end of the crack to remain closed. Closed form expressions are presented for the crack opening length and for the stress and displacements in the plane of the crack. The special case of pure bending is presented as an example and for this case the stress intensity factor is computed.
Green's operator for Hamiltonians with Coulomb plus polynomial potentials
NASA Astrophysics Data System (ADS)
Kelbert, E.; Hyder, A.; Demir, F.; Hlousek, Z. T.; Papp, Z.
2007-07-01
The Hamiltonian of a Coulomb plus polynomial potential in the Coulomb-Sturmian basis has an infinite symmetric band-matrix structure. A band matrix can always be considered as a block-tridiagonal matrix. So, the corresponding Green's operator can be given as a matrix-valued continued fraction. As examples, we calculate Green's operator for the Coulomb plus linear and quadratic confinement potential problems and determine the energy levels.
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.
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.
Fast polynomial transform and its implementation by computer
NASA Technical Reports Server (NTRS)
Reed, I. S.; Shao, H. M.; Truong, T. K.
1981-01-01
A fast polynomial transform (FPT) algorithm for computing two-dimensional cyclic convolutions on a general-purpose computer is demonstrated and compared with the FFT approach. An FPT program for two-dimensional convolutions written in FORTRAN is shown to be 20% faster than the conventional FFT algorithm. This higher speed advantage makes the FPT algorithm a candidate for many two-dimensional digital image filtering applications.
Conservation laws of generalized billiards that are polynomial in momenta
NASA Astrophysics Data System (ADS)
Kozlov, V. V.
2014-04-01
This paper deals with dynamics particles moving on a Euclidean n-dimensional torus or in an n-dimensional parallelepiped box in a force field whose potential is proportional to the characteristic function of the region D with a regular boundary. After reaching this region, the trajectory of the particle is refracted according to the law which resembles the Snell -Descartes law from geometrical optics. When the energies are small, the particle does not reach the region D and elastically bounces off its boundary. In this case, we obtain a dynamical system of billiard type (which was intensely studied with respect to strictly convex regions). In addition, the paper discusses the problem of the existence of nontrivial first integrals that are polynomials in momenta with summable coefficients and are functionally independent with the energy integral. Conditions for the geometry of the boundary of the region D under which the problem does not admit nontrivial polynomial first integrals are found. Examples of nonconvex regions are given; for these regions the corresponding dynamical system is obviously nonergodic for fixed energy values (including small ones), however, it does not admit polynomial conservation laws independent of the energy integral.
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.
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.
Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.
Shukla, Rahul; Dragotti, Pier Luigi; Do, Minh N; Vetterli, Martin
2005-03-01
This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R) - c(o)2(-c1R)), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(N log N). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(N log N). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp. PMID:15762332
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.
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.
Stochastic Integration of Renewable Energy Technologies Based on Polynomial Expa
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
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
Gherbi, Hassen; Markmann, Katharina; Svistoonoff, Sergio; Estevan, Joan; Autran, Daphné; Giczey, Gabor; Auguy, Florence; Péret, Benjamin; Laplaze, Laurent; Franche, Claudine; Parniske, Martin; Bogusz, Didier
2008-01-01
Root endosymbioses vitally contribute to plant nutrition and fitness worldwide. Nitrogen-fixing root nodulation, confined to four plant orders, encompasses two distinct types of associations, the interaction of legumes (Fabales) with rhizobia bacteria and actinorhizal symbioses, where the bacterial symbionts are actinomycetes of the genus Frankia. Although several genetic components of the host–symbiont interaction have been identified in legumes, the genetic basis of actinorhiza formation is unknown. Here, we show that the receptor-like kinase gene SymRK, which is required for nodulation in legumes, is also necessary for actinorhiza formation in the tree Casuarina glauca. This indicates that both types of nodulation symbiosis share genetic components. Like several other legume genes involved in the interaction with rhizobia, SymRK is also required for the interaction with arbuscular mycorrhiza (AM) fungi. We show that SymRK is involved in AM formation in C. glauca as well and can restore both nodulation and AM symbioses in a Lotus japonicus symrk mutant. Taken together, our results demonstrate that SymRK functions as a vital component of the genetic basis for both plant–fungal and plant–bacterial endosymbioses and is conserved between legumes and actinorhiza-forming Fagales. PMID:18316735
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
Rosche, Thomas M.; Siddique, Azeem; Larsen, Michelle H.; Figurski, David H.
