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.
Complex Chebyshev-polynomial-based unified model (CCPBUM) neural networks
NASA Astrophysics Data System (ADS)
Jeng, Jin-Tsong; Lee, Tsu-Tian
1998-03-01
In this paper, we propose complex Chebyshev Polynomial Based unified model neural network for the approximation of complex- valued function. Based on this approximate transformable technique, we have derived the relationship between the single-layered neural network and multi-layered perceptron neural network. It is shown that the complex Chebyshev Polynomial Based unified model neural network can be represented as a functional link network that are based on Chebyshev polynomial. We also derived a new learning algorithm for the proposed network. It turns out that the complex Chebyshev Polynomial Based unified model neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional complex feedforward/recurrent neural network.
Discontinuous Galerkin method based on non-polynomial approximation spaces
Yuan Ling . E-mail: lyuan@dam.brown.edu; Shu Chiwang . E-mail: shu@dam.brown.edu
2006-10-10
In this paper, we develop discontinuous Galerkin (DG) methods based on non-polynomial approximation spaces for numerically solving time dependent hyperbolic and parabolic and steady state hyperbolic and elliptic partial differential equations (PDEs). The algorithm is based on approximation spaces consisting of non-polynomial elementary functions such as exponential functions, trigonometric functions, etc., with the objective of obtaining better approximations for specific types of PDEs and initial and boundary conditions. It is shown that L {sup 2} stability and error estimates can be obtained when the approximation space is suitably selected. It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.
SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos
Ahlfeld, R. Belkouchi, B.; Montomoli, F.
2016-09-01
A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10
Fast complex memory polynomial-based adaptive digital predistorter
NASA Astrophysics Data System (ADS)
Singh Sappal, Amandeep; Singh Patterh, Manjeet; Sharma, Sanjay
2011-07-01
Today's 3G wireless systems require both high linearity and high power amplifier (PA) efficiency. The high peak-to-average ratios of the digital modulation schemes used in 3G wireless systems require that the RF PA maintain high linearity over a large range while maintaining this high efficiency; these two requirements are often at odds with each other with many of the traditional amplifier architectures. In this article, a fast and easy-to-implement adaptive digital predistorter has been presented for Wideband Code Division Multiplexed signals using complex memory polynomial work function. The proposed algorithm has been implemented to test a Motorola LDMOSFET PA. The proposed technique also takes care of the memory effects of the PA, which have been ignored in many proposed techniques in the literature. The results show that the new complex memory polynomial-based adaptive digital predistorter has better linearisation performance than conventional predistortion techniques.
Estimation of the entropy based on its polynomial representation.
Vinck, Martin; Battaglia, Francesco P; Balakirsky, Vladimir B; Vinck, A J Han; Pennartz, Cyriel M A
2012-05-01
Estimating entropy from empirical samples of finite size is of central importance for information theory as well as the analysis of complex statistical systems. Yet, this delicate task is marred by intrinsic statistical bias. Here we decompose the entropy function into a polynomial approximation function and a remainder function. The approximation function is based on a Taylor expansion of the logarithm. Given n observations, we give an unbiased, linear estimate of the first n power series terms based on counting sets of k coincidences. For the remainder function we use nonlinear Bayesian estimation with a nearly flat prior distribution on the entropy that was developed by Nemenman, Shafee, and Bialek. Our simulations show that the combined entropy estimator has reduced bias in comparison to other available estimators.
Estimation of the entropy based on its polynomial representation
NASA Astrophysics Data System (ADS)
Vinck, Martin; Battaglia, Francesco P.; Balakirsky, Vladimir B.; Vinck, A. J. Han; Pennartz, Cyriel M. A.
2012-05-01
Estimating entropy from empirical samples of finite size is of central importance for information theory as well as the analysis of complex statistical systems. Yet, this delicate task is marred by intrinsic statistical bias. Here we decompose the entropy function into a polynomial approximation function and a remainder function. The approximation function is based on a Taylor expansion of the logarithm. Given n observations, we give an unbiased, linear estimate of the first n power series terms based on counting sets of k coincidences. For the remainder function we use nonlinear Bayesian estimation with a nearly flat prior distribution on the entropy that was developed by Nemenman, Shafee, and Bialek. Our simulations show that the combined entropy estimator has reduced bias in comparison to other available estimators.
Enhanced Access Polynomial Based Self-healing Key Distribution
NASA Astrophysics Data System (ADS)
Dutta, Ratna; Mukhopadhyay, Sourav; Dowling, Tom
A fundamental concern of any secure group communication system is that of key management. Wireless environments create new key management problems and requirements to solve these problems. One such core requirement in these emerging networks is that of self-healing. In systems where users can be offline and miss updates self healing allows a user to recover lost keys and get back into the secure communication without putting extra burden on the group manager. Clearly self healing must be only available to authorized users and this creates more challenges in that we must ensure unauthorized or revoked users cannot, themselves or by means of collusion, avail of self healing. To this end we enhance the one-way key chain based self-healing key distribution of Dutta et al. by introducing a collusion resistance property between the revoked users and the newly joined users. Our scheme is based on the concept of access polynomials. These can be loosely thought of as white lists of authorized users as opposed to the more widely used revocation polynomials or black lists of revoked users. We also allow each user a pre-arranged life cycle distributed by the group manager. Our scheme provides better efficiency in terms of storage, and the communication and computation costs do not increase as the number of sessions grows as compared to most current schemes. We analyze our scheme in an appropriate security model and prove that the proposed scheme is computationally secure and not only achieving forward and backward secrecy, but also resisting collusion between the new joined users and the revoked users. Unlike most existing schemes the new scheme allows temporary revocation. Also unlike existing schemes, our construction does not collapse if the number of revoked users crosses a threshold value. This feature increases resilience against revocation based denial of service (DOS) attacks and thus improves availability of communication channel.
Luminance-Chrominance Gain Equalizer Based on Bernstein Polynomials
NASA Astrophysics Data System (ADS)
Chutchavong, Vanvisa; Sangaroon, Ornlarp; Benjangkaprasert, Chawalit; Janchitrapongvej, Kanok
This paper presents a linear luminance-chrominance gain equalizer for correcting the linear chrominance gain distortion in the color TV transmission system. The proposed gain equalizer was implemented based on Bernstein polynomials. As it is known that the Bernstein filter has flexible parameters to adjust the circuit performance for the best results. In addition, the modulated 20T sine-squared pulse test signal is generated for testing the performance of the proposed gain equalizer, which can be measured all three types of the linear chrominance distortions. As the results, the proposed gain equalizer is also proved to be efficient in equalizing both the low gain and the high gain chrominance distortions without degrading its phase characteristics.
Fast Minimum Variance Beamforming Based on Legendre Polynomials.
Bae, MooHo; Park, Sung Bae; Kwon, Sung Jae
2016-09-01
Currently, minimum variance beamforming (MV) is actively investigated as a method that can improve the performance of an ultrasound beamformer, in terms of the lateral and contrast resolution. However, this method has the disadvantage of excessive computational complexity since the inverse spatial covariance matrix must be calculated. Some noteworthy methods among various attempts to solve this problem include beam space adaptive beamforming methods and the fast MV method based on principal component analysis, which are similar in that the original signal in the element space is transformed to another domain using an orthonormal basis matrix and the dimension of the covariance matrix is reduced by approximating the matrix only with important components of the matrix, hence making the inversion of the matrix very simple. Recently, we proposed a new method with further reduced computational demand that uses Legendre polynomials as the basis matrix for such a transformation. In this paper, we verify the efficacy of the proposed method through Field II simulations as well as in vitro and in vivo experiments. The results show that the approximation error of this method is less than or similar to those of the above-mentioned methods and that the lateral response of point targets and the contrast-to-speckle noise in anechoic cysts are also better than or similar to those methods when the dimensionality of the covariance matrices is reduced to the same dimension.
NASA Astrophysics Data System (ADS)
Coelho, Rodrigo C. V.; Ilha, Anderson S.; Doria, Mauro M.
2016-10-01
A lattice Boltzmann method is proposed based on the expansion of the equilibrium distribution function in powers of a new set of generalized orthonormal polynomials which are here presented. The new polynomials are orthonormal under the weight defined by the equilibrium distribution function itself. The D-dimensional Hermite polynomials is a sub-case of the present ones, associated to the particular weight of a Gaussian function. The proposed lattice Boltzmann method allows for the treatment of semi-classical fluids, such as electrons in metals under the Drude-Sommerfeld model, which is a particular case that we develop and validate by the Riemann problem.
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
Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation.
Yuan, Lifeng; 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.
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
Mahmood, Zahid; Ning, Huansheng; Ghafoor, AtaUllah
2017-03-24
Wireless Sensor Networks (WSNs) consist of lightweight devices to measure sensitive data that are highly vulnerable to security attacks due to their constrained resources. In a similar manner, the internet-based lightweight devices used in the Internet of Things (IoT) are facing severe security and privacy issues because of the direct accessibility of devices due to their connection to the internet. Complex and resource-intensive security schemes are infeasible and reduce the network lifetime. In this regard, we have explored the polynomial distribution-based key establishment schemes and identified an issue that the resultant polynomial value is either storage intensive or infeasible when large values are multiplied. It becomes more costly when these polynomials are regenerated dynamically after each node join or leave operation and whenever key is refreshed. To reduce the computation, we have proposed an Efficient Key Management (EKM) scheme for multiparty communication-based scenarios. The proposed session key management protocol is established by applying a symmetric polynomial for group members, and the group head acts as a responsible node. The polynomial generation method uses security credentials and secure hash function. Symmetric cryptographic parameters are efficient in computation, communication, and the storage required. The security justification of the proposed scheme has been completed by using Rubin logic, which guarantees that the protocol attains mutual validation and session key agreement property strongly among the participating entities. Simulation scenarios are performed using NS 2.35 to validate the results for storage, communication, latency, energy, and polynomial calculation costs during authentication, session key generation, node migration, secure joining, and leaving phases. EKM is efficient regarding storage, computation, and communication overhead and can protect WSN-based IoT infrastructure.
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.
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.
A New and Improved Host-Independent Plasmid System for RK2-Based Conjugal Transfer
Strand, Trine Aakvik; Lale, Rahmi; Degnes, Kristin Fløgstad; Lando, Malin; Valla, Svein
2014-01-01
Bacterial conjugation is a process that is mediated either by a direct cell-to-cell junction or by formation of a bridge between the cells. It is often used to transfer DNA constructs designed in Escherichia coli to recipient bacteria, yeast, plants and mammalian cells. Plasmids bearing the RK2/RP4 origin of transfer (oriT) are mostly mobilized using the E. coli S17-1/SM10 donor strains, in which transfer helper functions are provided from a chromosomally integrated RP4::Mu. We have observed that large plasmids were occasionally modified after conjugal transfer when using E. coli S17-1 as a donor. All modified plasmids had increased in size, which most probably was a result of co-transfer of DNA from the chromosomally located oriT. It has earlier also been demonstrated that the bacteriophage Mu is silently transferred to recipient cells by these donor strains, and both occurrences are very likely to lead to mutations within the recipient DNA. Here we report the construction of a new biological system addressing both the above mentioned problems in which the transfer helper functions are provided by a plasmid lacking a functional oriT. This system is compatible with all other replicons commonly used in conjugation experiments and further enables the use of diverse bacterial strains as donors. Plasmids containing large inserts were successfully conjugated and the plasmid modifications observed when E. coli S17-1 was used as donor were eliminated by the use of the new host-independent vector system. PMID:24595202
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
Charge-based MOSFET model based on the Hermite interpolation polynomial
NASA Astrophysics Data System (ADS)
Colalongo, Luigi; Richelli, Anna; Kovacs, Zsolt
2017-04-01
An accurate charge-based compact MOSFET model is developed using the third order Hermite interpolation polynomial to approximate the relation between surface potential and inversion charge in the channel. This new formulation of the drain current retains the same simplicity of the most advanced charge-based compact MOSFET models such as BSIM, ACM and EKV, but it is developed without requiring the crude linearization of the inversion charge. Hence, the asymmetry and the non-linearity in the channel are accurately accounted for. Nevertheless, the expression of the drain current can be worked out to be analytically equivalent to BSIM, ACM and EKV. Furthermore, thanks to this new mathematical approach the slope factor is rigorously defined in all regions of operation and no empirical assumption is required.
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
2015-09-03
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.
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.
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
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.
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
Jiang, T; Li, Y
1997-01-01
In an earlier paper (1996), we proposed a set of generalized defuzzification strategies which can be characterized as single-mode-oriented strategies. A single-mode-oriented defuzzification strategy, although useful in many research projects and real world applications, cannot be applied to a multimode situation where two or more distinct possibility peaks exist in its membership function distribution. In this paper, for multimode-oriented generalized defuzzification applications, a multimode-oriented polynomial transformation based defuzzification strategy (M-PTD) is introduced. The new M-PTD strategy, which uses the Kalman filter in parameter learning procedure, offers a constraint-free and self-renewal defuzzification solution.
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…
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device.
A trans-dimensional polynomial-spline parameterization for gradient-based geoacoustic inversion.
Steininger, Gavin; Dosso, Stan E; Holland, Charles W; Dettmer, Jan
2014-10-01
This paper presents a polynomial spline-based parameterization for trans-dimensional geoacoustic inversion. The parameterization is demonstrated for both simulated and measured data and shown to be an effective method of representing sediment geoacoustic profiles dominated by gradients, as typically occur, for example, in muddy seabeds. Specifically, the spline parameterization is compared using the deviance information criterion (DIC) to the standard stack-of-homogeneous layers parameterization for the inversion of bottom-loss data measured at a muddy seabed experiment site on the Malta Plateau. The DIC is an information criterion that is well suited to trans-D Bayesian inversion and is introduced to geoacoustics in this paper. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile and provides smaller overall uncertainties in geoacoustic parameters. In addition, the spline parameterization is found to be more parsimonious, and hence preferred, according to the DIC. The trans-dimensional polynomial spline approach is general, and applicable to any inverse problem for gradient-based profiles. [Work supported by ONR.].
Regression-based adaptive sparse polynomial dimensional decomposition for sensitivity analysis
NASA Astrophysics Data System (ADS)
Tang, Kunkun; Congedo, Pietro; Abgrall, Remi
2014-11-01
Polynomial dimensional decomposition (PDD) is employed in this work for global sensitivity analysis and uncertainty quantification of stochastic systems subject to a large number of random input variables. Due to the intimate structure between PDD and Analysis-of-Variance, PDD is able to provide simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to polynomial chaos (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of the standard method unaffordable for real engineering applications. In order to address this problem of curse of dimensionality, this work proposes a variance-based adaptive strategy aiming to build a cheap meta-model by sparse-PDD with PDD coefficients computed by regression. During this adaptive procedure, the model representation by PDD only contains few terms, so that the cost to resolve repeatedly the linear system of the least-square regression problem is negligible. The size of the final sparse-PDD representation is much smaller than the full PDD, since only significant terms are eventually retained. Consequently, a much less number of calls to the deterministic model is required to compute the final PDD coefficients.
NASA Astrophysics Data System (ADS)
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.
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
2016-07-06
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.
NASA Astrophysics Data System (ADS)
Dragomirescu, Florica Ioana
2012-11-01
The main motivation for a temporal stability investigation of initially localized perturbations in a swirling flow stability problem consists in pointing out the critical frequencies at which instability can sets in, an important key in predicting and understanding the flow particularities. The linearized disturbance equations define a second order ordinary differential equation with non-constant coefficients which we solve in order to determine the critical frequency in different physical parameters spaces. A non-classical polynomials based spectral method is proposed for the numerical treatment of the resulting generalized eigenvalue problem governing the stability of the flow. Numerical investigation are performed in the inviscid case for a moderate level of swirl and dominant temporal instability modes are retrieved for each Fourier component pair. The obtained values of the growth rate associated with the most amplified wavenumber are compared with existing inviscid temporal instability evaluations and good agreements are found.
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.
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.
Orthogonal polynomial Schauder bases in C[-1,1] with optimal growth of degrees
Skopina, M A
2001-04-30
For each {epsilon}>0 an orthogonal Schauder basis of algebraic polynomials P{sub n} in C[-1,1] is constructed such that the degrees of the polynomials have the estimate n(1+{epsilon}). This growth rate is the lowest possible.
NASA Astrophysics Data System (ADS)
Jeng, Jin-Tsong; Lee, Tsu-Tian
1998-03-01
In this paper, we propose a neural network model with a faster learning speed and a good approximate capability in the function approximation for solving worst-case identification of nonlinear systems H(infinity ) problems. Specifically, via the approximate transformable technique, we develop a Chebyshev Polynomials Based unified model neural network for solving the worst-case identification of nonlinear systems H(infinity ) problems. Based on this approximate transformable technique, the relationship between the single-layered neural network and multi-layered perceptron neural network is derived. It is shown that the Chebyshev Polynomials Based unified model neural network can be represented as a functional link network that is based on Chebyshev polynomials. We also derive a new learning algorithm such that the infinity norm of the transfer function from the input to the output is under a prescribed level. It turns out that the Chebyshev Polynomials Based unified model neural network not only has the same capability of universal approximator, but also has a faster learning speed than multi-layered perceptron or the recurrent neural network in the deterministic worst-case identification of nonlinear systems H(infinity ) problems.
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
On the Standard Model prediction for RK and RK*
NASA Astrophysics Data System (ADS)
Pattori, A.
2016-11-01
In this article a recent work is reviewed, where we evaluated the impact of radiative corrections in RK and RK * . We find that, employing the cuts presently applied by the LHCb Collaboration, such corrections do not exceed a few percent. Moreover, their effect is well described (and corrected) by existing Monte Carlo codes. Our analysis reinforces the interest of these observables as clean probe of physics beyond the Standard Model.
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
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.
Vector quantizer based on brightness maps for image compression with the polynomial transform
NASA Astrophysics Data System (ADS)
Escalante-Ramirez, Boris; Moreno-Gutierrez, Mauricio; Silvan-Cardenas, Jose L.
2002-11-01
We present a vector quantization scheme acting on brightness fields based on distance/distortion criteria correspondent with psycho-visual aspects. These criteria quantify sensorial distortion between vectors that represent either portions of a digital image or alternatively, coefficients of a transform-based coding system. In the latter case, we use an image representation model, namely the Hermite transform, that is based on some of the main perceptual characteristics of the human vision system (HVS) and in their response to light stimulus. Energy coding in the brightness domain, determination of local structure, code-book training and local orientation analysis are all obtained by means of the Hermite transform. This paper, for thematic reasons, is divided in four sections. The first one will shortly highlight the importance of having newer and better compression algorithms. This section will also serve to explain briefly the most relevant characteristics of the HVS, advantages and disadvantages related with the behavior of our vision in front of ocular stimulus. The second section shall go through a quick review of vector quantization techniques, focusing their performance on image treatment, as a preview for the image vector quantizer compressor actually constructed in section 5. Third chapter was chosen to concentrate the most important data gathered on brightness models. The building of this so-called brightness maps (quantification of the human perception on the visible objects reflectance), in a bi-dimensional model, will be addressed here. The Hermite transform, a special case of polynomial transforms, and its usefulness, will be treated, in an applicable discrete form, in the fourth chapter. As we have learned from previous works 1, Hermite transform has showed to be a useful and practical solution to efficiently code the energy within an image block, deciding which kind of quantization is to be used upon them (whether scalar or vector). It will also be
Linear precoding based on polynomial expansion: reducing complexity in massive MIMO.
Mueller, Axel; Kammoun, Abla; Björnson, Emil; Debbah, Mérouane
Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
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.
Suwansukho, Kajpanya; Sumriddetchkajorn, Sarun; Buranasiri, Prathan
2014-04-01
With our single-wavelength spectral-imaging-based Thai jasmine rice identification system, we emphasize here that a combination of an appropriate polynomial fitting function on the determined chain code and a well-trained neural network configuration is highly sufficient in achieving a low false acceptance rate (FAR) and a low false rejection rate (FRR). Experimental demonstration shows promising results in identifying our desired Thai jasmine rice from six unwanted rice varieties with FAR and FRR values of 6.2% and 7.1%, respectively. Additional key performances include a much faster identification time of 30.5 s, chemical-free analysis, robustness, and adaptive learning.
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
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.
NASA Astrophysics Data System (ADS)
Suwansukho, Kajpanya; Sumriddetchkajorn, Sarun; Buranasiri, Prathan
2013-06-01
We previously showed that a combination of image thresholding, chain coding, elliptic Fourier descriptors, and artificial neural network analysis provided a low false acceptance rate (FAR) and a false rejection rate (FRR) of 11.0% and 19.0%, respectively, in identify Thai jasmine rice from three unwanted rice varieties. In this work, we highlight that only a polynomial function fitting on the determined chain code and the neural network analysis are highly sufficient in obtaining a very low FAR of < 3.0% and a very low 0.3% FRR for the separation of Thai jasmine rice from Chainat 1 (CNT1), Prathumtani 1 (PTT1), and Hom-Pitsanulok (HPSL) rice varieties. With this proposed approach, the analytical time is tremendously suppressed from 4,250 seconds down to 2 seconds, implying extremely high potential in practical deployment.
NASA Astrophysics Data System (ADS)
Wang, Y. P.; Lu, Z. P.; Sun, D. S.; Wang, N.
2016-01-01
In order to better express the characteristics of satellite clock bias (SCB) and improve SCB prediction precision, this paper proposed a new SCB prediction model which can take physical characteristics of space-borne atomic clock, the cyclic variation, and random part of SCB into consideration. First, the new model employs a quadratic polynomial model with periodic items to fit and extract the trend term and cyclic term of SCB; then based on the characteristics of fitting residuals, a time series ARIMA ~(Auto-Regressive Integrated Moving Average) model is used to model the residuals; eventually, the results from the two models are combined to obtain final SCB prediction values. At last, this paper uses precise SCB data from IGS (International GNSS Service) to conduct prediction tests, and the results show that the proposed model is effective and has better prediction performance compared with the quadratic polynomial model, grey model, and ARIMA model. In addition, the new method can also overcome the insufficiency of the ARIMA model in model recognition and order determination.
NASA Astrophysics Data System (ADS)
Lv, Qian; Su, Tao; Zheng, Jibin
2016-01-01
In inverse synthetic aperture radar (ISAR) imaging of targets with complex motion, the azimuth echoes have to be modeled as multicomponent cubic phase signals (CPSs) after motion compensation. For the CPS model, the chirp rate and the quadratic chirp rate deteriorate the ISAR image quality due to the Doppler frequency shift; thus, an effective parameter estimation algorithm is required. This paper focuses on a parameter estimation algorithm for multicomponent CPSs based on the local polynomial ambiguity function (LPAF), which is simple and can be easily implemented via the complex multiplication and fast Fourier transform. Compared with the existing parameter estimation algorithm for CPS, the proposed algorithm can achieve a better compromise between performance and computational complexity. Then, the high-quality ISAR image can be obtained by the proposed LPAF-based ISAR imaging algorithm. The results of the simulated data demonstrate the effectiveness of the proposed algorithm.
Karagiannis, Georgios Lin, Guang
2014-02-15
Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.
Karagiannis, Georgios; Lin, Guang
2014-02-15
Generalized polynomial chaos (gPC) expansions allow the representation of the solution of a stochastic system as a series of polynomial terms. The number of gPC terms increases dramatically with the dimension of the random input variables. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs if the evaluations of the system are expensive, the evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solution, both in spacial and random domains, by coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spacial points via (1) Bayesian model average or (2) medial probability model, and their construction as functions on the spacial domain via spline interpolation. The former accounts the model uncertainty and provides Bayes-optimal predictions; while the latter, additionally, provides a sparse representation of the solution by evaluating the expansion on a subset of dominating gPC bases when represented as a gPC expansion. Moreover, the method quantifies the importance of the gPC bases through inclusion probabilities. We design an MCMC sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed method is suitable for, but not restricted to, problems whose stochastic solution is sparse at the stochastic level with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the good performance of the proposed method and make comparisons with others on 1D, 14D and 40D in random space elliptic stochastic partial differential equations.
Improved polynomial remainder sequences for Ore polynomials.
Jaroschek, Maximilian
2013-11-01
Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders. Different ways have been studied to make these as small as possible. The subresultant sequence of two polynomials is a polynomial remainder sequence in which the size of the coefficients is optimal in the generic case, but when taking the input from applications, the coefficients are often larger than necessary. We generalize two improvements of the subresultant sequence to Ore polynomials and derive a new bound for the minimal coefficient size. Our approach also yields a new proof for the results in the commutative case, providing a new point of view on the origin of the extraneous factors of the coefficients.
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
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)
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)
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
NASA Astrophysics Data System (ADS)
Sraj, Ihab; Zedler, Sarah E.; Knio, Omar M.; Jackson, Charles S.; Hoteit, Ibrahim
2016-12-01
The authors present a Polynomial Chaos (PC)-based Bayesian inference method for quantifying the uncertainties of the K-Profile Parametrization (KPP) within the MIT General Circulation Model (MITgcm) of the tropical pacific. The inference of the uncertain parameters is based on a Markov Chain Monte Carlo (MCMC) scheme that utilizes a newly formulated test statistic taking into account the different components representing the structures of turbulent mixing on both daily and seasonal timescales in addition to the data quality, and filters for the effects of parameter perturbations over those due to changes in the wind. To avoid the prohibitive computational cost of integrating the MITgcm model at each MCMC iteration, we build a surrogate model for the test statistic using the PC method. To filter out the noise in the model predictions and avoid related convergence issues, we resort to a Basis-Pursuit-DeNoising (BPDN) compressed sensing approach to determine the PC coefficients of a representative surrogate model. The PC surrogate is then used to evaluate the test statistic in the MCMC step for sampling the posterior of the uncertain parameters. Results of the posteriors indicate good agreement with the default values for two parameters of the KPP model namely the critical bulk and gradient Richardson numbers; while the posteriors of the remaining parameters were barely informative.
NASA Astrophysics Data System (ADS)
Mahata, Avik; Mukhopadhyay, Tanmoy; Adhikari, Sondipon
2016-03-01
Nano-twinned structures are mechanically stronger, ductile and stable than its non-twinned form. We have investigated the effect of varying twin spacing and twin boundary width (TBW) on the yield strength of the nano-twinned copper in a probabilistic framework. An efficient surrogate modelling approach based on polynomial chaos expansion has been proposed for the analysis. Effectively utilising 15 sets of expensive molecular dynamics simulations, thousands of outputs have been obtained corresponding to different sets of twin spacing and twin width using virtual experiments based on the surrogates. One of the major outcomes of this work is that there exists an optimal combination of twin boundary spacing and twin width until which the strength can be increased and after that critical point the nanowires weaken. This study also reveals that the yield strength of nano-twinned copper is more sensitive to TBW than twin spacing. Such robust inferences have been possible to be drawn only because of applying the surrogate modelling approach, which makes it feasible to obtain results corresponding to 40 000 combinations of different twin boundary spacing and twin width in a computationally efficient framework.
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.
Notes on Schubert, Grothendieck and Key Polynomials
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2016-03-01
We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco-Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.
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.
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...
Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision.
Kukelova, Zuzana; Bujnak, Martin; Pajdla, Tomas
2012-07-01
We present a method for solving systems of polynomial equations appearing in computer vision. This method is based on polynomial eigenvalue solvers and is more straightforward and easier to implement than the state-of-the-art Gröbner basis method since eigenvalue problems are well studied, easy to understand, and efficient and robust algorithms for solving these problems are available. We provide a characterization of problems that can be efficiently solved as polynomial eigenvalue problems (PEPs) and present a resultant-based method for transforming a system of polynomial equations to a polynomial eigenvalue problem. We propose techniques that can be used to reduce the size of the computed polynomial eigenvalue problems. To show the applicability of the proposed polynomial eigenvalue method, we present the polynomial eigenvalue solutions to several important minimal relative pose problems.
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…
An Analytic Formula for the A_2 Jack Polynomials
NASA Astrophysics Data System (ADS)
Mangazeev, Vladimir V.
2007-01-01
In this letter I shall review my joint results with Vadim Kuznetsov and Evgeny Sklyanin [Indag. Math. 14 (2003), 451-482] on separation of variables (SoV) for the An Jack polynomials. This approach originated from the work [RIMS Kokyuroku 919 (1995), 27-34] where the integral representations for the A2 Jack polynomials was derived. Using special polynomial bases I shall obtain a more explicit expression for the A2 Jack polynomials in terms of generalised hypergeometric functions.
NASA Astrophysics Data System (ADS)
Carvalho, Luis A.
