Sample records for polynomial based rk

  1. Polynomial mixture method of solving ordinary differential equations

    NASA Astrophysics Data System (ADS)

    Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

    2017-11-01

    In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

  2. RK and RK* beyond the standard model

    NASA Astrophysics Data System (ADS)

    Hiller, Gudrun; Nišandžić, Ivan

    2017-08-01

    Measurements of the ratio of B →K*μ μ to B →K*e e branching fractions, RK*, by the LHCb Collaboration strengthen the hints from previous studies with pseudoscalar kaons, RK, for the breakdown of lepton universality, and therefore the Standard Model (SM), to ˜3.5 σ . Complementarity between RK and RK* allows us to pin down the Dirac structure of the new contributions to be predominantly SM-like chiral, with possible admixture of chirality-flipped contributions of up to O (few 10 %). Scalar and vector leptoquark representations (S3,V1,V3) plus possible (S˜2,V2) admixture can explain RK ,K* via tree-level exchange. Flavor models naturally predict leptoquark masses not exceeding a few TeV, with couplings to third-generation quarks at O (0.1 ), implying that this scenario can be directly tested at the LHC.

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

    PubMed

    Mafusire, Cosmas; Krüger, Tjaart P J

    2018-06-01

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

  4. Explaining the R_K and R_{K^*} anomalies

    NASA Astrophysics Data System (ADS)

    Ghosh, Diptimoy

    2017-10-01

    Recent LHCb results on R_{K^*}, the ratio of the branching fractions of B → K^* μ ^+ μ ^- to that of B → K^* e^+ e^-, for the dilepton invariant mass bins q^2 ≡ m_{ℓ ℓ }^2 = [0.045-1.1] GeV^2 and [1.1-6] GeV^2 show approximately 2.5 σ deviations from the corresponding Standard Model prediction in each of the bins. This, when combined with the measurement of R_K (q^2=[1-6] GeV^2), a similar ratio for the decay to a pseudo-scalar meson, highly suggests lepton non-universal new physics in semi-leptonic B meson decays. In this work, we perform a model independent analysis of these potential new physics signals and identify the operators that do the best job in satisfying all these measurements. We show that heavy new physics, giving rise to q^2 independent local 4-Fermi operators of scalar, pseudo-scalar, vector or axial-vector type, is unable to explain all the three measurements simultaneously, in particular R_{K^*} in the bin [0.045-1.1], within their experimental 1σ regions. We point out the possibility to explain R_{K^*} in the low bin by an additional light (≲ 20 {MeV}) vector boson with appropriate coupling strengths to (\\bar{b} s) and (\\bar{e} e).

  5. A polynomial based model for cell fate prediction in human diseases.

    PubMed

    Ma, Lichun; Zheng, Jie

    2017-12-21

    Cell fate regulation directly affects tissue homeostasis and human health. Research on cell fate decision sheds light on key regulators, facilitates understanding the mechanisms, and suggests novel strategies to treat human diseases that are related to abnormal cell development. In this study, we proposed a polynomial based model to predict cell fate. This model was derived from Taylor series. As a case study, gene expression data of pancreatic cells were adopted to test and verify the model. As numerous features (genes) are available, we employed two kinds of feature selection methods, i.e. correlation based and apoptosis pathway based. Then polynomials of different degrees were used to refine the cell fate prediction function. 10-fold cross-validation was carried out to evaluate the performance of our model. In addition, we analyzed the stability of the resultant cell fate prediction model by evaluating the ranges of the parameters, as well as assessing the variances of the predicted values at randomly selected points. Results show that, within both the two considered gene selection methods, the prediction accuracies of polynomials of different degrees show little differences. Interestingly, the linear polynomial (degree 1 polynomial) is more stable than others. When comparing the linear polynomials based on the two gene selection methods, it shows that although the accuracy of the linear polynomial that uses correlation analysis outcomes is a little higher (achieves 86.62%), the one within genes of the apoptosis pathway is much more stable. Considering both the prediction accuracy and the stability of polynomial models of different degrees, the linear model is a preferred choice for cell fate prediction with gene expression data of pancreatic cells. The presented cell fate prediction model can be extended to other cells, which may be important for basic research as well as clinical study of cell development related diseases.

  6. Coherent orthogonal polynomials

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

    Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

    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 relatemore » 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

  7. Gabor-based kernel PCA with fractional power polynomial models for face recognition.

    PubMed

    Liu, Chengjun

    2004-05-01

    This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power

  8. Cloning and characterization of a SnRK2 gene from Jatropha curcas L.

    PubMed

    Chun, J; Li, F-S; Ma, Y; Wang, S-H; Chen, F

    2014-12-19

    Although the SnRK2 class of Ser/Thr protein kinases is critical for signal transduction and abiotic stress resistance in plants, there have been no studies to examine SnRK2 in Jatropha curcas L. In the present study, JcSnRK2 was cloned from J. curcas using the rapid amplification of cDNA end technique and characterized. The JcSnRK2 genomic sequence is 2578 base pairs (bp), includes 10 exons and 9 introns, and the 1017-bp open reading frame encodes 338 amino acids. JcSnRK2 was transcribed in all examined tissues, with the highest transcription rate observed in the roots, followed by the leaves and stalks; the lowest rate was observed in flowers and seeds. JcSnRK2 expression increased following abscisic acid treatment, salinity, and drought stress. During a 48-h stress period, the expression of JcSnRK2 showed 2 peaks and periodic up- and downregulation. JcSnRK2 was rapidly activated within 1 h under salt and drought stress, but not under cold stress. Because of the gene sequence and expression similarity of JcSnRK2 to AtSnRK2.8, primarily in the roots, an eukaryotic expression vector containing the JcSnRK2 gene (pBI121-JcSnRK2) was constructed and introduced to the Arabidopsis AtSnRK2.8 mutant snf2.8. JcSnRK2-overexpressing plants exhibited higher salt and drought tolerance, further demonstrating the function of JcSnRK2 in the osmotic stress response. J. curcas is highly resistant to extreme salt and drought conditions and JcSnRK2 was found to be activated under these conditions. Thus, JcSnRK2 is potential candidate for improving crop tolerance to salt and drought stress.

  9. SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

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

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

    2016-09-01

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

  10. SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

  11. Nonredundant functions of Arabidopsis LecRK-V.2 and LecRK-VII.1 in controlling stomatal immunity and jasmonate-mediated stomatal closure.

    PubMed

    Yekondi, Shweta; Liang, Fu-Chun; Okuma, Eiji; Radziejwoski, Amandine; Mai, Hsien-Wei; Swain, Swadhin; Singh, Prashant; Gauthier, Mathieu; Chien, Hsiao-Chiao; Murata, Yoshiyuki; Zimmerli, Laurent

    2018-04-01

    Stomatal immunity restricts bacterial entry to leaves through the recognition of microbe-associated molecular patterns (MAMPs) by pattern-recognition receptors (PRRs) and downstream abscisic acid and salicylic acid signaling. Through a reverse genetics approach, we characterized the function of the L-type lectin receptor kinase-V.2 (LecRK-V.2) and -VII.1 (LecRK-VII.1). Analyses of interactions with the PRR FLAGELLIN SENSING2 (FLS2) were performed by co-immunoprecipitation and bimolecular fluorescence complementation and whole-cell patch-clamp analyses were used to evaluate guard cell Ca 2+ -permeable cation channels. The Arabidopsis thaliana LecRK-V.2 and LecRK-VII.1 and notably their kinase activities were required for full activation of stomatal immunity. Knockout lecrk-V.2 and lecrk-VII.1 mutants were hyper-susceptible to Pseudomonas syringae infection and showed defective stomatal closure in response to bacteria or to the MAMPs flagellin and EF-Tu. By contrast, Arabidopsis over-expressing LecRK-V.2 or LecRK-VII.1 demonstrated a potentiated stomatal immunity. LecRK-V.2 and LecRK-VII.1 are shown to be part of the FLS2 PRR complex. In addition, LecRK-V.2 and LecRK-VII.1 were critical for methyl jasmonate (MeJA)-mediated stomatal closure, notably for MeJA-induced activation of guard cell Ca 2+ -permeable cation channels. This study highlights the role of LecRK-V.2 and LecRK-VII.1 in stomatal immunity at the FLS2 PRR complex and in MeJA-mediated stomatal closure. © 2017 The Authors. New Phytologist © 2017 New Phytologist Trust.

  12. 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.

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

    PubMed

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

    2011-06-01

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

  14. A Polynomial Subset-Based Efficient Multi-Party Key Management System for Lightweight Device Networks.

    PubMed

    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.