2000-01-01
Replication of the broad-host-range, IncPα plasmid RK2 requires two plasmid loci: trfA, the replication initiator gene, and oriV, the origin of replication. While these determinants are sufficient for replication in a wide variety of bacteria, they do not confer the stable maintenance of parental RK2 observed in its hosts. The product of the incC gene has been proposed to function in the stable maintenance of RK2 because of its relatedness to the ParA family of ATPases, some of which are known to be involved in the active partition of plasmid and chromosomal DNA. Here we show that IncC has the properties expected of a component of an active partition system. The smaller polypeptide product of incC (IncC2) exhibits a strong, replicon-independent incompatibility phenotype with RK2. This incompatibility phenotype requires the global transcriptional repressor, KorB, and the target for incC-mediated incompatibility is a KorB-binding site (OB). We found that KorB and IncC interact in vivo by using the yeast two-hybrid system and in vitro by using partially purified proteins. Elevated expression of the incC and korB genes individually has no obvious effect on Escherichia coli cell growth, but their simultaneous overexpression is toxic, indicating a possible interaction of IncC-KorB complexes with a vital host target. A region of RK2 bearing incC, korB, and multiple KorB-binding sites is able to stabilize an unstable, heterologous plasmid in an incC-dependent manner. Finally, elevated levels of IncC2 cause RK2 to aggregate, indicating a possible role for IncC in plasmid pairing. These findings demonstrate that IncC, KorB, and at least one KorB-binding site are components of an active partition system for the promiscuous plasmid RK2. PMID:11029420
A new approach to self-organizing fuzzy polynomial neural networks guided by genetic optimization
NASA Astrophysics Data System (ADS)
Oh, Sung-Kwun; Pedrycz, Witold
2005-09-01
In this study, we introduce a new topology of Fuzzy Polynomial Neural Networks (FPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology. The underlying methodology involves mechanisms of genetic optimization, especially genetic algorithms (GAs). Let us recall that the design of the “conventional” FPNNs uses an extended Group Method of Data Handling (GMDH) and exploits a fixed fuzzy inference type located at each FPN of the FPNN as well as considers a fixed number of input nodes at FPNs (or nodes) located in each layer. The proposed FPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. The structural optimization is realized via GAs whereas in the case of the parametric optimization we proceed with a standard least square method based learning. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. The performance of the proposed gFPNN is quantified through experimentation that exploits standard data already being used in fuzzy modeling. The results reveal superiority of the proposed networks over the existing fuzzy and neural models.
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.
Dai, Fengzhao; Zheng, Yazhong; Bu, Yang; Wang, Xiangzhao
2016-08-01
A Zernike-polynomials-based wavefront reconstruction method for lateral shearing interferometry is proposed. Shear matrices are calculated using matrix transformation instead of mathematical derivation. Simulation results show that the shear matrices calculated using the proposed method are the same as those obtained from mathematical derivation. The advantage of the proposed method is that high order shear matrices can be obtained easily; thus, wavefront reconstruction can be extended to higher order Zernike terms, and reconstruction accuracy can be improved. PMID:27505367
NASA Astrophysics Data System (ADS)
Pagnacco, E.; de Cursi, E. Souza; Sampaio, R.
2016-07-01
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.
Wang, Pengcheng; Zhu, Jian-Kang; Lang, Zhaobo
2015-01-01
Nitric oxide (NO) plays important roles in plant development, and biotic and abiotic stress responses. In a recent study, we showed that endogenous NO negatively regulates abscisic acid (ABA) signaling in guard cells by inhibiting sucrose nonfermenting 1 (SNF1)-related protein kinase 2.6 (SnRK2.6)/open stomata 1(OST1) through S-nitrosylation. Application of NO breaks seed dormancy and alleviates the inhibitory effect of ABA on seed germination and early seedling growth, but it is unclear how NO functions at the stages of seed germination and early seedling development. Here, we show that like SnRK2.6, SnRK2.2 can be inactivated by S-nitrosoglutathione (GSNO) treatment through S-nitrosylation. SnRK2.2 and the closely related SnRK2.3 are known to play redundant roles in ABA inhibition of seed germination in Arabidopsis. We found that treatment with the NO donor SNP phenocopies the snrk2.2snrk2.3 double mutant in conferring ABA insensitivity at the stages of seed germination and early seedling growth. Our results suggest that NO negatively regulates ABA signaling in germination and early seedling growth through S-nitrosylation of SnRK2.2 and SnRK2.3.