2005-06-01
Zernike Polynomials have been successfully used for many years in optics. Nevertheless there are some recent discussions regarding their accuracy when applied to surfaces such as the human cornea. A set of synthetic surfaces resembling several common corneal anomalies was sampled and was also used to compute the optical path difference using a simple ray-tracing procedure. The Root Mean Square Error between the Zernike Polynomials fit and the theoretical elevation and WF error surface was computed for both surfaces and for all number of Zernike terms. We have found that RMSE for the simplest, most symmetric corneal surface (spherical shape) and for the most complex shape (post-radial keratotomy) both the optical path difference and surface elevation, for 1 through 36 Zernike terms, range from: 421.4 to 0.8 microns, and 421.4 to 8.2 microns, respectively; mean RMSE for maximum Zernike terms for both surfaces were 4.5 microns. Computations in this work suggest that, for surfaces such as post-RK, keratoconus or post-keratoplasty, even more than 36 terms may be necessary in order to obtain minimum precision requirements. We suggest that the number of Zernike Polynomial should not be a global fixed conventional value but rather based on specific surface properties.
Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials.
Lombardo, Rosaria; Beh, Eric J; Kroonenberg, Pieter M
2016-06-01
The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display-the polynomial biplot.
Uniform Asymptotics of Orthogonal Polynomials Arising from Coherent States
NASA Astrophysics Data System (ADS)
Dai, Dan; Hu, Weiying; Wang, Xiang-Sheng
2015-08-01
In this paper, we study a family of orthogonal polynomials {φ_n(z)} arising from nonlinear coherent states in quantum optics. Based on the three-term recurrence relation only, we obtain a uniform asymptotic expansion of φ_n(z) as the polynomial degree n tends to infinity. Our asymptotic results suggest that the weight function associated with the polynomials has an unusual singularity, which has never appeared for orthogonal polynomials in the Askey scheme. Our main technique is the Wang and Wong's difference equation method. In addition, the limiting zero distribution of the polynomials φ_n(z) is provided.
Distortion theorems for polynomials on a circle
Dubinin, V N
2000-12-31
Inequalities for the derivatives with respect to {phi}=arg z the functions ReP(z), |P(z)|{sup 2} and arg P(z) are established for an algebraic polynomial P(z) at points on the circle |z|=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.
Shan, Peng; Peng, Silong; Zhao, Yuhui; Tang, Liang
2016-03-01
An analysis of binary mixtures of hydroxyl compound by Attenuated Total Reflection Fourier transform infrared spectroscopy (ATR FT-IR) and classical least squares (CLS) yield large model error due to the presence of unmodeled components such as H-bonded components. To accommodate these spectral variations, polynomial-based least squares (LSP) and polynomial-based total least squares (TLSP) are proposed to capture the nonlinear absorbance-concentration relationship. LSP is based on assuming that only absorbance noise exists; while TLSP takes both absorbance noise and concentration noise into consideration. In addition, based on different solving strategy, two optimization algorithms (limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm and Levenberg-Marquardt (LM) algorithm) are combined with TLSP and then two different TLSP versions (termed as TLSP-LBFGS and TLSP-LM) are formed. The optimum order of each nonlinear model is determined by cross-validation. Comparison and analyses of the four models are made from two aspects: absorbance prediction and concentration prediction. The results for water-ethanol solution and ethanol-ethyl lactate solution show that LSP, TLSP-LBFGS, and TLSP-LM can, for both absorbance prediction and concentration prediction, obtain smaller root mean square error of prediction than CLS. Additionally, they can also greatly enhance the accuracy of estimated pure component spectra. However, from the view of concentration prediction, the Wilcoxon signed rank test shows that there is no statistically significant difference between each nonlinear model and CLS.
Efficient isolation of polynomial's real roots
NASA Astrophysics Data System (ADS)
Rouillier, Fabrice; Zimmermann, Paul
2004-01-01
This paper revisits an algorithm isolating the real roots of a univariate polynomial using Descartes' rule of signs. It follows work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick. Our first contribution is a generic algorithm which enables one to describe all the known algorithms based on Descartes' rule of sign and the bisection strategy in a unified framework. Using that framework, a new algorithm is presented, which is optimal in terms of memory usage and as fast as both Collins and Akritas' algorithm and Krandick's variant, independently of the input polynomial. From this new algorithm, we derive an adaptive semi-numerical version, using multi-precision interval arithmetic. We finally show that these critical optimizations have important consequences since our new algorithm still works with huge polynomials, including orthogonal polynomials of degree 1000 and more, which were out of reach of previous methods.
Chen, Huifang; Xie, Lei
2014-12-18
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.
NASA Astrophysics Data System (ADS)
Liu, Yang; Chen, Zhenyu; Yang, Zhile; Li, Kang; Tan, Jiubin
2016-12-01
The accuracy of surface measurement determines the manufacturing quality of membrane mirrors. Thus, an efficient and accurate measuring method is critical in membrane mirror fabrication. This paper formulates this measurement issue as a surface reconstruction problem and employs two-stage trained Zernike polynomials as an inline measuring tool to solve the optical surface measurement problem in the membrane mirror manufacturing process. First, all terms of the Zernike polynomial are generated and projected to a non-circular region as the candidate model pool. The training data are calculated according to the measured values of distance sensors and the geometrical relationship between the ideal surface and the installed sensors. Then the terms are selected by minimizing the cost function each time successively. To avoid the problem of ill-conditioned matrix inversion by the least squares method, the coefficient of each model term is achieved by modified elitist teaching-learning-based optimization. Subsequently, the measurement precision is further improved by a second stage of model refinement. Finally, every point on the membrane surface can be measured according to this model, providing more the subtle feedback information needed for the precise control of membrane mirror fabrication. Experimental results confirm that the proposed method is effective in a membrane mirror manufacturing system driven by negative pressure, and the measurement accuracy can achieve 15 µm.
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
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.
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…
Computing the roots of complex orthogonal and kernel polynomials
Saylor, P.E.; Smolarski, D.C.
1988-01-01
A method is presented to compute the roots of complex orthogonal and kernel polynomials. An important application of complex kernel polynomials is the acceleration of iterative methods for the solution of nonsymmetric linear equations. In the real case, the roots of orthogonal polynomials coincide with the eigenvalues of the Jacobi matrix, a symmetric tridiagonal matrix obtained from the defining three-term recurrence relationship for the orthogonal polynomials. In the real case kernel polynomials are orthogonal. The Stieltjes procedure is an algorithm to compute the roots of orthogonal and kernel polynomials bases on these facts. In the complex case, the Jacobi matrix generalizes to a Hessenberg matrix, the eigenvalues of which are roots of either orthogonal or kernel polynomials. The resulting algorithm generalizes the Stieljes procedure. It may not be defined in the case of kernel polynomials, a consequence of the fact that they are orthogonal with respect to a nonpositive bilinear form. (Another consequence is that kernel polynomials need not be of exact degree.) A second algorithm that is always defined is presented for kernel polynomials. Numerical examples are described.
Bouwmeester, Klaas; Han, Miao; Blanco-Portales, Rosario; Song, Wei; Weide, Rob; Guo, Li-Yun; van der Vossen, Edwin A G; Govers, Francine
2014-01-01
Late blight caused by the plant pathogenic oomycete Phytophthora infestans is known as one of the most destructive potato diseases. Plant breeders tend to employ NB-LRR-based resistance for introducing genetically controlled late blight resistance in their breeding lines. However, P. infestans is able to rapidly escape this type of resistance, and hence, NB-LRR-based resistance in potato cultivars is often not durable. Previously, we identified a novel type of Phytophthora resistance in Arabidopsis. This resistance is mediated by the cell surface receptor LecRK-I.9, which belongs to the family of L-type lectin receptor kinases. In this study, we report that expression of the Arabidopsis LecRK-I.9 gene in potato and Nicotiana benthamiana results in significantly enhanced late blight resistance. Transcriptional profiling showed strong reduction in salicylic acid (SA)-mediated defence gene expression in LecRK-I.9 transgenic potato lines (TPLs). In contrast, transcripts of two protease inhibitor genes accumulated to extreme high levels, suggesting that LecRK-I.9-mediated late blight resistance is relying on a defence response that includes activation of protease inhibitors. These results demonstrate that the functionality of LecRK-I.9 in Phytophthora resistance is maintained after interfamily transfer to potato and N. benthamiana and suggest that this novel type of LecRK-based resistance can be exploited in breeding strategies to improve durable late blight resistance in Solanaceous crops.
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
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.
Factoring Polynomials Modulo Composites,
2007-11-02
xA. This is an appropriate time to introduce the Sylvester Matrix . Definition 3.9 Given polynomials f,g as above, the Sylvester matrix off and g is...the coefficient matrix of the above system of equations. We denote this Sylvester matrix as S(f, g) by the following (1 + m) x (1 + m) matrix a, bm a11...bin-i bm S(f,g) = ao at : b- C R(l+m)x(l+m) aq-1 bo ao b0 the empty spaces are filled by zeros. The Sylvester matrix is the coefficient matrix of
Decidability of classes of algebraic systems in polynomial time
Anokhin, M I
2002-02-28
For some classes of algebraic systems several kinds of polynomial-time decidability are considered, which use an oracle performing signature operations and computing predicates. Relationships between various kinds of decidability are studied. Several results on decidability and undecidability in polynomial time are proved for some finitely based varieties of universal algebras.
Superoscillations with arbitrary polynomial shape
NASA Astrophysics Data System (ADS)
Chremmos, Ioannis; Fikioris, George
2015-07-01
We present a method for constructing superoscillatory functions the superoscillatory part of which approximates a given polynomial with arbitrarily small error in a fixed interval. These functions are obtained as the product of the polynomial with a sufficiently flat, bandlimited envelope function whose Fourier transform has at least N-1 continuous derivatives and an Nth derivative of bounded variation, N being the order of the polynomial. Polynomials of arbitrarily high order can be approximated if the Fourier transform of the envelope is smooth, i.e. a bump function.
Chaves, Rafael
2016-01-08
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
NASA Astrophysics Data System (ADS)
Chaves, Rafael
2016-01-01
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
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…
On a Perplexing Polynomial Puzzle
ERIC Educational Resources Information Center
Richmond, Bettina
2010-01-01
It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…
Estrada index and Chebyshev polynomials
NASA Astrophysics Data System (ADS)
Ginosar, Yuval; Gutman, Ivan; Mansour, Toufik; Schork, Matthias
2008-03-01
Let G be a graph whose eigenvalues are λ1, λ2,…, λn. The Estrada index of G is equal to ∑i=1ne. We point out certain classes of graphs whose characteristic polynomials are closely connected to the Chebyshev polynomials of the second kind. Various relations, in particular approximations, for the Estrada index of these graphs are obtained.
Controlling General Polynomial Networks
NASA Astrophysics Data System (ADS)
Cuneo, N.; Eckmann, J.-P.
2014-06-01
We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the motion of each particle is 1D. For polynomial interactions, we give sufficient conditions for Hörmander's "bracket condition" to hold, which implies the uniqueness of the steady state (if it exists), as well as the controllability of the associated system in control theory. These conditions are constructive; they are formulated in terms of inequivalence of the forces (modulo translations) and/or conditions on the topology of the connections. We illustrate our results with examples, including "conducting chains" of variable cross-section. This then extends the results for a simple chain obtained in Eckmann et al. in (Commun Math Phys 201:657-697, 1999).
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)
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.
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.
Numerical constructions involving Chebyshev polynomials
NASA Astrophysics Data System (ADS)
Lyakhovsky, V. D.
2017-02-01
We propose a new algorithm for the character expansion of tensor products of finite-dimensional irreducible representations of simple Lie algebras. The algorithm produces valid results for the algebras B 3, C 3, and D 3. We use the direct correspondence between Weyl anti-invariant functions and multivariate second-kind Chebyshev polynomials. We construct the triangular trigonometric polynomials for the algebra D 3.
Stochastic Estimation via Polynomial Chaos
2015-10-01
Program Manager Lethality, Vulnerability and Survivability Branch This report is published in the interest of scientific and technical...initial conditions for partial differential equations. Here, the elementary theory of the polynomial chaos is presented followed by the details of a...the elementary theory of the polynomial chaos is presented followed by the details of a number of example calculations where the statistical mean and
Polynomial force approximations and multifrequency atomic force microscopy.
Platz, Daniel; Forchheimer, Daniel; Tholén, Erik A; Haviland, David B
2013-01-01
We present polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip-surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high-resolution surface-property maps of polymer blend samples. The polynomial method is described as a special example of a more general approximative force reconstruction, where the aim is to determine model parameters that best approximate the measured force spectrum. This approximative approach is not limited to spectral data, and we demonstrate how it can be adapted to a force quadrature picture.
Properties of Leach-Flessas-Gorringe polynomials
NASA Astrophysics Data System (ADS)
Pursey, D. L.
1990-09-01
A generating function is obtained for the polynomials recently introduced by Leach, Flessas, and Gorringe [J. Math. Phys. 30, 406 (1989)], and is then used to relate the Leach-Flessas-Gorringe (or LFG) polynomials to Hermite polynomials. The generating function is also used to express a number of integrals involving the LFG polynomials as finite sums of parabolic cylinder functions.
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.
Multi-particle dynamical systems and polynomials
NASA Astrophysics Data System (ADS)
Demina, Maria V.; Kudryashov, Nikolai A.
2016-05-01
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi-particle dynamical system by finding polynomial solutions of partial differential equations is introduced. The method enables one to integrate a wide class of polynomial multi-particle dynamical systems. The general solutions of certain dynamical systems related to linear second-order partial differential equations are found. As a by-product of our results, new families of orthogonal polynomials are derived.
Quantum Hurwitz numbers and Macdonald polynomials
NASA Astrophysics Data System (ADS)
Harnad, J.
2016-11-01
Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.
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.
Chromatic polynomials of random graphs
NASA Astrophysics Data System (ADS)
Van Bussel, Frank; Ehrlich, Christoph; Fliegner, Denny; Stolzenberg, Sebastian; Timme, Marc
2010-04-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
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.
2015-06-01
cient parallel code for applying the operator. Our method constructs a polynomial preconditioner using a nonlinear least squares (NLLS) algorithm. We show...apply the underlying operator. Such a preconditioner can be very attractive in scenarios where one has a highly efficient parallel code for applying...repeatedly solve a large system of linear equations where one has an extremely fast parallel code for applying an underlying fixed linear operator
Li, Bing; Wang, Jia-Jia; Zhao, Yan; Kong, Fan-Mei; Guo, Ying
2017-01-01
Sucrose non-fermenting 1-related protein kinases (SnRKs) comprise a major family of signaling genes in plants and are associated with metabolic regulation, nutrient utilization and stress responses. This gene family has been proposed to be involved in sucrose signaling. In the present study, we cloned three copies of the TaSnRK2.10 gene from bread wheat on chromosomes 4A, 4B and 4D. The coding sequence (CDS) is 1086 bp in length and encodes a protein of 361 amino acids that exhibits functional domains shared with SnRK2s. Based on the haplotypes of TaSnRK2.10-4A (Hap-4A-H and Hap-4A-L), a cleaved amplified polymorphic sequence (CAPS) marker designated TaSnRK2.10-4A-CAPS was developed and mapped between the markers D-1092101 and D-100014232 using a set of recombinant inbred lines (RILs). The TaSnRK2.10-4B alleles (Hap-4B-G and Hap-4B-A) were transformed into allele-specific PCR (AS-PCR) markers TaSnRK2.10-4B-AS1 and TaSnRK2.10-4B-AS2, which were located between the markers D-1281577 and S-1862758. No diversity was found for TaSnRK2.10-4D. An association analysis using a natural population consisting of 128 winter wheat varieties in multiple environments showed that the thousand grain weight (TGW) and spike length (SL) of Hap-4A-H were significantly higher than those of Hap-4A-L, but pant height (PH) was significantly lower. PMID:28355304
Zhang, Zhao-Gui; Lv, Guang-de; Li, Bing; Wang, Jia-Jia; Zhao, Yan; Kong, Fan-Mei; Guo, Ying; Li, Si-Shen
2017-01-01
Sucrose non-fermenting 1-related protein kinases (SnRKs) comprise a major family of signaling genes in plants and are associated with metabolic regulation, nutrient utilization and stress responses. This gene family has been proposed to be involved in sucrose signaling. In the present study, we cloned three copies of the TaSnRK2.10 gene from bread wheat on chromosomes 4A, 4B and 4D. The coding sequence (CDS) is 1086 bp in length and encodes a protein of 361 amino acids that exhibits functional domains shared with SnRK2s. Based on the haplotypes of TaSnRK2.10-4A (Hap-4A-H and Hap-4A-L), a cleaved amplified polymorphic sequence (CAPS) marker designated TaSnRK2.10-4A-CAPS was developed and mapped between the markers D-1092101 and D-100014232 using a set of recombinant inbred lines (RILs). The TaSnRK2.10-4B alleles (Hap-4B-G and Hap-4B-A) were transformed into allele-specific PCR (AS-PCR) markers TaSnRK2.10-4B-AS1 and TaSnRK2.10-4B-AS2, which were located between the markers D-1281577 and S-1862758. No diversity was found for TaSnRK2.10-4D. An association analysis using a natural population consisting of 128 winter wheat varieties in multiple environments showed that the thousand grain weight (TGW) and spike length (SL) of Hap-4A-H were significantly higher than those of Hap-4A-L, but pant height (PH) was significantly lower.
Macdonald Polynomials in Superspace: Conjectural Definition and Positivity Conjectures
NASA Astrophysics Data System (ADS)
Blondeau-Fournier, Olivier; Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2012-07-01
We introduce a conjectural construction for an extension to superspace of the Macdonald polynomials. The construction, which depends on certain orthogonality and triangularity relations, is tested for high degrees. We conjecture a simple form for the norm of the Macdonald polynomials in superspace and a rather non-trivial expression for their evaluation. We study the limiting cases q = 0 and q = ∞, which lead to two families of Hall-Littlewood polynomials in superspace. We also find that the Macdonald polynomials in superspace evaluated at q = t = 0 or q = t = ∞ seem to generalize naturally the Schur functions. In particular, their expansion coefficients in the corresponding Hall-Littlewood bases appear to be polynomials in t with nonnegative integer coefficients. More strikingly, we formulate a generalization of the Macdonald positivity conjecture to superspace: the expansion coefficients of the Macdonald superpolynomials expanded into a modified version of the Schur superpolynomial basis (the q = t = 0 family) are polynomials in q and t with nonnegative integer coefficients.
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.
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).
Korobov polynomials of the first kind
NASA Astrophysics Data System (ADS)
Dolgy, D. V.; Kim, D. S.; Kim, T.
2017-01-01
In this paper, we study Korobov polynomials of the first kind from the viewpoint of umbral calculus and give new identities for them, associated with special polynomials which are derived from umbral calculus. Bibliography: 12 titles.
The Chebyshev Polynomials: Patterns and Derivation
ERIC Educational Resources Information Center
Sinwell, Benjamin
2004-01-01
The Chebyshev polynomials named after a Russian mathematician, Pafnuty Lvovich Chebyshev, have various mathematical applications. A process for obtaining Chebyshev polynomials, and a mathematical inquiry into the patterns they generate, is presented.
A New Generalisation of Macdonald Polynomials
NASA Astrophysics Data System (ADS)
Garbali, Alexandr; de Gier, Jan; Wheeler, Michael
2017-01-01
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q, t) and polynomial in a further two parameters (u, v). We evaluate these polynomials explicitly as a matrix product. At u = v = 0 they reduce to Macdonald polynomials, while at q = 0, u = v = s they recover a family of inhomogeneous symmetric functions originally introduced by Borodin.
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
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.
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.
Avila-Curiel, A; Shamah, T; Barragán, L; Chávez, A; Avila, Maria; Juárez, L
2004-03-01
A nutritional status index was built by modeling the mathematical function of the mean Z scores of weight for age, from 60,079 children under five years of age, selected in a probabilistic fashion from the Mexican population. The most precise mathematical model was a fifth degree polynomial. The correlation coefficient was between .937
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.
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
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.
NASA Astrophysics Data System (ADS)
Notaris, Sotirios
1995-03-01
Given a fixed n≥1, and a (monic) orthogonal polynomial πn(·)Dπn(·;dσ) relative to a positive measuredσ on the interval [a, b], one can define the nonnegative measure , to which correspond the (monic) orthogonal polynomials . The coefficients in the three-term recurrence relation for , whendσ is a Chebyshev measure of any of the four kinds, were obtained analytically in closed form by Gautschi and Li. Here, we give explicit formulae for the Stieltjes polynomials whendσ is any of the four Chebyshev measures. In addition, we show that the corresponding Gauss-Kronrod quadrature formulae for each of these , based on the zeros of and , have all the desirable properties of the interlacing of nodes, their inclusion in [-1, 1], and the positivity of all quadrature weights. Exceptions occur only for the Chebyshev measuredσ of the third or fourth kind andn even, in which case the inclusion property fails. The precise degree of exactness for each of these formulae is also determined.
Nägele, Thomas; Weckwerth, Wolfram
2014-01-01
Sucrose and trehalose-6-phosphate (T6P) are central compounds in the regulation and orchestration of whole plant metabolism, growth, development, and flowering. To evaluate their highly complex and regulatory interaction with the two conserved sugar and energy sensors Snf1-related protein kinase 1 (SnRK1), an AMPK-related protein kinase, and hexokinase (Hxk), we developed a kinetic model which demonstrates the subtle metabolic control of sugar homeostasis in a wide range of concentrations without the need for changes in gene expression or protein concentrations. Our model approach is based on a comprehensive set of published metabolite concentrations under various conditions and coupled enzyme kinetics accounting for the role of SnRK1 and Hxk in the sugar and energy homeostasis. This allowed us to investigate interactions between sugar phosphates, such as T6P, which are metabolic inhibitors of SnRK1 and Hxk, and sucrose synthesis during the transition from carbon deficiency to availability. Model simulations and sensitivity analyses indicated that slight changes in SnRK1 activity induced by allosteric effectors may be sufficient to explain a dramatic readjustment of metabolic homeostasis. This may comprise up to 10-fold changes in metabolite concentrations. Further, the Hxk/T6P/SnRK1 interaction implemented in the model supports the interpretation of phenotypic and transcriptomic changes observed in Hxk overexpressing plants. Finally, our approach presents a theoretical framework to kinetically link metabolic networks to underlying regulatory instances. PMID:25120550
Freeform surface of progressive addition lens represented by Zernike polynomials
NASA Astrophysics Data System (ADS)
Li, Yiyu; Xia, Risheng; Chen, Jiaojie; Feng, Haihua; Yuan, Yimin; Zhu, Dexi; Li, Chaohong
2016-10-01
We used the explicit expression of Zernike polynomials in Cartesian coordinates to fit and describe the freeform surface of progressive addition lens (PAL). The derivatives of Zernike polynomials can easily be calculated from the explicit expression and used to calculate the principal curvatures of freeform surface based on differential geometry. The surface spherical power and surface astigmatism of the freeform surface were successfully derived from the principal curvatures. By comparing with the traditional analytical method, Zernike polynomials with order of 20 is sufficient to represent the freeform surface with nanometer accuracy if dense sampling of the original surface is achieved. Therefore, the data files which contain the massive sampling points of the freeform surface for the generation of the trajectory of diamond tool tip required by diamond machine for PAL manufacture can be simplified by using a few Zernike coefficients.
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.
The stable computation of formal orthogonal polynomials
NASA Astrophysics Data System (ADS)
Beckermann, Bernhard
1996-12-01
For many applications - such as the look-ahead variants of the Lanczos algorithm - a sequence of formal (block-)orthogonal polynomials is required. Usually, one generates such a sequence by taking suitable polynomial combinations of a pair of basis polynomials. These basis polynomials are determined by a look-ahead generalization of the classical three term recurrence, where the polynomial coefficients are obtained by solving a small system of linear equations. In finite precision arithmetic, the numerical orthogonality of the polynomials depends on a good choice of the size of the small systems; this size is usually controlled by a heuristic argument such as the condition number of the small matrix of coefficients. However, quite often it happens that orthogonality gets lost.
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.
Explaining the RK and RD(*) anomalies with vector leptoquarks
NASA Astrophysics Data System (ADS)
Sahoo, Suchismita; Mohanta, Rukmani; Giri, Anjan K.
2017-02-01
Recently, the B factories BABAR and Belle as well as the LHCb experiment have reported several anomalies in the semileptonic B meson decays, such as the RK and RD(*) etc. We investigate these deviations by considering the vector leptoquarks relevant for both b →s l+l- and b →c l ν¯ l transitions. The leptoquark parameter space is constrained by using the experimentally measured branching ratios of Bs→l+l- , B ¯ →Xsl+l-(ν ν ¯ ) , and Bu+→l+νl processes. Using the constrained leptoquark couplings, we compute the branching ratios, forward-backward asymmetries, τ , and D* polarization parameters in the B ¯ →D(*)l ν¯ l processes. We find that the vector leptoquarks can explain both the RD(*) and RK anomalies, simultaneously. Furthermore, we study the rare leptonic Bu,c *→l ν ¯ decay processes in this model.
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.
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.
Tsallis p, q-deformed Touchard polynomials and Stirling numbers
NASA Astrophysics Data System (ADS)
Herscovici, O.; Mansour, T.
2017-01-01
In this paper, we develop and investigate a new two-parametrized deformation of the Touchard polynomials, based on the definition of the NEXT q-exponential function of Tsallis. We obtain new generalizations of the Stirling numbers of the second kind and of the binomial coefficients and represent two new statistics for the set partitions.
Sauerbrei, Willi; Royston, Patrick; Look, Maxime
2007-06-01
The Cox proportional hazards model has become the standard for the analysis of survival time data in cancer and other chronic diseases. In most studies, proportional hazards (PH) are assumed for covariate effects. With long-term follow-up, the PH assumption may be violated, leading to poor model fit. To accommodate non-PH effects, we introduce a new procedure, MFPT, an extension of the multivariable fractional polynomial (MFP) approach, to do the following: (1) select influential variables; (2) determine a sensible dose-response function for continuous variables; (3) investigate time-varying effects; (4) model such time-varying effects on a continuous scale. Assuming PH initially, we start with a detailed model-building step, including a search for possible non-linear functions for continuous covariates. Sometimes a variable with a strong short-term effect may appear weak or non-influential if 'averaged' over time under the PH assumption. To protect against omitting such variables, we repeat the analysis over a restricted time-interval. Any additional prognostic variables identified by this second analysis are added to create our final time-fixed multivariable model. Using a forward-selection algorithm we search for possible improvements in fit by adding time-varying covariates. The first part to create a final time-fixed model does not require the use of MFP. A model may be given from 'outside' or a different strategy may be preferred for this part. This broadens the scope of the time-varying part. To motivate and illustrate the methodology, we create prognostic models from a large database of patients with primary breast cancer. Non-linear time-fixed effects are found for progesterone receptor status and number of positive lymph nodes. Highly statistically significant time-varying effects are present for progesterone receptor status and tumour size.
Fractal Trigonometric Polynomials for Restricted Range Approximation
NASA Astrophysics Data System (ADS)
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016-05-01
One-sided approximation tackles the problem of approximation of a prescribed function by simple traditional functions such as polynomials or trigonometric functions that lie completely above or below it. In this paper, we use the concept of fractal interpolation function (FIF), precisely of fractal trigonometric polynomials, to construct one-sided uniform approximants for some classes of continuous functions.
Polynomial solutions of nonlinear integral equations
NASA Astrophysics Data System (ADS)
Dominici, Diego
2009-05-01
We analyze the polynomial solutions of a nonlinear integral equation, generalizing the work of Bender and Ben-Naim (2007 J. Phys. A: Math. Theor. 40 F9, 2008 J. Nonlinear Math. Phys. 15 (Suppl. 3) 73). We show that, in some cases, an orthogonal solution exists and we give its general form in terms of kernel polynomials.
New pole placement algorithm - Polynomial matrix approach
NASA Technical Reports Server (NTRS)
Shafai, B.; Keel, L. H.
1990-01-01
A simple and direct pole-placement algorithm is introduced for dynamical systems having a block companion matrix A. The algorithm utilizes well-established properties of matrix polynomials. Pole placement is achieved by appropriately assigning coefficient matrices of the corresponding matrix polynomial. This involves only matrix additions and multiplications without requiring matrix inversion. A numerical example is given for the purpose of illustration.
Tutte polynomial in functional magnetic resonance imaging
NASA Astrophysics Data System (ADS)
García-Castillón, Marlly V.
2015-09-01
Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.
DIFFERENTIAL CROSS SECTION ANALYSIS IN KAON PHOTOPRODUCTION USING ASSOCIATED LEGENDRE POLYNOMIALS
P. T. P. HUTAURUK, D. G. IRELAND, G. ROSNER
2009-04-01
Angular distributions of differential cross sections from the latest CLAS data sets,6 for the reaction γ + p→K+ + Λ have been analyzed using associated Legendre polynomials. This analysis is based upon theoretical calculations in Ref. 1 where all sixteen observables in kaon photoproduction can be classified into four Legendre classes. Each observable can be described by an expansion of associated Legendre polynomial functions. One of the questions to be addressed is how many associated Legendre polynomials are required to describe the data. In this preliminary analysis, we used data models with different numbers of associated Legendre polynomials. We then compared these models by calculating posterior probabilities of the models. We found that the CLAS data set needs no more than four associated Legendre polynomials to describe the differential cross section data. In addition, we also show the extracted coefficients of the best model.