  15. SABIO-RK: an updated resource for manually curated biochemical reaction kinetics

    PubMed Central

    Rey, Maja; Weidemann, Andreas; Kania, Renate; Müller, Wolfgang

    2018-01-01

    Abstract SABIO-RK (http://sabiork.h-its.org/) is a manually curated database containing data about biochemical reactions and their reaction kinetics. The data are primarily extracted from scientific literature and stored in a relational database. The content comprises both naturally occurring and alternatively measured biochemical reactions and is not restricted to any organism class. The data are made available to the public by a web-based search interface and by web services for programmatic access. In this update we describe major improvements and extensions of SABIO-RK since our last publication in the database issue of Nucleic Acid Research (2012). (i) The website has been completely revised and (ii) allows now also free text search for kinetics data. (iii) Additional interlinkages with other databases in our field have been established; this enables users to gain directly comprehensive knowledge about the properties of enzymes and kinetics beyond SABIO-RK. (iv) Vice versa, direct access to SABIO-RK data has been implemented in several systems biology tools and workflows. (v) On request of our experimental users, the data can be exported now additionally in spreadsheet formats. (vi) The newly established SABIO-RK Curation Service allows to respond to specific data requirements. PMID:29092055

  16. A Polynomial Subset-Based Efficient Multi-Party Key Management System for Lightweight Device Networks

    PubMed Central

    Mahmood, Zahid; Ning, Huansheng; Ghafoor, AtaUllah

    2017-01-01

    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. PMID:28338632

  17. Genome-wide identification and characterization of SnRK2 gene family in cotton (Gossypium hirsutum L.).

    PubMed

    Liu, Zhao; Ge, Xiaoyang; Yang, Zuoren; Zhang, Chaojun; Zhao, Ge; Chen, Eryong; Liu, Ji; Zhang, Xueyan; Li, Fuguang

    2017-06-12

    Sucrose non-fermenting-1-related protein kinase 2 (SnRK2) is a plant-specific serine/threonine kinase family involved in the abscisic acid (ABA) signaling pathway and responds to osmotic stress. A genome-wide analysis of this protein family has been conducted previously in some plant species, but little is known about SnRK2 genes in upland cotton (Gossypium hirsutum L.). The recent release of the G. hirsutum genome sequence provides an opportunity to identify and characterize the SnRK2 kinase family in upland cotton. We identified 20 putative SnRK2 sequences in the G. hirsutum genome, designated as GhSnRK2.1 to GhSnRK2.20. All of the sequences encoded hydrophilic proteins. Phylogenetic analysis showed that the GhSnRK2 genes were classifiable into three groups. The chromosomal location and phylogenetic analysis of the cotton SnRK2 genes indicated that segmental duplication likely contributed to the diversification and evolution of the genes. The gene structure and motif composition of the cotton SnRK2 genes were analyzed. Nine exons were conserved in length among all members of the GhSnRK2 family. Although the C-terminus was divergent, seven conserved motifs were present. All GhSnRK2s genes showed expression patterns under abiotic stress based on transcriptome data. The expression profiles of five selected genes were verified in various tissues by quantitative real-time RT-PCR (qRT-PCR). Transcript levels of some family members were up-regulated in response to drought, salinity or ABA treatments, consistent with potential roles in response to abiotic stress. This study is the first comprehensive analysis of SnRK2 genes in upland cotton. Our results provide the fundamental information for the functional dissection of GhSnRK2s and vital availability for the improvement of plant stress tolerance using GhSnRK2s.

  18. A Fast lattice-based polynomial digital signature system for m-commerce

    NASA Astrophysics Data System (ADS)

    Wei, Xinzhou; Leung, Lin; Anshel, Michael

    2003-01-01

    The privacy and data integrity are not guaranteed in current wireless communications due to the security hole inside the Wireless Application Protocol (WAP) version 1.2 gateway. One of the remedies is to provide an end-to-end security in m-commerce by applying application level security on top of current WAP1.2. The traditional security technologies like RSA and ECC applied on enterprise's server are not practical for wireless devices because wireless devices have relatively weak computation power and limited memory compared with server. In this paper, we developed a lattice based polynomial digital signature system based on NTRU's Polynomial Authentication and Signature Scheme (PASS), which enabled the feasibility of applying high-level security on both server and wireless device sides.

  19. Hydrodynamics-based functional forms of activity metabolism: a case for the power-law polynomial function in animal swimming energetics.

    PubMed

    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.

  20. Simple Proof of Jury Test for Complex Polynomials

    NASA Astrophysics Data System (ADS)

    Choo, Younseok; Kim, Dongmin

    Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouché's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

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

    NASA Astrophysics Data System (ADS)

    Li, Tuanjie; Shi, Jiachen; Tang, Yaqiong

    2018-04-01

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

  2. Poly-Frobenius-Euler polynomials

    NASA Astrophysics Data System (ADS)

    Kurt, Burak

    2017-07-01

    Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

  3. SnRK1A-Interacting Negative Regulators Modulate the Nutrient Starvation Signaling Sensor SnRK1 in Source-Sink Communication in Cereal Seedlings under Abiotic Stress[C][W

    PubMed Central

    Lin, Chien-Ru; Lee, Kuo-Wei; Chen, Chih-Yu; Hong, Ya-Fang; Chen, Jyh-Long; Lu, Chung-An; Chen, Ku-Ting; Ho, Tuan-Hua David; Yu, Su-May

    2014-01-01

    In plants, source-sink communication plays a pivotal role in crop productivity, yet the underlying regulatory mechanisms are largely unknown. The SnRK1A protein kinase and transcription factor MYBS1 regulate the sugar starvation signaling pathway during seedling growth in cereals. Here, we identified plant-specific SnRK1A-interacting negative regulators (SKINs). SKINs antagonize the function of SnRK1A, and the highly conserved GKSKSF domain is essential for SKINs to function as repressors. Overexpression of SKINs inhibits the expression of MYBS1 and hydrolases essential for mobilization of nutrient reserves in the endosperm, leading to inhibition of seedling growth. The expression of SKINs is highly inducible by drought and moderately by various stresses, which is likely related to the abscisic acid (ABA)–mediated repression of SnRK1A under stress. Overexpression of SKINs enhances ABA sensitivity for inhibition of seedling growth. ABA promotes the interaction between SnRK1A and SKINs and shifts the localization of SKINs from the nucleus to the cytoplasm, where it binds SnRK1A and prevents SnRK1A and MYBS1 from entering the nucleus. Our findings demonstrate that SnRK1A plays a key role regulating source-sink communication during seedling growth. Under abiotic stress, SKINs antagonize the function of SnRK1A, which is likely a key factor restricting seedling vigor. PMID:24569770

  4. 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.

  5. A transfectant RK13 cell line permissive to classical caprine scrapie prion propagation.

    PubMed

    Dassanayake, Rohana P; Zhuang, Dongyue; Truscott, Thomas C; Madsen-Bouterse, Sally A; O'Rourke, Katherine I; Schneider, David A

    2016-03-03

    To assess scrapie infectivity associated with caprine-origin tissues, bioassay can be performed using kids, lambs or transgenic mice expressing caprine or ovine prion (PRNP) alleles, but the incubation periods are fairly long. Although several classical ovine scrapie prion permissive cell lines with the ability to detect brain-derived scrapie prion have been available, no classical caprine scrapie permissive cell line is currently available. Therefore, the aims of this study were to generate a rabbit kidney epithelial cell line (RK13) stably expressing caprine wild-type PRNP (cpRK13) and then to assess permissiveness of cpRK13 cells to classical caprine scrapie prion propagation. The cpRK13 and plasmid control RK13 (pcRK13) cells were incubated with brain-derived classical caprine scrapie inocula prepared from goats or ovinized transgenic mice (Tg338, express ovine VRQ allele) infected with caprine scrapie. Significant PrP(Sc) accumulation, which is indicative of scrapie prion propagation, was detected by TSE ELISA and immunohistochemistry in cpRK13 cells inoculated with classical caprine scrapie inocula. Western blot analysis revealed the typical proteinase K-resistant 3 PrP(res) isoforms in the caprine scrapie prion inoculated cpRK13 cell lysate. Importantly, PrP(Sc) accumulation was not detected in similarly inoculated pcRK13 cells, whether by TSE ELISA, immunohistochemistry, or western blot. These findings suggest that caprine scrapie prions can be propagated in cpRK13 cells, thus this cell line may be a useful tool for the assessment of classical caprine prions in the brain tissues of goats.

  6. 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)

  7. 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.

  8. Genome-Wide Identification and Characterization of the GmSnRK2 Family in Soybean

    PubMed Central

    Zhao, Wei; Cheng, Yi-Hui; Zhang, Chi; Shen, Xin-Jie; You, Qing-Bo; Guo, Wei; Li, Xiang; Song, Xue-Jiao; Zhou, Xin-An

    2017-01-01

    Sucrose non-fermenting-1 (SNF1)-related protein kinase 2s (SnRK2s) that were reported to be involved in the transduction of abscisic acid (ABA) signaling, play important roles in response to biotic and abiotic stresses in plants. Compared to the systemic investigation of SnRK2s in Arabidopsis thaliana and Oryza sativa, little is known regarding SnRK2s in soybean, which is one of the most important oil and protein crops. In the present study, we performed genome-wide identification and characterization of GmSnRK2s in soybean. In summary, 22 GmSnRK2s were identified and clustered into four groups. Phylogenetic analysis indicated the expansion of SnRK2 gene family during the evolution of soybean. Various cis-acting elements such as ABA Response Elements (ABREs) were identified and analyzed in the promoter regions of GmSnRK2s. The results of RNA sequencing (RNA-Seq) data for different soybean tissues showed that GmSnRK2s exhibited spatio-temporally specific expression patterns during soybean growth and development. Certain GmSnRK2s could respond to the treatments including salinity, ABA and strigolactones. Our results provide a foundation for the further elucidation of the function of GmSnRK2 genes in soybean. PMID:28832544

  9. Genome-Wide Identification and Characterization of the GmSnRK2 Family in Soybean.

    PubMed

    Zhao, Wei; Cheng, Yi-Hui; Zhang, Chi; Shen, Xin-Jie; You, Qing-Bo; Guo, Wei; Li, Xiang; Song, Xue-Jiao; Zhou, Xin-An; Jiao, Yong-Qing

    2017-08-23

    Sucrose non-fermenting-1 (SNF1)-related protein kinase 2s (SnRK2s) that were reported to be involved in the transduction of abscisic acid (ABA) signaling, play important roles in response to biotic and abiotic stresses in plants. Compared to the systemic investigation of SnRK2s in Arabidopsis thaliana and Oryza sativa , little is known regarding SnRK2s in soybean, which is one of the most important oil and protein crops. In the present study, we performed genome-wide identification and characterization of GmSnRK2s in soybean. In summary, 22 GmSnRK2s were identified and clustered into four groups. Phylogenetic analysis indicated the expansion of SnRK2 gene family during the evolution of soybean. Various cis -acting elements such as ABA Response Elements (ABREs) were identified and analyzed in the promoter regions of GmSnRK2s . The results of RNA sequencing (RNA-Seq) data for different soybean tissues showed that GmSnRK2s exhibited spatio-temporally specific expression patterns during soybean growth and development. Certain GmSnRK2s could respond to the treatments including salinity, ABA and strigolactones. Our results provide a foundation for the further elucidation of the function of GmSnRK2 genes in soybean.