Huang, Pin-Yao; Yeh, Yu-Hung; Liu, An-Chi; Cheng, Chiu-Ping; Zimmerli, Laurent
2014-07-01
Pattern-triggered immunity (PTI) is broad spectrum and manipulation of PTI is believed to represent an attractive way to engineer plants with broad-spectrum disease resistance. PTI is activated upon perception of microbe-associated molecular patterns (MAMPs) by pattern-recognition receptors (PRRs). We have recently demonstrated that the L-type lectin receptor kinase-VI.2 (LecRK-VI.2) positively regulates Arabidopsis thaliana PTI. Here we show through in vitro pull-down, bimolecular fluorescence complementation and co-immunoprecipitation analyses that LecRK-VI.2 associates with the PRR FLS2. We also demonstrated that LecRK-VI.2 from the cruciferous plant Arabidopsis remains functional after interfamily transfer to the Solanaceous plant Nicotiana benthamiana. Wild tobacco plants ectopically expressing LecRK-VI.2 were indeed more resistant to virulent hemi-biotrophic and necrotrophic bacteria, but not to the fungal pathogen Botrytis cinerea suggesting that, as with Arabidopsis, the LecRK-VI.2 protective effect in N. benthamiana is bacteria specific. Ectopic expression of LecRK-VI.2 in N. benthamiana primed PTI-mediated reactive oxygen species production, mitogen-activated protein kinase (MAPK) activity, callose deposition and gene expression upon treatment with the MAMP flagellin. Our findings identified LecRK-VI.2 as a member of the FLS2 receptor complex and suggest that heterologous expression of components of PRR complexes can be used as tools to engineer plant disease resistance to bacteria.
Wang, Pengcheng; Zhu, Jian-Kang; Lang, Zhaobo
2015-01-01
Nitric oxide (NO) plays important roles in plant development, and biotic and abiotic stress responses. In a recent study, we showed that endogenous NO negatively regulates abscisic acid (ABA) signaling in guard cells by inhibiting sucrose nonfermenting 1 (SNF1)-related protein kinase 2.6 (SnRK2.6)/open stomata 1(OST1) through S-nitrosylation. Application of NO breaks seed dormancy and alleviates the inhibitory effect of ABA on seed germination and early seedling growth, but it is unclear how NO functions at the stages of seed germination and early seedling development. Here, we show that like SnRK2.6, SnRK2.2 can be inactivated by S-nitrosoglutathione (GSNO) treatment through S-nitrosylation. SnRK2.2 and the closely related SnRK2.3 are known to play redundant roles in ABA inhibition of seed germination in Arabidopsis. We found that treatment with the NO donor SNP phenocopies the snrk2.2snrk2.3 double mutant in conferring ABA insensitivity at the stages of seed germination and early seedling growth. Our results suggest that NO negatively regulates ABA signaling in germination and early seedling growth through S-nitrosylation of SnRK2.2 and SnRK2.3. PMID:26024299
Anticoagulants and the Björk-Shiley prosthesis. Experience of 390 patients.
Sutton, M G; Miller, G A; Oldershaw, P J; Paneth, M
1978-01-01
From September 1972 to January 1975, 390 patients underwent valve replacement using the Björk-Shiley tilting disc prosthesis. For the group as a whole hospital mortality was 13.3 per cent and was lowest in those undergoing isolated mitral or aortic valve replacement (5.3 and 9.4%, respectively). Available for follow-up were 209 patients of whom 123 were maintained on dipyridamole and 96 on warfarin. Thromboembolic complications were significantly (P less than 0.01) commoner in the dipyridamole (28 of 123, 22%) than warfarin (6 of 86, 7%) treated group. In the dipyridamole treated group the incidence of thromboembolic complications was similar whichever valve was replaced and thromboembolic complications were responsible for 14 of the 28 late deaths. In the warfarin treated group thromboembolic complications only occurred in patients with a mitral prosthesis. Anticoagulation is indicated for all patients with this prosthesis wherever inserted. PMID:656224
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.