M-Interval Orthogonal Polynomial Estimators with Applications
NASA Astrophysics Data System (ADS)
Jaroszewicz, Boguslaw Emanuel
In this dissertation, adaptive estimators of various statistical nonlinearities are constructed and evaluated. The estimators are based on classical orthogonal polynomials which allows an exact computation of convergence rates. The first part of the dissertation is devoted to the estimation of one- and multi-dimensional probability density functions. The most attractive computationally is the Legendre estimator, which corresponds to the mean square segmented polynomial approximation of a pdf. Exact bounds for two components of the estimation error--deterministic bias and random error--are derived for all the polynomial estimators. The bounds on the bias are functions of the "smoothness" of the estimated pdf as measured by the number of continuous derivatives the pdf possesses. Adaptively estimated the optimum number of orthonormal polynomials minimizes the total error. In the second part, the theory of polynomial estimators is applied to the estimation of derivatives of pdf and regression functions. The optimum detectors for small signals in nongaussian noise, as well as any kind of statistical filtering involving likelihood function, are based on the nonlinearity which is a ratio of the derivative of the pdf and the pdf itself. Several different polynomial estimators of this nonlinearity are developed and compared. The theory of estimation is then extended to the multivariable case. The partial derivative nonlinearity is used for detection of signals in dependent noise. When the dimensionality of the nonlinearity is very large, the transformed Hermite estimators are particularly useful. The estimators can be viewed as two-stage filters: the first stage is a pre -whitening filter optimum in gaussian noise and the second stage is a nonlinear filter, which improves performance in nongaussian noise. Filtering of this type can be applied to predictive coding, nonlinear identification and other estimation problems involving a conditional expected value. In the third
Central suboptimal H ∞ control design for nonlinear polynomial systems
NASA Astrophysics Data System (ADS)
Basin, Michael V.; Shi, Peng; Calderon-Alvarez, Dario
2011-05-01
This article presents the central finite-dimensional H ∞ regulator for nonlinear polynomial systems, which is suboptimal for a given threshold γ with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, the article reduces the original H ∞ control problem to the corresponding optimal H 2 control problem, using this technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), 'State-space Solutions to Standard H 2 and H ∞ Control Problems', IEEE Transactions on Automatic Control, 34, 831-847]. This article yields the central suboptimal H ∞ regulator for nonlinear polynomial systems in a closed finite-dimensional form, based on the optimal H 2 regulator obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008b), 'Optimal Controller for Uncertain Stochastic Polynomial Systems', Journal of the Franklin Institute, 345, 293-302]. Numerical simulations are conducted to verify performance of the designed central suboptimal regulator for nonlinear polynomial systems against the central suboptimal H ∞ regulator available for the corresponding linearised system.
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
Konakli, Katerina Sudret, Bruno
2016-09-15
The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely 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
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
NASA Astrophysics Data System (ADS)
Ben Mahmoud, B. Karem
2009-05-01
In this paper, a temperature dynamical profiling inside vacuum-insulated Hydrogen cryogenic vessels is yielded. The theoretical investigations are based on the similarity between the convective heat equation and the characteristic differential equation of the Boubaker polynomials.
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.
Adapted polynomial chaos expansion for failure detection
NASA Astrophysics Data System (ADS)
Paffrath, M.; Wever, U.
2007-09-01
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.
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.
Gauss-Lobatto to Bernstein polynomials transformation
NASA Astrophysics Data System (ADS)
Coluccio, Loredana; Eisinberg, Alfredo; Fedele, Giuseppe
2008-12-01
The aim of this paper is to transform a polynomial expressed as a weighted sum of discrete orthogonal polynomials on Gauss-Lobatto nodes into Bernstein form and vice versa. Explicit formulas and recursion expressions are derived. Moreover, an efficient algorithm for the transformation from Gauss-Lobatto to Bernstein is proposed. Finally, in order to show the robustness of the proposed algorithm, experimental results are reported.
The Chinese Remainder Problem and Polynomial Interpolation.
1986-08-01
27709 86a 10 7 16 UNIVERSITY OF WISCONSIN-MADISON MATEMATICS RESEARCH CENTER THE CHINESE REMAINDER PROBLEM AND POLYNOMIAL INTERPOLATION Isaac J...Classifications: lOA10, 41A10 Key Words: Chinese Remainder Theorem, Polynomial Interpolation Work Unit Number 3 (Numerical Analysis and Scientific...Street Wisconsin Numerical Analysis and Madison, Wisconsin 53705 Scientific Computing " 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE U. S
WalRK two component system of Bacillus anthracis responds to temperature and antibiotic stress.
Dhiman, Alisha; Gopalani, Monisha; Bhatnagar, Rakesh
2015-04-17
WalRK Two Component System (TCS) of Bacillus anthracis forms a functional TCS. This report elaborates upon the WalRK genomic architecture, promoter structure, promoter activity and expression under various stress conditions in B. anthracis. 5' RACE located the WalRK functional promoter within 317 bp region upstream of WalR. Reporter gene assays demonstrated maximal promoter activity during early growth phases indicating utility in exponential stages of growth. qRT-PCR showed upregulation of WalRK transcripts during temperature and antibiotic stress. However, WalR overexpression did not affect the tested antibiotic MIC values in B. anthracis. Collectively, these results confirm that WalRK responds to cell envelope stress in B. anthracis.
Baxter Operator Formalism for Macdonald Polynomials
NASA Astrophysics Data System (ADS)
Gerasimov, Anton; Lebedev, Dimitri; Oblezin, Sergey
2013-11-01
We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely, we construct a bispectral pair of mutually commuting Baxter operators such that the Macdonald polynomials are their common eigenfunctions. The bispectral pair of Baxter operators is closely related to the bispectral pair of recursive operators for Macdonald polynomials leading to various families of their integral representations. We also construct the Baxter operator formalism for the q-deformed {{gl}_{ell+1}} -Whittaker functions and the Jack polynomials obtained by degenerations of the Macdonald polynomials associated with the type A ℓ root system. This note provides a generalization of our previous results on the Baxter operator formalism for the Whittaker functions. It was demonstrated previously that Baxter operator formalism for the Whittaker functions has deep connections with representation theory. In particular, the Baxter operators should be considered as elements of appropriate spherical Hecke algebras and their eigenvalues are identified with local Archimedean L-factors associated with admissible representations of reductive groups over {{R}}. We expect that the Baxter operator formalism for the Macdonald polynomials has an interpretation in representation theory over higher-dimensional local/global fields.
Extending Romanovski polynomials in quantum mechanics
NASA Astrophysics Data System (ADS)
Quesne, C.
2013-12-01
Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schrödinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.
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.
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
Sun, Liang; Wang, Yan-Ping; Chen, Pei; Ren, Jie; Ji, Kai; Li, Qian; Li, Ping; Dai, Sheng-Jie; Leng, Ping
2011-11-01
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.
On λ-Bell polynomials associated with umbral calculus
NASA Astrophysics Data System (ADS)
Kim, T.; Kim, D. S.
2017-01-01
In this paper, we introduce some new λ-Bell polynomials and Bell polynomials of the second kind and investigate properties of these polynomials. Using our investigation, we derive some new identities for the two kinds of λ-Bell polynomials arising from umbral calculus.
Modeling a Temporally Evolving Atmosphere with Zernike Polynomials
2012-09-01
Systems, SPIE Press, 2010 5. J.W. Goodman , Statistical Optics , John Wiley & Sons, Inc., New York, NY, 1985 6. R. J. Noll, "Zernike Polynomials and...temporal model of phase screen generation. The long standing Fourier transform (FT) based method assumes the frozen flow hypothesis holds, where... optical tilt. 1. INTRODUCTION For conventional imaging systems, Geosynchronous Earth Orbit (GEO) space objects cannot be resolved due to
Quantum circuits and low-degree polynomials over {{{F}}_\\mathsf{2}}
NASA Astrophysics Data System (ADS)
Montanaro, Ashley
2017-02-01
In this work we explore a correspondence between quantum circuits and low-degree polynomials over the finite field {{{F}}2} . Any quantum circuit made up of Hadamard, Z, controlled-Z and controlled-controlled-Z gates gives rise to a degree-3 polynomial over {{{F}}2} such that calculating quantum circuit amplitudes is equivalent to counting zeroes of the corresponding polynomial. We exploit this connection, which is especially clean and simple for this particular gate set, in two directions. First, we give proofs of classical hardness results based on quantum circuit concepts. Second, we find efficient classical simulation algorithms for certain classes of quantum circuits based on efficient algorithms for classes of polynomials.
Quasi-kernel polynomials and convergence results for quasi-minimal residual iterations
NASA Technical Reports Server (NTRS)
Freund, Roland W.
1992-01-01
Recently, Freund and Nachtigal have proposed a novel polynominal-based iteration, the quasi-minimal residual algorithm (QMR), for solving general nonsingular non-Hermitian linear systems. Motivated by the QMR method, we have introduced the general concept of quasi-kernel polynomials, and we have shown that the QMR algorithm is based on a particular instance of quasi-kernel polynomials. In this paper, we continue our study of quasi-kernel polynomials. In particular, we derive bounds for the norms of quasi-kernel polynomials. These results are then applied to obtain convergence theorems both for the QMR method and for a transpose-free variant of QMR, the TFQMR algorithm.
Knot polynomials in the first non-symmetric representation
NASA Astrophysics Data System (ADS)
Anokhina, A.; Mironov, A.; Morozov, A.; Morozov, And.
2014-05-01
We describe the explicit form and the hidden structure of the answer for the HOMFLY polynomial for the figure-8 and some other 3-strand knots in representation [21]. This is the first result for non-torus knots beyond (anti)symmetric representations, and its evaluation is far more complicated. We provide a whole variety of different arguments, allowing one to guess the answer for the figure-8 knot, which can be also partly used in more complicated situations. Finally we report the result of exact calculation for figure-8 and some other 3-strand knots based on the previously developed sophisticated technique of multi-strand calculations. We also discuss a formula for the superpolynomial in representation [21] for the figure-8 knot, which heavily relies on the conjectural form of superpolynomial expansion nearby the special polynomial point. Generalizations and details will be presented elsewhere.
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.
Cusp Catastrophe Polynomial Model: Power and Sample Size Estimation
Chen, Ding-Geng(Din); Chen, Xinguang(Jim); Lin, Feng; Tang, Wan; Lio, Y. L.; Guo, (Tammy) Yuanyuan
2016-01-01
Guastello’s polynomial regression method for solving cusp catastrophe model has been widely applied to analyze nonlinear behavior outcomes. However, no statistical power analysis for this modeling approach has been reported probably due to the complex nature of the cusp catastrophe model. Since statistical power analysis is essential for research design, we propose a novel method in this paper to fill in the gap. The method is simulation-based and can be used to calculate statistical power and sample size when Guastello’s polynomial regression method is used to cusp catastrophe modeling analysis. With this novel approach, a power curve is produced first to depict the relationship between statistical power and samples size under different model specifications. This power curve is then used to determine sample size required for specified statistical power. We verify the method first through four scenarios generated through Monte Carlo simulations, and followed by an application of the method with real published data in modeling early sexual initiation among young adolescents. Findings of our study suggest that this simulation-based power analysis method can be used to estimate sample size and statistical power for Guastello’s polynomial regression method in cusp catastrophe modeling. PMID:27158562
Chemical Reaction Networks for Computing Polynomials.
Salehi, Sayed Ahmad; Parhi, Keshab K; Riedel, Marc D
2017-01-20
Chemical reaction networks (CRNs) provide a fundamental model in the study of molecular systems. Widely used as formalism for the analysis of chemical and biochemical systems, CRNs have received renewed attention as a model for molecular computation. This paper demonstrates that, with a new encoding, CRNs can compute any set of polynomial functions subject only to the limitation that these functions must map the unit interval to itself. These polynomials can be expressed as linear combinations of Bernstein basis polynomials with positive coefficients less than or equal to 1. In the proposed encoding approach, each variable is represented using two molecular types: a type-0 and a type-1. The value is the ratio of the concentration of type-1 molecules to the sum of the concentrations of type-0 and type-1 molecules. The proposed encoding naturally exploits the expansion of a power-form polynomial into a Bernstein polynomial. Molecular encoders for converting any input in a standard representation to the fractional representation as well as decoders for converting the computed output from the fractional to a standard representation are presented. The method is illustrated first for generic CRNs; then chemical reactions designed for an example are mapped to DNA strand-displacement reactions.
A robust polynomial principal component analysis for seismic noise attenuation
NASA Astrophysics Data System (ADS)
Wang, Yuchen; Lu, Wenkai; Wang, Benfeng; Liu, Lei
2016-12-01
Random and coherent noise attenuation is a significant aspect of seismic data processing, especially for pre-stack seismic data flattened by normal moveout correction or migration. Signal extraction is widely used for pre-stack seismic noise attenuation. Principle component analysis (PCA), one of the multi-channel filters, is a common tool to extract seismic signals, which can be realized by singular value decomposition (SVD). However, when applying the traditional PCA filter to seismic signal extraction, the result is unsatisfactory with some artifacts when the seismic data is contaminated by random and coherent noise. In order to directly extract the desired signal and fix those artifacts at the same time, we take into consideration the amplitude variation with offset (AVO) property and thus propose a robust polynomial PCA algorithm. In this algorithm, a polynomial constraint is used to optimize the coefficient matrix. In order to simplify this complicated problem, a series of sub-optimal problems are designed and solved iteratively. After that, the random and coherent noise can be effectively attenuated simultaneously. Applications on synthetic and real data sets note that our proposed algorithm can better suppress random and coherent noise and have a better performance on protecting the desired signals, compared with the local polynomial fitting, conventional PCA and a L1-norm based PCA method.
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.
Supersymmetric pairing of kinks for polynomial nonlinearities
Rosu, H.C.; Cornejo-Perez, O.
2005-04-01
We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on reaction-diffusion equations in the traveling frame and damped-anharmonic-oscillator equations. We also report an interesting pairing of the kink solutions, a result obtained by reversing the factorization brackets in the supersymmetric quantum-mechanical style. In this way, one gets ordinary differential equations with a different polynomial nonlinearity possessing kink solutions of different width but propagating at the same velocity as the kinks of the original equation. This pairing of kinks could have many applications. We illustrate the mathematical procedure with several important cases, among which are the generalized Fisher equation, the FitzHugh-Nagumo equation, and the polymerization fronts of microtubules.
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.
Enhancing sparsity of Hermite polynomial expansions by iterative rotations
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.
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
Parabolic Refined Invariants and Macdonald Polynomials
NASA Astrophysics Data System (ADS)
Chuang, Wu-yen; Diaconescu, Duiliu-Emanuel; Donagi, Ron; Pantev, Tony
2015-05-01
A string theoretic derivation is given for the conjecture of Hausel, Letellier and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of a local root stack, generalizing previous work of the first two authors in collaboration with Pan. Haiman's geometric construction for Macdonald polynomials is shown to emerge naturally in this context via geometric engineering. In particular this yields a new conjectural relation between Macdonald polynomials and refined local orbifold curve counting invariants. The string theoretic approach also leads to a new spectral cover construction for parabolic Higgs bundles in terms of holomorphic symplectic orbifolds.
Source emission-pattern polynomial representation
NASA Astrophysics Data System (ADS)
Flores-Hernandez, Ricardo; De Villa, Francisco
1990-12-01
A method to obtain accurate thickness data to characterize the emission patterns of evaporation sources is described. Thickness data is obtained through digital image processing algorithms applied to the monochromatic transmission bands digitized from a set of multilayer Fabry-Perot filters deposited on large flat circular substrates. These computer image-processed taper-thickness patterns are reduced to orthonormal polynomial series expansions in two steps, using Tschebyshev and associated Legendre polynomials. The circular glass substrates employed to characterize each type of evaporation source are kept stationary during the evaporation process of evaporation of each layer to obtain the specific thickness distribution for each type of source.
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
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
2012-01-06
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.
Real-time task recognition in cataract surgery videos using adaptive spatiotemporal polynomials.
Quellec, Gwénolé; Lamard, Mathieu; Cochener, Béatrice; Cazuguel, Guy
2015-04-01
This paper introduces a new algorithm for recognizing surgical tasks in real-time in a video stream. The goal is to communicate information to the surgeon in due time during a video-monitored surgery. The proposed algorithm is applied to cataract surgery, which is the most common eye surgery. To compensate for eye motion and zoom level variations, cataract surgery videos are first normalized. Then, the motion content of short video subsequences is characterized with spatiotemporal polynomials: a multiscale motion characterization based on adaptive spatiotemporal polynomials is presented. The proposed solution is particularly suited to characterize deformable moving objects with fuzzy borders, which are typically found in surgical videos. Given a target surgical task, the system is trained to identify which spatiotemporal polynomials are usually extracted from videos when and only when this task is being performed. These key spatiotemporal polynomials are then searched in new videos to recognize the target surgical task. For improved performances, the system jointly adapts the spatiotemporal polynomial basis and identifies the key spatiotemporal polynomials using the multiple-instance learning paradigm. The proposed system runs in real-time and outperforms the previous solution from our group, both for surgical task recognition ( Az = 0.851 on average, as opposed to Az = 0.794 previously) and for the joint segmentation and recognition of surgical tasks ( Az = 0.856 on average, as opposed to Az = 0.832 previously).
On Arithmetic-Geometric-Mean Polynomials
ERIC Educational Resources Information Center
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
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.
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…
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.
Least squares polynomial fits and their accuracy
NASA Technical Reports Server (NTRS)
Lear, W. M.
1977-01-01
Equations are presented which attempt to fit least squares polynomials to tables of date. It is concluded that much data are needed to reduce the measurement error standard deviation by a significant amount, however at certain points great accuracy is attained.
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.
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.
Multiple Representations and the Understanding of Taylor Polynomials
ERIC Educational Resources Information Center
Habre, Samer
2009-01-01
The study of Maclaurin and Taylor polynomials entails the comprehension of various new mathematical ideas. Those polynomials are initially discussed at the college level in a calculus class and then again in a course on numerical methods. This article investigates the understanding of these polynomials by students taking a numerical methods class…
The Gibbs Phenomenon for Series of Orthogonal Polynomials
ERIC Educational Resources Information Center
Fay, T. H.; Kloppers, P. Hendrik
2006-01-01
This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…
Inverse of polynomial matrices in the irreducible form
NASA Technical Reports Server (NTRS)
Chang, Fan R.; Shieh, Leang S.; Mcinnis, Bayliss C.
1987-01-01
An algorithm is developed for finding the inverse of polynomial matrices in the irreducible form. The computational method involves the use of the left (right) matrix division method and the determination of linearly dependent vectors of the remainders. The obtained transfer function matrix has no nontrivial common factor between the elements of the numerator polynomial matrix and the denominator polynomial.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Global Monte Carlo Simulation with High Order Polynomial Expansions
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-12-13
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, possibly increasing the communication across a loosely coupled system and thereby improving convergence over the conventional fission bank approach used in most production Monte Carlo codes. The project examined a number of basis functions, including global Legendre polynomials as well as “local” piecewise polynomials such as finite element hat functions and higher order versions. The global FET showed an improvement in convergence over the conventional fission bank approach. The local FET methods showed some advantages versus global polynomials in handling geometries with discontinuous material properties. The conventional finite element hat functions had the disadvantage that the expansion coefficients could not be estimated directly but had to be obtained by solving a linear system whose matrix elements were estimated. An alternative fission matrix-based response matrix algorithm was formulated. Studies were made of two alternative applications of the FET, one based on the kernel density estimator and one based on Arnoldi’s method of minimized iterations. Preliminary results for both methods indicate improvements in fission source convergence. These developments indicate that the FET has promise for speeding up Monte Carlo fission source
Polynomial search and global modeling: Two algorithms for modeling chaos.
Mangiarotti, S; Coudret, R; Drapeau, L; Jarlan, L
2012-10-01
Global modeling aims to build mathematical models of concise description. Polynomial Model Search (PoMoS) and Global Modeling (GloMo) are two complementary algorithms (freely downloadable at the following address: http://www.cesbio.ups-tlse.fr/us/pomos_et_glomo.html) designed for the modeling of observed dynamical systems based on a small set of time series. Models considered in these algorithms are based on ordinary differential equations built on a polynomial formulation. More specifically, PoMoS aims at finding polynomial formulations from a given set of 1 to N time series, whereas GloMo is designed for single time series and aims to identify the parameters for a selected structure. GloMo also provides basic features to visualize integrated trajectories and to characterize their structure when it is simple enough: One allows for drawing the first return map for a chosen Poincaré section in the reconstructed space; another one computes the Lyapunov exponent along the trajectory. In the present paper, global modeling from single time series is considered. A description of the algorithms is given and three examples are provided. The first example is based on the three variables of the Rössler attractor. The second one comes from an experimental analysis of the copper electrodissolution in phosphoric acid for which a less parsimonious global model was obtained in a previous study. The third example is an exploratory case and concerns the cycle of rainfed wheat under semiarid climatic conditions as observed through a vegetation index derived from a spatial sensor.
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.
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.
Jack polynomial fractional quantum Hall states and their generalizations
NASA Astrophysics Data System (ADS)
Baratta, Wendy; Forrester, Peter J.
2011-02-01
In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=-(r-1)/(k+1), (r-1) and (k+1) relatively prime, and with partition given in terms of its frequencies by [n0k0k0k⋯0m] satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.
Polynomial chaos representation of databases on manifolds
NASA Astrophysics Data System (ADS)
Soize, C.; Ghanem, R.
2017-04-01
Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
A polynomial function of gait performance.
Giaquinto, Salvatore; Galli, Manuela; Nolfe, Giuseppe
2007-01-01
A mathematical data processing method is presented that represents a further step in gait analysis. The proposed polynomial regression analysis is reliable in assessing differences in the same patient and even on the same day. The program also calculates the confidence interval of the whole curve. The procedure was applied to normal subjects in order to collect normative data. When a new subject is tested, the polynomial function obtained is graphically superimposed on control data. Should the new curve fall within the limits described by normative data, it is considered to be equivalent. The procedure can be applied to the same subject, either normal or pathological, for retesting kinematic characteristics. The gait cycle is analyzed as a whole, not point-by-point. Ten normal subjects and two patients, one with recent- and the other with late-onset hemiplegia, were tested. Multiple baseline evaluation is recommended before the start of a rehabilitation program.
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.
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…
Trigonometric Polynomials For Estimation Of Spectra
NASA Technical Reports Server (NTRS)
Greenhall, Charles A.
1990-01-01
Orthogonal sets of trigonometric polynomials used as suboptimal substitutes for discrete prolate-spheroidal "windows" of Thomson method of estimation of spectra. As used here, "windows" denotes weighting functions used in sampling time series to obtain their power spectra within specified frequency bands. Simplified windows designed to require less computation than do discrete prolate-spheroidal windows, albeit at price of some loss of accuracy.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
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.
The polynomial form of the scattering equations
NASA Astrophysics Data System (ADS)
Dolan, Louise; Goddard, Peter
2014-07-01
The scattering equations, recently proposed by Cachazo, He and Yuan as providing a kinematic basis for describing tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons), are reformulated in polynomial form. The scattering equations for N particles are shown to be equivalent to a Möbius invariant system of N - 3 equations, m = 0, 2 ≤ m ≤ N - 2, in N variables, where m is a homogeneous polynomial of degree m, with the exceptional property of being linear in each variable taken separately. Fixing the Möbius invariance appropriately, yields polynomial equations h m = 0, 1 ≤ m ≤ N - 3, in N - 3 variables, where h m has degree m. The linearity of the equations in the individual variables facilitates computation, e.g. the elimination of variables to obtain single variable equations determining the solutions. Expressions are given for the tree amplitudes in terms of the m and h m . The extension to the massive case for scalar particles is described and the special case of four dimensional space-time is discussed.
Simplified Storm Surge Simulations Using Bernstein Polynomials
NASA Astrophysics Data System (ADS)
Beisiegel, Nicole; Behrens, Jörn
2016-04-01
Storm surge simulations are vital for forecasting, hazard assessment and eventually improving our understanding of Earth system processes. Discontinuous Galerkin (DG) methods have recently been explored in that context, because they are locally mass-conservative and in combination with suitable robust nodal filtering techniques (slope limiters) positivity-preserving and well-balanced for the still water state at rest. These filters manipulate interpolation point values in every time step in order to retain the desirable properties of the scheme. In particular, DG methods are able to represent prognostic variables such as the fluid height at high-order accuracy inside each element (triangle). For simulations that include wetting and drying, however, the high-order accuracy will destabilize the numerical model because point values on quadrature points may become negative during the computation if they do not coincide with interpolation points. This is why the model that we are presenting utilizes Bernstein polynomials as basis functions to model the wetting and drying. This has the advantage that negative pointvalues away from interpolation points are prevented, the model is stabilized and no additional time step restriction is introduced. Numerical tests show that the model is capable of simulating simplified storm surges. Furthermore, a comparison of model results with third-order Bernstein polynomials with results using traditional nodal Lagrange polynomials reveals an improvement in numerical convergence.
Polynomials and Neural Networks for Gas Turbine Monitoring: a Comparative Study
NASA Astrophysics Data System (ADS)
Loboda, Igor; Feldshteyn, Yakov
2011-09-01
Gas turbine health monitoring includes the common stages of problem detection, fault identification, and prognostics. To extract useful diagnostic information from raw recorded data, these stages require a preliminary operation of computing differences between measurements and an engine baseline, which is a function of engine operating conditions. These deviations of measured values from the baseline data can be good indicators of engine health. However, their quality and the success of all diagnostic stages strongly depend on the adequacy of the baseline model employed and, in particular, on the mathematical techniques applied to create it. To create a baseline model, we have applied polynomials and the least squares method for computing the coefficients over a long period of time. Methods were proposed to enhance such a polynomial-based model. The resulting accuracy was sufficient for reliable monitoring of gas turbine deterioration effects. The polynomials previously investigated thus far are used in the present study as a standard for evaluating artificial neural networks, a very popular technique in gas turbine diagnostics. The focus of this comparative study is to verify whether the use of networks results in a better description of the engine baseline. Extensive field data for two different industrial gas turbines were used to compare these two techniques under various conditions. The deviations were computed for all available data, and the quality of the resulting deviation plots was compared visually. The mean error of the baseline model was used as an additional criterion for comparing the techniques. To find the best network configurations, many network variations were realised and compared with the polynomials. Although the neural networks studied were found to be close to the polynomials in accuracy, they did not exceed the polynomials in any variation. In this way, it seems that polynomials can be successfully used for engine monitoring, at least for
Long-time uncertainty propagation using generalized polynomial chaos and flow map composition
Luchtenburg, Dirk M.; Brunton, Steven L.; Rowley, Clarence W.
2014-10-01
We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The composition of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.
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.
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.
Wu, Peng; Wang, Wenli; Duan, Weike; Li, Ying; Hou, Xilin
2017-01-01
The CDPK-SnRK (calcium-dependent protein kinase/Snf1-related protein kinase) gene superfamily plays important roles in signaling pathways for disease resistance and various stress responses, as indicated by emerging evidence. In this study, we constructed comparative analyses of gene structure, retention, expansion, whole-genome duplication (WGD) and expression patterns of CDPK-SnRK genes in Brassica rapa and their evolution in plants. A total of 49 BrCPKs, 14 BrCRKs, 3 BrPPCKs, 5 BrPEPRKs, and 56 BrSnRKs were identified in B. rapa. All BrCDPK-SnRK proteins had highly conserved kinase domains. By statistical analysis of the number of CDPK-SnRK genes in each species, we found that the expansion of the CDPK-SnRK gene family started from angiosperms. Segmental duplication played a predominant role in CDPK-SnRK gene expansion. The analysis showed that PEPRK was more preferentially retained than other subfamilies and that CPK was retained similarly to SnRK. Among the CPKs and SnRKs, CPKIII and SnRK1 genes were more preferentially retained than other groups. CRK was closest to CPK, which may share a common evolutionary origin. In addition, we identified 196 CPK genes and 252 SnRK genes in 6 species, and their different expansion and evolution types were discovered. Furthermore, the expression of BrCDPK-SnRK genes is dynamic in different tissues as well as in response to abiotic stresses, demonstrating their important roles in development in B. rapa. In summary, this study provides genome-wide insight into the evolutionary history and mechanisms of CDPK-SnRK genes following whole-genome triplication in B. rapa. PMID:28239387
Shaping plant development through the SnRK1-TOR metabolic regulators.
Baena-González, Elena; Hanson, Johannes
2017-02-01
SnRK1 (Snf1-related protein kinase 1) and TOR (target of rapamycin) are evolutionarily conserved protein kinases that lie at the heart of energy sensing, playing central and antagonistic roles in the regulation of metabolism and gene expression. Increasing evidence links these metabolic regulators to numerous aspects of plant development, from germination to flowering and senescence. This prompts the hypothesis that SnRK1 and TOR modify developmental programs according to the metabolic status to adjust plant growth to a specific environment. The aim of this review is to provide support to this hypothesis and to incentivize further studies on this topic by summarizing the work that establishes a genetic connection between SnRK1-TOR and plant development.