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

    NASA Astrophysics Data System (ADS)

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

    2018-07-01

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

  11. On polynomial preconditioning for indefinite Hermitian matrices

    NASA Technical Reports Server (NTRS)

    Freund, Roland W.

    1989-01-01

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

  12. Cylinder surface test with Chebyshev polynomial fitting method

    NASA Astrophysics Data System (ADS)

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

    2017-10-01

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

  13. Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map

    PubMed Central

    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

  14. Model-based multi-fringe interferometry using Zernike polynomials

    NASA Astrophysics Data System (ADS)

    Gu, Wei; Song, Weihong; Wu, Gaofeng; Quan, Haiyang; Wu, Yongqian; Zhao, Wenchuan

    2018-06-01

    In this paper, a general phase retrieval method is proposed, which is based on one single interferogram with a small amount of fringes (either tilt or power). Zernike polynomials are used to characterize the phase to be measured; the phase distribution is reconstructed by a non-linear least squares method. Experiments show that the proposed method can obtain satisfactory results compared to the standard phase-shifting interferometry technique. Additionally, the retrace errors of proposed method can be neglected because of the few fringes; it does not need any auxiliary phase shifting facilities (low cost) and it is easy to implement without the process of phase unwrapping.

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

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

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

    2016-09-15

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

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

    NASA Astrophysics Data System (ADS)

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

    2018-02-01

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

  17. RK-33 Radiosensitizes Prostate Cancer Cells by Blocking the RNA Helicase DDX3

    PubMed Central

    Xie, Min; Vesuna, Farhad; Tantravedi, Saritha; Bol, Guus M.; Heerma van Voss, Marise R.; Nugent, Katriana; Malek, Reem; Gabrielson, Kathleen; van Diest, Paul J.; Tran, Phuoc T.; Raman, Venu

    2017-01-01

    Despite advances in diagnosis and treatment, prostate cancer is the most prevalent cancer in males and the second highest cause of cancer-related mortality. We identified an RNA helicase gene, DDX3 (DDX3X), which is overexpressed in prostate cancers, and whose expression is directly correlated with high Gleason scores. Knockdown of DDX3 in the aggressive prostate cancer cell lines DU145 and 22Rv1 resulted in significantly reduced clonogenicity. To target DDX3, we rationally designed a small molecule, RK-33, which docks into the ATP-binding domain of DDX3. Functional studies indicated that RK-33 preferentially bound to DDX3 and perturbed its activity. RK-33 treatment of prostate cancer cell lines DU145, 22Rv1, and LNCaP (which have high DDX3 levels) decreased proliferation and induced a G1 phase cell-cycle arrest. Conversely, the low DDX3–expressing cell line, PC3, exhibited few changes following RK-33 treatment. Importantly, combination studies using RK-33 and radiation exhibited synergistic effects both in vitro and in a xenograft model of prostate cancer demonstrating the role of RK-33 as a radiosensitizer. Taken together, these results indicate that blocking DDX3 by RK-33 in combination with radiation treatment is a viable option for treating locally advanced prostate cancer. PMID:27634756

  18. Umbral orthogonal polynomials

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

    Lopez-Sendino, J. E.; del Olmo, M. A.

    2010-12-23

    We present an umbral operator version of the classical orthogonal polynomials. We obtain three families which are the umbral counterpart of the Jacobi, Laguerre and Hermite polynomials in the classical case.

  19. Multiple zeros of polynomials

    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.

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

    PubMed

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

    2012-10-01

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

  1. The complex becomes more complex: protein-protein interactions of SnRK1 with DUF581 family proteins provide a framework for cell- and stimulus type-specific SnRK1 signaling in plants.

    PubMed

    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.

  2. The complex becomes more complex: protein-protein interactions of SnRK1 with DUF581 family proteins provide a framework for cell- and stimulus type-specific SnRK1 signaling in plants

    PubMed Central

    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

  3. Solutions of interval type-2 fuzzy polynomials using a new ranking method

    NASA Astrophysics Data System (ADS)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

    2015-10-01

    A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

  4. Cosmographic analysis with Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

  5. Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

    PubMed

    Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

    2014-10-01

    Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

  6. A model-based 3D phase unwrapping algorithm using Gegenbauer polynomials.

    PubMed

    Langley, Jason; Zhao, Qun

    2009-09-07

    The application of a two-dimensional (2D) phase unwrapping algorithm to a three-dimensional (3D) phase map may result in an unwrapped phase map that is discontinuous in the direction normal to the unwrapped plane. This work investigates the problem of phase unwrapping for 3D phase maps. The phase map is modeled as a product of three one-dimensional Gegenbauer polynomials. The orthogonality of Gegenbauer polynomials and their derivatives on the interval [-1, 1] are exploited to calculate the expansion coefficients. The algorithm was implemented using two well-known Gegenbauer polynomials: Chebyshev polynomials of the first kind and Legendre polynomials. Both implementations of the phase unwrapping algorithm were tested on 3D datasets acquired from a magnetic resonance imaging (MRI) scanner. The first dataset was acquired from a homogeneous spherical phantom. The second dataset was acquired using the same spherical phantom but magnetic field inhomogeneities were introduced by an external coil placed adjacent to the phantom, which provided an additional burden to the phase unwrapping algorithm. Then Gaussian noise was added to generate a low signal-to-noise ratio dataset. The third dataset was acquired from the brain of a human volunteer. The results showed that Chebyshev implementation and the Legendre implementation of the phase unwrapping algorithm give similar results on the 3D datasets. Both implementations of the phase unwrapping algorithm compare well to PRELUDE 3D, 3D phase unwrapping software well recognized for functional MRI.

  7. Numerical solutions for Helmholtz equations using Bernoulli polynomials

    NASA Astrophysics Data System (ADS)

    Bicer, Kubra Erdem; Yalcinbas, Salih

    2017-07-01

    This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

  8. miRNAs mediate SnRK1-dependent energy signaling in Arabidopsis

    PubMed Central

    Confraria, Ana; Martinho, Cláudia; Elias, Alexandre; Rubio-Somoza, Ignacio; Baena-González, Elena

    2013-01-01

    The SnRK1 protein kinase, the plant ortholog of mammalian AMPK and yeast Snf1, is activated by the energy depletion caused by adverse environmental conditions. Upon activation, SnRK1 triggers extensive transcriptional changes to restore homeostasis and promote stress tolerance and survival partly through the inhibition of anabolism and the activation of catabolism. Despite the identification of a few bZIP transcription factors as downstream effectors, the mechanisms underlying gene regulation, and in particular gene repression by SnRK1, remain mostly unknown. microRNAs (miRNAs) are 20–24 nt RNAs that regulate gene expression post-transcriptionally by driving the cleavage and/or translation attenuation of complementary mRNA targets. In addition to their role in plant development, mounting evidence implicates miRNAs in the response to environmental stress. Given the involvement of miRNAs in stress responses and the fact that some of the SnRK1-regulated genes are miRNA targets, we postulated that miRNAs drive part of the transcriptional reprogramming triggered by SnRK1. By comparing the transcriptional response to energy deprivation between WT and dcl1-9, a mutant deficient in miRNA biogenesis, we identified 831 starvation genes misregulated in the dcl1-9 mutant, out of which 155 are validated or predicted miRNA targets. Functional clustering analysis revealed that the main cellular processes potentially co-regulated by SnRK1 and miRNAs are translation and organelle function and uncover TCP transcription factors as one of the most highly enriched functional clusters. TCP repression during energy deprivation was impaired in miR319 knockdown (MIM319) plants, demonstrating the involvement of miR319 in the stress-dependent regulation of TCPs. Altogether, our data indicates that miRNAs are components of the SnRK1 signaling cascade contributing to the regulation of specific mRNA targets and possibly tuning down particular cellular processes during the stress response

  9. SnRK1 activates autophagy via the TOR signaling pathway in Arabidopsis thaliana

    PubMed Central

    Soto-Burgos, Junmarie

    2017-01-01

    Autophagy is a degradation process in which cells break down and recycle their cytoplasmic contents when subjected to environmental stress or during cellular remodeling. The Arabidopsis thaliana SnRK1 complex is a protein kinase that senses changes in energy levels and triggers downstream responses to enable survival. Its mammalian ortholog, AMPK, and yeast ortholog, Snf-1, activate autophagy in response to low energy conditions. We therefore hypothesized that SnRK1 may play a role in the regulation of autophagy in response to nutrient or energy deficiency in Arabidopsis. To test this hypothesis, we determined the effect of overexpression or knockout of the SnRK1 catalytic subunit KIN10 on autophagy activation by abiotic stresses, including nutrient deficiency, salt, osmotic, oxidative, and ER stress. While wild-type plants had low basal autophagy activity in control conditions, KIN10 overexpression lines had increased autophagy under these conditions, indicating activation of autophagy by SnRK1. A kin10 mutant had a basal level of autophagy under control conditions similar to wild-type plants, but activation of autophagy by most abiotic stresses was blocked, indicating that SnRK1 is required for autophagy induction by a wide variety of stress conditions. In mammals, TOR is a negative regulator of autophagy, and AMPK acts to activate autophagy both upstream of TOR, by inhibiting its activity, and in a parallel pathway. Inhibition of Arabidopsis TOR leads to activation of autophagy; inhibition of SnRK1 did not block this activation. Furthermore, an increase in SnRK1 activity was unable to induce autophagy when TOR was also activated. These results demonstrate that SnRK1 acts upstream of TOR in the activation of autophagy in Arabidopsis. PMID:28783755

  10. SnRK1 activates autophagy via the TOR signaling pathway in Arabidopsis thaliana

    DOE PAGES

    Soto-Burgos, Junmarie; Bassham, Diane C.