Maria-Ferreira, Daniele; da Silva, Luisa Mota; Mendes, Daniel Augusto Gasparin Bueno; Cabrini, Daniela de Almeida; Nascimento, Adamara Machado; Iacomini, Marcello; Cipriani, Thales Ricardo; Santos, Adair Roberto Soares; de Paula Werner, Maria Fernanda; Baggio, Cristiane Hatsuko
2014-01-01
A rhamnogalacturonan (RGal) isolated from Acmella oleracea (L.) R.K. Jansen administered by oral route showed gastroprotective activity against acute lesions induced by ethanol. In this study, we investigated the gastric ulcer healing effect of RGal and its mechanisms of action. Intraperitoneal treatment of animals with RGal protected the gastric mucosa against acute lesions induced by ethanol, with participation of gastric mucus. Furthermore, in the chronic ulcer model, oral administration of RGal accelerates the gastric ulcer healing, accompanied by increasing of cellular proliferation and gastric mucus content, reducing inflammatory parameters and oxidative stress. In addition, the repeated 7 days-treatment of animals with RGal did not show alterations of clinical and behavioral symptoms, body and organs weights or plasmatic biochemical parameters. Collectively, these results showed that RGal has an interesting antiulcerogenic activity and could constitute an attractive molecule of interest for the development of new antiulcer agents. PMID:24416280
Maria-Ferreira, Daniele; da Silva, Luisa Mota; Mendes, Daniel Augusto Gasparin Bueno; Cabrini, Daniela de Almeida; Nascimento, Adamara Machado; Iacomini, Marcello; Cipriani, Thales Ricardo; Santos, Adair Roberto Soares; Werner, Maria Fernanda de Paula; Baggio, Cristiane Hatsuko
2014-01-01
A rhamnogalacturonan (RGal) isolated from Acmella oleracea (L.) R.K. Jansen administered by oral route showed gastroprotective activity against acute lesions induced by ethanol. In this study, we investigated the gastric ulcer healing effect of RGal and its mechanisms of action. Intraperitoneal treatment of animals with RGal protected the gastric mucosa against acute lesions induced by ethanol, with participation of gastric mucus. Furthermore, in the chronic ulcer model, oral administration of RGal accelerates the gastric ulcer healing, accompanied by increasing of cellular proliferation and gastric mucus content, reducing inflammatory parameters and oxidative stress. In addition, the repeated 7 days-treatment of animals with RGal did not show alterations of clinical and behavioral symptoms, body and organs weights or plasmatic biochemical parameters. Collectively, these results showed that RGal has an interesting antiulcerogenic activity and could constitute an attractive molecule of interest for the development of new antiulcer agents.
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
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
Woo, Joo Yong; Jeong, Kwang Ju; Kim, Young Jin; Paek, Kyung-Hee
2016-01-01
In Arabidopsis, several L-type lectin receptor kinases (LecRKs) have been identified as putative immune receptors. However, to date, there have been few analyses of LecRKs in crop plants. Virus-induced gene silencing of CaLecRK-S.5 verified the role of CaLecRK-S.5 in broad-spectrum resistance. Compared with control plants, CaLecRK-S.5-silenced plants showed reduced hypersensitive response, reactive oxygen species burst, secondary metabolite production, mitogen-activated protein kinase activation, and defense-related gene expression in response to Tobacco mosaic virus pathotype P0 (TMV-P0) infection. Suppression of CaLecRK-S.5 expression significantly enhanced the susceptibility to Pepper mild mottle virus pathotype P1,2,3, Xanthomonas campestris pv. vesicatoria, Phytophthora capsici, as well as TMV-P0. Additionally, β-aminobutyric acid treatment and a systemic acquired resistance assay revealed that CaLecRK-S.5 is involved in priming of plant immunity. Pre-treatment with β-aminobutyric acid before viral infection restored the reduced disease resistance phenotypes shown in CaLecRK-S.5-silenced plants. Systemic acquired resistance was also abolished in CaLecRK-S.5-silenced plants. Finally, RNA sequencing analysis indicated that CaLecRK-S.5 positively regulates plant immunity at the transcriptional level. Altogether, these results suggest that CaLecRK-S.5-mediated broad-spectrum resistance is associated with the regulation of priming. PMID:27647723
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
Physical analysis of the Björk-Shiley prosthetic valve sound.