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
Maximum of the Characteristic Polynomial of Random Unitary Matrices
NASA Astrophysics Data System (ADS)
Arguin, Louis-Pierre; Belius, David; Bourgade, Paul
2017-01-01
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.
Classification by using Prony's method with a polynomial model
NASA Astrophysics Data System (ADS)
Mueller, R.; Lee, W.; Okamitsu, J.
2012-06-01
Prony's Method with a Polynomial Model (PMPM) is a novel way of doing classification. Given a number of training samples with features and labels, it assumes a Gaussian mixture model for each feature, and uses Prony's method to determine a method of moments solution for the means and priors of the Gaussian distributions in the Gaussian mixture model. The features are then sorted in descending order by their relative performance. Based on the Gaussian mixture model of the first feature, training samples are partitioned into clusters by determining which Gaussian distribution each training sample is most likely from. Then with the training samples in each cluster, a new Gaussian mixture model is built for the next most powerful feature. This process repeats until a Gaussian mixture model is built for each feature, and a tree is thus grown with the training data partitioned into several final clusters. A "leaf" model for each final cluster is the weighted least squares solution (regression) for approximating a polynomial function of the features to the truth labels. Testing consists of determining for each testing sample a likelihood that the testing sample belongs to each cluster, and then regressions are weighted by their likelihoods and averaged to produce the test confidence. Evaluation of PMPM is done by extracting features from data collected by both Ground Penetrating Radar and Metal Detector of a robot-mounted land-mine detection system, training PMPM models, and testing in a cross-validation fashion.
Myers, N.J.
1994-12-31
The author gives a hybrid method for the iterative solution of linear systems of equations Ax = b, where the matrix (A) is nonsingular, sparse and nonsymmetric. As in a method developed by Starke and Varga the method begins with a number of steps of the Arnoldi method to produce some information on the location of the spectrum of A. This method then switches to an iterative method based on the Faber polynomials for an annular sector placed around these eigenvalue estimates. The Faber polynomials for an annular sector are used because, firstly an annular sector can easily be placed around any eigenvalue estimates bounded away from zero, and secondly the Faber polynomials are known analytically for an annular sector. Finally the author gives three numerical examples, two of which allow comparison with Starke and Varga`s results. The third is an example of a matrix for which many iterative methods would fall, but this method converges.
Lüchow, Arne; Sturm, Alexander; Schulte, Christoph; Haghighi Mood, Kaveh
2015-02-28
Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a few examples that the new Jastrow factor achieves 85%–90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.
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.
Specht, D F
1990-01-01
Two methods for classification based on the Bayes strategy and nonparametric estimators for probability density functions are reviewed. The two methods are named the probabilistic neural network (PNN) and the polynomial Adaline. Both methods involve one-pass learning algorithms that can be implemented directly in parallel neural network architectures. The performances of the two methods are compared with multipass backpropagation networks, and relative advantages and disadvantages are discussed. PNN and the polynomial Adaline are complementary techniques because they implement the same decision boundaries but have different advantages for applications. PNN is easy to use and is extremely fast for moderate-sized databases. For very large databases and for mature applications in which classification speed is more important than training speed, the polynomial equivalent can be found.
Li, Guangjie; Peng, Futian; Zhang, Lin; Shi, Xingzheng; Wang, Zhaoyan
2010-02-01
Sucrose non-fermenting-1-related protein kinase-1 (SnRK1) plays an important role in metabolic regulation in plant. To understand the molecular mechanism of amino acids and carbohydrate metabolism in Malus hupehensis Rehd. var. pinyiensis Jiang (Pingyi Tiancha, PYTC), a full-length cDNA clone encoding homologue of SnRK1 was isolated from PYTC by Rapid Amplification of cDNA Ends (RACE). The clone, designated as MhSnRK1, contains 2063 nucleotides with an open reading frame of 1548 nucleotides. The deduced 515 amino acids showed high identities with other plant SnRK1 genes. Quantitative real-time PCR analysis revealed this gene was expressed in roots, stems and leaves. Exposing seedlings to nitrate caused and initial decrease in expression of the MhSnRK1 gene in roots, leaves and stems in short term. Ectopic expression of MhSnRK1 in tomato mainly resulted in higher starch content in leaf and red-ripening fruit than wild-type plants. This result supports the hypothesis that overexpression of SnRK1 causes the accumulation of starch in plant cells. All the results suggest that MhSnRK1 may play important roles in carbohydrate and amino acid metabolisms.
Momentum space orthogonal polynomial projection quantization
NASA Astrophysics Data System (ADS)
Handy, C. R.; Vrinceanu, D.; Marth, C. B.; Gupta, R.
2016-04-01
The orthogonal polynomial projection quantization (OPPQ) is an algebraic method for solving Schrödinger’s equation by representing the wave function as an expansion {{\\Psi }}(x)={\\displaystyle \\sum }n{{{Ω }}}n{P}n(x)R(x) in terms of polynomials {P}n(x) orthogonal with respect to a suitable reference function R(x), which decays asymptotically not faster than the bound state wave function. The expansion coefficients {{{Ω }}}n are obtained as linear combinations of power moments {μ }{{p}}=\\int {x}p{{\\Psi }}(x) {{d}}x. In turn, the {μ }{{p}}'s are generated by a linear recursion relation derived from Schrödinger’s equation from an initial set of low order moments. It can be readily argued that for square integrable wave functions representing physical states {{lim}}n\\to ∞ {{{Ω }}}n=0. Rapidly converging discrete energies are obtained by setting Ω coefficients to zero at arbitrarily high order. This paper introduces an extention of OPPQ in momentum space by using the representation {{Φ }}(k)={\\displaystyle \\sum }n{{{\\Xi }}}n{Q}n(k)T(k), where Q n (k) are polynomials orthogonal with respect to a suitable reference function T(k). The advantage of this new representation is that it can help solving problems for which there is no coordinate space moment equation. This is because the power moments in momentum space are the Taylor expansion coefficients, which are recursively calculated via Schrödinger’s equation. We show the convergence of this new method for the sextic anharmonic oscillator and an algebraic treatment of Gross-Pitaevskii nonlinear equation.
Khader, M M
2013-10-01
In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.
A polynomial f(R) inflation model
Huang, Qing-Guo
2014-02-01
Motivated by the ultraviolet complete theory of quantum gravity, for example the string theory, we investigate a polynomial f(R) inflation model in detail. We calculate the spectral index and tensor-to-scalar ratio in the f(R) inflation model with the form of f(R) = R + (R{sup 2})/6M{sup 2} + (λn)/2n (R{sup n})/(3M{sup 2}){sup n-1}. Compared to Planck 2013, we find that R{sup n} term should be exponentially suppressed, i.e. |λ{sub n}|∼<10{sup −2n+2.6}.
A polynomial f(R) inflation model
Huang, Qing-Guo
2014-02-19
Motivated by the ultraviolet complete theory of quantum gravity, for example the string theory, we investigate a polynomial f(R) inflation model in detail. We calculate the spectral index and tensor-to-scalar ratio in the f(R) inflation model with the form of f(R)=R+((R{sup 2})/(6M{sup 2}))+((λ{sub n})/(2n))((R{sup n})/((3M{sup 2}){sup n−1})). Compared to Planck 2013, we find that R{sup n} term should be exponentially suppressed, i.e. |λ{sub n}|≲10{sup −2n+2.6}.
Polynomial Local Improvement Algorithms in Combinatorial Optimization.
1981-11-01
NUMBER SOL 81- 21 IIS -J O 15 14. TITLE (am#Su&Utl & YEO RPR ERO OEE Polynomial Local Improvement Algorithms in TcnclRpr Combinatorial Optimization 6...Stanford, CA 94305 II . CONTROLLING OFFICE NAME AND ADDRESS It. REPORT DATE Office of Naval Research - Dept. of the Navy November 1981 800 N. Qu~incy Street...corresponds to a node of the tree. ii ) The father of a vertex is its optimal adjacent vertex; if a vertex is a local optimum, it has no father. The tree is
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.
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.
Polynomial compensation, inversion, and approximation of discrete time linear systems
NASA Technical Reports Server (NTRS)
Baram, Yoram
1987-01-01
The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.
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
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.
Return times of polynomials as meta-Fibonacci numbers
NASA Astrophysics Data System (ADS)
Emerson, Nathaniel D.
We consider generalized closest return times of a complex polynomial of degree at least two. Most previous studies on this subject have focused on the properties of polynomials with particular return times, especially the Fibonacci numbers. We study the general form of these closest return times. The main result of this paper is that these closest return times are meta-Fibonacci numbers. In particular, this result applies to the return times of a principal nest of a polynomial. Furthermore, we show that an analogous result holds in a tree with dynamics that is associated with a polynomial.
Some properties of multiple orthogonal polynomials associated with Macdonald functions
NASA Astrophysics Data System (ADS)
Coussement, Els; van Assche, Walter
2001-08-01
Multiple orthogonal polynomials corresponding to two weights on [0,[infinity]) associated with modified Bessel functions (Macdonald functions) K[nu] and K[nu]+1 were introduced in Van Assche, Yakubovich (Integral Transforms Special Funct. 9 (2000) 229-244) and recently also studied by Ben Cheikh, Douak (Meth. Appl. Anal., to appear). We obtain explicit formulas for type I vector polynomials (An,n,Bn,n) and (An+1,n,Bn+1,n) and for type II polynomials Pn,n and Pn+1,n. We also obtain generating functions for types I and II 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.
Application of field dependent polynomial model
NASA Astrophysics Data System (ADS)
Janout, Petr; Páta, Petr; Skala, Petr; Fliegel, Karel; Vítek, Stanislav; Bednář, Jan
2016-09-01
Extremely wide-field imaging systems have many advantages regarding large display scenes whether for use in microscopy, all sky cameras, or in security technologies. The Large viewing angle is paid by the amount of aberrations, which are included with these imaging systems. Modeling wavefront aberrations using the Zernike polynomials is known a longer time and is widely used. Our method does not model system aberrations in a way of modeling wavefront, but directly modeling of aberration Point Spread Function of used imaging system. This is a very complicated task, and with conventional methods, it was difficult to achieve the desired accuracy. Our optimization techniques of searching coefficients space-variant Zernike polynomials can be described as a comprehensive model for ultra-wide-field imaging systems. The advantage of this model is that the model describes the whole space-variant system, unlike the majority models which are partly invariant systems. The issue that this model is the attempt to equalize the size of the modeled Point Spread Function, which is comparable to the pixel size. Issues associated with sampling, pixel size, pixel sensitivity profile must be taken into account in the design. The model was verified in a series of laboratory test patterns, test images of laboratory light sources and consequently on real images obtained by an extremely wide-field imaging system WILLIAM. Results of modeling of this system are listed in this article.
Tabulating knot polynomials for arborescent knots
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Morozov, A.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A.
2017-02-01
Arborescent knots are those which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is sufficient for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site (http://knotebook.org). Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the ‘family’ approach, suggested in Mironov and Morozov (2015 Nucl. Phys. B 899 395–413), and apply it to arborescent knots in the Rolfsen table by developing a Feynman diagram technique, associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY-PT polynomials.
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.
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.
Simulation of Experimental Parameters of RC Beams by Employing the Polynomial Regression Method
NASA Astrophysics Data System (ADS)
Sayin, B.; Sevgen, S.; Samli, R.
2016-07-01
A numerical model based on the method polynomial regression is developed to simulate the mechanical behavior of reinforced concrete beams strengthened with a carbon-fiber-reinforced polymer and subjected to four-point bending. The results obtained are in good agreement with data of laboratory tests.
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.
Lotus japonicus symRK-14 uncouples the cortical and epidermal symbiotic program.
Kosuta, Sonja; Held, Mark; Hossain, Md Shakhawat; Morieri, Giulia; Macgillivary, Amanda; Johansen, Christopher; Antolín-Llovera, Meritxell; Parniske, Martin; Oldroyd, Giles E D; Downie, Allan J; Karas, Bogumil; Szczyglowski, Krzysztof
2011-09-01
SYMRK is a leucine-rich-repeat (LRR)-receptor kinase that mediates intracellular symbioses of legumes with rhizobia and arbuscular mycorrhizal fungi. It participates in signalling events that lead to epidermal calcium spiking, an early cellular response that is typically considered as central for intracellular accommodation and nodule organogenesis. Here, we describe the Lotus japonicus symRK-14 mutation that alters a conserved GDPC amino-acid sequence in the SYMRK extracellular domain. Normal infection of the epidermis by fungal or bacterial symbionts was aborted in symRK-14. Likewise, epidermal responses of symRK-14 to bacterial signalling, including calcium spiking, NIN gene expression and infection thread formation, were significantly reduced. In contrast, no major negative effects on the formation of nodule primordia and cortical infection were detected. Cumulatively, our data show that the symRK-14 mutation uncouples the epidermal and cortical symbiotic program, while indicating that the SYMRK extracellular domain participates in transduction of non-equivalent signalling events. The GDPC sequence was found to be highly conserved in LRR-receptor kinases in legumes and non-legumes, including the evolutionarily distant bryophytes. Conservation of the GDPC sequence in nearly one-fourth of LRR-receptor-like kinases in the genome of Arabidopsis thaliana suggests, however, that this sequence might also play an important non-symbiotic function in this plant.
The VicRK system of Streptococcus mutans responds to oxidative stress.
Deng, D M; Liu, M J; ten Cate, J M; Crielaard, W
2007-07-01
In Streptococcus mutans, virulence and cariogenicity may be modulated via the two-component regulatory system VicRK. Environmental signals, sensed by VicK, inducing this modulation are still unclear, however, and were investigated in the present study. We found that VicRK displays homology with protein-domains that, in other bacteria, are involved in redox-sensing. After constructing a VicRK-promoter GFP-reporter strain, we showed increased fluorescence intensity under oxidative stress. Potential interference of alternative signals and experimental conditions on GFP expression was excluded by the use of negative and positive control strains. Finally, we constructed a clean vicK knockout mutant, which proved to be more sensitive to H(2)O(2) than the wild-type. In conclusion, this study showed that the VicRK system responds to and protects against oxidative stress. As a result, a link between oxidative/redox stress and the cariogenic nature of S. mutans can be hypothesized.
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.
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
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.
D-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization
NASA Astrophysics Data System (ADS)
Ali, S. Twareque; Bagarello, Fabio; Gazeau, Jean Pierre
2015-10-01
The D-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group GL(2,C) of invertible 2 × 2 matrices with complex entries. It reveals interesting aspects of these representations. The second example is based on a pseudo-bosonic generalization of operator-valued functions of a complex variable which resolves the identity. We show that such a generalization allows one to obtain a quantum pseudo-bosonic version of the complex plane viewed as the canonical phase space and to understand functions of the pseudo-bosonic operators as the quantized versions of functions of a complex variable.
Lagrange-Lobatto interpolating polynomials in the discrete variable representation.
Rayson, M J
2007-08-01
The discrete variable representation (DVR) is a well known and widely used computational technique in many areas of physics. Recently, the Lagrange-Lobatto basis has attracted increasing attention, especially for radial Hamiltonians with a singular potential at the origin and finite element DVR constructions. However, unlike standard DVR functions, the Lagrange-Lobatto basis functions are not orthogonal. The overlap matrix is usually approximated as the identity using the same quadrature approximation as for the potential. Based on the special properties of overlap matrix of Lagrange-Lobatto polynomials, an explanation of the success of the identity approximation, including error bounds, is presented. Results for hydrogen and the more nontrivial potentials of self-consistent all-electron density functional atomic calculations are also given.
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.
Detergent-Like Activity and α-Helical Structure of Warnericin RK, an Anti-Legionella Peptide
Verdon, Julien; Falge, Mirjam; Maier, Elke; Bruhn, Heike; Steinert, Michael; Faber, Cornelius; Benz, Roland; Héchard, Yann
2009-01-01
Abstract Warnericin RK is the first antimicrobial peptide known to be active against Legionella pneumophila, a pathogen bacterium that is responsible for severe pneumonia. Strikingly, this peptide displays a very narrow range of antimicrobial activity, almost limited to the Legionella genus, and a hemolytic activity. A similar activity has been described for δ-lysin, a well-known hemolytic peptide of Staphylococci that has not been described as antimicrobial. In this study we aimed to understand the mode of action of warnericin RK and to explain its particular target specificity. We found that warnericin RK permeabilizes artificial membranes in a voltage-independent manner. Osmotic protection experiments on erythrocytes showed that warnericin RK does not form well-defined pores, suggesting a detergent-like mode of action, as previously described for δ-lysin at high concentrations. Warnericin RK also permeabilized Legionella cells, and these cells displayed a high sensitivity to detergents. Depending on the detergent used, Legionella was from 10- to 1000-fold more sensitive than the other bacteria tested. Finally, the structure of warnericin RK was investigated by means of circular dichroism and NMR spectroscopy. The peptide adopted an amphiphilic α-helical structure, consistent with the proposed mode of action. We conclude that the specificity of warnericin RK toward Legionella results from both the detergent-like mode of action of the peptide and the high sensitivity of these bacteria to detergents. PMID:19804724
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…
The evolution of piecewise polynomial wave functions
NASA Astrophysics Data System (ADS)
Andrews, Mark
2017-01-01
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite region), but they immediately extend over all available space as they evolve. The simplest splines are the square and triangular wave functions in one dimension, but very complicated splines have been used in physics. In general the evolution of such spline wave functions can be expressed in terms of antiderivatives of the propagator; in the case of a free particle or an oscillator, all the evolutions are expressed exactly in terms of Fresnel integrals. Some extensions of these methods to two and three dimensions are discussed.
Polynomial Monogamy Relations for Entanglement Negativity
NASA Astrophysics Data System (ADS)
Allen, Grant W.; Meyer, David A.
2017-02-01
The notion of nonclassical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations—the church of the smaller Hilbert space only accepts monogamous congregants. We demonstrate how to characterize the limits of what is quantum mechanically possible with a computable measure, entanglement negativity. We show that negativity only saturates the standard linear monogamy inequality in trivial cases implied by its monotonicity under local operations and classical communication, and derive a necessary and sufficient inequality which, for the first time, is a nonlinear higher degree polynomial. For very large quantum systems, we prove that the negativity can be distributed at least linearly for the tightest constraint and conjecture that it is at most linear.
Schur polynomials and biorthogonal random matrix ensembles
NASA Astrophysics Data System (ADS)
Tierz, Miguel
2010-06-01
The study of the average of Schur polynomials over a Stieltjes-Wigert ensemble has been carried out by Dolivet and Tierz [J. Math. Phys. 48, 023507 (2007); e-print arXiv:hep-th/0609167], where it was shown that it is equal to quantum dimensions. Using the same approach, we extend the result to the biorthogonal case. We also study, using the Littlewood-Richardson rule, some particular cases of the quantum dimension result. Finally, we show that the notion of Giambelli compatibility of Schur averages, introduced by Borodin et al. [Adv. Appl. Math. 37, 209 (2006); e-print arXiv:math-ph/0505021], also holds in the biorthogonal setting.
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.
Properties of the zeros of generalized basic hypergeometric polynomials
NASA Astrophysics Data System (ADS)
Bihun, Oksana; Calogero, Francesco
2015-11-01
We define the generalized basic hypergeometric polynomial of degree N in terms of the generalized basic hypergeometric function, by choosing one of its parameters to allow the termination of the series after a finite number of summands. In this paper, we obtain a set of nonlinear algebraic equations satisfied by the N zeros of the polynomial. Moreover, we obtain an N × N matrix M defined in terms of the zeros of the polynomial, which, in turn, depend on the parameters of the polynomial. The eigenvalues of this remarkable matrix M are given by neat expressions that depend only on some of the parameters of the polynomial; that is, the matrix M is isospectral. Moreover, in case the parameters that appear in the expressions for the eigenvalues of M are rational, the matrix M has rational eigenvalues, a Diophantine property.
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.
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.
Chen, Sheng; Hong, Xia; Khalaf, Emad F; Alsaadi, Fuad E; Harris, Chris J
2016-09-23
Complex-valued (CV) B-spline neural network approach offers a highly effective means for identifying and inverting practical Hammerstein systems. Compared with its conventional CV polynomial-based counterpart, a CV B-spline neural network has superior performance in identifying and inverting CV Hammerstein systems, while imposing a similar complexity. This paper reviews the optimality of the CV B-spline neural network approach. Advantages of B-spline neural network approach as compared with the polynomial based modeling approach are extensively discussed, and the effectiveness of the CV neural network-based approach is demonstrated in a real-world application. More specifically, we evaluate the comparative performance of the CV B-spline and polynomial-based approaches for the nonlinear iterative frequency-domain decision feedback equalization (NIFDDFE) of single-carrier Hammerstein channels. Our results confirm the superior performance of the CV B-spline-based NIFDDFE over its CV polynomial-based counterpart.
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.
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.
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
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
SO(N) restricted Schur polynomials
Kemp, Garreth
2015-02-15
We focus on the 1/4-BPS sector of free super Yang-Mills theory with an SO(N) gauge group. This theory has an AdS/CFT (an equivalence between a conformal field theory in d-1 dimensions and type II string theory defined on an AdS space in d-dimensions) dual in the form of type IIB string theory with AdS{sub 5}×RP{sup 5} geometry. With the aim of studying excited giant graviton dynamics, we construct an orthogonal basis for this sector of the gauge theory in this work. First, we demonstrate that the counting of states, as given by the partition function, and the counting of restricted Schur polynomials match by restricting to a particular class of Young diagram labels. We then give an explicit construction of these gauge invariant operators and evaluate their two-point function exactly. This paves the way to studying the spectral problem of these operators and their D-brane duals.
Polynomial Method for PLL Controller Optimization†
Wang, Ta-Chung; Lall, Sanjay; Chiou, Tsung-Yu
2011-01-01
The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach. PMID:22163973
Strut fracture in the new Bjørk-Shiley mitral valve prosthesis.
Brubakk, O; Simonsen, S; Källman, L; Fredriksen, A
1981-04-01
The case of a patient with the new type Bjørk-Shiley aortic and mitral valve prosthesis is described. Three months after implant she suffered acute heart failure and died. Post-mortem examination revealed a fractured outlet strut in the mitral valve prosthesis with dislocation of the disc. The fracture was regarded as due to excessive brittleness caused by demonstrated deposition of chromium-tungsten-carbide.
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.
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.
Generalized Rayleigh and Jacobi Processes and Exceptional Orthogonal Polynomials
NASA Astrophysics Data System (ADS)
Chou, C.-I.; Ho, C.-L.
2013-09-01
We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.
On polynomial integrability of the Euler equations on so(4)
NASA Astrophysics Data System (ADS)
Llibre, Jaume; Yu, Jiang; Zhang, Xiang
2015-10-01
In this paper we prove that the Euler equations on the Lie algebra so(4) with a diagonal quadratic Hamiltonian either satisfy the Manakov condition, or have at most four functionally independent polynomial first integrals.
Fitting discrete aspherical surface sag data using orthonormal polynomials.
Hilbig, David; Ceyhan, Ufuk; Henning, Thomas; Fleischmann, Friedrich; Knipp, Dietmar
2015-08-24
Characterizing real-life optical surfaces usually involves finding the best-fit of an appropriate surface model to a set of discrete measurement data. This process can be greatly simplified by choosing orthonormal polynomials for the surface description. In case of rotationally symmetric aspherical surfaces, new sets of orthogonal polynomials were introduced by Forbes to replace the numerical unstable standard description. From these, for the application of surface retrieval using experimental ray tracing, the sag orthogonal Q(con)-polynomials are of particular interest. However, these are by definition orthogonal over continuous data and may not be orthogonal for discrete data. In this case, the simplified solution is not valid. Hence, a Gram-Schmidt orthonormalization of these polynomials over the discrete data set is proposed to solve this problem. The resulting difference will be presented by a performance analysis and comparison to the direct matrix inversion method.
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.
Design of robust differential microphone arrays with orthogonal polynomials.
Pan, Chao; Benesty, Jacob; Chen, Jingdong
2015-08-01
Differential microphone arrays have the potential to be widely deployed in hands-free communication systems thanks to their frequency-invariant beampatterns, high directivity factors, and small apertures. Traditionally, they are designed and implemented in a multistage way with uniform linear geometries. This paper presents an approach to the design of differential microphone arrays with orthogonal polynomials, more specifically with Jacobi polynomials. It first shows how to express the beampatterns as a function of orthogonal polynomials. Then several differential beamformers are derived and their performance depends on the parameters of the Jacobi polynomials. Simulations show the great flexibility of the proposed method in terms of designing any order differential microphone arrays with different beampatterns and controlling white noise gain.
Asymptotic expansions of Feynman integrals of exponentials with polynomial exponent
NASA Astrophysics Data System (ADS)
Kravtseva, A. K.; Smolyanov, O. G.; Shavgulidze, E. T.
2016-10-01
In the paper, an asymptotic expansion of path integrals of functionals having exponential form with polynomials in the exponent is constructed. The definition of the path integral in the sense of analytic continuation is considered.
Symmetric polynomials in information theory: Entropy and subentropy
Jozsa, Richard; Mitchison, Graeme
2015-06-15
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.
Orthogonal sets of data windows constructed from trigonometric polynomials
NASA Technical Reports Server (NTRS)
Greenhall, C. A.
1989-01-01
Suboptimal, easily computable substitutes for the discrete prolate-spheroidal windows used by Thomson for spectral estimation are given. Trigonometric coefficients and energy leakages of the window polynomials are tabulated.
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.
Performance comparison of polynomial representations for optimizing optical freeform systems
NASA Astrophysics Data System (ADS)
Brömel, A.; Gross, H.; Ochse, D.; Lippmann, U.; Ma, C.; Zhong, Y.; Oleszko, M.
2015-09-01
Optical systems can benefit strongly from freeform surfaces, however the choice of the right representation isn`t an easy one. Classical representations like X-Y-polynomials, as well as Zernike-polynomials are often used for such systems, but should have some disadvantage regarding their orthogonality, resulting in worse convergence and reduced quality in final results compared to newer representations like the Q-polynomials by Forbes. Additionally the supported aperture is a circle, which can be a huge drawback in case of optical systems with rectangular aperture. In this case other representations like Chebyshev-or Legendre-polynomials come into focus. There are a larger number of possibilities; however the experience with these newer representations is rather limited. Therefore in this work the focus is on investigating the performance of four widely used representations in optimizing two ambitious systems with very different properties: Three-Mirror-Anastigmat and an anamorphic System. The chosen surface descriptions offer support for circular or rectangular aperture, as well as different grades of departure from rotational symmetry. The basic shapes are for example a conic or best-fit-sphere and the polynomial set is non-, spatial or slope-orthogonal. These surface representations were chosen to evaluate the impact of these aspects on the performance optimization of the two example systems. Freeform descriptions investigated here were XY-polynomials, Zernike in Fringe representation, Q-polynomials by Forbes, as well as 2-dimensional Chebyshev-polynomials. As a result recommendations for the right choice of freeform surface representations for practical issues in the optimization of optical systems can be given.
A robust polynomial fitting approach for contact angle measurements.
Atefi, Ehsan; Mann, J Adin; Tavana, Hossein
2013-05-14
Polynomial fitting to drop profile offers an alternative to well-established drop shape techniques for contact angle measurements from sessile drops without a need for liquid physical properties. Here, we evaluate the accuracy of contact angles resulting from fitting polynomials of various orders to drop profiles in a Cartesian coordinate system, over a wide range of contact angles. We develop a differentiator mask to automatically find a range of required number of pixels from a drop profile over which a stable contact angle is obtained. The polynomial order that results in the longest stable regime and returns the lowest standard error and the highest correlation coefficient is selected to determine drop contact angles. We find that, unlike previous reports, a single polynomial order cannot be used to accurately estimate a wide range of contact angles and that a larger order polynomial is needed for drops with larger contact angles. Our method returns contact angles with an accuracy of <0.4° for solid-liquid systems with θ < ~60°. This compares well with the axisymmetric drop shape analysis-profile (ADSA-P) methodology results. Above about 60°, we observe significant deviations from ADSA-P results, most likely because a polynomial cannot trace the profile of drops with close-to-vertical and vertical segments. To overcome this limitation, we implement a new polynomial fitting scheme by transforming drop profiles into polar coordinate system. This eliminates the well-known problem with high curvature drops and enables estimating contact angles in a wide range with a fourth-order polynomial. We show that this approach returns dynamic contact angles with less than 0.7° error as compared to ADSA-P, for the solid-liquid systems tested. This new approach is a powerful alternative to drop shape techniques for estimating contact angles of drops regardless of drop symmetry and without a need for liquid properties.
Polynomial Interpolation and Sums of Powers of Integers
ERIC Educational Resources Information Center
Cereceda, José Luis
2017-01-01
In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, P[subscript k](n) and Q[subscript k](n), such that P[subscript k](n) = Q[subscript k](n) = f[subscript k](n) for n = 1, 2,… , k, where f[subscript k](1), f[subscript k](2),… , f[subscript k](k) are k arbitrarily chosen…
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.