    2017-08-04

    Autophagy is a degradation process in which cells break down and recycle their cytoplasmic contents when subjected to environmental stress or during cellular remodeling. The Arabidopsis thaliana SnRK1 complex is a protein kinase that senses changes in energy levels and triggers downstream responses to enable survival. Its mammalian ortholog, AMPK, and yeast ortholog, Snf-1, activate autophagy in response to low energy conditions. We therefore hypothesized that SnRK1 may play a role in the regulation of autophagy in response to nutrient or energy deficiency in Arabidopsis. To test this hypothesis, we determined the effect of overexpression or knockout of the SnRK1more » catalytic subunit KIN10 on autophagy activation by abiotic stresses, including nutrient deficiency, salt, osmotic, oxidative, and ER stress. While wild-type plants had low basal autophagy activity in control conditions, KIN10 overexpression lines had increased autophagy under these conditions, indicating activation of autophagy by SnRK1. A kin10 mutant had a basal level of autophagy under control conditions similar to wild-type plants, but activation of autophagy by most abiotic stresses was blocked, indicating that SnRK1 is required for autophagy induction by a wide variety of stress conditions. In mammals, TOR is a negative regulator of autophagy, and AMPK acts to activate autophagy both upstream of TOR, by inhibiting its activity, and in a parallel pathway. Inhibition of Arabidopsis TOR leads to activation of autophagy; inhibition of SnRK1 did not block this activation. Furthermore, an increase in SnRK1 activity was unable to induce autophagy when TOR was also activated. The results presented here demonstrate that SnRK1 acts upstream of TOR in the activation of autophagy in Arabidopsis.« less

  11. SnRK1 activates autophagy via the TOR signaling pathway in Arabidopsis thaliana

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

    Soto-Burgos, Junmarie; Bassham, Diane C.

    Autophagy is a degradation process in which cells break down and recycle their cytoplasmic contents when subjected to environmental stress or during cellular remodeling. The Arabidopsis thaliana SnRK1 complex is a protein kinase that senses changes in energy levels and triggers downstream responses to enable survival. Its mammalian ortholog, AMPK, and yeast ortholog, Snf-1, activate autophagy in response to low energy conditions. We therefore hypothesized that SnRK1 may play a role in the regulation of autophagy in response to nutrient or energy deficiency in Arabidopsis. To test this hypothesis, we determined the effect of overexpression or knockout of the SnRK1more » catalytic subunit KIN10 on autophagy activation by abiotic stresses, including nutrient deficiency, salt, osmotic, oxidative, and ER stress. While wild-type plants had low basal autophagy activity in control conditions, KIN10 overexpression lines had increased autophagy under these conditions, indicating activation of autophagy by SnRK1. A kin10 mutant had a basal level of autophagy under control conditions similar to wild-type plants, but activation of autophagy by most abiotic stresses was blocked, indicating that SnRK1 is required for autophagy induction by a wide variety of stress conditions. In mammals, TOR is a negative regulator of autophagy, and AMPK acts to activate autophagy both upstream of TOR, by inhibiting its activity, and in a parallel pathway. Inhibition of Arabidopsis TOR leads to activation of autophagy; inhibition of SnRK1 did not block this activation. Furthermore, an increase in SnRK1 activity was unable to induce autophagy when TOR was also activated. The results presented here demonstrate that SnRK1 acts upstream of TOR in the activation of autophagy in Arabidopsis.« less

  12. 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.

  13. Production of a conjugate between the rK346 antigen from Leishmania infantum and the horseradish peroxidase C for the detection of rK346 antibodies.

    PubMed

    Rengifo-González, Juan; Medina-Mora, Yollyseth; Silva-Barrios, Sasha; Márquez-Contreras, María Elizabeth; Tibisay Ruiz, María; Cáceres, Ana J; Concepción, Juan Luis; Quiñones, Wilfredo

    2016-06-01

    It was designed and characterized a reporter system to be captured by an- tibodies bound to ELISA plates. The system was designed with the rK346 from Leishmania infantum, a highly antigenic and specific protein. The rK346 was coupled to the horseradish peroxidase C (HRPc) from Armoracia rusticana using glutaraldehyde or sulfo-SMCC. Gluta- raldehyde conjugation was performed in two steps. Separation of conjugates was carried out using a Sepharose S-200 in size exclusion chromatography (SEC); fractions were analyzed via HRPc activity and through ELISA plates sensitized with polyclonal anti-rK346 IgG puri- fied from rabbit serum. A heterogeneous population of conjugates rK346-HRPc was obtained with molecular weights ranging between 109.7 ± 16.5 to 67.6 ± 10.1 kDa; with rK346-HRPe stoichiometries of 1:2; 2:1; 3:1; and 2:2. Conjugation using sulfo-SMCC was carried out first by introducing -SH groups onto the HRPc using the SATA reagent and the antigen was modi- fied with sulfo-SMCC during 45 min. Separation and analysis of conjugates was performed similarly as with glutaraldehyde, resulting in a heterogeneous population of conjugates rK346- HRPc with molecular weights between 150.5 ± 22.6 to 80.0 ± 12.0 kDa; with rK346-HRPC stoichiometries of 2:1; 1:2; 2:2; and 1:3, with an increased conjugation efficiency in compari- son with glutaraldehyde. This enables sulfo-SMCC to be used as a potential reagent for cou- pling the antigen to the HRPc, to design an economic, specific and easy method to apply as a reporter system, available to assess individuals at risk and/or at early and late stages of visceral leishmaniasis.

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

    NASA Astrophysics Data System (ADS)

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

    2017-10-01

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

  15. Structural basis for basal activity and autoactivation of abscisic acid (ABA) signaling SnRK2 kinases

    PubMed Central

    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

  16. Do r/K reproductive strategies apply to human differences?

    PubMed

    Rushton, J P

    1988-01-01

    This article discusses the r/K theory of Social Biology and how it relates to humans. The symbols r and K originate in the mathematics of population biology and refer to 2 ends of a continuum in which a compensatory exchange occurs between gamete production (the r-strategy) and longevity (the K-strategy). Both across and within species, r and K strategists differ in a suite of correlated characteristics. Humans are the most K of all. K's supposedly have a longer gestation period, a higher birthweight, a more delayed sexual maturation, a lower sex drive, and a longer life. Studies providing evidence for the expected covariation among K attributes are presented. Additional evidence for r/K theory comes from the comparison of human population known to differ in gamete production. The pattern of racial differences observed to occur in sexual behavior has also been found to exist on numerous other indices of K. For instance, there are racial differences in brain size, intelligence, and maturation rate, among others. The findings suggest that, on the average, Mongoloids are more K than Caucasoids, who in turn, are more K than Negroids. Recently conducted studies have extended the data in favor of r/K theory, and further research is currently underway, including whether r/K attributes underlie individual and social class differences in health and longevity.

  17. Polynomial Chaos Based Acoustic Uncertainty Predictions from Ocean Forecast Ensembles

    NASA Astrophysics Data System (ADS)

    Dennis, S.

    2016-02-01

    Most significant ocean acoustic propagation occurs at tens of kilometers, at scales small compared basin and to most fine scale ocean modeling. To address the increased emphasis on uncertainty quantification, for example transmission loss (TL) probability density functions (PDF) within some radius, a polynomial chaos (PC) based method is utilized. In order to capture uncertainty in ocean modeling, Navy Coastal Ocean Model (NCOM) now includes ensembles distributed to reflect the ocean analysis statistics. Since the ensembles are included in the data assimilation for the new forecast ensembles, the acoustic modeling uses the ensemble predictions in a similar fashion for creating sound speed distribution over an acoustically relevant domain. Within an acoustic domain, singular value decomposition over the combined time-space structure of the sound speeds can be used to create Karhunen-Loève expansions of sound speed, subject to multivariate normality testing. These sound speed expansions serve as a basis for Hermite polynomial chaos expansions of derived quantities, in particular TL. The PC expansion coefficients result from so-called non-intrusive methods, involving evaluation of TL at multi-dimensional Gauss-Hermite quadrature collocation points. Traditional TL calculation from standard acoustic propagation modeling could be prohibitively time consuming at all multi-dimensional collocation points. This method employs Smolyak order and gridding methods to allow adaptive sub-sampling of the collocation points to determine only the most significant PC expansion coefficients to within a preset tolerance. Practically, the Smolyak order and grid sizes grow only polynomially in the number of Karhunen-Loève terms, alleviating the curse of dimensionality. The resulting TL PC coefficients allow the determination of TL PDF normality and its mean and standard deviation. In the non-normal case, PC Monte Carlo methods are used to rapidly establish the PDF. This work was

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

    PubMed

    Dehmer, Matthias; Emmert-Streib, Frank; Shi, Yongtang; Stefu, Monica; Tripathi, Shailesh

    2015-01-01

    In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164-168]. We demonstrate that by using the new functional matrix approach, exhaustively generated graphs can be discriminated more uniquely than shown in the mentioned previous work.

  19. Orbifold E-functions of dual invertible polynomials

    NASA Astrophysics Data System (ADS)

    Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi

    2016-08-01

    An invertible polynomial is a weighted homogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search for mirror symmetric orbifold Landau-Ginzburg models, P. Berglund and M. Henningson considered a pair (f , G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f ˜ , G ˜) . We consider the so-called orbifold E-function of such a pair (f , G) which is a generating function for the exponents of the monodromy action on an orbifold version of the mixed Hodge structure on the Milnor fibre of f. We prove that the orbifold E-functions of Berglund-Henningson dual pairs coincide up to a sign depending on the number of variables and a simple change of variables. The proof is based on a relation between monomials (say, elements of a monomial basis of the Milnor algebra of an invertible polynomial) and elements of the whole symmetry group of the dual polynomial.

  20. Hadamard Factorization of Stable Polynomials

    NASA Astrophysics Data System (ADS)

    Loredo-Villalobos, Carlos Arturo; Aguirre-Hernández, Baltazar

    2011-11-01

    The stable (Hurwitz) polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p,q ∈ R[x]:p(x) = anxn+an-1xn-1+...+a1x+a0q(x) = bmx m+bm-1xm-1+...+b1x+b0the Hadamard product (p × q) is defined as (p×q)(x) = akbkxk+ak-1bk-1xk-1+...+a1b1x+a0b0where k = min(m,n). Some results (see [16]) shows that if p,q ∈R[x] are stable polynomials then (p×q) is stable, also, i.e. the Hadamard product is closed; however, the reciprocal is not always true, that is, not all stable polynomial has a factorization into two stable polynomials the same degree n, if n> 4 (see [15]).In this work we will give some conditions to Hadamard factorization existence for stable polynomials.