Schöndube, F; Keusen, H; Messmer, B J
1983-07-01
The closing sound of an implanted Björk-Shiley heart valve prosthesis can be heard clearly in the proximity of the patient. A clinical interrogation of 35 patients showed that 16 (46%) were disturbed by the clicking noise and 10 (29%) reported disturbance of those nearby. A silent prosthesis would be preferred by 15 (43%) patients, eight (23%) declined such a valve for reasons of their own security, and 12 (34%) patients were undecided. The frequency spectrum of the metallic closing sound and its loudness were measured by noninvasive techniques in 20 patients. In the aortic as well as in the mitral position, a high peak of the sound pressure level was registered at 9.8 kHz. In 20 patients the average value of the sound pressure level was 35 dbA measured at a distance of 10 cm from the patient's chest. In vitro studies demonstrated a high peak of the sound pressure level at 9.5 kHz for the Björk-Shiley valve when recorded in free air and at 7 kHz in a standardized valve chamber of a mock circulatory system filled with blood or water. A decrease of the sound pressure level could be achieved by a textile wrap around the chest which damps frequencies around 10 kHz. This protects those nearby but not the patient, who hears the clicking mainly through internal conduction. This unpleasant valve noise can be eliminated only during construction of a new prosthesis provided that such "minor" side effects are measured and taken into consideration.
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.
Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model.
Altmann, Yoann; Dobigeon, Nicolas; Tourneret, Jean-Yves
2013-04-01
This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.
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.
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
NASA Astrophysics Data System (ADS)
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
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.
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.
Design of a recursive vector processor using polynomial splines
NASA Technical Reports Server (NTRS)
Kim, C. S.; Shen, C. N.
1980-01-01
The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.
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.
Multi-dimensional Hermite polynomials in quantum optics
NASA Astrophysics Data System (ADS)
Kok, Pieter; Braunstein, Samuel L.
2001-08-01
We study a class of optical circuits with vacuum input states consisting of Gaussian sources without coherent displacements such as down-converters and squeezers, together with photo-detectors and passive interferometry (beamsplitters, polarization rotations, phase-shifters, etc). We show that the outgoing state leaving the optical circuit can be expressed in terms of so-called multi-dimensional Hermite polynomials and give their recursion and orthogonality relations. We show how quantum teleportation of single-photon polarization states can be modelled using this description.
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.
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.
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
Sobecky, P A; Easter, C L; Bear, P D; Helinski, D R
1996-01-01
A 3.2-kb fragment encoding five genes, parCBA/DE, in two divergently transcribed operons promotes stable maintenance of the replicon of the broad-host-range plasmid RK2 in a vector-independent manner in Escherichia coli. The parDE operon has been shown to contribute to stabilization through the postsegregational killing of plasmid-free daughter cells, while the parCBA operon encodes a resolvase, ParA, that mediates the resolution of plasmid multimers through site-specific recombination. To date, evidence indicates that multimer resolution alone does not play a significant role in RK2 stable maintenance by the parCBA operon in E. coli. It has been proposed, instead, that the parCBA region encodes an additional stability mechanism, a partition system, that ensures that each daughter cell receives a plasmid copy at cell division. However, studies carried out to date have not directly determined the plasmid stabilization activity of the parCBA operon alone. An assessment was made of the relative contributions of postsegregational killing (parDE) and the putative partitioning system (parCBA) to the stabilization of mini-RK2 replicons in E. coli. Mini-RK2 replicons carrying either the entire 3.2-kb (parCBA/DE) fragment or the 2.3-kb parCBA region alone were found to be stably maintained in two E. coli strains tested. The stabilization found is not due to resolution of multimers. The stabilizing effectiveness of parCBA was substantially reduced when the plasmid copy number was lowered, as in the case of E. coli cells carrying a temperature-sensitive mini-RK2 replicon grown at a nonpermissive temperature. The presence of the entire 3.2-kb region effectively stabilized the replicon, however, under both low- and high-copy-number-conditions. In those instances of decreased plasmid copy number, the postsegregational killing activity, encoded by parDE, either as part of the 3.2-kb fragment or alone played the major role in the stabilization of mini-RK2 replicons within the
The distribution of zeros of general q-polynomials
NASA Astrophysics Data System (ADS)
Álvarez-Nodarse, R.; Buendía, E.; Dehesa, J. S.
1997-10-01
A general system of q-orthogonal polynomials is defined by means of its three-term recurrence relation. This system encompasses many of the known families of q-polynomials, among them the q-analogue of the classical orthogonal polynomials. The asymptotic density of zeros of the system is shown to be a simple and compact expression of the parameters which characterize the asymptotic behaviour of the coefficients of the recurrence relation. This result is applied to specific classes of polynomials known by the names q-Hahn, q-Kravchuk, q-Racah, q-Askey and Wilson, Al Salam - Carlitz and the celebrated little and big q-Jacobi.