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.
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.
One-parameter extension of the Doi-Peliti formalism and its relation with orthogonal polynomials.
Ohkubo, Jun
2012-10-01
An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected to orthogonal polynomials. We show that two different orthogonal polynomials, i.e., Charlier polynomials and Hermite polynomials, can be used to express the Doi-Peliti formalism explicitly.
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.
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.
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.
Dynamic Harmony Search with Polynomial Mutation Algorithm for Valve-Point Economic Load Dispatch.
Karthikeyan, M; Raja, T Sree Ranga
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.
Ding, A Adam; Wu, Hulin
2014-10-01
We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.
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.
A Topological Framework for the Computation of the HOMFLY Polynomial and Its Application to Proteins
Comoglio, Federico; Rinaldi, Maurizio
2011-01-01
Polymers can be modeled as open polygonal paths and their closure generates knots. Knotted proteins detection is currently achieved via high-throughput methods based on a common framework insensitive to the handedness of knots. Here we propose a topological framework for the computation of the HOMFLY polynomial, an handedness-sensitive invariant. Our approach couples a multi-component reduction scheme with the polynomial computation. After validation on tabulated knots and links the framework was applied to the entire Protein Data Bank along with a set of selected topological checks that allowed to discard artificially entangled structures. This led to an up-to-date table of knotted proteins that also includes two newly detected right-handed trefoil knots in recently deposited protein structures. The application range of our framework is not limited to proteins and it can be extended to the topological analysis of biological and synthetic polymers and more generally to arbitrary polygonal paths. PMID:21533239
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
On modeling of tool wear using sensor fusion and polynomial classifiers
NASA Astrophysics Data System (ADS)
Deiab, Ibrahim; Assaleh, Khaled; Hammad, Firas
2009-07-01
With increased global competition, the manufacturing sector is vigorously working on enhancing the efficiency of manufacturing processes in terms of cost, quality, and environmental impact. This work presents a novel approach to model and predict cutting tool wear using statistical signal analysis, pattern recognition, and sensor fusion. The data are acquired from two sources: an acoustic emission sensor (AE) and a tool post dynamometer. The pattern recognition used here is based on two methods: Artificial Neural Networks (ANN) and Polynomial Classifiers (PC). Cutting tool wear values predicted by neural network (ANN) and polynomial classifiers (PC) are compared. For the case study presented, PC proved to significantly reduce the required training time compared to that required by an ANN without compromising the prediction accuracy. The predicted results compared well with the measured tool wear values.
González-Cardel, Mario; Arguijo, Pedro; Díaz-Uribe, Rufino
2013-06-01
A method for approximating the inverse error function involved in the determination of the radius of a Gaussian beam is proposed. It is based on a polynomial inversion that can be developed to any desired degree, according to an a priori defined error budget. Analytic expressions are obtained and used to determine the radius of a TEM(oo) He-Ne laser beam from intensity measurements experimentally obtained by using the knife edge method. The error and the interval of validity of the approximation are determined for polynomials of different degrees. The analysis of the theoretical and experimental errors is also presented.
NASA Astrophysics Data System (ADS)
Isah, Abdulnasir; Chang, Phang
2016-06-01
In this article we propose the wavelet operational method based on shifted Legendre polynomial to obtain the numerical solutions of non-linear systems of fractional order differential equations (NSFDEs). The operational matrix of fractional derivative derived through wavelet-polynomial transformation are used together with the collocation method to turn the NSFDEs to a system of non-linear algebraic equations. Illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques.
Zhang, Yan; Sahinidis, Nikolaos V.
2013-03-06
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.
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
Generalized coherent states for polynomial Weyl-Heisenberg algebras
NASA Astrophysics Data System (ADS)
Kibler, Maurice R.; Daoud, Mohammed
2012-08-01
It is the aim of this paper to show how to construct á la Perelomov and á la Barut-Girardello coherent states for a polynomial Weyl-Heisenberg algebra. This algebra depends on r parameters. For some special values of the parameter corresponding to r = 1, the algebra covers the cases of the su(1,1) algebra, the su(2) algebra and the ordinary Weyl-Heisenberg or oscillator algebra. For r arbitrary, the generalized Weyl-Heisenberg algebra admits finite or infinite-dimensional representations depending on the values of the parameters. Coherent states of the Perelomov type are derived in finite and infinite dimensions through a Fock-Bargmann approach based on the use of complex variables. The same approach is applied for deriving coherent states of the Barut-Girardello type in infinite dimension. In contrast, the construction of á la Barut-Girardello coherent states in finite dimension can be achieved solely at the price to replace complex variables by generalized Grassmann variables. Finally, some preliminary developments are given for the study of Bargmann functions associated with some of the coherent states obtained in this work.
Convergent series for lattice models with polynomial interactions
NASA Astrophysics Data System (ADS)
Ivanov, Aleksandr S.; Sazonov, Vasily K.
2017-01-01
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of the perturbative expansions by a certain interacting model or regularizing original lattice integrals, one can construct desired convergent series. In this paper we develop methods, which are based on the joint and separate utilization of the regularization and new initial approximation. We prove, that the convergent series exist and can be expressed as re-summed standard perturbation theory for any model on the finite lattice with the polynomial interaction of even degree. We discuss properties of such series and study their applicability to practical computations on the example of the lattice ϕ4-model. We calculate <ϕn2 > expectation value using the convergent series, the comparison of the results with the Borel re-summation and Monte Carlo simulations shows a good agreement between all these methods.
Rodriguez-Cardenas, Yalil Augusto; Arriola-Guillen, Luis Ernesto; Flores-Mir, Carlos
2014-01-01
OBJECTIVE: The objective of this study was to evaluate the Björk and Jabarak cephalometric analysis generated from cone-beam computed tomography (CBCT) synthesized lateral cephalograms in adults with different sagittal skeletal patterns. METHODS: The sample consisted of 46 CBCT synthesized cephalograms obtained from patients between 16 and 40 years old. A Björk and Jarabak cephalometric analysis among different sagittal skeletal classes was performed. Analysis of variance (ANOVA), multiple range test of Tukey, Kruskal-Wallis test, and independent t-test were used as appropriate. RESULTS: In comparison to the standard values: Skeletal Class III had increased gonial and superior gonial angles (P < 0.001). This trend was also evident when sex was considered. For Class I males, the sella angle was decreased (P = 0.041), articular angle increased (P = 0.027) and gonial angle decreased (P = 0.002); whereas for Class III males, the gonial angle was increased (P = 0.012). For Class I females, the articular angle was increased (P = 0.029) and the gonial angle decreased (P = 0.004). Björk's sum and Björk and Jabarak polygon sum showed no significant differences. The facial biotype presented in the three sagittal classes was mainly hypodivergent and neutral. CONCLUSIONS: In this sample, skeletal Class III malocclusion was strongly differentiated from the other sagittal classes, specifically in the mandible, as calculated through Björk and Jarabak analysis. PMID:25628079
The AMPK/SNF1/SnRK1 fuel gauge and energy regulator: structure, function and regulation.
Ghillebert, Ruben; Swinnen, Erwin; Wen, Jing; Vandesteene, Lies; Ramon, Matthew; Norga, Koen; Rolland, Filip; Winderickx, Joris
2011-11-01
All life forms on earth require a continuous input and monitoring of carbon and energy supplies. The AMP-activated kinase (AMPK)/sucrose non-fermenting1 (SNF1)/Snf1-related kinase1 (SnRK1) protein kinases are evolutionarily conserved metabolic sensors found in all eukaryotic organisms from simple unicellular fungi (yeast SNF1) to animals (AMPK) and plants (SnRK1). Activated by starvation and energy-depleting stress conditions, they enable energy homeostasis and survival by up-regulating energy-conserving and energy-producing catabolic processes, and by limiting energy-consuming anabolic metabolism. In addition, they control normal growth and development as well as metabolic homeostasis at the organismal level. As such, the AMPK/SNF1/SnRK1 kinases act in concert with other central signaling components to control carbohydrate uptake and metabolism, fatty acid and lipid biosynthesis and the storage of carbon energy reserves. Moreover, they have a tremendous impact on developmental processes that are triggered by environmental changes such as nutrient depletion or stress. Although intensive research by many groups has partly unveiled the factors that regulate AMPK/SNF1/SnRK1 kinase activity as well as the pathways and substrates they control, several fundamental issues still await to be clarified. In this review, we will highlight these issues and focus on the structure, function and regulation of the AMPK/SNF1/SnRK1 kinases.
NJ cluster analysis of the SnRK2, PYR/PYL/RCAR, and ABF genes in Tibetan hulless barley.
Yuan, H J; Wang, Y L; Wei, Z X; Xu, Q J; Zeng, X Q; Tang, Y W; Nyima, T S
2016-11-03
The abscisic acid (ABA) signaling pathway is known as one of the most important signaling pathways in plants and is mediated by multiple regulators. The genes SnRK2, PYR/PYL/RCAR, and ABF are relevant to both ABA-dependent and -independent signaling pathways. To elucidate the profile of these genes from Tibetan hulless barley (Hordeum vulgare L. var. nudum Hook. f.), we collected available sequences from RNA-Seq data, together with NCBI data from five other model plant species (Arabidopsis thaliana, Brachypodium distachyon, Oryza sativa, Populus trichocarpa, and Sorghum bicolor). Gene trees of SnRK2, PYR/PYL/RCAR, and ABF were constructed using a neighbor joining (NJ) method. For all genes, we identified a dominant group in which all six species were represented. Three, four, and five groups were found in the NJ trees of SnRK2, PYR/PYL/RCAR, and ABF, respectively. For each gene, Tibetan hulless barley was divided into three groups. Our analyses indicated that Tibetan hulless barley was associated with B. distachyon. The NJ cluster analysis also suggested that Tibetan hulless barley was affiliated with S. bicolor (SnRK2), A. thaliana (PYR/PYL/RCAR), and O. sativa (ABF). These results illustrate a diverse expression of genes SnRK2, PYR/PYL/RCAR, and ABF, and suggest a relationship among the six species studied. Collectively, our characterization of the three components of the ABA signaling pathway may contribute to improve stress tolerance in Tibetan hulless barley.
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.
Isothermal titration calorimetry: general formalism using binding polynomials.
Freire, Ernesto; Schön, Arne; Velazquez-Campoy, Adrian
2009-01-01
The theory of the binding polynomial constitutes a very powerful formalism by which many experimental biological systems involving ligand binding can be analyzed under a unified framework. The analysis of isothermal titration calorimetry (ITC) data for systems possessing more than one binding site has been cumbersome because it required the user to develop a binding model to fit the data. Furthermore, in many instances, different binding models give rise to identical binding isotherms, making it impossible to discriminate binding mechanisms using binding data alone. One of the main advantages of the binding polynomials is that experimental data can be analyzed by employing a general model-free methodology that provides essential information about the system behavior (e.g., whether there exists binding cooperativity, whether the cooperativity is positive or negative, and the magnitude of the cooperative energy). Data analysis utilizing binding polynomials yields a set of binding association constants and enthalpy values that conserve their validity after the correct model has been determined. In fact, once the correct model is validated, the binding polynomial parameters can be immediately translated into the model specific constants. In this chapter, we describe the general binding polynomial formalism and provide specific theoretical and experimental examples of its application to isothermal titration calorimetry.
Failure of a Björk-Shiley mitral valve prosthesis to open: clinical recognition.
Saunders, C R; Rossi, N P; Rittenhouse, E A
1977-01-01
Failure of a Björk-Shiley mitral valve prosthesis to open was recognized early in the postoperative period and required immediate replacement. The clinical finding was sudden, intermittent, severe hypotension associated with absent poppet sounds and simultaneous elevation in left atrial pressure. This unique and unusual hemodynamic picture was duplicated in four animal experiments. Routine monitoring of left atrial pressure is a useful postoperative adjunct that can provide early documentation of obstruction to left atrial outflow. Early recognition of the problem and immediate operative correction are mandatory.
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
Kodali, Vidya P; Perali, Ramu S; Sen, R
2011-08-26
An exopolysaccharide (EPS) was isolated from Bacillus coagulans RK-02 and purified by size exclusion chromatography. The purified, homogeneous EPS had an average molecular weight of ∼3 × 10⁴ Da by comparison with FITC-labeled dextran standards. In vivo evaluations showed that, like other reported polysaccharides, this EPS displayed significant antioxidant activity. FTIR spectroscopy analysis showed the presence of hydroxy, carboxy, and α-glycosidic linkages and a mannose residue. GC analysis indicated that the EPS was a heteropolymer composed of glucose, mannose, galactose, glucosamine, and fucose as monomeric constituent units. Partial elucidation of the structure of the carbohydrate biopolymer based on GC-MS and NMR analysis showed the presence of two unique sets of tetrasaccharide repeating units that have 1→3 and 1→6 glycosidic linkages. This is also the first report of a Gram-positive bacterial polysaccharide with both fucose as a sugar monomer and 1→3 and 1→6 glycosidic linkages in the molecular backbone.
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.
Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion
NASA Astrophysics Data System (ADS)
Perkó, Zoltán; van der Voort, Sebastian R.; van de Water, Steven; Hartman, Charlotte M. H.; Hoogeman, Mischa; Lathouwers, Danny
2016-06-01
The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications.
Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion.
Perkó, Zoltán; van der Voort, Sebastian R; van de Water, Steven; Hartman, Charlotte M H; Hoogeman, Mischa; Lathouwers, Danny
2016-06-21
The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications.
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.
Zaunders, John; Jing, Junmei; Leipold, Michael; Maecker, Holden; Kelleher, Anthony D; Koch, Inge
2016-01-01
Many methods have been described for automated clustering analysis of complex flow cytometry data, but so far the goal to efficiently estimate multivariate densities and their modes for a moderate number of dimensions and potentially millions of data points has not been attained. We have devised a novel approach to describing modes using second order polynomial histogram estimators (SOPHE). The method divides the data into multivariate bins and determines the shape of the data in each bin based on second order polynomials, which is an efficient computation. These calculations yield local maxima and allow joining of adjacent bins to identify clusters. The use of second order polynomials also optimally uses wide bins, such that in most cases each parameter (dimension) need only be divided into 4-8 bins, again reducing computational load. We have validated this method using defined mixtures of up to 17 fluorescent beads in 16 dimensions, correctly identifying all populations in data files of 100,000 beads in <10 s, on a standard laptop. The method also correctly clustered granulocytes, lymphocytes, including standard T, B, and NK cell subsets, and monocytes in 9-color stained peripheral blood, within seconds. SOPHE successfully clustered up to 36 subsets of memory CD4 T cells using differentiation and trafficking markers, in 14-color flow analysis, and up to 65 subpopulations of PBMC in 33-dimensional CyTOF data, showing its usefulness in discovery research. SOPHE has the potential to greatly increase efficiency of analysing complex mixtures of cells in higher dimensions.
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).
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.
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.
Model Fractional Quantum Hall States and Jack Polynomials
Bernevig, B. Andrei; Haldane, F. D. M.
2008-06-20
We describe an occupation-number-like picture of fractional quantum Hall states in terms of polynomial wave functions characterized by a dominant occupation-number configuration. The bosonic variants of single-component Abelian and non-Abelian fractional quantum Hall states are modeled by Jack symmetric polynomials (Jacks), characterized by dominant occupation-number configurations satisfying a generalized Pauli principle. In a series of well-known quantum Hall states, including the Laughlin, Read-Moore, and Read-Rezayi, the Jack polynomials naturally implement a ''squeezing rule'' that constrains allowed configurations to be restricted to those obtained by squeezing the dominant configuration. The Jacks presented in this Letter describe new trial uniform states, but it is yet to be determined to which actual experimental fractional quantum Hall effect states they apply.
Broad-host-range plasmid pRK340 delivers Tn5 into the Legionella pneumophila chromosome.
Keen, M G; Street, E D; Hoffman, P S
1985-01-01
Transposon Tn5 was introduced into Legionella pneumophila on plasmid pRK340, which is temperature sensitive for plasmid maintenance. The presence of plasmid DNA was confirmed by agarose gel electrophoresis and by conjugal transfer of the plasmid to Escherichia coli. Tn5 insertions were obtained by culturing L. pneumophila at the nonpermissive temperature (43 degrees C) on buffered charcoal-yeast extract agar containing kanamycin. Of the 260 kanamycin-resistant colonies picked, 220 failed to conjugate pRK340 to E. coli. Plasmid DNA was not visualized from eight randomly picked Tn5-containing strains, and Southern hybridizations indicated that Tn5, but not pRK340, inserted into multiple sites in the Legionella chromosome. In addition, the streptomycin resistance determinant on Tn5 was expressed in L. pneumophila. Images PMID:2987191
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
Diagnostic accuracy of rKLO8 versus rK26 ELISAs for screening of canine visceral leishmaniasis.
Martínez Abad, Lily P; Almeida, Caroline S; Mattos, Ana Márcia M; Mendonça, Ana Carolina P; Alves, Márcio J M; Pinheiro, Aimara C; Porrozzi, Renato; Abass, Elfadil; Steinhoff, Ulrich; Teixeira, Henrique C
2017-02-01
Canine visceral leishmaniasis (CVL) represents an important public health issue. Despite numerous diagnostic tests available, CVL diagnosis still needs to be improved to achieve a more accurate detection rate. Recently, rKLO8, a new antigenic protein of Sudanese Leishmania donovani, was studied for the first time in diagnosis of human visceral leishmaniasis (HVL) and showed good performance. The present study aimed to evaluate serum reactivity to rKL08 and the reference antigen rK26, and to compare both diagnostic proteins with the combined DPP(®) CVL rapid test and ELISA (EIE-Bio-Manguinhos) confirmatory test, which are both recommended for the diagnosis of CVL in Brazil. Serum samples of dogs were grouped into: (I) DPP(®)/EIE negative (n=100) and (II) DPP(®)/EIE positive sera (n=100). Enhanced levels of IgG, mainly IgG2, to both rKLO8 and rK26 were found in group II. Sensitivity was 68% and 77% and specificity was 92% and 91%, for rKLO8 and rK26 antigens, respectively. Moreover, the combination of rKLO8 and rK26 antigens (rKLO8+rK26) exhibited higher sensitivity (85%) and specificity (93%). Thus, our results show that apart from the improved diagnostic power of rKLO8 in HVL, this new antigen is also suitable for the diagnosis of CVL. Further, the combination of rKLO8 and rK26 antigens increases the diagnostic accuracy of CVL.
Hand, Erin S; Haller, Sherry L; Peng, Chen; Rothenburg, Stefan; Hersperger, Adam R
2015-01-01
As a group, poxviruses have been shown to infect a wide variety of animal species. However, there is individual variability in the range of species able to be productively infected. In this study, we observed that ectromelia virus (ECTV) does not replicate efficiently in cultured rabbit RK13 cells. Conversely, vaccinia virus (VACV) replicates well in these cells. Upon infection of RK13 cells, the replication cycle of ECTV is abortive in nature, resulting in a greatly reduced ability to spread among cells in culture. We observed ample levels of early gene expression but reduced detection of virus factories and severely blunted production of enveloped virus at the cell surface. This work focused on two important host range genes, named E3L and K3L, in VACV. Both VACV and ECTV express a functional protein product from the E3L gene, but only VACV contains an intact K3L gene. To better understand the discrepancy in replication capacity of these viruses, we examined the ability of ECTV to replicate in wild-type RK13 cells compared to cells that constitutively express E3 and K3 from VACV. The role these proteins play in the ability of VACV to replicate in RK13 cells was also analyzed to determine their individual contribution to viral replication and PKR activation. Since E3L and K3L are two relevant host range genes, we hypothesized that expression of one or both of them may have a positive impact on the ability of ECTV to replicate in RK13 cells. Using various methods to assess virus growth, we did not detect any significant differences with respect to the replication of ECTV between wild-type RK13 compared to versions of this cell line that stably expressed VACV E3 alone or in combination with K3. Therefore, there remain unanswered questions related to the factors that limit the host range of ECTV.
Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics
NASA Astrophysics Data System (ADS)
Engliš, Miroslav; Ali, S. Twareque
2015-07-01
Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.
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.
On solutions of polynomial growth of ordinary differential equations
NASA Astrophysics Data System (ADS)
van den Berg, I. P.
We present a theorem on the existence of solutions of polynomial growth of ordinary differential equations of type E: {dY}/{dX} = F(X, Y) , where F is of class C1. We show that the asymptotic behaviour of these solutions and the variation of neighbouring solutions are obtained by solving an asymptotic functional equation related to E, and that this method has practical value. The theorem is standard; its nonstandard proof uses macroscope and microscope techniques. The result is an extension of results by F. and M. Diener and G. Reeb on solutions of polynomial growth of rational differential equations.
Polynomial approximation of Poincare maps for Hamiltonian system
NASA Technical Reports Server (NTRS)
Froeschle, Claude; Petit, Jean-Marc
1992-01-01
Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.
Riemann hypothesis for period polynomials of modular forms
Jin, Seokho; Ma, Wenjun; Ono, Ken; Soundararajan, Kannan
2016-01-01
The period polynomial rf(z) for an even weight k≥4 newform f∈Sk(Γ0(N)) is the generating function for the critical values of L(f,s). It has a functional equation relating rf(z) to rf(−1Nz). We prove the Riemann hypothesis for these polynomials: that the zeros of rf(z) lie on the circle |z|=1/N. We prove that these zeros are equidistributed when either k or N is large. PMID:26903628
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…
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.
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.
FEDOROVA,A.; ZEITLIN,M.; PARSA,Z.
2000-03-31
In this paper the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to a variational approach in the general case they have the solution as a multiresolution (multiscales) expansion on the base of compactly supported wavelet basis. They give an extension of their results to the cases of periodic orbital particle motion and arbitrary variable coefficients. Then they consider more flexible variational method which is based on a biorthogonal wavelet approach. Also they consider a different variational approach, which is applied to each scale.
The complexity of class polynomial computation via floating point approximations
NASA Astrophysics Data System (ADS)
Enge, Andreas
2009-06-01
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of modular functions in several arguments. The fastest one of the presented approaches uses a technique devised by Dupont to evaluate modular functions by Newton iterations on an expression involving the arithmetic-geometric mean. Under the heuristic assumption, justified by experiments, that the correctness of the result is not perturbed by rounding errors, the algorithm runs in time O left( sqrt {\\vert D\\vert} log^3 \\vert D\\vert M left( sq... ...arepsilon} \\vert D\\vert right) subseteq O left( h^{2 + \\varepsilon} right) for any \\varepsilon > 0 , where D is the CM discriminant, h is the degree of the class polynomial and M (n) is the time needed to multiply two n -bit numbers. Up to logarithmic factors, this running time matches the size of the constructed polynomials. The estimate also relies on a new result concerning the complexity of enumerating the class group of an imaginary quadratic order and on a rigorously proven upper bound for the height of class polynomials.
Two-variable Hermite Polynomial State and Its Wigner Function
NASA Astrophysics Data System (ADS)
Meng, Xiang-Guo; Wang, Ji-Suo; Liang, Bao-Long
2009-08-01
In this paper we obtain the Wigner functions of two-variable Hermite polynomial states (THPS) and their marginal distribution using the entangled state |ξ> representation. Also we obtain tomogram of THPS by virtue of the Radon transformation between the Wigner operator and the projection operator of another entangled state |η,τ 1,τ 2>.
Cubic Polynomials with Real or Complex Coefficients: The Full Picture
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2016-01-01
The cubic polynomial with real coefficients has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance…
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.
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)
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.
Computational Technique for Teaching Mathematics (CTTM): Visualizing the Polynomial's Resultant
ERIC Educational Resources Information Center
Alves, Francisco Regis Vieira
2015-01-01
We find several applications of the Dynamic System Geogebra--DSG related predominantly to the basic mathematical concepts at the context of the learning and teaching in Brasil. However, all these works were developed in the basic level of Mathematics. On the other hand, we discuss and explore, with DSG's help, some applications of the polynomial's…
Chemical Equilibrium and Polynomial Equations: Beware of Roots.
ERIC Educational Resources Information Center
Smith, William R.; Missen, Ronald W.
1989-01-01
Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…
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.
Effects of Polynomial Trends on Detrending Moving Average Analysis
NASA Astrophysics Data System (ADS)
Shao, Ying-Hui; Gu, Gao-Feng; Jiang, Zhi-Qiang; Zhou, Wei-Xing
2015-07-01
The detrending moving average (DMA) algorithm is one of the best performing methods to quantify the long-term correlations in nonstationary time series. As many long-term correlated time series in real systems contain various trends, we investigate the effects of polynomial trends on the scaling behaviors and the performances of three widely used DMA methods including backward algorithm (BDMA), centered algorithm (CDMA) and forward algorithm (FDMA). We derive a general framework for polynomial trends and obtain analytical results for constant shifts and linear trends. We find that the behavior of the CDMA method is not influenced by constant shifts. In contrast, linear trends cause a crossover in the CDMA fluctuation functions. We also find that constant shifts and linear trends cause crossovers in the fluctuation functions obtained from the BDMA and FDMA methods. When a crossover exists, the scaling behavior at small scales comes from the intrinsic time series while that at large scales is dominated by the constant shifts or linear trends. We also derive analytically the expressions of crossover scales and show that the crossover scale depends on the strength of the polynomial trends, the Hurst index, and in some cases (linear trends for BDMA and FDMA) the length of the time series. In all cases, the BDMA and the FDMA behave almost the same under the influence of constant shifts or linear trends. Extensive numerical experiments confirm excellently the analytical derivations. We conclude that the CDMA method outperforms the BDMA and FDMA methods in the presence of polynomial trends.
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
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.
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.
A comparison of companion matrix methods to find roots of a trigonometric polynomial
NASA Astrophysics Data System (ADS)
Boyd, John P.
2013-08-01
A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements
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)
Huang, Li
2016-11-01
Inspired by the recently proposed Legendre orthogonal polynomial representation for imaginary-time Green’s functions G(τ), we develop an alternate and superior representation for G(τ) and implement it in the hybridization expansion continuous-time quantum Monte Carlo impurity solver. This representation is based on the kernel polynomial method, which introduces some integral kernel functions to filter the numerical fluctuations caused by the explicit truncations of polynomial expansion series and can improve the computational precision significantly. As an illustration of the new representation, we re-examine the imaginary-time Green’s functions of the single-band Hubbard model in the framework of dynamical mean-field theory. The calculated results suggest that with carefully chosen integral kernel functions, whether the system is metallic or insulating, the Gibbs oscillations found in the previous Legendre orthogonal polynomial representation have been vastly suppressed and remarkable corrections to the measured Green’s functions have been obtained. Project supported by the National Natural Science Foundation of China (Grant No. 11504340).
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
Torres-Escobar, Ascención; Juárez-Rodríguez, María Dolores; Lamont, Richard J; Demuth, Donald R
2013-01-01
Autoinducer-2 (AI-2) is required for biofilm formation and virulence of the oral pathogen Aggregatibacter actinomycetemcomitans, and we previously showed that lsrB codes for a receptor for AI-2. The lsrB gene is expressed as part of the lsrACDBFG operon, which is divergently transcribed from an adjacent lsrRK operon. In Escherichia coli, lsrRK encodes a repressor and AI-2 kinase that function to regulate lsrACDBFG. To determine if lsrRK controls lsrACDBFG expression and influences biofilm growth of A. actinomycetemcomitans, we first defined the promoters for each operon. Transcriptional reporter plasmids containing the 255-bp lsrACDBFG-lsrRK intergenic region (IGR) fused to lacZ showed that essential elements of lsrR promoter reside 89 to 255 bp upstream from the lsrR start codon. Two inverted repeat sequences that represent potential binding sites for LsrR and two sequences resembling the consensus cyclic AMP receptor protein (CRP) binding site were identified in this region. Using electrophoretic mobility shift assay (EMSA), purified LsrR and CRP proteins were shown to bind probes containing these sequences. Surprisingly, the 255-bp IGR did not contain the lsrA promoter. Instead, a fragment encompassing nucleotides +1 to +159 of lsrA together with the 255-bp IGR was required to promote lsrA transcription. This suggests that a region within the lsrA coding sequence influences transcription, or alternatively that the start codon of A. actinomycetemcomitans lsrA has been incorrectly annotated. Transformation of ΔlsrR, ΔlsrK, ΔlsrRK, and Δcrp deletion mutants with lacZ reporters containing the lsrA or lsrR promoter showed that LsrR negatively regulates and CRP positively regulates both lsrACDBFG and lsrRK. However, in contrast to what occurs in E. coli, deletion of lsrK had no effect on the transcriptional activity of the lsrA or lsrR promoters, suggesting that another kinase may be capable of phosphorylating AI-2 in A. actinomycetemcomitans. Finally, biofilm
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…
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.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Stróżyna, Ewa
2015-12-01
We study the problem of formal classification of the vector fields of the form x ˙ = ax2 + bxy + cy2 + … , y ˙ = dx2 + exy + fy2 + … using formal changes of the coordinates, but not using the changes of the time. We focus on one special case (which is the most complex one): when the quadratic homogeneous part has a polynomial first integral. In the proofs we avoid complicated calculations. The method we use is effective and it is based on the method introduced in our previous work concerning the Bogdanov-Takens singularity.