  1. 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.

  2. 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…

  3. On universal knot polynomials

    NASA Astrophysics Data System (ADS)

    Mironov, A.; Mkrtchyan, R.; Morozov, A.

    2016-02-01

    We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

  4. Absolute Radiometric Calibration of the GÖKTÜRK-2 Satellite Sensor Using Tuz GÖLÜ (landnet Site) from Ndvi Perspective

    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

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

    PubMed Central

    Dehmer, Matthias; Emmert-Streib, Frank; Shi, Yongtang; Stefu, Monica; Tripathi, Shailesh

    2015-01-01

    In this paper, we study the discrimination power of graph measures that are based on graph-theoretical matrices. The paper generalizes the work of [M. Dehmer, M. Moosbrugger. Y. Shi, Encoding structural information uniquely with polynomial-based descriptors by employing the Randić matrix, Applied Mathematics and Computation, 268(2015), 164–168]. We demonstrate that by using the new functional matrix approach, exhaustively generated graphs can be discriminated more uniquely than shown in the mentioned previous work. PMID:26479495

  6. Learning polynomial feedforward neural networks by genetic programming and backpropagation.

    PubMed

    Nikolaev, N Y; Iba, H

    2003-01-01

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

  7. Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.

    PubMed

    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. © 2011 IEEE

  8. A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation

    NASA Astrophysics Data System (ADS)

    Oruç, Ömer

    2018-04-01

    In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.

  9. Determinants with orthogonal polynomial entries

    NASA Astrophysics Data System (ADS)

    Ismail, Mourad E. H.

    2005-06-01

    We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. We also study the Hankel determinants which start with pn on the top left-hand corner. As examples we evaluate the Hankel determinants whose entries are q-ultraspherical or Al-Salam-Chihara polynomials.

  10. Distortion theorems for polynomials on a circle

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

    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.

  11. Characterization of a common wheat (Triticum aestivum L.) TaSnRK2.7 gene involved in abiotic stress responses

    PubMed Central

    Zhang, Hongying; Mao, Xinguo; Jing, Ruilian; Chang, Xiaoping; Xie, Huimin

    2011-01-01

    Sucrose non-fermenting-1-related protein kinase 2 (SnRK2) plays a key role in the plant stress signalling transduction pathway via phosphorylation. Here, a SnRK2 member of common wheat, TaSnRK2.7, was cloned and characterized. Southern blot analysis suggested that the common wheat genome contains three copies of TaSnRK2.7. Subcellular localization showed the presence of TaSnRK2.7 in the cell membrane, cytoplasm, and nucleus. Expression patterns revealed that TaSnRK2.7 is expressed strongly in roots, and responds to polyethylene glycol, NaCl, and cold stress, but not to abscisic acid (ABA) application, suggesting that TaSnRK2.7 might participate in non-ABA-dependent signal transduction pathways. TaSnRK2.7 was transferred to Arabidopsis under the control of the CaMV-35S promoter. Function analysis showed that TaSnRK2.7 is involved in carbohydrate metabolism, decreasing osmotic potential, enhancing photosystem II activity, and promoting root growth. Its overexpression results in enhanced tolerance to multi-abiotic stress. Therefore, TaSnRK2.7 is a multifunctional regulatory factor in plants, and has the potential to be utilized in transgenic breeding to improve abiotic stress tolerance in crop plants. PMID:21030389

  12. Polynomial Conjoint Analysis of Similarities: A Model for Constructing Polynomial Conjoint Measurement Algorithms.

    ERIC Educational Resources Information Center

    Young, Forrest W.

    A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

  13. 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.

  14. 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…

  15. Stochastic Estimation via Polynomial Chaos

    DTIC Science & Technology

    2015-10-01

    AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

  16. 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)

  17. Distortion theorems for polynomials on a circle

    NASA Astrophysics Data System (ADS)

    Dubinin, V. N.

    2000-12-01

    Inequalities for the derivatives with respect to \\varphi=\\arg z the functions \\operatorname{Re}P(z), \\vert P(z)\\vert^2 and \\arg P(z) are established for an algebraic polynomial P(z) at points on the circle \\vert z\\vert=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.

  18. Polynomial probability distribution estimation using the method of moments

    PubMed Central

    Mattsson, Lars; Rydén, Jesper

    2017-01-01

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

  19. Polynomial probability distribution estimation using the method of moments.

    PubMed

    Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

    2017-01-01

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

  20. a Comprehensive Review of Pansharpening Algorithms for GÖKTÜRK-2 Satellite Images

    NASA Astrophysics Data System (ADS)

    Kahraman, S.; Ertürk, A.

    2017-11-01

    In this paper, a comprehensive review and performance evaluation of pansharpening algorithms for GÖKTÜRK-2 images is presented. GÖKTÜRK-2 is the first high resolution remote sensing satellite of Turkey which was designed and built in Turkey, by The Ministry of Defence, TUBITAK-UZAY and Turkish Aerospace Industry (TUSAŞ) collectively. GÖKTÜRK-2 was launched at 18th. December 2012 in Jinguan, China and provides 2.5 meter panchromatic (PAN) and 5 meter multispectral (MS) spatial resolution satellite images. In this study, a large number of pansharpening algorithms are implemented and evaluated for performance on multiple GÖKTÜRK-2 satellite images. Quality assessments are conducted both qualitatively through visual results and quantitatively using Root Mean Square Error (RMSE), Correlation Coefficient (CC), Spectral Angle Mapper (SAM), Erreur Relative Globale Adimensionnelle de Synthése (ERGAS), Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM) and Universal Image Quality Index (UIQI).

  1. Multi-indexed (q-)Racah polynomials

    NASA Astrophysics Data System (ADS)

    Odake, Satoru; Sasaki, Ryu

    2012-09-01

    As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

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

    PubMed

    Lam, H K

    2012-02-01

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

  3. Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

    NASA Astrophysics Data System (ADS)

    Milstead, Jonathan

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

  4. Genome-wide identification and expression profiling of the SnRK2 gene family in Malus prunifolia.

    PubMed

    Shao, Yun; Qin, Yuan; Zou, Yangjun; Ma, Fengwang

    2014-11-15

    Sucrose non-fermenting-1-related protein kinase 2 (SnRK2) constitutes a small plant-specific serine/threonine kinase family with essential roles in the abscisic acid (ABA) signal pathway and in responses to osmotic stress. Although a genome-wide analysis of this family has been conducted in some species, little is known about SnRK2 genes in apple (Malus domestica). We identified 14 putative sequences encoding 12 deduced SnRK2 proteins within the apple genome. Gene chromosomal location and synteny analysis of the apple SnRK2 genes indicated that tandem and segmental duplications have likely contributed to the expansion and evolution of these genes. All 12 full-length coding sequences were confirmed by cloning from Malus prunifolia. The gene structure and motif compositions of the apple SnRK2 genes were analyzed. Phylogenetic analysis showed that MpSnRK2s could be classified into four groups. Profiling of these genes presented differential patterns of expression in various tissues. Under stress conditions, transcript levels for some family members were up-regulated in the leaves in response to drought, salinity, or ABA treatments. This suggested their possible roles in plant response to abiotic stress. Our findings provide essential information about SnRK2 genes in apple and will contribute to further functional dissection of this gene family. Copyright © 2014 Elsevier B.V. All rights reserved.

  5. An algorithmic approach to solving polynomial equations associated with quantum circuits

    NASA Astrophysics Data System (ADS)

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

    2009-12-01

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

  6. Identification and functional characterization of the Arabidopsis Snf1-related protein kinase SnRK2.4 phosphatidic acid-binding domain.

    PubMed

    Julkowska, Magdalena M; McLoughlin, Fionn; Galvan-Ampudia, Carlos S; Rankenberg, Johanna M; Kawa, Dorota; Klimecka, Maria; Haring, Michel A; Munnik, Teun; Kooijman, Edgar E; Testerink, Christa

    2015-03-01

    Phosphatidic acid (PA) is an important signalling lipid involved in various stress-induced signalling cascades. Two SnRK2 protein kinases (SnRK2.4 and SnRK2.10), previously identified as PA-binding proteins, are shown here to prefer binding to PA over other anionic phospholipids and to associate with cellular membranes in response to salt stress in Arabidopsis roots. A 42 amino acid sequence was identified as the primary PA-binding domain (PABD) of SnRK2.4. Unlike the full-length SnRK2.4, neither the PABD-YFP fusion protein nor the SnRK2.10 re-localized into punctate structures upon salt stress treatment, showing that additional domains of the SnRK2.4 protein are required for its re-localization during salt stress. Within the PABD, five basic amino acids, conserved in class 1 SnRK2s, were found to be necessary for PA binding. Remarkably, plants overexpressing the PABD, but not a non-PA-binding mutant version, showed a severe reduction in root growth. Together, this study biochemically characterizes the PA-SnRK2.4 interaction and shows that functionality of the SnRK2.4 PABD affects root development. © 2014 The Authors. Plant, Cell & Environment published by John Wiley & Sons Ltd.

  7. Equivalences of the multi-indexed orthogonal polynomials

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

    Odake, Satoru

    2014-01-15

    Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

  8. A Formally-Verified Decision Procedure for Univariate Polynomial Computation Based on Sturm's Theorem

    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.

  9. Linear precoding based on polynomial expansion: reducing complexity in massive MIMO.

    PubMed

    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.

  10. Sucrose non-ferment 1 related protein kinase 2 (SnRK2) genes could mediate the stress responses in potato (Solanum tuberosum L.).