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.
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.
Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials
Ho, Choon-Lin
2011-04-15
Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it is also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.
Korobov polynomials of the third kind and of the fourth kind.
Kim, Taekyun; Kim, Dae San
2015-01-01
The first degenerate version of the Bernoulli polynomials of the second kind appeared in the paper by Korobov (Math Notes 2:77-19, 1996; Proceedings of the IV international conference modern problems of number theory and its applications, pp 40-49, 2001). In this paper, we study two degenerate versions of the Bernoulli polynomials of the second kind which will be called Korobov polynomials of third kind and of the fourth kind. Some properties, identities, recurrence relations and connections with other polynomials are investigated by using umbral calculus.
Local Polynomial Regression for Symmetric Positive Definite Matrices.
Yuan, Ying; Zhu, Hongtu; Lin, Weili; Marron, J S
2012-09-01
Local polynomial regression has received extensive attention for the nonparametric estimation of regression functions when both the response and the covariate are in Euclidean space. However, little has been done when the response is in a Riemannian manifold. We develop an intrinsic local polynomial regression estimate for the analysis of symmetric positive definite (SPD) matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space. The primary motivation and application of the proposed methodology is in computer vision and medical imaging. We examine two commonly used metrics, including the trace metric and the Log-Euclidean metric on the space of SPD matrices. For each metric, we develop a cross-validation bandwidth selection method, derive the asymptotic bias, variance, and normality of the intrinsic local constant and local linear estimators, and compare their asymptotic mean square errors. Simulation studies are further used to compare the estimators under the two metrics and to examine their finite sample performance. We use our method to detect diagnostic differences between diffusion tensors along fiber tracts in a study of human immunodeficiency virus.
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.
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.
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.
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.
Polynomial Decay of Correlations in the Generalized Baker's Transformation
NASA Astrophysics Data System (ADS)
Bose, Christopher; Murray, Rua
2013-08-01
We introduce a family of area preserving generalized baker's transformations acting on the unit square and having sharp polynomial rates of mixing for Holder data. The construction is geometric, relying on the graph of a single variable "cut function". Each baker's map B is non-uniformly hyperbolic and while the exact mixing rate depends on B, all polynomial rates can be attained. The analysis of mixing rates depends on building a suitable Young tower for an expanding factor. The mechanisms leading to a slow rate of correlation decay are especially transparent in our examples due to the simple geometry in the construction. For this reason we propose this class of maps as an excellent testing ground for new techniques for the analysis of decay of correlations in non-uniformly hyperbolic systems. Finally, some of our examples can be seen to be extensions of certain 1-D non-uniformly expanding maps that have appeared in the literature over the last twenty years thereby providing a unified treatment of these interesting and well-studied examples.
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.
Hwang, F-N Wei, Z-H Huang, T-M Wang Weichung
2010-04-20
We develop a parallel Jacobi-Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi-Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc's efficient and various parallel operations, linear solvers, preconditioning schemes, and easy usages. The parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by Schroedinger's equations. We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi-Davidson algorithm, very efficiently in parallel. Besides, the overall performance is quite satisfactory. We have observed near perfect superlinear speedup by using up to 320 processors. The parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 Intel 3.0 GHz processors.
Fujita, Yasunari; Yoshida, Takuya; Yamaguchi-Shinozaki, Kazuko
2013-01-01
Water availability is one of the main limiting factors for plant growth and development. The phytohormone abscisic acid (ABA) fulfills a critical role in coordinating the responses to reduced water availability as well as in multiple developmental processes. Endogenous ABA levels increase in response to osmotic stresses such as drought and high salinity, and ABA activates the expression of many genes via ABA-responsive elements (ABREs) in their promoter regions. ABRE-binding protein/ABRE-binding factor (AREB/ABF) transcription factors (TFs) regulate the ABRE-mediated transcription of downstream target genes. Three subclass III sucrose non-fermenting-1 related protein kinase 2 (SnRK2) protein kinases (SRK2D/SnRK2.2, SRK2E/SnRK2.6/OST1 and SRK2I/SnRK2.3) phosphorylate and positively control the AREB/ABF TFs. Substantial progress has been made in our understanding of the ABA-sensing system mediated by Pyrabactin resistance1/PYR1-like/regulatory components of ABA receptor (PYR/PYL/RCAR)-protein phosphatase 2C complexes. In addition to PP2C-PYR/PYL/RCAR ABAreceptor complex, the AREB/ABF-SnRK2 pathway, which is well conserved in land plants, was recently shown to play a major role as a positive regulator of ABA/stress signaling through ABRE-mediated transcription of target genes implicated in the osmotic stress response. This review focuses on current progress in the study of the AREB/ABF-SnRK2 positive regulatory pathway in plants and describes additional signaling factors implicated in the AREB/ABF-SnRK2 pathway. Moreover, to help promote the link between basic and applied studies, the nomenclature and phylogenetic relationships between the AREB/ABFs and SnRK2s are summarized and discussed.