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.
A general resolution of intractable problems in polynomial time through DNA Computing.
Sanches, C A A; Soma, N Y
2016-12-01
Based on a set of known biological operations, a general resolution of intractable problems in polynomial time through DNA Computing is presented. This scheme has been applied to solve two NP-Hard problems (Minimization of Open Stacks Problem and Matrix Bandwidth Minimization Problem) and three co-NP-Complete problems (associated with Hamiltonian Path, Traveling Salesman and Hamiltonian Circuit), which have not been solved with this model. Conclusions and open questions concerning the computational capacity of this model are presented, and research topics are suggested.
Krzywińska, Ewa; Kulik, Anna; Bucholc, Maria; Fernandez, Maria A.; Rodriguez, Pedro L.; Dobrowolska, Grażyna
2016-01-01
ABSTRACT Protein phosphatases 2C (PP2Cs) are important regulators of plant responses to abiotic stress. It is established that clade A PP2Cs inhibit ABA-activated SNF1-related protein kinases 2 (SnRK2s). Our recently published results show that ABI1, a member of clade A of PP2C is also a negative regulator of SnRK2.4, a kinase not activated in response to ABA. Here, we show that another member of this clade - PP2CA, interacts with and inhibits SnRK2.4. The salt-induced SnRK2.4/SnRK2.10 activity is higher in abi1–2 pp2ca-1 mutant than in wild type or single abi1 or pp2ca mutants, indicating that both phosphatases are inhibitors of SnRK2.4 and are at least partially redundant. Moreover, PP2CA together with ABI1 and SnRK2.4 regulates root growth in response to salinity. PMID:27901636
Painlevé V and time-dependent Jacobi polynomials
NASA Astrophysics Data System (ADS)
Basor, Estelle; Chen, Yang; Ehrhardt, Torsten
2010-01-01
In this paper we study the simplest deformation on a sequence of orthogonal polynomials. This in turn induces a deformation on the moment matrix of the polynomials and associated Hankel determinant. We replace the original (or reference) weight w0(x) (supported on \\mathbb {R} or subsets of \\mathbb {R}) by w0(x) e-tx. It is a well-known fact that under such a deformation the recurrence coefficients denoted as αn and βn evolve in t according to the Toda equations, giving rise to the time-dependent orthogonal polynomials and time-dependent determinants, using Sogo's terminology. If w0 is the normal density e^{-x^2},\\;x\\in \\mathbb {R}, or the gamma density xα e-x, x\\in \\mathbb {R}_{+}, α > -1, then the initial value problem of the Toda equations can be trivially solved. This is because under elementary scaling and translation the orthogonality relations reduce to the original ones. However, if w0 is the beta density (1 - x)α(1 + x)β, x in [ - 1, 1], α, β > -1, the resulting 'time-dependent' Jacobi polynomials will again satisfy a linear second-order ode, but no longer in the Sturm-Liouville form, which is to be expected. This deformation induces an irregular singular point at infinity in addition to three regular singular points of the hypergeometric equation satisfied by the Jacobi polynomials. We will show that the coefficients of this ode, as well as the Hankel determinant, are intimately related to a particular Painlevé V. In particular we show that \\\\textsf {p}_1(n,t), where \\\\textsf {p}_1(n,t) is the coefficient of zn-1 of the monic orthogonal polynomials associated with the 'time-dependent' Jacobi weight, satisfies, up to a translation in t, the Jimbo-Miwa σ-form of the same PV; while a recurrence coefficient αn(t) is up to a translation in t and a linear fractional transformation PV(α2/2, - β2/2, 2n + 1 + α + β, - 1/2). These results are found from combining a pair of nonlinear difference equations and a pair of Toda equations. This
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.
Simulating Nonequilibrium Radiation via Orthogonal Polynomial Refinement
2015-01-07
from data bases which are derived from quantum physics and transmit across the two different coordinates by a nearest neighbor search algorithm [7,8...complex radiative simulation must be built on the interaction of quantum physics, chemical kinetics, aerodynamics, and radiation transfer. The most...created a space partition algorithm for the nearest neighbor search optimization on both structured/unstructured grids and integrated with the high
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
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
Woo, Joo Yong; Jeong, Kwang Ju; Kim, Young Jin; Paek, Kyung-Hee
2016-10-01
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.
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.
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.
Estimation of asymptotic stability regions via composite homogeneous polynomial Lyapunov functions
NASA Astrophysics Data System (ADS)
Pang, Guochen; Zhang, Kanjian
2015-03-01
In this article, we present a new method to estimate the asymptotic stability regions for a class of nonlinear systems via composite homogeneous polynomial Lyapunov functions, where these nonlinear systems are approximated as a convex hull of some linear systems. Since level set of the composite homogeneous polynomial Lyapunov functions is a union set of several homogeneous polynomial functions, the composite homogeneous polynomial Lyapunov functions are nonconservative compared with quadratic or homogeneous polynomial Lyapunov functions. Numerical examples are used to illustrate the effectiveness of our method.
Miao, Lili; Mao, Xinguo; Wang, Jingyi; Liu, Zicheng; Zhang, Bin; Li, Weiyu; Chang, Xiaoping; Reynolds, Matthew; Wang, Zhenhua; Jing, Ruilian
2017-01-01
Plant-specific protein kinase SnRK2s play crucial roles in response to various environmental stimuli. TaSnRK2.3, a SnRK2 member, was involved in the response to multiple abiotic stresses in wheat. To facilitate the use of TaSnRK2.3 in wheat breeding, the three genomic sequences of TaSnRK2.3, originating from the A, B, and D genomes of hexaploid wheat, were obtained. Sequence polymorphism assays showing 4 and 10 variations were detected at TaSnRK2.3-1A and at TaSnRK2.3-1B, respectively, yet no variation was identified at TaSnRK2.3-1D. Three haplotypes for A genome, and two main haplotypes for B genome of TaSnRK2.3 were identified in 32 genotypes. Functional markers (2.3AM1, 2.3AM2, 2.3BM1, 2.3BM2) were successfully developed to distinguish different haplotypes. Association analysis was performed with the general linear model in TASSEL 2.1. The results showed that both TaSnRK2.3-1A and TaSnRK2.3-1B were significantly associated with plant height (PH), length of peduncle and penultimate node, as well as 1,000-grain weight (TGW) under different environments. Additionally, TaSnRK2.3-1B was significantly associated with stem water-soluble carbohydrates at flowering and mid-grain filling stages. Hap-1A-1 had higher TGW and lower PH; Hap-1B-1 had higher TGW and stem water-soluble carbohydrates, as well as lower PH, thus the two haplotypes were considered as elite haplotypes. Geographic distribution and allelic frequencies indicated that the two preferred haplotypes Hap-1A-1 and Hap-1B-1 were positively selected in the process of Chinese wheat breeding. These results could be valuable for genetic improvement and germplasm enhancement using molecular marker assisted selection in wheat breeding.
Using the network reliability polynomial to characterize and design networks
EUBANK, STEPHEN; YOUSSEF, MINA; KHORRAMZADEH, YASAMIN
2015-01-01
We consider methods for solving certain network characterization and design problems that arise in network epidemiology. We argue that the network reliability polynomial introduced by Moore and Shannon is a useful framework in which to reason about these problems. Specifically, we show how efficient estimation of the polynomial permits characterizing and distinguishing very large networks in ways that are are dynamically relevant. Furthermore, a generalization of flows and cuts to structures that determine the reliability suggests a new measure of edge or vertex centrality that we call criticality. We describe how criticality is related to the more common notion of betweenness and illustrate its application to targeting interventions to control outbreaks of infectious disease. Although our applications are to infectious disease outbreaks, the methods we develop are applicable to many other diffusive dynamical systems over complex networks. PMID:26085930
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.
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.
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.
Piecewise quartic polynomial curves with a local shape parameter
NASA Astrophysics Data System (ADS)
Han, Xuli
2006-10-01
Piecewise quartic polynomial curves with a local shape parameter are presented in this paper. The given blending function is an extension of the cubic uniform B-splines. The changes of a local shape parameter will only change two curve segments. With the increase of the value of a shape parameter, the curves approach a corresponding control point. The given curves possess satisfying shape-preserving properties. The given curve can also be used to interpolate locally the control points with GC2 continuity. Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon. As an application, the piecewise polynomial curves can intersect an ellipse at different knot values by choosing the value of the shape parameter. The given curve can approximate an ellipse from the both sides and can then yield a tight envelope for an ellipse. Some computing examples for curve design are given.
Quaternionic polynomials with multiple zeros: A numerical point of view
NASA Astrophysics Data System (ADS)
Falcão, M. I.; Miranda, F.; Severino, R.; Soares, M. J.
2017-01-01
In the ring of quaternionic polynomials there is no easy solution to the problem of finding a suitable definition of multiplicity of a zero. In this paper we discuss different notions of multiple zeros available in the literature and add a computational point of view to this problem, by taking into account the behavior of the well known Newton's method in the presence of such roots.
Evaluation of the tensor polynomial failure criterion for composite materials
NASA Technical Reports Server (NTRS)
Tennyson, R. C.; Macdonald, D.; Nanyaro, A. P.
1978-01-01
A comprehensive experimental and analytical evaluation of the tensor polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of laminated composite structures subject to a plane stress state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion.
Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations
2014-07-01
non- linear hybrid systems by linear algebraic methods. In Radhia Cousot and Matthieu Martel, editors, SAS, volume 6337 of LNCS, pages 373–389. Springer...Tarski. A decision method for elementary algebra and geometry. Bulletin of the American Mathematical Society, 59, 1951. [36] Wolfgang Walter. Ordinary...Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 July 2014
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.
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.
An exponential polynomial observer for synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Mata-Machuca, J. L.; Martínez-Guerra, R.; Aguilar-López, R.
2010-12-01
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation.
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.
From Jack to Double Jack Polynomials via the Supersymmetric Bridge
NASA Astrophysics Data System (ADS)
Lapointe, Luc; Mathieu, Pierre
2015-07-01
The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine {widehat{sl}_2} algebra.
Torus HOMFLYPT as the Hall-Littlewood polynomials
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Shakirov, Sh
2012-09-01
We show that the HOMFLYPT polynomials for the torus knots T[m, n] in all fundamental representations are equal to the Hall-Littlewood polynomials in a representation which depends on m, and with a quantum parameter, which depends on n. This makes the long-anticipated interpretation of Wilson averages in 3d Chern-Simons theory as characters precise, at least for the torus knots, and calls for further studies in this direction. This fact is deeply related to the Hall-Littlewood-MacDonald duality of character expansion of superpolynomials found in Mironov et al (2012 J. Geom. Phys. 62 148-55). In fact, the relation continues to hold for extended polynomials, but the symmetry between m and n is broken; then m is the number of strands in the braid. Besides the HOMFLYPT case with q = t, the torus superpolynomials are reduced to the single Hall-Littlewood characters in the two other distinguished cases: q = 0 and t = 0.
Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan
2015-01-01
An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient. PMID:26501287
Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan
2015-10-16
An important class of complementary metal-oxide-semiconductor (CMOS) image sensors are those where pixel responses are monotonic nonlinear functions of light stimuli. This class includes various logarithmic architectures, which are easily capable of wide dynamic range imaging, at video rates, but which are vulnerable to image quality issues. To minimize fixed pattern noise (FPN) and maximize photometric accuracy, pixel responses must be calibrated and corrected due to mismatch and process variation during fabrication. Unlike literature approaches, which employ circuit-based models of varying complexity, this paper introduces a novel approach based on low-degree polynomials. Although each pixel may have a highly nonlinear response, an approximately-linear FPN calibration is possible by exploiting the monotonic nature of imaging. Moreover, FPN correction requires only arithmetic, and an optimal fixed-point implementation is readily derived, subject to a user-specified number of bits per pixel. Using a monotonic spline, involving cubic polynomials, photometric calibration is also possible without a circuit-based model, and fixed-point photometric correction requires only a look-up table. The approach is experimentally validated with a logarithmic CMOS image sensor and is compared to a leading approach from the literature. The novel approach proves effective and efficient.
NASA Astrophysics Data System (ADS)
Shen, Xiang; Liu, Bin; Li, Qing-Quan
2017-03-01
The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates
Traversa, Fabio L; Di Ventra, Massimiliano
2017-02-01
We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP = P question related to constraints of poly-resources resolvability.
NASA Astrophysics Data System (ADS)
Traversa, Fabio L.; Di Ventra, Massimiliano
2017-02-01
We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP = P question related to constraints of poly-resources resolvability.
Torres-Escobar, Ascención; Juárez-Rodríguez, María Dolores; Demuth, Donald R
2014-04-01
We previously showed that the Aggregatibacter actinomycetemcomitans lsrACDBFG and lsrRK operons are regulated by LsrR and cyclic AMP receptor protein (CRP) and that proper regulation of the lsr locus is required for optimal biofilm growth by A. actinomycetemcomitans. Here, we identified sequences that reside immediately upstream from both the lsrA and lsrR start codons that closely resemble the consensus recognition sequence of Escherichia coli integration host factor (IHF) protein. A. actinomycetemcomitans IHFα and IHFβ were expressed and purified as hexahistidine fusion proteins, and using electrophoretic mobility shift assays (EMSAs), the IHFα-IHFβ protein complex was shown to bind to probes containing the putative IHF recognition sequences. In addition, single-copy chromosomal insertions of lsrR promoter-lacZ and lsrA promoter-lacZ transcriptional fusions in wild-type A. actinomycetemcomitans and ΔihfA and ΔihfB mutant strains showed that IHF differentially regulates the lsr locus and functions as a negative regulator of lsrRK and a positive regulator of lsrACDBFG. Deletion of ihfA or ihfB also reduced biofilm formation and altered biofilm architecture relative to the wild-type strain, and these phenotypes were partially complemented by a plasmid-borne copy of ihfA or ihfB. Finally, using 5' rapid amplification of cDNA ends (RACE), two transcriptional start sites (TSSs) and two putative promoters were identified for lsrRK and three TSSs and putative promoters were identified for lsrACDBFG. The function of the two lsrRK promoters and the positive regulatory role of IHF in regulating lsrACDBFG expression were confirmed with a series of lacZ transcriptional fusion constructs. Together, our results highlight the complex transcriptional regulation of the lsrACDBFG and lsrRK operons and suggest that multiple promoters and the architecture of the lsrACDBFG-lsrRK intergenic region may control the expression of these operons.
Benhammouda, Brahim
2015-01-01
The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the solution of two classes of higher-index Hessenberg DAEs. The method is based on Adomian polynomials and the differential transform method (DTM). First, the DTM is applied to the DAE where the differential transforms of nonlinear terms are calculated using Adomian polynomials. Then, based on the index condition, the resulting recursion system is transformed into a nonsingular linear algebraic system. This system is then solved to obtain the coefficients of the power series solution. The main advantage of the proposed technique is that it does not require an index reduction nor a linearization. Two test problems are solved to demonstrate the effectiveness of the method. In addition, to extend the domain of convergence of the approximate series solution, we propose a post-treatment with Laplace-Padé resummation method.
NASA Astrophysics Data System (ADS)
Bazargan, Hamid; Christie, Mike; Elsheikh, Ahmed H.; Ahmadi, Mohammad
2015-12-01
Markov Chain Monte Carlo (MCMC) methods are often used to probe the posterior probability distribution in inverse problems. This allows for computation of estimates of uncertain system responses conditioned on given observational data by means of approximate integration. However, MCMC methods suffer from the computational complexities in the case of expensive models as in the case of subsurface flow models. Hence, it is of great interest to develop alterative efficient methods utilizing emulators, that are cheap to evaluate, in order to replace the full physics simulator. In the current work, we develop a technique based on sparse response surfaces to represent the flow response within a subsurface reservoir and thus enable efficient exploration of the posterior probability density function and the conditional expectations given the data. Polynomial Chaos Expansion (PCE) is a powerful tool to quantify uncertainty in dynamical systems when there is probabilistic uncertainty in the system parameters. In the context of subsurface flow model, it has been shown to be more accurate and efficient compared with traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution when the order of the PCE is increased can be proved for the random variables with finite variances. However, the major drawback of PCE is related to the curse of dimensionality as the number of terms to be estimated grows drastically with the number of the input random variables. This renders the computational cost of classical PCE schemes unaffordable for reservoir simulation purposes when the deterministic finite element model is expensive to evaluate. To address this issue, we propose the reduced-terms polynomial chaos representation which uses an impact factor to only retain the most relevant terms of the PCE decomposition. Accordingly, the reduced-terms polynomial chaos proxy can be used as the pseudo
NASA Astrophysics Data System (ADS)
Dada, M.; Awojoyogbe, O. B.; Boubaker, K.
2011-04-01
In this study, we have used dimensional analysis to solve the heat equation inside an experimental laser welding setup. The solution for the heat equation is based on the assumption that heat energy diffuses equally on both sides of the laser beam axis and that the temperature along the axis through which the laser beam moves is constant. The amount of heat energy delivered by the laser to the keyhole is analyzed using the Boubaker polynomial expansion scheme BPES.
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.
NASA Astrophysics Data System (ADS)
Ishizuka, Hiroaki; Udagawa, Masafumi; Motome, Yukitoshi
2013-12-01
We present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized spins on a geometrically frustrated lattice. The method enables us to reduce the calculation amount by using the Chebyshev polynomial expansion of the density of states compared to a conventional Monte Carlo technique based on the exact diagonalization of the fermion Hamiltonian matrix. Further reduction is brought about by a real-space truncation of the vector-matrix operations. We apply the method to the model with spin-ice type Ising spins on a three-dimensional pyrochlore lattice and carefully examine the convergence in terms of the order of polynomials and the truncation distance. We find that, in a wide range of electron density at a relatively weak Kondo coupling compared to the noninteracting bandwidth, the results by the polynomial expansion method show good convergence to those by the conventional method within reasonable numbers of polynomials. This enables us to study the systems up to 4×83=2048 sites, while the previous study by the conventional method was limited to 4×43=256 sites. On the other hand, the real-space truncation is not helpful in reducing the calculation amount for the system sizes that we reached, as the sufficient convergence is obtained when most of the sites are involved within the truncation distance. The necessary truncation distance, however, appears not to show significant system size dependence, suggesting that the truncation method becomes efficient for larger system sizes.
Rapid induction of malignant tumor in Sprague-Dawley rats by injection of RK3E-ras cells.
Kim, Soo-A; Kim, Hyun-Woo; Kim, Do-Kyung; Kim, Su-Gwan; Park, Joo-Cheol; Kang, Dong-Wan; Kim, Si-Wouk; Ahn, Sang-Gun; Yoon, Jung-Hoon
2006-04-08
Several tumor animal models have been provided as a tool for developing cancer therapy. Here, we developed rapid, easy-to use, and cost-effective new rat animal model for invasion and metastasis of cancer using genetically k-ras-induced rat kidney cells (RK3E-ras). We observed tumor as early as 3 days after injection of RK3E-ras cells in subcutaneous of Sprague-Dawley rats. Tumor size and volume were increased exponentially for 2 weeks. The tail vein injected rats obtained the lethal infiltration in the lung within 2 weeks. This tumor animal model has great potential for studying cancer processes and short-term screening of variable cancer therapy strategy.
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).
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.
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.
MLK-3 activates the SAPK/JNK and p38/RK pathways via SEK1 and MKK3/6.
Tibbles, L A; Ing, Y L; Kiefer, F; Chan, J; Iscove, N; Woodgett, J R; Lassam, N J
1996-01-01
Mixed lineage kinase-3 (MLK-3) is a 97 kDa serine/threonine kinase with multiple interaction domains, including a Cdc42 binding motif, but unknown function. Cdc42 and the related small GTP binding protein Rac1 can activate the SAPK/JNK and p38/RK stress-responsive kinase cascades, suggesting that MLK-3 may have a role in upstream regulation of these pathways. In support of this role, we demonstrate that MLK-3 can specifically activate the SAPK/JNK and p38/RK pathways, but has no effect on the activation of ERKs. Immunoprecipitated MLK-3 catalyzed the phosphorylation of SEK1 in vitro, and co-transfected MLK-3 induced phosphorylation of SEK1 and MKK3 at sites required for activation, suggesting direct regulation of these protein kinases. Furthermore, interactions between MLK-3 and SEK and MLK-3 and MKK6 were observed in co-precipitation experiments. Finally, kinase-dead mutants of MLK-3 blocked activation of the SAPK pathway by a newly identified mammalian analog of Ste20, germinal center kinase, but not by MEKK, suggesting that MLK-3 functions to activate the SAPK/JNK and p38/RK cascades in response to stimuli transduced by Ste20-like kinases. Images PMID:9003778
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.
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.
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.
NASA Astrophysics Data System (ADS)
Shang, Fang; Liu, Yungang
2014-03-01
In this paper, the adaptive disturbance attenuation via output feedback is investigated for a class of nonlinear systems with uncertain control coefficients. Notably, the considered systems depend on unmeasured states with polynomial-of-output growth rate, and hence the systems have severe unknowns. Due to the existence of both the virtual and actual uncertain control coefficients, we first introduce a suitable state transformation, such that the control design becomes convenient. Then, we construct an appropriate and simple state observer with two important gains, and one gain is large enough to handle the constants appeared in the design procedure, and the other is updated on-line to deal with the polynomial-of-output growth rate of the system. After that, an output feedback controller is proposed based on the observer in a step-by-step manner. Finally, it is shown that, by appropriate choice of the design parameters, the states of the closed-loop system are globally bounded, and the disturbance attenuation is achieved in the sense of ?-gain.
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.
Assessment of mitral Björk-Shiley prosthetic dysfunction using digitised M mode echocardiography.
Dawkins, K D; Cotter, L; Gibson, D G
1984-01-01
Digitised M mode echocardiograms were analysed in 22 patients with possible Björk-Shiley mitral prosthetic dysfunction. Patients with paraprosthetic mitral regurgitation had a significantly greater shortening fraction, an increased peak rate of dimension change during systole, and an increased peak velocity of circumferential fibre shortening than those with poor left ventricular function. Patients with a clotted prosthesis had lower values for shortening fraction and peak rate of dimension change during systole than patients with paraprosthetic regurgitation. In this latter group, the peak rate of dimension change during diastole and peak lengthening rate were greater than in either those patients with poor left ventricular function or those with a clotted prosthesis. In addition, the peak lengthening rate was greater in those with a clotted prosthesis than in those with poor left ventricular function. Thus M mode echocardiography is a useful method of assessing mitral prosthetic dysfunction and allows patients with paraprosthetic regurgitation to be distinguished from those with either poor left ventricular function or a clotted prosthesis. PMID:6691866
N-Myristoylation Regulates the SnRK1 Pathway in Arabidopsis[W
Pierre, Michèle; Traverso, José A.; Boisson, Bertrand; Domenichini, Séverine; Bouchez, David; Giglione, Carmela; Meinnel, Thierry
2007-01-01
Cotranslational and posttranslational modifications are increasingly recognized as important in the regulation of numerous essential cellular functions. N-myristoylation is a lipid modification ensuring the proper function and intracellular trafficking of proteins involved in many signaling pathways. Arabidopsis thaliana, like human, has two tightly regulated N-myristoyltransferase (NMT) genes, NMT1 and NMT2. Characterization of knockout mutants showed that NMT1 was strictly required for plant viability, whereas NMT2 accelerated flowering. NMT1 impairment induced extremely severe defects in the shoot apical meristem during embryonic development, causing growth arrest after germination. A transgenic plant line with an inducible NMT1 gene demonstrated that NMT1 expression had further effects at later stages. NMT2 did not compensate for NMT1 in the nmt1-1 mutant, but NMT2 overexpression resulted in shoot and root meristem abnormalities. Various data from complementation experiments in the nmt1-1 background, using either yeast or human NMTs, demonstrated a functional link between the developmental arrest of nmt1-1 mutants and the myristoylation state of an extremely small set of protein targets. We show here that protein N-myristoylation is systematically associated with shoot meristem development and that SnRK1 (for SNF1-related kinase) is one of its essential primary targets. PMID:17827350
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.
A subset polynomial neural networks approach for breast cancer diagnosis.
O'Neill, T J; Penm, Jack; Penm, Jonathan
2007-01-01
Breast cancer is a very common and serious cancer for women that is diagnosed in one of every eight Australian women before the age of 85. The conventional method of breast cancer diagnosis is mammography. However, mammography has been reported to have poor diagnostic capability. In this paper we have used subset polynomial neural network techniques in conjunction with fine needle aspiration cytology to undertake this difficult task of predicting breast cancer. The successful findings indicate that adoption of NNs is likely to lead to increased survival of women with breast cancer, improved electronic healthcare, and enhanced quality of life.
The BQP-hardness of approximating the Jones polynomial
NASA Astrophysics Data System (ADS)
Aharonov, Dorit; Arad, Itai
2011-03-01
A celebrated important result due to Freedman et al (2002 Commun. Math. Phys. 227 605-22) states that providing additive approximations of the Jones polynomial at the kth root of unity, for constant k=5 and k>=7, is BQP-hard. Together with the algorithmic results of Aharonov et al (2005) and Freedman et al (2002 Commun. Math. Phys. 227 587-603), this gives perhaps the most natural BQP-complete problem known today and motivates further study of the topic. In this paper, we focus on the universality proof; we extend the result of Freedman et al (2002) to ks that grow polynomially with the number of strands and crossings in the link, thus extending the BQP-hardness of Jones polynomial approximations to all values to which the AJL algorithm applies (Aharonov et al 2005), proving that for all those values, the problems are BQP-complete. As a side benefit, we derive a fairly elementary proof of the Freedman et al density result, without referring to advanced results from Lie algebra representation theory, making this important result accessible to a wider audience in the computer science research community. We make use of two general lemmas we prove, the bridge lemma and the decoupling lemma, which provide tools for establishing the density of subgroups in SU(n). Those tools seem to be of independent interest in more general contexts of proving the quantum universality. Our result also implies a completely classical statement, that the multiplicative approximations of the Jones polynomial, at exactly the same values, are #P-hard, via a recent result due to Kuperberg (2009 arXiv:0908.0512). Since the first publication of those results in their preliminary form (Aharonov and Arad 2006 arXiv:quant-ph/0605181), the methods we present here have been used in several other contexts (Aharonov and Arad 2007 arXiv:quant-ph/0702008; Peter and Stephen 2008 Quantum Inf. Comput. 8 681). The present paper is an improved and extended version of the results presented by Aharonov and Arad
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.
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.
NASA Astrophysics Data System (ADS)
Vignat, C.; Lamberti, P. W.
2009-10-01
Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.
Mahajan, Virendra N
2012-06-20
In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as
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.
Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
NASA Astrophysics Data System (ADS)
Manno, Gianni; Pavlov, Maxim V.
2017-03-01
Starting from a homogeneous polynomial in momenta of arbitrary order we extract multi-component hydrodynamic-type systems which describe 2-dimensional geodesic flows admitting the initial polynomial as integral. All these hydrodynamic-type systems are semi-Hamiltonian, thus implying that they are integrable according to the generalized hodograph method. Moreover, they are integrable in a constructive sense as polynomial first integrals allow to construct generating equations of conservation laws. According to the multiplicity of the roots of the polynomial integral, we separate integrable particular cases.
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.
Evolutionary polynomial regression applied to rainfall triggered landslide reactivation alert
NASA Astrophysics Data System (ADS)
Simeone, Vincenzo; Doglioni, Angelo; Fiorillo, Francesco
2010-05-01
Evolutionary Polynomial Regression (EPR) is a hybrid evolutionary modelling paradigm, which allows for the construction of explicit model equations, starting from measured data. It was successfully applied to multiple cases study as well as to different model aims, i.e. dynamic natural systems, pipe burst analysis, geotechnical soil characterization, etc. A landslide located on a slope on the Adriatic coast of south Italy, close to the small town of Petacciato, is here investigated. In particular, starting from the rainfall data, which are available for the last 110 years as daily records, and from 11 activation episodes which range between 1932 and 2009, a data-driven model aimed at describing the reactivation as function of cumulative rainfall values was identified. Petacciato landslide is a deep large landslide; it lays on a slope characterized by outcropping Pleistocenic blue clays, which are somewhere spaced out of thin loamy-sandy layers. Moving towards the upper part of the slope, which is closer to the town, blue clays are progressively replaced by sand and conglomerates. The slope is also characterized by frequent terraces which show slope inversions. The landslide is quite wide and the slope is characterized by a low steepness. In addition, the bottom of the sea, close to the shore, is very gently deepening, thus excluding an effect of water on the slope stability. For these reasons, the dynamic of Petacciato landslide is quite difficult to be interpreted. The particular mechanism of the landslide as well as the exceptional data availability, in particular in terms of reactivations, make it possible to cope with this system according to a data mining approach. It was observed that the landslide reactivated after long rainy periods, and then rainfall was assumed as a triggering factor. Therefore, cumulative rainfall values were constructed in order to account with long periods, up to 500 days. These were used as candidate inputs for the construction of a
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.