    PubMed

    Bai, Jiangping; Mao, Juan; Yang, Hongyu; Khan, Awais; Fan, Aqi; Liu, Siyan; Zhang, Junlian; Wang, Di; Gao, Huijuan; Zhang, Jinlin

    2017-05-15

    The SnRKs (sucrose non-fermenting 1 related protein kinase) are a gene family coding for Ser/Thr protein kinases and play important roles in linking the tolerance and metabolic responses of plants to abiotic stresses. To date, no genome-wide characterization of the sucrose non-ferment 1 related protein kinase 2 (SnRK2) subfamily has been conducted in potato (Solanum tuberosum L.). In this study, eight StSnRK2 genes (StSnRK2.1- StSnRK2.8) were identified in the genome of the potato (Solanum tuberosum L.) cultivar 'Longshu 3', with similar characteristics to SnRK2 from other plant species in gene structure, motif distribution and secondary structures. The C-terminal regions were highly divergent among StSnRK2s, while they all carried the similar Ser/Thr protein kinase domain. The fluorescence of GFP fused with StSnRK2.1, StSnRK2.2, StSnRK2.6, StSnRK2.7 and StSnRK2.8 was detected in the nucleus and cytoplasm of onion epidermal cells with StSnRK2.3 and StSnRK2.4 mainly associated to the nucleus while StSnRK2.5 to subcellular organelles. Expression level analysis by qRT-PCR showed that StSnRK2.1, 2.2, 2.5 and 2.6 were more than 1 fold higher in the root than in the leaf, tuber and stem tissues. The expressions of StSnRK2.3, 2.7, and 2.8 were at least 1.5 folds higher in the leaf and stem than in the root, but lower in the tuber. The expression of StSnRK2.4 was also significantly (P < 0.05) higher in leaf, stem, and tuber than in the root. From the perspective of the relative expressions of StSnRK2 genes in potato, ABA treatment had a different effect from NaCl and PEG treatments. In the present study, we identified and characterized eight SnRK2s in the potato genome. The eight StSnRK2s exhibit similar gene structure and secondary structures in potato to the SnRK2s found in other plant species. The relative expression of eight genes varied among various tissues (roots, leaves, tubers, and stems) and abiotic stresses (ABA, NaCl and PEG-6000) with the prolongation of

  11. Bayer Demosaicking with Polynomial Interpolation.

    PubMed

    Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil

    2016-08-30

    Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.

  12. Constructing general partial differential equations using polynomial and neural networks.

    PubMed

    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. Copyright © 2015 Elsevier Ltd. All rights reserved.

  13. Health Information in Turkish (Türkçe)

    MedlinePlus

    ... Expand Section Salmonella Infections Vaccine Information Statement (VIS) -- Typhoid Vaccines: What You Need to Know - English PDF Vaccine Information Statement (VIS) -- Typhoid Vaccines: What You Need to Know - Türkçe (Turkish) ...

  14. Interactions of ABA signaling core components (SlPYLs, SlPP2Cs, and SlSnRK2s) in tomato (Solanum lycopersicon).

    PubMed

    Chen, Pei; Sun, Yu-Fei; Kai, Wen-Bin; Liang, Bin; Zhang, Yu-Shu; Zhai, Xia-Wan; Jiang, Li; Du, Yang-Wei; Leng, Ping

    2016-10-20

    Abscisic acid (ABA) regulates fruit development and ripening via its signaling. However, the exact role of ABA signaling core components in fruit have not yet been clarified. In this study, we investigated the potential interactions of tomato (Solanum lycopersicon) ABA signaling core components using yeast two-hybrid analysis, with or without ABA at different concentrations. The results showed that among 12 PYR/PYL/RCAR ABA receptors (SlPYLs), SlPYL1, SlPYL2, SlPYL4, SlPYL5, SlPYL 7, SlPYL8, SlPYL9, SlPYL10, SlPYL11, and SlPYL13 were ABA-dependent receptors, while SlPYL3 and SlPYL12 were ABA-independent receptors. Among five SlPP2Cs (type 2C protein phosphatases) and seven SlSnRK2s (subfamily 2 of SNF1-related kinases), all SlSnRK2s could interact with SlPP2C2, while SlSnRK2.8 also interacted with SlPP2C3. SlSnRK2.5 could interact with SlABF2/4 (ABA-responsive element binding factors). Expressions of SlPYL1, SlPYL2, SlPYL8, and SlPYL10 were upregulated under exogenous ABA but downregulated under nordihydroguaiaretic acid (NDGA) at the mature green stage of fruit ripening. The expressions of SlPP2C1, SlPP2C2, SlPP2C3, and SlPP2C5 were upregulated in ABA-treated fruit, but downregulated in NDGA-treated fruit at the mature green stage. The expressions of SlSnRK2.4, SlSnRK2.5, SlSnRK2.6, and SlSnRK2.7 were upregulated by ABA, but downregulated by NDGA. However, SlSnRK2.2 was down regulated by ABA. Expression of SlABF2/3/4 was enhanced by ABA but decreased by NDGA. Based on these results, we concluded that the majority of ABA receptor PYLs interact with SlPP2Cs in an ABA-dependent manner. SlPP2C2 and SlPP2C3 can interact with SlSnRK2s. SlSnRK2.5 could interact with SlABF2/4. Most ABA signaling core components respond to exogenous ABA. Copyright © 2016 Elsevier GmbH. All rights reserved.

  15. Extending Romanovski polynomials in quantum mechanics

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

    Quesne, C.

    2013-12-15

    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 ofmore » 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.« less

  16. Purification and antibacterial activity of recombinant warnericin RK expressed in Escherichia coli.

    PubMed

    Verdon, Julien; Girardin, Nicolas; Marchand, Adrienne; Héchard, Yann; Berjeaud, Jean-Marc

    2013-06-01

    Warnericin RK is a small cationic peptide produced by Staphylococcus warneri RK. This peptide has an antimicrobial spectrum of activity almost restricted to the Legionella genus. It is a membrane-active peptide with a proposed detergent-like mechanism of action at high concentration. Moreover, the fatty acids content of Legionella was shown to modulate the peptide activity. In order to decipher the mode of action in details using solid-state NMR spectroscopy, large amount of an isotopic labeled peptide is required. Since it is less expensive to obtain such a peptide biologically, we report here methods to express warnericin RK in Escherichia coli with or without a fusion partner and to purify resulting recombinant peptides. The cDNA fragment encoding warnericin RK was synthesized and ligated into three expression vectors. Two fusion peptides, carrying polyhistidine tag in N- or C-terminal and a native peptide, without tag, were expressed in E. coli cells. Fusion peptides were purified, with a yield of 3 mg/l, by affinity chromatography and reverse-phase HPLC. The recombinant native peptide was purified using a two-step purification method consisting of a hydrophobic chromatography followed by a reverse-phase HPLC step with a yield of 1.4 mg/l. However, the anti-Legionella activity was lower for both tagged peptide probably because of structural modifications. So, the native recombinant peptide was preferentially chosen for (15)N-labeling experiments. Our results suggest that the developed production and purification procedures will be useful in obtaining a large quantity of recombinant isotope-labeled warnericin RK for further studies.

  17. Isolation, phylogeny and evolution of the SymRK gene in the legume genus Lupinus L.

    PubMed

    Mahé, Frédéric; Markova, Dragomira; Pasquet, Rémy; Misset, Marie-Thérèse; Aïnouche, Abdelkader

    2011-07-01

    SymRK is one of the key genes involved in initial steps of legume symbiotic association with fungi (mycorrhization) and nitrogen-fixing bacteria (nodulation). A large portion of the sequence encoding the extracellular domain of SYMRK was obtained for 38 lupine accessions and 2 outgroups in order to characterize this region, to evaluate its phylogenetic utility, and to examine whether its molecular evolutionary pattern is correlated with rhizobial diversity and specificity in Lupinus. The data suggested that, in Lupinus, SymRK is a single copy gene that shows good phylogenetic potential. Accordingly, SymRK provided additional support to previous molecular phylogenies, and shed additional light on relationships within the Old World group of Lupinus, especially among the African species. Similar to results of other studies, analyses of SymRK sequences were unable to resolve placement of the Florida unifoliolate lineage, whose relationship was weakly supported to either the Old or the New World lupines. Our data are consistent with strong purifying selection operating on SymRK in Lupinus, preserving rather than diversifying its function. Thus, although SymRK was demonstrated to be a vital gene in the early stages of the root-bacterial symbiotic associations, no evidence from present analyses indicate that this gene is involved in changes in rhizobial specificity in Lupinus. Copyright © 2011 Elsevier Inc. All rights reserved.

  18. Regulatory functions of SnRK1 in stress-responsive gene expression and in plant growth and development.

    PubMed

    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.

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

    NASA Astrophysics Data System (ADS)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim

    2014-07-01

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

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

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

    Seshadhri, Comandur; Saxena, Nitin

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

  1. 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 as the polynomials of degree for which Eq. (1) has a polynomial solution of some degree k. In this paper, we compute the limiting distribution, as well as the limiting mean level spacings distribution of the zeros of any Van Vleck polynomial as N --> ∞.

  2. On Certain Wronskians of Multiple Orthogonal Polynomials

    NASA Astrophysics Data System (ADS)

    Zhang, Lun; Filipuk, Galina

    2014-11-01

    We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szegő. There are two applications of our results. The first application arises from the observation that the m-th moment of the average characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal polynomials. Hence, it is straightforward to obtain the distinct behavior of the moments for odd and even m in a special multiple orthogonal ensemble - the AT ensemble. As the second application, we derive some Turán type inequalities for m! ultiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have regular configurations in the complex plane, which might be of independent interest.