Wu, Tingquan; Wang, Rui; Xu, Xiaomei; He, Xiaoming; Sun, Baojuan; Zhong, Yujuan; Liang, Zhaojuan; Luo, Shaobo; Lin, Yu'e
2014-10-10
L-type lectin receptor kinase (LecRK) proteins are an important family involved in diverse biological processes such as pollen development, senescence, wounding, salinity and especially in innate immunity in model plants such as Arabidopsis and tobacco. Till date, LecRK proteins or genes of cucumber have not been reported. In this study, a total of 25 LecRK genes were identified in the cucumber genome, unequally distributed across its seven chromosomes. According to similarity comparison of their encoded proteins, the Cucumis sativus LecRK (CsLecRK) genes were classified into six major clades (from Clade I to CladeVI). Expression of CsLecRK genes were tested using QRT-PCR method and the results showed that 25 CsLecRK genes exhibited different responses to abiotic (water immersion) and biotic (Phytophthora melonis and Phytophthora capsici inoculation) stresses, as well as that between disease resistant cultivar (JSH) and disease susceptible cultivar (B80). Among the 25 CsLecRK genes, we found CsLecRK6.1 was especially induced by P. melonis and P. capsici in JSH plants. All these results suggested that CsLecRK genes may play important roles in biotic and abiotic stresses.
Masatcioğlu, Tuğrul M; Avşar, Yahya K
2005-07-01
The objectives of this study were to determine the cumulative effects of flavorings (chili pepper, thyme, mint, cumin, nutmeg, allspice, clove, cinnamon, black pepper, salt, and hot red pepper paste), storage conditions, and storage time on the survival of Staphylococcus aureus in Sürk cheese and to monitor the associated chemical changes. Sürk cheese, a traditional Turkish cheese, was produced by heating diluted nonfat yogurt and adding flavorings to the resultant acid-heat curd. The cheese was later inoculated with S. aureus, shaped conically, and stored aerobically for mold growth and anaerobically in olive oil for 30 days at room temperature. The moisture content of aerobically stored cheese decreased over time and led to increases in total solids, salt, salt-in-moisture, and ash content during ripening (P < 0.05). The presence or absence of the flavorings had no significant effect, whereas storage conditions and storage duration decreased the survival of S. aureus (P < 0.05).
Karadede, Hülya; Oymak, Seyit Ahmet; Unlü, Erhan
2004-04-01
The distribution of some heavy metals in three different organs of mullet, Liza abu, and catfish, Silurus triostegus, from Atatürk Dam Lake located on Euphrates (Turkey) was studied. Co and Mo concentrations were below limits of detection in all fish organs, whereas Ni was also below limits in organs of mullet. The metal accumulation in the liver and gill of L. abu and S. triostegus was found to be quite high in comparison with the muscle. In general, the concentrations are similar to those previously observed on other fish studied in Atatürk Dam Lake and lower than those determined in Tigris River. The analysed metals (Co, Cu, Fe, Mn, Mo, Ni and Zn) were found in fish muscle at mean concentrations under the permissible limits proposed by FAO.