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.
Colored HOMFLY polynomials of knots presented as double fat diagrams
NASA Astrophysics Data System (ADS)
Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar
2015-07-01
Many knots and links in S 3 can be drawn as gluing of three manifolds with one or more four-punctured S 2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four -strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants which cannot be distinguished by [21] representation. The difference between the [21]-colored HOMFLY of two mutants seems to have a general form, with A-dependence completely defined by the old conjecture due to Morton and Cromwell. In particular, we check it for an entire multi-parametric family of mutant knots evaluated using evolution method.
Predicting Physical Time Series Using Dynamic Ridge Polynomial Neural Networks
Al-Jumeily, Dhiya; Ghazali, Rozaida; Hussain, Abir
2014-01-01
Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques. PMID:25157950
Application of Designer Polynomials to the Soft-Coulomb Potential
NASA Astrophysics Data System (ADS)
Weatherford, Charles; Wynn, Albert, III; Red, Eddie; Mathis, Clausell
2004-05-01
In a recent article [C.A. Weatherford, E. Red, A. Wynn III, International Journal of Quantum Chemistry 90, 1289-1294 (2002)], an algorithm was described whereby a synthetic weighted polynomial basis may be constructed which is adapted (designed) to a particular potential. It was applied therein to the Schroedinger equation with a coulomb potential in one dimension (-1/|x| ). A weighted polynomial basis with weight function w(x)=exp(-a|x|) was employed. It was observed that this potential had no even parity solutions - only odd parity solutions. The question arises as to the relationship of the solutions (eigenfunctions and eigenvalues) for this hard coulomb potential to the solutions for the soft coulomb potential (-1/ √x^2+b^2^1/2 ). In particular, since the soft coulomb potential is clearly expected to possess both even and odd parity solutions, how do these solutions behave as b->0 and thus what happens to the even solutions. This problem is deceptively difficult none of the standard basis sets produce a variational minimum as a function of 'a' for nonzero 'b'. This is apparently why this problem has never been done before. A new orthonormal basis was designed with weight function w(x)=exp(-a√x^2+b^2) which did produce a variational minimum for variable a and arbitrary fixed 'b'. The present paper describes these solutions and clearly indicates how they behave as b->0 .
Numerical solution of DGLAP equations using Laguerre polynomials expansion and Monte Carlo method.
Ghasempour Nesheli, A; Mirjalili, A; Yazdanpanah, M M
2016-01-01
We investigate the numerical solutions of the DGLAP evolution equations at the LO and NLO approximations, using the Laguerre polynomials expansion. The theoretical framework is based on Furmanski et al.'s articles. What makes the content of this paper different from other works, is that all calculations in the whole stages to extract the evolved parton distributions, are done numerically. The employed techniques to do the numerical solutions, based on Monte Carlo method, has this feature that all the results are obtained in a proper wall clock time by computer. The algorithms are implemented in FORTRAN and the employed coding ideas can be used in other numerical computations as well. Our results for the evolved parton densities are in good agreement with some phenomenological models. They also indicate better behavior with respect to the results of similar numerical calculations.
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.
Balagué, Claudine; Gouget, Anne; Bouchez, Olivier; Souriac, Camille; Haget, Nathalie; Boutet-Mercey, Stéphanie; Govers, Francine; Roby, Dominique; Canut, Hervé
2016-07-11
On microbial attack, plants can detect invaders and activate plant innate immunity. For the detection of pathogen molecules or cell wall damage, plants employ receptors that trigger the activation of defence responses. Cell surface proteins that belong to large families of lectin receptor kinases are candidates to function as immune receptors. Here, the function of LecRK-I.9 (At5g60300), a legume-type lectin receptor kinase involved in cell wall-plasma membrane contacts and in extracellular ATP (eATP) perception, was studied through biochemical, gene expression and reverse genetics approaches. In Arabidopsis thaliana, LecRK-I.9 expression is rapidly, highly and locally induced on inoculation with avirulent strains of Pseudomonas syringae pv. tomato (Pst). Two allelic lecrk-I.9 knock-out mutants showed decreased resistance to Pst. Conversely, over-expression of LecRK-I.9 led to increased resistance to Pst. The analysis of defence gene expression suggests an alteration of both the salicylic acid (SA) and jasmonic acid (JA) signalling pathways. In particular, LecRK-I.9 expression during plant-pathogen interaction was dependent on COI1 (CORONATINE INSENSITIVE 1) and JAR1 (JASMONATE RESISTANT 1) components, and JA-responsive transcription factors (TFs) showed altered levels of expression in plants over-expressing LecRK-I.9. A similar misregulation of these TFs was obtained by JA treatment. This study identified LecRK-I.9 as necessary for full resistance to Pst and demonstrated its involvement in the control of defence against pathogens through a regulation of JA signalling components. The role of LecRK-I.9 is discussed with regard to the potential molecular mechanisms linking JA signalling to cell wall damage and/or eATP perception.
Li, Jia; Zhang, Shengli; Huang, Shiping; Wang, Peng; Tian, Huiping
2013-02-15
R{sub 3}ZnH{sub 5} (R=K, Rb, Cs) series have been investigated with respect to the crystal structure, electronic and thermodynamic properties using first-principle methods based on density functional theory with generalized gradient approximation. The optimized structures and atomic coordinates are in good agreement with the experimental data. The strong covalent interactions are obtained between Zn and H atoms in the 18-electron [ZnH{sub 4}]{sup 2-} complex, while an ionic interaction is found between [ZnH{sub 4}]{sup 2-} and R atom. The formation enthalpies show that the formations of R{sub 3}ZnH{sub 5} hydrides are all exothermic at 298 K. The vibration free energies of R{sub 3}ZnH{sub 5} show that the thermodynamic stabilities of R{sub 3}ZnH{sub 5} hydrides decrease with the increasing diameter of R atom. Two possible decomposition reactions of R{sub 3}ZnH{sub 5} series have been suggested in our work. One (reaction one) is that R{sub 3}ZnH{sub 5} hydrides decomposes to elements directly, and the other (reaction two) is that R{sub 3}ZnH{sub 5} hydrides decomposes to RH hydride. The results show that the first decomposition reaction is more favorable one. The spontaneous decomposition reaction of K{sub 3}ZnH{sub 5} hydrides occur upon 465 K via reaction one, and 564 K via reaction two, respectively. - Graphical abstract: Total charge density of K{sub 3}ZnH{sub 5}. Highlights: Black-Right-Pointing-Pointer Electronic and thermodynamic properties of R{sub 3}ZnH{sub 5} (R=K, Rb, Cs) were calculated. Black-Right-Pointing-Pointer The formations of R{sub 3}ZnH{sub 5} hydrides are all exothermic at 298 K. Black-Right-Pointing-Pointer The thermodynamic stabilities decrease with the increasing diameter of R atom. Black-Right-Pointing-Pointer Two possible decomposition pathways of R{sub 3}ZnH{sub 5} were investigated.
NASA Astrophysics Data System (ADS)
Bukweli Kyemba, J. D.; Hounkonnou, M. N.
2012-06-01
This paper addresses a new characterization of ({ R},p,q)-deformed Rogers-Szegö polynomials by providing their three-term recurrence relation and the associated quantum algebra built with corresponding creation and annihilation operators. The whole construction is performed in a unified way, generalizing all known relevant results which are straightforwardly derived as particular cases. Continuous ({ R},p,q)-deformed Hermite polynomials and their recurrence relation are also deduced. Novel relations are provided and discussed.
Ananieva, Elitsa A; Gillaspy, Glenda E; Ely, Amanda; Burnette, Ryan N; Erickson, F Les
2008-12-01
In plants, myoinositol signaling pathways have been associated with several stress, developmental, and physiological processes, but the regulation of these pathways is largely unknown. In our efforts to better understand myoinositol signaling pathways in plants, we have found that the WD40 repeat region of a myoinositol polyphosphate 5-phosphatase (5PTase13; At1g05630) interacts with the sucrose nonfermenting-1-related kinase (SnRK1.1) in the yeast two-hybrid system and in vitro. Plant SnRK1 proteins (also known as AKIN10/11) have been described as central integrators of sugar, metabolic, stress, and developmental signals. Using mutants defective in 5PTase13, we show that 5PTase13 can act as a regulator of SnRK1 activity and that regulation differs with different nutrient availability. Specifically, we show that under low-nutrient or -sugar conditions, 5PTase13 acts as a positive regulator of SnRK1 activity. In contrast, under severe starvation conditions, 5PTase13 acts as a negative regulator of SnRK1 activity. To delineate the regulatory interaction that occurs between 5PTase13 and SnRK1.1, we used a cell-free degradation assay and found that 5PTase13 is required to reduce the amount of SnRK1.1 targeted for proteasomal destruction under low-nutrient conditions. This regulation most likely involves a 5PTase13-SnRK1.1 interaction within the nucleus, as a 5PTase13:green fluorescent protein was localized to the nucleus. We also show that a loss of function in 5PTase13 leads to nutrient level-dependent reduction of root growth, along with abscisic acid (ABA) and sugar insensitivity. 5ptase13 mutants accumulate less inositol 1,4,5-trisphosphate in response to sugar stress and have alterations in ABA-regulated gene expression, both of which are consistent with the known role of inositol 1,4,5-trisphosphate in ABA-mediated signaling. We propose that by forming a protein complex with SnRK1.1 protein, 5PTase13 plays a regulatory role linking inositol, sugar, and stress
Multifidelity, Multidisciplinary Design Under Uncertainty with Non-Intrusive Polynomial Chaos
NASA Technical Reports Server (NTRS)
West, Thomas K., IV; Gumbert, Clyde
2017-01-01
The primary objective of this work is to develop an approach for multifidelity uncertainty quantification and to lay the framework for future design under uncertainty efforts. In this study, multifidelity is used to describe both the fidelity of the modeling of the physical systems, as well as the difference in the uncertainty in each of the models. For computational efficiency, a multifidelity surrogate modeling approach based on non-intrusive polynomial chaos using the point-collocation technique is developed for the treatment of both multifidelity modeling and multifidelity uncertainty modeling. Two stochastic model problems are used to demonstrate the developed methodologies: a transonic airfoil model and multidisciplinary aircraft analysis model. The results of both showed the multifidelity modeling approach was able to predict the output uncertainty predicted by the high-fidelity model as a significant reduction in computational cost.
Ibañez, Diego Rodríguez; Gómez-Pedrero, José A; Alonso, Jose; Quiroga, Juan A
2016-03-21
A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.
Identification of nonlinear vibrating structures by polynomial expansion in the z-domain
NASA Astrophysics Data System (ADS)
Fasana, Alessandro; Garibaldi, Luigi; Marchesiello, Stefano
2017-02-01
A new method in the frequency domain for the identification of nonlinear vibrating structures is described, by adopting the perspective of nonlinearities as internal feedback forces. The technique is based on a polynomial expansion representation of the frequency response function of the underlying linear system, relying on a z-domain formulation. A least squares approach is adopted to take into account the information of all the frequency response functions but, when large data sets are used, the solution of the resulting system of algebraic linear equations can be a difficult task. A procedure to drastically reduce the matrix dimensions and consequently the computational cost - which largely depends on the number of spectral lines - is adopted, leading to a compact and well conditioned problem. The robustness and numerical performances of the method are demonstrated by its implementation on simulated data from single and two degree of freedom systems with typical nonlinear characteristics.
The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
Jafarov, E. I.; Van der Jeugt, J.
2013-10-15
We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg–Weyl superalgebra or “the algebra of supersymmetric quantum mechanics,” and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter γ. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C{sub n} with parameter γ{sup 2}. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.
A weighted ℓ{sub 1}-minimization approach for sparse polynomial chaos expansions
Peng, Ji; Hampton, Jerrad; Doostan, Alireza
2014-06-15
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ{sub 1}-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weightedℓ{sub 1}-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with a random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.
A model of flexion-extension movement in hip joint using polynomial interpolation
NASA Astrophysics Data System (ADS)
Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan
2013-10-01
The study proposes a mathematical model of flexion-extension movement in hip joint based on Lagrange polynomial interpolation. In order to develop and validate the proposed model the angle of flexion-extension (F-E) in hip joint was analyzed. The two main reasons of this option rely on the importance of the hip joint in human locomotion and the fact that flexion-extension movement is developed in most of the human joints. The mathematical model of joint movement allows developing a more detailed kinematic analysis of the joint movements. The raw data representing the variation of the flexion-extension angle in hip joint was achieved by experimental kinematic analysis of a lot of ten young healthy subjects.
Shen, Qingtang; Liu, Zhou; Song, Fengming; Xie, Qi; Hanley-Bowdoin, Linda; Zhou, Xueping
2011-11-01
The βC1 protein of tomato yellow leaf curl China β-satellite functions as a pathogenicity determinant. To better understand the molecular basis of βC1 in pathogenicity, a yeast two-hybrid screen of a tomato (Solanum lycopersicum) cDNA library was carried out using βC1 as bait. βC1 interacted with a tomato SUCROSE-NONFERMENTING1-related kinase designated as SlSnRK1. Their interaction was confirmed using a bimolecular fluorescence complementation assay in Nicotiana benthamiana cells. Plants overexpressing SnRK1 were delayed for symptom appearance and contained lower levels of viral and satellite DNA, while plants silenced for SnRK1 expression developed symptoms earlier and accumulated higher levels of viral DNA. In vitro kinase assays showed that βC1 is phosphorylated by SlSnRK1 mainly on serine at position 33 and threonine at position 78. Plants infected with βC1 mutants containing phosphorylation-mimic aspartate residues in place of serine-33 and/or threonine-78 displayed delayed and attenuated symptoms and accumulated lower levels of viral DNA, while plants infected with phosphorylation-negative alanine mutants contained higher levels of viral DNA. These results suggested that the SlSnRK1 protein attenuates geminivirus infection by interacting with and phosphorylating the βC1 protein.
Why the Faulhaber Polynomials Are Sums of Even or Odd Powers of (n + 1/2)
ERIC Educational Resources Information Center
Hersh, Reuben
2012-01-01
By extending Faulhaber's polynomial to negative values of n, the sum of the p'th powers of the first n integers is seen to be an even or odd polynomial in (n + 1/2) and therefore expressible in terms of the sum of the first n integers.
Root-cubing and general root-powering methods for finding the zeros of polynomials
NASA Technical Reports Server (NTRS)
Bareiss, E. H.
1969-01-01
Mathematical analysis technique generalizes a root squaring and root cubing method into a general root powering method. The introduction of partitioned polynomials into this general root powering method simplifies the coding of the polynomial transformations into input data suitable for processing by computer. The method includes analytic functions.
NASA Astrophysics Data System (ADS)
Slavyanov, S. Yu.; Satco, D. A.; Ishkhanyan, A. M.; Rotinyan, T. A.
2016-12-01
We discuss several examples of generating apparent singular points as a result of differentiating particular homogeneous linear ordinary differential equations with polynomial coefficients and formulate two general conjectures on the generation and removal of apparent singularities in arbitrary Fuchsian differential equations with polynomial coefficients. We consider a model problem in polymer physics.
Pointwise convergence of derivatives of Lagrange interpolation polynomials for exponential weights
NASA Astrophysics Data System (ADS)
Damelin, S. B.; Jung, H. S.
2005-01-01
For a general class of exponential weights on the line and on (-1,1), we study pointwise convergence of the derivatives of Lagrange interpolation. Our weights include even weights of smooth polynomial decay near +/-[infinity] (Freud weights), even weights of faster than smooth polynomial decay near +/-[infinity] (Erdos weights) and even weights which vanish strongly near +/-1, for example Pollaczek type weights.
Hardness Results for Agnostically Learning Low-Degree Polynomial Threshold Functions
2011-01-01
anti-concentration result for low-degree polynomials over Gaussian ran- dom variables, due to Carbery and Wright: Theorem A.2 ([5]). Let p : Rn → R be...puter Science, 350(1):24–39, January 2006. [5] A. Carbery and J. Wright. Distributional and Lq norm inequalities for polynomials over convex bodies in
On ambiguity in knot polynomials for virtual knots
NASA Astrophysics Data System (ADS)
Morozov, A.; Morozov, And.; Popolitov, A.
2016-06-01
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual q and A =qN. These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conveniently observed in the hypercube formalism: then they substitute q-dimensions of certain fat graphs, which are not constrained by recursion and can be chosen arbitrarily. The number of these new topological invariants seems to grow fast with the number of non-virtual crossings: 0, 1, 1, 5, 15, 91, 784, 9160, ... This number can be decreased by imposing the factorization requirement for composites, in addition to topological invariance - still freedom remains. None of these new parameters, however, appears in HOMFLY for Kishino unknot, which thus remains unseparated from the ordinary unknots even by this enriched set of knot invariants.
Absorption and Fluorescence Lineshape Theory for Polynomial Potentials.
Anda, André; De Vico, Luca; Hansen, Thorsten; Abramavičius, Darius
2016-12-13
The modeling of vibrations in optical spectra relies heavily on the simplifications brought about by using harmonic oscillators. However, realistic molecular systems can deviate substantially from this description. We develop two methods which show that the extension to arbitrarily shaped potential energy surfaces is not only straightforward, but also efficient. These methods are applied to an electronic two-level system with potential energy surfaces of polynomial form and used to study anharmonic features such as the zero-phonon line shape and mirror-symmetry breaking between absorption and fluorescence spectra. The first method, which constructs vibrational wave functions as linear combinations of the harmonic oscillator wave functions, is shown to be extremely robust and can handle large anharmonicities. The second method uses the cumulant expansion, which is readily solved, even at high orders, thanks to an ideally suited matrix theorem.
Representation of videokeratoscopic height data with Zernike polynomials
NASA Astrophysics Data System (ADS)
Schwiegerling, Jim; Greivenkamp, John E.; Miller, Joseph M.
1995-10-01
Videokeratoscopic data are generally displayed as a color-coded map of corneal refractive power, corneal curvature, or surface height. Although the merits of the refractive power and curvature methods have been extensively debated, the display of corneal surface height demands further investigation. A significant drawback to viewing corneal surface height is that the spherical and cylindrical components of the cornea obscure small variations in the surface. To overcome this drawback, a methodology for decomposing corneal height data into a unique set of Zernike polynomials is presented. Repeatedly removing the low-order Zernike terms reveals the hidden height variations. Examples of the decomposition-and-display technique are shown for cases of astigmatism, keratoconus, and radial keratotomy. Copyright (c) 1995 Optical Society of America
Virasoro constraints and polynomial recursion for the linear Hodge integrals
NASA Astrophysics Data System (ADS)
Guo, Shuai; Wang, Gehao
2016-11-01
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.
Virasoro constraints and polynomial recursion for the linear Hodge integrals
NASA Astrophysics Data System (ADS)
Guo, Shuai; Wang, Gehao
2017-04-01
The Hodge tau-function is a generating function for the linear Hodge integrals. It is also a tau-function of the KP hierarchy. In this paper, we first present the Virasoro constraints for the Hodge tau-function in the explicit form of the Virasoro equations. The expression of our Virasoro constraints is simply a linear combination of the Virasoro operators, where the coefficients are restored from a power series for the Lambert W function. Then, using this result, we deduce a simple version of the Virasoro constraints for the linear Hodge partition function, where the coefficients are restored from the Gamma function. Finally, we establish the equivalence relation between the Virasoro constraints and polynomial recursion formula for the linear Hodge integrals.
Simulation of massive public health data by power polynomials
Demirtas, Hakan; Hedeker, Donald; Mermelstein, Robin J.
2013-01-01
Situations in which multiple outcomes and predictors of different distributional types are collected are becoming increasingly common in public health practice, and joint modeling of mixed types has been gaining popularity in recent years. Evaluation of various statistical techniques that have been developed for mixed data in simulated environments necessarily requires joint generation of multiple variables. Most massive public health data sets include different types of variables. For instance in clustered or longitudinal designs, often multiple variables are measured or observed for each individual or at each occasion. This work is motivated by a need to jointly generate binary and possibly non-normal continuous variables. We illustrate the use of power polynomials to simulate multivariate mixed data on the basis of a real adolescent smoking study. We believe that our proposed technique for simulating such intensive data has potential to be a handy methodological addition to public health researchers’ toolkit. PMID:22532052
Coulomb branch Hilbert series and Hall-Littlewood polynomials
NASA Astrophysics Data System (ADS)
Cremonesi, Stefano; Hanany, Amihay; Mekareeya, Noppadol; Zaffaroni, Alberto
2014-09-01
There has been a recent progress in understanding the chiral ring of 3d = 4 superconformal gauge theories by explicitly constructing an exact generating function (Hilbert series) counting BPS operators on the Coulomb branch. In this paper we introduce Coulomb branch Hilbert series in the presence of background magnetic charges for flavor symmetries, which are useful for computing the Hilbert series of more general theories through gluing techniques. We find a simple formula of the Hilbert series with background magnetic charges for T ρ ( G) theories in terms of Hall-Littlewood polynomials. Here G is a classical group and ρ is a certain partition related to the dual group of G. The Hilbert series for vanishing background magnetic charges show that Coulomb branches of T ρ ( G) theories are complete intersections. We also demonstrate that mirror symmetry maps background magnetic charges to baryonic charges.
Orthogonal polynomial projection quantization: a new Hill determinant method
NASA Astrophysics Data System (ADS)
Handy, C. R.; Vrinceanu, D.
2013-04-01
Accurate energy eigenvalues are obtained by simply projecting the unknown bound state wave function on, essentially, arbitrary sets of orthogonal polynomials, and setting a subset of these to zero. The projection integrals are represented in terms of the power moments of the wave function, obtained recursively by transforming Schrödinger’s equation into a moment equation. Because unbounded wave functions do not have power moments, all solutions are guaranteed to be L2, resulting in a more robust, rapidly converging and stable method when compared with configuration space Hill determinant methods. More importantly, our approach permits the use of arbitrary, nonanalytic, positive reference functions, including those that manifest the true asymptotic behavior of the discrete states. These advantages are not usually possible with the standard Hill approach. The formulation presented here can be applied to any problem for which Schrödinger’s equation can be transformed into a moment equation. In this regard it is related to the L2 quantization prescription developed by Tymczak et al (1998 Phys. Rev. Lett. 80 3674; 1998 Phys. Rev. A 58 2708) corresponding to the Hill determinant method in momentum space, and to the eigenvalue moment method (Handy and Bessis 1985 Phys. Rev. Lett. 55 931; Handy et al 1988 Phys. Rev. Lett. 60 253), the first use of semidefinite programming related analysis in quantum physics. The latter method can be used to generate the ground state, whose orthogonal polynomials can serve to generate even more rapidly converging estimates for the excited discrete state energies. We demonstrate the power of this new approach on the sextic and quartic anharmonic oscillators, as well as on recently studied one- and two-dimensional pseudo-Hermitian Hamiltonians.
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Perkó, Zoltán Gilli, Luca Lathouwers, Danny Kloosterman, Jan Leen
2014-03-01
The demand for accurate and computationally affordable sensitivity and uncertainty techniques is constantly on the rise and has become especially pressing in the nuclear field with the shift to Best Estimate Plus Uncertainty methodologies in the licensing of nuclear installations. Besides traditional, already well developed methods – such as first order perturbation theory or Monte Carlo sampling – Polynomial Chaos Expansion (PCE) has been given a growing emphasis in recent years due to its simple application and good performance. This paper presents new developments of the research done at TU Delft on such Polynomial Chaos (PC) techniques. Our work is focused on the Non-Intrusive Spectral Projection (NISP) approach and adaptive methods for building the PCE of responses of interest. Recent efforts resulted in a new adaptive sparse grid algorithm designed for estimating the PC coefficients. The algorithm is based on Gerstner's procedure for calculating multi-dimensional integrals but proves to be computationally significantly cheaper, while at the same it retains a similar accuracy as the original method. More importantly the issue of basis adaptivity has been investigated and two techniques have been implemented for constructing the sparse PCE of quantities of interest. Not using the traditional full PC basis set leads to further reduction in computational time since the high order grids necessary for accurately estimating the near zero expansion coefficients of polynomial basis vectors not needed in the PCE can be excluded from the calculation. Moreover the sparse PC representation of the response is easier to handle when used for sensitivity analysis or uncertainty propagation due to the smaller number of basis vectors. The developed grid and basis adaptive methods have been implemented in Matlab as the Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm and were tested on four analytical problems. These show consistent good performance both
Observer-based controller for nonlinear analytical systems
NASA Astrophysics Data System (ADS)
Elloumi, S.; Belhouane, M. M.; Benhadj Braiek, N.
2016-06-01
In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.
Generalization of the Bollobás-Riordan polynomial for tensor graphs
NASA Astrophysics Data System (ADS)
Tanasa, Adrian
2011-07-01
Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial T encoding the supplementary topological information. This polynomial is a natural generalization of the Bollobás-Riordan polynomial (used to characterize matrix graphs) and is different from the Gurău polynomial [R. Gurău, Ann. Henri Poincare 11, 565 (2010)], 10.1007/s00023-010-0035-6, defined for a particular class of tensor graphs, the colorable ones. The polynomial T is defined for both colorable and non-colorable graphs and it is proved to satisfy the deletion/contraction relation. A non-trivial example of a non-colorable graphs is analyzed.
NASA Astrophysics Data System (ADS)
Baldi, Antonio; Bertolino, Filippo
2013-10-01
It is well known that displacement components estimated using digital image correlation are affected by a systematic error due to the polynomial interpolation required by the numerical algorithm. The magnitude of bias depends on the characteristics of the speckle pattern (i.e., the frequency content of the image), on the fractional part of displacements and on the type of polynomial used for intensity interpolation. In literature, B-Spline polynomials are pointed out as being able to introduce the smaller errors, whereas bilinear and cubic interpolants generally give the worst results. However, the small bias of B-Spline polynomials is partially counterbalanced by a somewhat larger execution time. We will try to improve the accuracy of lower order polynomials by a posteriori correcting their results so as to obtain a faster and more accurate analysis.
2012-01-01
Background The rice roots are highly salt-sensitive organ and primary root growth is rapidly suppressed by salt stress. Sucrose nonfermenting 1-related protein kinase2 (SnRK2) family is one of the key regulator of hyper-osmotic stress signalling in various plant cells. To understand early salt response of rice roots and identify SnRK2 signaling components, proteome changes of transgenic rice roots over-expressing OSRK1, a rice SnRK2 kinase were investigated. Results Proteomes were analyzed by two-dimensional electrophoresis and protein spots were identified by LC-MS/MS from wild type and OSRK1 transgenic rice roots exposed to 150 mM NaCl for either 3 h or 7 h. Fifty two early salt -responsive protein spots were identified from wild type rice roots. The major up-regulated proteins were enzymes related to energy regulation, amino acid metabolism, methylglyoxal detoxification, redox regulation and protein turnover. It is noted that enzymes known to be involved in GA-induced root growth such as fructose bisphosphate aldolase and methylmalonate semialdehyde dehydrogenase were clearly down-regulated. In contrast to wild type rice roots, only a few proteins were changed by salt stress in OSRK1 transgenic rice roots. A comparative quantitative analysis of the proteome level indicated that forty three early salt-responsive proteins were magnified in transgenic rice roots at unstressed condition. These proteins contain single or multiple potential SnRK2 recognition motives. In vitro kinase assay revealed that one of the identified proteome, calreticulin is a good substrate of OSRK1. Conclusions Our present data implicate that rice roots rapidly changed broad spectrum of energy metabolism upon challenging salt stress, and suppression of GA signaling by salt stress may be responsible for the rapid arrest of root growth and development. The broad spectrum of functional categories of proteins affected by over-expression of OSRK1 indicates that OSRK1 is an upstream regulator of
NASA Astrophysics Data System (ADS)
Li, Jia; Zhang, Shengli; Huang, Shiping; Wang, Peng; Tian, Huiping
2013-02-01
R3ZnH5 (R=K, Rb, Cs) series have been investigated with respect to the crystal structure, electronic and thermodynamic properties using first-principle methods based on density functional theory with generalized gradient approximation. The optimized structures and atomic coordinates are in good agreement with the experimental data. The strong covalent interactions are obtained between Zn and H atoms in the 18-electron [ZnH4]2- complex, while an ionic interaction is found between [ZnH4]2- and R atom. The formation enthalpies show that the formations of R3ZnH5 hydrides are all exothermic at 298 K. The vibration free energies of R3ZnH5 show that the thermodynamic stabilities of R3ZnH5 hydrides decrease with the increasing diameter of R atom. Two possible decomposition reactions of R3ZnH5 series have been suggested in our work. One (reaction one) is that R3ZnH5 hydrides decomposes to elements directly, and the other (reaction two) is that R3ZnH5 hydrides decomposes to RH hydride. The results show that the first decomposition reaction is more favorable one. The spontaneous decomposition reaction of K3ZnH5 hydrides occur upon 465 K via reaction one, and 564 K via reaction two, respectively.
NASA Astrophysics Data System (ADS)
Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.