  3. An Apple Protein Kinase MdSnRK1.1 Interacts with MdCAIP1 to Regulate ABA Sensitivity.

    PubMed

    Liu, Xiao-Juan; Liu, Xin; An, Xiu-Hong; Han, Peng-Liang; You, Chun-Xiang; Hao, Yu-Jin

    2017-10-01

    ABA is a crucial phytohormone for development and stress responses in plants. Snf1-related protein kinase 1.1 (SnRK1.1) is involved in the ABA response. However, the molecular mechanism underlying the SnRK1.1 response to ABA is largely unknown. Here, it was found that overexpression of the apple MdSnRK1.1 gene enhanced ABA sensitivity in both transgenic apple calli and Arabidopsis seedlings. Subsequently, a yeast two-hybrid screen demonstrated that MdCAIP1 (C2-domain ABA Insensitive Protein1) interacted with MdSnRK1.1. Their interaction was further confirmed by pull-down and co-immunoprecipitation assays. Expression of the MdCAIP1 gene was positively induced by ABA. Its overexpression enhanced ABA sensitivity in transgenic apple calli. Furthermore, it was found that MdSnRK1.1 phosphorylated the MdCAIP1 protein in vivo and promoted its degradation in vitro and in vivo. As a result, MdSnRK1.1 inhibited MdCAIP1-mediated ABA sensitivity, and MdCAIP1 partially reduced MdSnRK1.1-mediated ABA sensitivity. Our findings indicate that MdSnRK1.1 plays an important role in the ABA response, partially by controlling the stability of the MdCAIP1 protein. © The Author 2017. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: journals.permissions@oup.com.

  4. 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…

  5. Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies

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

    Hampton, Jerrad; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

    2015-01-01

    Sampling orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models with random inputs, using Polynomial Chaos (PC) expansions. It is known that bounding a probabilistic parameter, referred to as coherence, yields a bound on the number of samples necessary to identify coefficients in a sparse PC expansion via solution to an ℓ{sub 1}-minimization problem. Utilizing results for orthogonal polynomials, we bound the coherence parameter for polynomials of Hermite and Legendre type under their respective natural sampling distribution. In both polynomial bases we identify an importance sampling distribution which yields a bound with weaker dependence onmore » the order of the approximation. For more general orthonormal bases, we propose the coherence-optimal sampling: a Markov Chain Monte Carlo sampling, which directly uses the basis functions under consideration to achieve a statistical optimality among all sampling schemes with identical support. We demonstrate these different sampling strategies numerically in both high-order and high-dimensional, manufactured PC expansions. In addition, the quality of each sampling method is compared in the identification of solutions to two differential equations, one with a high-dimensional random input and the other with a high-order PC expansion. In both cases, the coherence-optimal sampling scheme leads to similar or considerably improved accuracy.« less

  6. Vector-valued Jack polynomials and wavefunctions on the torus

    NASA Astrophysics Data System (ADS)

    Dunkl, Charles F.

    2017-06-01

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

  7. Light resonances and the low-q2 bin of RK*$$ {R}_{K^{*}} $$

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

    Altmannshofer, Wolfgang; Baker, Michael J.; Gori, Stefania

    LHCb has reported hints of lepton-flavor universality violation in the rare decaysmore » $$B \\to K^{(*)} \\ell^+\\ell^-$$, both in high- and low-$q^2$ bins. Although the high-$q^2$ hint may be explained by new short-ranged interactions, the low-$q^2$ one cannot. We thus explore the possibility that the latter is explained by a new light resonance. We find that LHCb's central value of $$R_{K^*}$$ in the low-$q^2$ bin is achievable in a restricted parameter space of new-physics scenarios in which the new, light resonance decays preferentially to electrons and has a mass within approximately $10$ MeV of the di-muon threshold. Interestingly, such an explanation can have a kinematic origin and does not require a source of lepton-flavor universality violation. A model-independent prediction is a narrow peak in the differential $$B \\to K^* e^+e^-$$ rate close to the di-muon threshold. If such a peak is observed, other observables, such as the differential $$B \\to K e^+e^-$$ rate and $$R_K$$, may be employed to distinguish between models. However, if a low-mass resonance is not observed and the low-$q^2$ anomaly increases in significance, then the case for an experimental origin of the lepton-flavor universality violating anomalies would be strengthened. Finally, to further explore this, we also point out that, in analogy to $$J/\\psi$$ decays, $e^+e^-$ and $$\\mu^+\\mu^-$$ decays of $$\\phi$$ mesons can be used as a cross check of lepton-flavor universality by LHCb with $5$ fb$$^{-1}$$ of integrated luminosity.« less

  8. Light resonances and the low-q2 bin of RK*$$ {R}_{K^{*}} $$

    DOE PAGES

    Altmannshofer, Wolfgang; Baker, Michael J.; Gori, Stefania; ...

    2018-03-29

    LHCb has reported hints of lepton-flavor universality violation in the rare decaysmore » $$B \\to K^{(*)} \\ell^+\\ell^-$$, both in high- and low-$q^2$ bins. Although the high-$q^2$ hint may be explained by new short-ranged interactions, the low-$q^2$ one cannot. We thus explore the possibility that the latter is explained by a new light resonance. We find that LHCb's central value of $$R_{K^*}$$ in the low-$q^2$ bin is achievable in a restricted parameter space of new-physics scenarios in which the new, light resonance decays preferentially to electrons and has a mass within approximately $10$ MeV of the di-muon threshold. Interestingly, such an explanation can have a kinematic origin and does not require a source of lepton-flavor universality violation. A model-independent prediction is a narrow peak in the differential $$B \\to K^* e^+e^-$$ rate close to the di-muon threshold. If such a peak is observed, other observables, such as the differential $$B \\to K e^+e^-$$ rate and $$R_K$$, may be employed to distinguish between models. However, if a low-mass resonance is not observed and the low-$q^2$ anomaly increases in significance, then the case for an experimental origin of the lepton-flavor universality violating anomalies would be strengthened. Finally, to further explore this, we also point out that, in analogy to $$J/\\psi$$ decays, $e^+e^-$ and $$\\mu^+\\mu^-$$ decays of $$\\phi$$ mesons can be used as a cross check of lepton-flavor universality by LHCb with $5$ fb$$^{-1}$$ of integrated luminosity.« less

  9. Algorithms for Solvents and Spectral Factors of Matrix Polynomials

    DTIC Science & Technology

    1981-01-01

    spectral factors of matrix polynomials LEANG S. SHIEHt, YIH T. TSAYt and NORMAN P. COLEMANt A generalized Newton method , based on the contracted gradient...of a matrix poly- nomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial...estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right

  10. Approximating exponential and logarithmic functions using polynomial interpolation

    NASA Astrophysics Data System (ADS)

    Gordon, Sheldon P.; Yang, Yajun

    2017-04-01

    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 analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

  11. DIFFERENTIAL CROSS SECTION ANALYSIS IN KAON PHOTOPRODUCTION USING ASSOCIATED LEGENDRE POLYNOMIALS

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

    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 thenmore » 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.« less

  12. Percolation critical polynomial as a graph invariant

    DOE PAGES

    Scullard, Christian R.

    2012-10-18

    Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

  13. 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.

  14. Transfer matrix computation of generalized critical polynomials in percolation

    DOE PAGES

    Scullard, Christian R.; Jacobsen, Jesper Lykke

    2012-09-27

    Percolation thresholds have recently been studied by means of a graph polynomial PB(p), henceforth referred to as the critical polynomial, that may be defined on any periodic lattice. The polynomial depends on a finite subgraph B, called the basis, and the way in which the basis is tiled to form the lattice. The unique root of P B(p) in [0, 1] either gives the exact percolation threshold for the lattice, or provides an approximation that becomes more accurate with appropriately increasing size of B. Initially P B(p) was defined by a contraction-deletion identity, similar to that satisfied by the Tuttemore » polynomial. Here, we give an alternative probabilistic definition of P B(p), which allows for much more efficient computations, by using the transfer matrix, than was previously possible with contraction-deletion. We present bond percolation polynomials for the (4, 82), kagome, and (3, 122) lattices for bases of up to respectively 96, 162, and 243 edges, much larger than the previous limit of 36 edges using contraction-deletion. We discuss in detail the role of the symmetries and the embedding of B. For the largest bases, we obtain the thresholds p c(4, 82) = 0.676 803 329 · · ·, p c(kagome) = 0.524 404 998 · · ·, p c(3, 122) = 0.740 420 798 · · ·, comparable to the best simulation results. We also show that the alternative definition of P B(p) can be applied to study site percolation problems.« less

  15. SCFAtPP2-B11 modulates ABA signaling by facilitating SnRK2.3 degradation in Arabidopsis thaliana

    PubMed Central

    Ren, Ziyin; Zhi, Liya; Yao, Bin; Su, Chao; Liu, Liu; Li, Xia

    2017-01-01

    The phytohormone abscisic acid (ABA) is an essential part of the plant response to abiotic stressors such as drought. Upon the perception of ABA, pyrabactin resistance (PYR)/PYR1-like (PYL)/regulatory components of ABA receptor (RCAR) proteins interact with co-receptor protein phosphatase type 2Cs to permit activation Snf1-related protein kinase2 (SnRK2) kinases, which switch on ABA signaling by phosphorylating various target proteins. Thus, SnRK2 kinases are central regulators of ABA signaling. However, the mechanisms that regulate SnRK2 degradation remain elusive. Here, we show that SnRK2.3 is degradated by 26S proteasome system and ABA promotes its degradation. We found that SnRK2.3 interacts with AtPP2-B11 directly. AtPP2-B11 is an F-box protein that is part of a SKP1/Cullin/F-box E3 ubiquitin ligase complex that negatively regulates plant responses to ABA by specifically promoting the degradation of SnRK2.3. AtPP2-B11 was induced by ABA, and the knockdown of AtPP2-B11 expression markedly increased the ABA sensitivity of plants during seed germination and postgerminative development. Overexpression of AtPP2-B11 does not affect ABA sensitivity, but inhibits the ABA hypersensitive phenotypes of SnRK2.3 overexpression lines. These results reveal a novel mechanism through which AtPP2-B11 specifically degrades SnRK2.3 to attenuate ABA signaling and the abiotic stress response in Arabidopsis. PMID:28787436

  16. Molecular mimicry regulates ABA signaling by SnRK2 kinases and PP2C phosphatases.

    PubMed

    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.

  17. Quantitative phosphoproteomics identifies SnRK2 protein kinase substrates and reveals the effectors of abscisic acid action.