Indrasumunar, Arief; Wilde, Julia; Hayashi, Satomi; Li, Dongxue; Gresshoff, Peter M
2015-03-15
Association between legumes and rhizobia results in the formation of root nodules, where symbiotic nitrogen fixation occurs. The early stages of this association involve a complex of signalling events between the host and microsymbiont. Several genes dealing with early signal transduction have been cloned, and one of them encodes the leucine-rich repeat (LRR) receptor kinase (SymRK; also termed NORK). The Symbiosis Receptor Kinase gene is required by legumes to establish a root endosymbiosis with Rhizobium bacteria as well as mycorrhizal fungi. Using degenerate primer and BAC sequencing, we cloned duplicated SymRK homeologues in soybean called GmSymRKα and GmSymRKβ. These duplicated genes have high similarity of nucleotide (96%) and amino acid sequence (95%). Sequence analysis predicted a malectin-like domain within the extracellular domain of both genes. Several putative cis-acting elements were found in promoter regions of GmSymRKα and GmSymRKβ, suggesting a participation in lateral root development, cell division and peribacteroid membrane formation. The mutant of SymRK genes is not available in soybean; therefore, to know the functions of these genes, RNA interference (RNAi) of these duplicated genes was performed. For this purpose, RNAi construct of each gene was generated and introduced into the soybean genome by Agrobacterium rhizogenes-mediated hairy root transformation. RNAi of GmSymRKβ gene resulted in an increased reduction of nodulation and mycorrhizal infection than RNAi of GmSymRKα, suggesting it has the major activity of the duplicated gene pair. The results from the important crop legume soybean confirm the joint phenotypic action of GmSymRK genes in both mycorrhizal and rhizobial infection seen in model legumes.
Coello, Patricia; Martínez-Barajas, Eleazar
2014-01-01
Phaseolus vulgaris seeds can grow and develop at the expense of the pod reserves after the fruits have been removed from the plant (Fountain etal., 1989). Because this process involves sensing the reduction of nutrients and the remobilisation of pod reserves, we investigated the effect on sucrose non-fermenting related kinase 1 (SnRK1) activity during this process. Bean fruits removed from the plant at 20 days after flowering (DAF) demonstrated active remobilisation of nutrients from the pod to the seeds. After 5 days, the pod dry weight was reduced by 50%. The process was characterized by a rapid degradation of starch, with the greatest decrease observed on day 1 after the fruits were removed. The pod nutrients were insufficient for the needs of all the seeds, and only some seeds continued their development. Those seeds exhibited a transient reduction in sucrose levels on day 1 after the fruits were removed. However, the normal level of sucrose was recovered, and the rate of starch synthesis was identical to that of a seed developed under normal conditions. Removing the fruits from the plant had no effect on the activity of SnRK1 in the pods, whereas in the seeds, the activity was increased by 35%. Simultaneously, a large reduction in seed sucrose levels was observed. The increase in SnRK1 activity was observed in both the cotyledon and embryo axes, but it was higher in the cotyledon. At 20–25 DAF, cotyledons actively accumulate storage materials. It is possible that the increase in SnRK1 activity observed in seeds developed in fruits that have been removed from the plant is part of the mechanism required for nutrient remobilisation under conditions of stress. PMID:24860586
NASA Astrophysics Data System (ADS)
Das, Diganta; Hati, Chandan; Kumar, Girish; Mahajan, Namit
2016-09-01
We present a unified explanation for the B -decay anomalies in RD(*) and RK together with the anomalous muon magnetic moment, consistent with the constraints from the current measurements of leptonic decay rates and D0-D¯ 0 , Bs0-B¯s 0 mixings, within the framework of a minimal left-right symmetric gauge theory motivated by one of the low-energy subgroups of E6 naturally accommodating leptoquarks.
Sari, Deniz; Ozkurt, Nesimi; Akdag, Ali; Kutukoglu, Murat; Gurarslan, Aliye
2014-06-01
Airport noise and its impact on the surrounding areas are major issues in the aviation industry. The İstanbul Atatürk Airport is a major global airport with passenger numbers increasing rapidly per annum. The noise levels for day, evening and night times were modeled around the İstanbul Atatürk Airport according to the European Noise Directive using the actual data records for the year 2011. The "ECAC Doc. 29-Interim" method was used for the computation of the aircraft traffic noise. In the setting the noise model for the local airport topography was taken into consideration together with the noise source data, the airport loadings, features of aircraft and actual air traffic data. Model results were compared with long-term noise measurement values for calibration. According to calibration results, classifications of the aircraft type and flight tracks were revised. For noise model validation, the daily noise measurements at four additional locations were used during the verification period. The input data was re-edited only for these periods and the model was validated. A successful model performance was obtained in several zones around the airport. The validated noise model of the İstanbul Atatürk Airport can be now utilized both for determining the noise levels in the future and for producing new strategies which are about the land use planning, operational considerations for the air traffic management and the noise abatement procedures.
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Rossow, C.-C.
2008-01-01
A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.