2006-10-01
In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.
Jain, Mukesh; Li, Qin-Bao; Chourey, Prem S
2008-09-01
A full-length cDNA clone, SbSnRK1b (1530 bp, GenBank accession no. EF544393), encoding a putative serine/threonine protein kinase homologue of yeast (Saccharomyces cerevisiae) SNF1, was isolated from developing endosperm of sorghum [Sorghum bicolor (L.) Moench]. Multiple sequence alignment data showed a phylogenetic affiliation of the sorghum clone with the SnRK1b group of protein kinases that are highly expressed in cereal seed endosperm. The DNA gel blot analyses indicated that SbSnRK1b gene is present as a single- or low copy number gene in sorghum. The RNA and protein gel blot analyses confirmed the expression of SbSnRK1b in developing sorghum caryopses, overlapping with the starch biosynthesis phase, 12-24 days after fertilization. In situ hybridization and immunolocalization data resolved the spatial specificity of SbSnRK1b expression in the basal endosperm transfer cell layer, the unique port of assimilate unloading in the growing sorghum seed. Expression of SbSnRK1b was also evident in the developing sorghum microspores, coincident with the onset of starch deposition phase. As in sorghum, similar spatiotemporal specificity of SnRK1b expression was observed during maize (Zea mays L.) seed development. However, discordant in situ hybridization and immunolocalization data indicated that the expression of SbSnRK1b homologue in maize is under posttranscriptional control during endosperm development.
Björk-Shiley strut fracture and disc escape: literature review and a method of disc retrieval.
Hendel, P N
1989-03-01
Embolization of a prosthetic valve poppet is a rare but life-threatening event. It was reported sporadically before the introduction of the Björk-Shiley 70-degree convexoconcave prosthesis in 1980. Since that time, there have been a large number of reported mechanical failures with disc escape. The rate for the 29-mm to 33-mm mitral valves is estimated as 5.2%. In 29 of 35 patients (including the 2 presented here) in whom the site of disc lodgment could be determined, the disc was in the descending or abdominal aorta. Fifteen of these patients died. Six survivors had the disc removed at the same operation and 6 at a later operation. In 2 patients, the disc was not removed. In 2 patients in whom the disc was not removed initially, it was thought to contribute to postoperative complications. Two more cases of structural failure of the Björk-Shiley convexoconcave prosthesis are presented. A transpericardial approach to the descending aorta on bypass is described. It allows easy removal of the disc and eliminates the need for a second operation.
Broeckx, Tom; Hulsmans, Sander; Rolland, Filip
2016-12-01
The SnRK1 (SNF1-related kinase 1) kinases are the plant cellular fuel gauges, activated in response to energy-depleting stress conditions to maintain energy homeostasis while also gatekeeping important developmental transitions for optimal growth and survival. Similar to their opisthokont counterparts (animal AMP-activated kinase, AMPK, and yeast Sucrose Non-Fermenting 1, SNF), they function as heterotrimeric complexes with a catalytic (kinase) α subunit and regulatory β and γ subunits. Although the overall configuration of the kinase complexes is well conserved, plant-specific structural modifications (including a unique hybrid βγ subunit) and associated differences in regulation reflect evolutionary divergence in response to fundamentally different lifestyles. While AMP is the key metabolic signal activating AMPK in animals, the plant kinases appear to be allosterically inhibited by sugar-phosphates. Their function is further fine-tuned by differential subunit expression, localization, and diverse post-translational modifications. The SnRK1 kinases act by direct phosphorylation of key metabolic enzymes and regulatory proteins, extensive transcriptional regulation (e.g. through bZIP transcription factors), and down-regulation of TOR (target of rapamycin) kinase signaling. Significant progress has been made in recent years. New tools and more directed approaches will help answer important fundamental questions regarding their structure, regulation, and function, as well as explore their potential as targets for selection and modification for improved plant performance in a changing environment.
NASA Technical Reports Server (NTRS)
Pototzky, Anthony S.
2008-01-01
A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.
NASA Astrophysics Data System (ADS)
Jacquelin, E.; Adhikari, S.; Sinou, J.-J.; Friswell, M. I.
2015-11-01
Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken's transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken's transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken's method are enough. This latter result is improved if a generalization of Aitken's method (recursive Aitken's transformation, Shank's transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response.
On the Use of the Polynomial Annihilation Edge Detection for Locating Cracks in Beam-Like Structures
Saxena, Rishu; Surace, Cecilia; Archibald, Richard K
2013-01-01
A crack in a structure causes a discontinuity in the first derivative of the mode shapes: On this basis, a numerical method for detecting discontinuities in smooth piecewise functions and their derivatives, based on a polynomial annihilation technique, has been applied to the problem of crack detection and localisation in beam-like structures for which only post-damage mode shapes are available. Using a finite-element model of a cracked beam, the performance of this methodology has been analysed for different crack depths and increasing amounts of noise. Given the crack position, a procedure to estimate its depth is also proposed and corresponding results shown.
Le Pape, Sylvain; Dimitrova, Elena; Hannaert, Patrick; Konovalov, Alexander; Volmer, Romain; Ron, David; Thuillier, Raphaël; Hauet, Thierry
2014-08-25
The unfolded protein response (UPR)--the endoplasmic reticulum stress response--is found in various pathologies including ischemia-reperfusion injury (IRI). However, its role during IRI is still unclear. Here, by combining two different bioinformatical methods--a method based on ordinary differential equations (Time Series Network Inference) and an algebraic method (probabilistic polynomial dynamical systems)--we identified the IRE1α-XBP1 and the ATF6 pathways as the main UPR effectors involved in cell's adaptation to IRI. We validated these findings experimentally by assessing the impact of their knock-out and knock-down on cell survival during IRI.
NASA Astrophysics Data System (ADS)
Nikolic, Milena; Benítez, Pablo; Narasimhan, Bharathwaj; Grabovickic, Dejan; Liu, Jayao; Miñano, Juan C.
2016-07-01
Several applications of freeform optics call for deeper analysis of systems with rectangular apertures. We study the behavior of a freeform mirror system by comparing four orthogonal polynomial surface representations through local optimization. We compare polynomials with different orthogonal areas (rectangular-circular) and different metrics (sag-gradient). Polynomials orthogonal inside a rectangle converge faster or to a better local minimum than those orthogonal inside a circle in the example considered. This is the most likely due to the loss of the good properties of orthogonality when the orthogonality area does not coincide with the surface area used.
Explicit polynomial formulas for solutions of the matrix equation AX-XA=C
Demenchuk, Alexandr K.; Makarov, Evgenii K.
2009-08-15
We provide some mathematical tool to analyze the possible theoretical structure of Hamiltonian reconstructed from von Neumann or Heisenberg's equation for a finite-dimensional quantum system. To this end, we give an explicit polynomial representation for the general solution of the matrix equation AX-XA=C together with some (also polynomial) solvability conditions when A and C are some complex square matrices of the same size and the matrix A is semisimple. When the matrix A is normal, we derive a polynomial existence condition for Hermitian solutions and a similar formula for all solutions of this type.
Indirect searches of dark matter via polynomial spectral features
Garcia-Cely, Camilo; Heeck, Julian
2016-08-11
We derive the spectra arising from non-relativistic dark matter annihilations or decays into intermediary particles with arbitrary spin, which subsequently produce neutrinos or photons via two-body decays. Our approach is model independent and predicts spectral features restricted to a kinematic box. The overall shape within that box is a polynomial determined by the polarization of the decaying particle. We illustrate our findings with two examples. First, with the neutrino spectra arising from dark matter annihilations into the massive Standard Model gauge bosons. Second, with the gamma-ray and neutrino spectra generated by dark matter annihilations into hypothetical massive spin-2 particles. Our results are in particular applicable to the 750 GeV diphoton excess observed at the LHC if interpreted as a spin-0 or spin-2 particle coupled to dark matter. We also derive limits on the dark matter annihilation cross section into this resonance from the non-observation of the associated gamma-ray spectral features by the H.E.S.S. telescope.
Polynomials for crystal frameworks and the rigid unit mode spectrum
Power, S. C.
2014-01-01
To each discrete translationally periodic bar-joint framework in , we associate a matrix-valued function defined on the d-torus. The rigid unit mode (RUM) spectrum of is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function and also to the set of wavevectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to being square, the determinant of gives rise to a unique multi-variable polynomial . For ideal zeolites, the algebraic variety of zeros of on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealized framework rigidity and flexibility, and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions two and three, direct proofs are given to show the maximal floppy mode property (order N). In particular, this is the case for the cubic symmetry sodalite framework and some other idealized zeolites. PMID:24379422
Extremal polynomials and methods of optimization of numerical algorithms
Lebedev, V I
2004-10-31
Chebyshev-Markov-Bernstein-Szegoe polynomials C{sub n}(x) extremal on [-1,1] with weight functions w(x)=(1+x){sup {alpha}}(1- x){sup {beta}}/{radical}(S{sub l}(x)) where {alpha},{beta}=0,1/2 and S{sub l}(x)={pi}{sub k=1}{sup m}(1-c{sub k}T{sub l{sub k}}(x))>0 are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight p(x)=w{sup 2}(x)(1-x{sup 2}){sup -1/2}. The parameters of optimal Chebyshev iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko-Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshev filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.
Computing Role Assignments of Proper Interval Graphs in Polynomial Time
NASA Astrophysics Data System (ADS)
Heggernes, Pinar; van't Hof, Pim; Paulusma, Daniël
A homomorphism from a graph G to a graph R is locally surjective if its restriction to the neighborhood of each vertex of G is surjective. Such a homomorphism is also called an R-role assignment of G. Role assignments have applications in distributed computing, social network theory, and topological graph theory. The Role Assignment problem has as input a pair of graphs (G,R) and asks whether G has an R-role assignment. This problem is NP-complete already on input pairs (G,R) where R is a path on three vertices. So far, the only known non-trivial tractable case consists of input pairs (G,R) where G is a tree. We present a polynomial time algorithm that solves Role Assignment on all input pairs (G,R) where G is a proper interval graph. Thus we identify the first graph class other than trees on which the problem is tractable. As a complementary result, we show that the problem is Graph Isomorphism-hard on chordal graphs, a superclass of proper interval graphs and trees.
A Polynomial Time, Numerically Stable Integer Relation Algorithm
NASA Technical Reports Server (NTRS)
Ferguson, Helaman R. P.; Bailey, Daivd H.; Kutler, Paul (Technical Monitor)
1998-01-01
Let x = (x1, x2...,xn be a vector of real numbers. X is said to possess an integer relation if there exist integers a(sub i) not all zero such that a1x1 + a2x2 + ... a(sub n)Xn = 0. Beginning in 1977 several algorithms (with proofs) have been discovered to recover the a(sub i) given x. The most efficient of these existing integer relation algorithms (in terms of run time and the precision required of the input) has the drawback of being very unstable numerically. It often requires a numeric precision level in the thousands of digits to reliably recover relations in modest-sized test problems. We present here a new algorithm for finding integer relations, which we have named the "PSLQ" algorithm. It is proved in this paper that the PSLQ algorithm terminates with a relation in a number of iterations that is bounded by a polynomial in it. Because this algorithm employs a numerically stable matrix reduction procedure, it is free from the numerical difficulties, that plague other integer relation algorithms. Furthermore, its stability admits an efficient implementation with lower run times oil average than other algorithms currently in Use. Finally, this stability can be used to prove that relation bounds obtained from computer runs using this algorithm are numerically accurate.
On the Characteristic Polynomial of a Random Unitary Matrix
NASA Astrophysics Data System (ADS)
Hughes, C. P.; Keating, J. P.; O'Connell, Neil
We present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial Z of a random N×N unitary matrix, as N-->∞. First we show that , evaluated at a finite set of distinct points, is asymptotically a collection of i.i.d. complex normal random variables. This leads to a refinement of a recent central limit theorem due to Keating and Snaith, and also explains the covariance structure of the eigenvalue counting function. Next we obtain a central limit theorem for ln Z in a Sobolev space of generalised functions on the unit circle. In this limiting regime, lower-order terms which reflect the global covariance structure are no longer negligible and feature in the covariance structure of the limiting Gaussian measure. Large deviations results for ln Z/A, evaluated at a finite set of distinct points, can be obtained for . For higher-order scalings we obtain large deviations results for ln Z/A evaluated at a single point. There is a phase transition at A= ln N (which only applies to negative deviations of the real part) reflecting a switch from global to local conspiracy.
Indirect searches of dark matter via polynomial spectral features
NASA Astrophysics Data System (ADS)
Garcia-Cely, Camilo; Heeck, Julian
2016-08-01
We derive the spectra arising from non-relativistic dark matter annihilations or decays into intermediary particles with arbitrary spin, which subsequently produce neutrinos or photons via two-body decays. Our approach is model independent and predicts spectral features restricted to a kinematic box. The overall shape within that box is a polynomial determined by the polarization of the decaying particle. We illustrate our findings with two examples. First, with the neutrino spectra arising from dark matter annihilations into the massive Standard Model gauge bosons. Second, with the gamma-ray and neutrino spectra generated by dark matter annihilations into hypothetical massive spin-2 particles. Our results are in particular applicable to the 750 GeV diphoton excess observed at the LHC if interpreted as a spin-0 or spin-2 particle coupled to dark matter. We also derive limits on the dark matter annihilation cross section into this resonance from the non-observation of the associated gamma-ray spectral features by the H.E.S.S. telescope.
Universal Associated Legendre Polynomials and Some Useful Definite Integrals
NASA Astrophysics Data System (ADS)
Chen, Chang-Yuan; You, Yuan; Lu, Fa-Lin; Sun, Dong-Sheng; Dong, Shi-Hai
2016-08-01
We first introduce the universal associated Legendre polynomials, which are occurred in studying the non-central fields such as the single ring-shaped potential and then present definite integrals IA ±(a, τ) = ∫-1 +1 xa[Pl‧ m‧ (x)]2/(1 ± x)τ dx, a = 0, 1, 2, 3, 4, 5, 6, τ = 1, 2, 3, IB(b, σ) = ∫-1 +1 xb[Pl‧ m‧ (x)]2/(1 - x2)σ dx, b = 0, 2, 4, 6, 8, σ = 1, 2, 3, and IC ±(c, κ) = ∫-1 +1 xc[Pl‧ m‧ (x)]2/[(1 - x2)κ (1 ± x)] dx, c = 0, 1, 2, 3, 4, 5, 6, 7, 8, κ = 1, 2. The superindices “±” in IA ±(a, τ) and IC ± (c, κ) correspond to those of the factor (1 ± x) involved in weight functions. The formulas obtained in this work and also those for integer quantum numbers l‧ and m‧ are very useful and unavailable in classic handbooks. Supported by the National Natural Science Foundation of China under Grant No. 11275165 and partially by 20160978-SIP-IPN, Mexico.
Celeste, Ricardo; Maringolo, Milena P; Comar, Moacyr; Viana, Rommel B; Guimarães, Amanda R; Haiduke, Roberto L A; da Silva, Albérico B F
2015-10-01
Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations.
Cameron, David R.; Jiang, Jhih-Hang; Kostoulias, Xenia; Foxwell, Daniel J.; Peleg, Anton Y.
2016-01-01
The treatment of infections caused by methicillin-resistant Staphylococcus aureus is complicated by the emergence of strains with intermediate-level resistance to vancomycin (termed VISA). We have characterised a molecular pathway involved in the in vivo evolution of VISA mediated by the regulatory proteins YycH and YycI. In contrast to their function in other bacterial species, we report a positive role for these auxiliary proteins in regulation of the two-component regulator WalRK. Transcriptional profiling of yycH and yycI deletion mutants revealed downregulation of the ‘WalRK regulon’ including cell wall hydrolase genes atlA and sle1, with functional autolysis assays supporting these data by showing an impaired autolytic phenotype for each deletion strain. Using bacterial-two hybrid assays, we showed that YycH and YycI interact, and that YycHI also interacts with the sensor kinase WalK, forming a ternary protein complex. Mutation to YycH or YycI associated with clinical VISA strains had a deleterious impact on the YycHI/WalK complex, suggesting that the interaction is important for the regulation of WalRK. Taken together, we have described a novel antibiotic resistance strategy for the human pathogen S. aureus, whereby YycHI mutations are selected for in vivo leading to reduced WalRK activation, impaired cell wall turnover and ultimately reduced vancomycin efficacy. PMID:27600558
Bradley, Ritu R; Terajima, Masanori
2005-12-01
The K1L protein of vaccinia virus is required for its growth in certain cell lines (RK-13 and human). The cowpox host-range protein CP77 has been shown to complement K1L function in RK-13 cells, despite a lack of homology between the two proteins except for ankyrin repeats. We investigated the role of ankyrin repeats of K1L protein in RK-13 cells. The growth of a recombinant vaccinia virus, with K1L gene mutated in the most conserved ankyrin repeat, was severely impaired. Infection with the mutant virus caused shutdown of cellular and viral protein synthesis early in infection. We also investigated the interaction of K1L protein with cellular proteins and found that K1L interacts with the rabbit homologue of human ACAP2, a GTPase-activating protein with ankyrin repeats. Our result suggests the importance of ankyrin repeat for host-range function of K1L in RK-13 cells and identifies ACAP2 as a cellular protein, which may be interacting with K1L.
Schuck, Stefan; Baldwin, Ian T.; Bonaventure, Gustavo
2013-01-01
Nicotiana attenuata HSPRO (NaHSPRO) is a negative regulator of seedling growth promoted by the fungus Piriformospora indica. Homologs of NaHSPRO in Arabidopsis thaliana (i.e., AtHSPRO1 and AtHSPRO2) are known to physically interact with the AKINβγ subunit of the SnRK1 complex.2 To investigate whether NaHSPRO is associated with SnRK1 function during the stimulation of seedling growth by P. indica, we studied N. attenuata plants silenced in the expression of NaGAL83 (as-gal83 plants)—a gene that encodes for the regulatory β-subunit of SnRK1—and plants silenced in the expression of both NaHSPRO and NaGAL83 (ir-hspro/as-gal83 plants). The results showed that P. indica differentially stimulated the growth of both as-gal83 and ir-hspro/as-gal83 seedlings compared with control seedlings, with a magnitude similar to that observed in ir-hspro seedlings. Thus, we showed that, similar to NaHSPRO, NaGAL83 is a negative regulator of seedling growth stimulated by P. indica. We propose that the effect of NaHSPRO on seedling growth is associated with SnRK1 signaling. PMID:23333980
Moulin, Jean-Claude; Silvano, Jérémy; Barban, Véronique; Riou, Patrice; Allain, Caroline
2013-07-01
The neurovirulence of two new candidate 17D-204 Stamaril™ working seed lots and that of two reference preparations were compared. The Stamaril™ working seed lots have been used for more than twenty years for the manufacturing of vaccines of acceptable safety and efficacy. The preparation designated RK 168-73 and provided by the Robert Koch Institute was used as a reference. It was confirmed that RK 168-73 strain was not a good virus control in our study because it has a very low neurovirulence regarding both the clinical and histopathological scores in comparison with Stamaril™ strain and is not representative of a vaccine known to be satisfactory in use. The results were reinforced by the phenotypic characterization by plaque assay demonstrating that RK 168-73 was very different from the Stamaril™ vaccine, and by sequencing results showing 4 mutations between Stamaril™ and RK 168-73 viruses leading to amino acid differences in the NS4B and envelop proteins.
Wilson polynomials and the Lorentz transformation properties of the parity operator
Bender, Carl M.; Meisinger, Peter N.; Wang Qinghai
2005-05-01
The parity operator for a parity-symmetric quantum field theory transforms as an infinite sum of irreducible representations of the homogeneous Lorentz group. These representations are connected with Wilson polynomials.
C. ALLEN
2000-08-01
We consider halo formation in continuous beams oscillating at natural modes by inspecting particle trajectories. Trajectory equations containing field nonlinearities are derived from a weighted polynomial expansion. We then use perturbational techniques to further analyze particle motion.
Orthogonality Measure on the Torus for Vector-Valued Jack Polynomials
NASA Astrophysics Data System (ADS)
Dunkl, Charles F.
2016-03-01
For each irreducible module of the symmetric group on N objects there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to certain Hermitian forms. These polynomials were studied by the author and J.-G. Luque using a Yang-Baxter graph technique. This paper constructs a matrix-valued measure on the N-torus for which the polynomials are mutually orthogonal. The construction uses Fourier analysis techniques. Recursion relations for the Fourier-Stieltjes coefficients of the measure are established, and used to identify parameter values for which the construction fails. It is shown that the absolutely continuous part of the measure satisfies a first-order system of differential equations.
q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials
NASA Astrophysics Data System (ADS)
Coulembier, K.; Sommen, F.
2010-03-01
We define a q-deformation of the Dirac operator, inspired by the one-dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator. This allows us to construct q-deformed Schrödinger equations in higher dimensions. The equivalence of these Schrödinger equations with those defined on q-Euclidean space in quantum variables is shown. We also define the m-dimensional q-Clifford-Hermite polynomials and show their connection with the q-Laguerre polynomials. These polynomials are orthogonal with respect to an m-dimensional q-integration, which is related to integration on q-Euclidean space. The q-Laguerre polynomials are the eigenvectors of an suq(1|1)-representation.
A pair of Fibonacci-like polynomials arising from a special mapping
NASA Astrophysics Data System (ADS)
Griffiths, Martin; Griffiths, Jonny
2016-02-01
We study here a pair of sequences of polynomials that arise from a particular iterated mapping on the plane. We show how these sequences come about, and give some of their interesting mathematical properties.
NASA Technical Reports Server (NTRS)
Dayawansa, W. P.; Martin, C. F.
1989-01-01
Consideration is given to three-dimensional homogeneous polynomial systems, and some sufficient conditions for their asymptotic stability are derived by using homogeneous feedback. The tests given are geometric in nature.
Tang, Kunkun; Congedo, Pietro M.; Abgrall, Rémi
2016-06-01
The Polynomial Dimensional Decomposition (PDD) is employed in this work for the global sensitivity analysis and uncertainty quantification (UQ) of stochastic systems subject to a moderate to large number of input random variables. Due to the intimate connection between the PDD and the Analysis of Variance (ANOVA) approaches, PDD is able to provide a simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to the Polynomial Chaos expansion (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of standard methods unaffordable for real engineering applications. In order to address the problem of the curse of dimensionality, this work proposes essentially variance-based adaptive strategies aiming to build a cheap meta-model (i.e. surrogate model) by employing the sparse PDD approach with its coefficients computed by regression. Three levels of adaptivity are carried out in this paper: 1) the truncated dimensionality for ANOVA component functions, 2) the active dimension technique especially for second- and higher-order parameter interactions, and 3) the stepwise regression approach designed to retain only the most influential polynomials in the PDD expansion. During this adaptive procedure featuring stepwise regressions, the surrogate model representation keeps containing few terms, so that the cost to resolve repeatedly the linear systems of the least-squares regression problem is negligible. The size of the finally obtained sparse PDD representation is much smaller than the one of the full expansion, since only significant terms are eventually retained. Consequently, a much smaller number of calls to the deterministic model is required to compute the final PDD coefficients.
High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials
NASA Astrophysics Data System (ADS)
>Jesper Lykke Jacobsen,
2014-04-01
The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow-tie lattices. Jacobsen and Scullard have defined a graph polynomial PB(q, v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = eK - 1 provide increasingly accurate approximations to the critical manifolds upon increasing the size of B. Using transfer matrix techniques, these authors computed PB(q, v) for large bases (up to 243 edges), obtaining determinations of the ferromagnetic critical point vc > 0 for the (4, 82), kagome, and (3, 122) lattices to a precision (of the order 10-8) slightly superior to that of the best available Monte Carlo simulations. In this paper we describe a more efficient transfer matrix approach to the computation of PB(q, v) that relies on a formulation within the periodic Temperley-Lieb algebra. This makes possible computations for substantially larger bases (up to 882 edges), and the precision on vc is hence taken to the range 10-13. We further show that a large variety of regular lattices can be cast in a form suitable for this approach. This includes all Archimedean lattices, their duals and their medials. For all these lattices we tabulate high-precision estimates of the bond percolation thresholds pc and Potts critical points vc. We also trace and discuss the full Potts critical manifold in the (q, v) plane, paying special attention to the antiferromagnetic region v < 0. Finally, we adapt the technique to site percolation as well, and compute the polynomials PB(p) for certain Archimedean and dual lattices (those having only cubic and quartic vertices), using very large bases (up to 243 vertices). This produces the site percolation thresholds pc to a precision of the order of 10-9.
Design and development of thin quartz glass WFXT polynomial mirror shells by direct polishing
NASA Astrophysics Data System (ADS)
Proserpio, L.; Campana, S.; Citterio, O.; Civitani, M.; Combrinck, H.; Conconi, P.; Cotroneo, V.; Freeman, R.; Langstrof, P.; Mattaini, E.; Morton, R.; Oberle, B.; Pareschi, G.; Parodi, G.; Pels, C.; Schenk, C.; Stock, R.; Tagliaferri, G.
2010-07-01
The Wide Field X-ray Telescope (WFXT) is a medium class mission for X-ray surveys of the sky with an unprecedented area and sensitivity. In order to meet the effective area requirement, the design of the optical system is based on very thin mirror shells, with thicknesses in the 1-2 mm range. In order to get the desired angular resolution (10 arcsec requirement, 5 arcsec goal) across the entire 1x1 degree FOV (Field Of View), the design of the optical system is based on nested modified grazing incidence Wolter-I mirrors realized with polynomial profiles, focal plane curvature and plate scale corrections. This design guarantees an increased angular resolution at large off-axis angle with respect to the normally used Wolter I configuration, making WFXT ideal for survey purposes. The WFXT X-ray Telescope Assembly is composed by three identical mirror modules of 78 nested shells each, with diameter up to 1.1 m. The epoxy replication process with SiC shells has already been proved to be a valuable technology to meet the angular resolution requirement of 10 arcsec. To further mature the telescope manufacturing technology and to achieve the goal of 5 arcsec, a deterministic direct polishing method is under investigation. The direct polishing method has already been used for past missions (as Einstein, Rosat, Chandra): the technological challenge now is to apply it for almost ten times thinner shells. Under investigation is quartz glass (fused silica), a well-known material with good thermo-mechanical and polishability characteristics that could meet our goal in terms of mass and stiffness, with significant cost and time saving with respect to SiC. Our approach is based on two main steps: first quartz glass tubes available on the market are grinded to conical profiles, and second the obtained shells are polished to the required polynomial profiles by CNC (Computer Numerical Control) polishing machine. In this paper, the first results of the direct grinding and polishing of
A robust and efficient stepwise regression method for building sparse polynomial chaos expansions
NASA Astrophysics Data System (ADS)
Abraham, Simon; Raisee, Mehrdad; Ghorbaniasl, Ghader; Contino, Francesco; Lacor, Chris
2017-03-01
Polynomial Chaos (PC) expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters. The computational cost of classical PC solution schemes is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension. This considerably restricts the practical use of PC at the industrial level. A common approach to address such problems is to make use of sparse PC expansions. This paper presents a non-intrusive regression-based method for building sparse PC expansions. The most important PC contributions are detected sequentially through an automatic search procedure. The variable selection criterion is based on efficient tools relevant to probabilistic method. Two benchmark analytical functions are used to validate the proposed algorithm. The computational efficiency of the method is then illustrated by a more realistic CFD application, consisting of the non-deterministic flow around a transonic airfoil subject to geometrical uncertainties. To assess the performance of the developed methodology, a detailed comparison is made with the well established LAR-based selection technique. The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem. Moreover, the most important stochastic features are captured at a reduced computational cost compared to the LAR method. The results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs.
Schmidt-Kalman Filter with Polynomial Chaos Expansion for Orbit Determination of Space Objects
NASA Astrophysics Data System (ADS)
Yang, Y.; Cai, H.; Zhang, K.
2016-09-01
Parameter errors in orbital models can result in poor orbit determination (OD) using a traditional Kalman filter. One approach to account for these errors is to consider them in the so-called Schmidt-Kalman filter (SKF), by augmenting the state covariance matrix (CM) with additional parameter covariance rather than additively estimating these so-called "consider" parameters. This paper introduces a new SKF algorithm with polynomial chaos expansion (PCE-SKF). The PCE approach has been proved to be more efficient than Monte Carlo method for propagating the input uncertainties onto the system response without experiencing any constraints of linear dynamics, or Gaussian distributions of the uncertainty sources. The state and covariance needed in the orbit prediction step are propagated using PCE. An inclined geosynchronous orbit scenario is set up to test the proposed PCE-SKF based OD algorithm. The satellite orbit is propagated based on numerical integration, with the uncertain coefficient of solar radiation pressure considered. The PCE-SKF solutions are compared with extended Kalman filter (EKF), SKF and PCE-EKF (EKF with PCE) solutions. It is implied that the covariance propagation using PCE leads to more precise OD solutions in comparison with those based on linear propagation of covariance.
Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials
Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane
2014-01-01
In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293