    PubMed

    Wang, Pengcheng; Xue, Liang; Batelli, Giorgia; Lee, Shinyoung; Hou, Yueh-Ju; Van Oosten, Michael J; Zhang, Huiming; Tao, W Andy; Zhu, Jian-Kang

    2013-07-02

    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.

  18. 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.

  19. CaLecRK-S.5, a pepper L-type lectin receptor kinase gene, confers broad-spectrum resistance by activating priming

    PubMed Central

    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

  20. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    NASA Astrophysics Data System (ADS)

    Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

    2003-07-01

    Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

  1. Identification of novel interactors and potential phosphorylation substrates of GsSnRK1 from wild soybean (Glycine soja).

    PubMed

    Song, Yu; Zhang, Hang; You, Hongguang; Liu, Yuanming; Chen, Chao; Feng, Xu; Yu, Xingyu; Wu, Shengyang; Wang, Libo; Zhong, Shihua; Li, Qiang; Zhu, Yanming; Ding, Xiaodong

    2018-04-17

    The plant sucrose nonfermenting kinase 1 (SnRK1) kinases play the central roles in the processes of energy balance, hormone perception, stress resistance, metabolism, growth, and development. However, the functions of these kinases are still elusive. In this study, we used GsSnRK1 of wild soybean as bait to perform library-scale screens by the means of yeast two-hybrid to identify its interacting proteins. The putative interactions were verified by yeast retransformation and β-galactosidase assays, and the selected interactions were further confirmed in planta by bimolecular fluorescence complementation and biochemical Co-IP assays. Protein phosphorylation analyses were carried out by phos-tag assay and anti-phospho-(Ser/Thr) substrate antibodies. Finally, we obtained 24 GsSnRK1 interactors and several putative substrates that can be categorized into SnRK1 regulatory β subunit, protein modification, biotic and abiotic stress-related, hormone perception and signalling, gene expression regulation, water and nitrogen transport, metabolism, and unknown proteins. Intriguingly, we first discovered that GsSnRK1 interacted with and phosphorylated the components of soybean nodulation and symbiotic nitrogen fixation. The interactions and potential functions of GsSnRK1 and its associated proteins were extensively discussed and analysed. This work provides plausible clues to elucidate the novel functions of SnRK1 in response to variable environmental, metabolic, and physiological requirements. © 2018 John Wiley & Sons Ltd.

  2. On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

    NASA Technical Reports Server (NTRS)

    Fischer, Bernd; Freund, Roland W.

    1992-01-01

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

  3. Weierstrass method for quaternionic polynomial root-finding

    NASA Astrophysics Data System (ADS)

    Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana

    2018-01-01

    Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.

  4. Molecular Mimicry Regulates ABA Signaling by SnRK2 Kinases and PP2C Phosphatases

    PubMed Central

    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

  5. Molecular Mimicry Regulates ABA Signaling by SnRK2 Kinases and PP2C Phosphatases

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

    Soon, Fen-Fen; Ng, Ley-Moy; Zhou, X. Edward

    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 mechanismmore » 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.« less

  6. Overexpression of a Common Wheat Gene TaSnRK2.8 Enhances Tolerance to Drought, Salt and Low Temperature in Arabidopsis

    PubMed Central

    Zhang, Hongying; Mao, Xinguo; Wang, Chengshe; Jing, Ruilian

    2010-01-01

    Drought, salinity and low temperatures are major factors limiting crop productivity and quality. Sucrose non-fermenting1-related protein kinase 2 (SnRK2) plays a key role in abiotic stress signaling in plants. In this study, TaSnRK2.8, a SnRK2 member in wheat, was cloned and its functions under multi-stress conditions were characterized. Subcellular localization showed the presence of TaSnRK2.8 in the cell membrane, cytoplasm and nucleus. Expression pattern analyses in wheat revealed that TaSnRK2.8 was involved in response to PEG, NaCl and cold stresses, and possibly participates in ABA-dependent signal transduction pathways. To investigate its role under various environmental stresses, TaSnRK2.8 was transferred to Arabidopsis under control of the CaMV-35S promoter. Overexpression of TaSnRK2.8 resulted in enhanced tolerance to drought, salt and cold stresses, further confirmed by longer primary roots and various physiological characteristics, including higher relative water content, strengthened cell membrane stability, significantly lower osmotic potential, more chlorophyll content, and enhanced PSII activity. Meanwhile, TaSnRK2.8 plants had significantly lower total soluble sugar levels under normal growing conditions, suggesting that TaSnRK2.8 might be involved in carbohydrate metabolism. Moreover, the transcript levels of ABA biosynthesis (ABA1, ABA2), ABA signaling (ABI3, ABI4, ABI5), stress-responsive genes, including two ABA-dependent genes (RD20A, RD29B) and three ABA-independent genes (CBF1, CBF2, CBF3), were generally higher in TaSnRK2.8 plants than in WT/GFP controls under normal/stress conditions. Our results suggest that TaSnRK2.8 may act as a regulatory factor involved in a multiple stress response pathways. PMID:21209856

  7. Comparative Study of rK39 Leishmania Antigen for Serodiagnosis of Visceral Leishmaniasis: Systematic Review with Meta-Analysis

    PubMed Central

    Maia, Zuinara; Lírio, Monique; Mistro, Sóstenes; Mendes, Carlos Maurício Cardeal; Mehta, Sanjay R.; Badaro, Roberto

    2012-01-01

    Background The rK39 recombinant protein is derived from a specific antigen produced by the Leishmania donovani complex, and has been used in the last two decades for the serodiagnosis of visceral leishmaniasis. We present here a systematic review and meta-analysis of studies evaluating serologic assays to diagnose visceral leishmaniasis to determine the accuracy of rK39 antigen in comparison to the use of other antigen preparations. Methodology/Principal Findings A systematic review with meta-analysis of the literature was performed to compare the rK39 strip-test and ELISA formats against serological tests using promastigote antigens derived from whole or soluble parasites for Direct Aglutination Test (DAT), Indirect Immunofluorescence test (IFAT) and ELISA with a promastigote antigen preparation (p-ELISA). Gold standard diagnosis was defined by the demonstration of amastigotes on hematological specimens. A database search was performed on Medline, Lilacs, Scopus, Isi Web of Science, and Cochrane Library. Quality of data was assessed using the QUADAS questionnaire. A search of the electronic databases found 352 papers of which only 14 fulfilled the selection criteria. Three evaluated the rK39 ELISA, while 13 evaluated the rK39 immunochromatographic strip test. The summarized sensitivity for the rK39-ELISA was 92% followed by IFAT 88% and p-ELISA 87%. The summarized specificity for the three diagnostic tests was 81%, 90%, and 77%. Studies comparing the rK39 strip test with DAT found a similar sensitivity of 94%, although the DAT had a slightly higher specificity. The rK39 strip test was more sensitive and specific than the IFAT and p-ELISA. We did not detect any difference in the sensitivity and specificity between strips produced by different manufacturers. Conclusions The rK39 protein used either in a strip test or in an ELISA, and the DAT are the best choices for implementation of rapid, easy and efficient test for serodiagnosis of VL. PMID:22303488

  8. Comparative study of rK39 Leishmania antigen for serodiagnosis of visceral leishmaniasis: systematic review with meta-analysis.

    PubMed

    Maia, Zuinara; Lírio, Monique; Mistro, Sóstenes; Mendes, Carlos Maurício Cardeal; Mehta, Sanjay R; Badaro, Roberto

    2012-01-01

    The rK39 recombinant protein is derived from a specific antigen produced by the Leishmania donovani complex, and has been used in the last two decades for the serodiagnosis of visceral leishmaniasis. We present here a systematic review and meta-analysis of studies evaluating serologic assays to diagnose visceral leishmaniasis to determine the accuracy of rK39 antigen in comparison to the use of other antigen preparations. A systematic review with meta-analysis of the literature was performed to compare the rK39 strip-test and ELISA formats against serological tests using promastigote antigens derived from whole or soluble parasites for Direct Aglutination Test (DAT), Indirect Immunofluorescence test (IFAT) and ELISA with a promastigote antigen preparation (p-ELISA). Gold standard diagnosis was defined by the demonstration of amastigotes on hematological specimens. A database search was performed on Medline, Lilacs, Scopus, Isi Web of Science, and Cochrane Library. Quality of data was assessed using the QUADAS questionnaire. A search of the electronic databases found 352 papers of which only 14 fulfilled the selection criteria. Three evaluated the rK39 ELISA, while 13 evaluated the rK39 immunochromatographic strip test. The summarized sensitivity for the rK39-ELISA was 92% followed by IFAT 88% and p-ELISA 87%. The summarized specificity for the three diagnostic tests was 81%, 90%, and 77%. Studies comparing the rK39 strip test with DAT found a similar sensitivity of 94%, although the DAT had a slightly higher specificity. The rK39 strip test was more sensitive and specific than the IFAT and p-ELISA. We did not detect any difference in the sensitivity and specificity between strips produced by different manufacturers. The rK39 protein used either in a strip test or in an ELISA, and the DAT are the best choices for implementation of rapid, easy and efficient test for serodiagnosis of VL.

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

    PubMed

    Robin, Eric; Valle, Valéry; Brémand, Fabrice

    2005-12-01

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

  10. Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation.

    PubMed

    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.

  11. Discrete Tchebycheff orthonormal polynomials and applications

    NASA Technical Reports Server (NTRS)

    Lear, W. M.

    1980-01-01

    Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

  12. Wavefront reconstruction algorithm based on Legendre polynomials for radial shearing interferometry over a square area and error analysis.

    PubMed

    Kewei, E; Zhang, Chen; Li, Mengyang; Xiong, Zhao; Li, Dahai

    2015-08-10

    Based on the Legendre polynomials expressions and its properties, this article proposes a new approach to reconstruct the distorted wavefront under test of a laser beam over square area from the phase difference data obtained by a RSI system. And the result of simulation and experimental results verifies the reliability of the method proposed in this paper. The formula of the error propagation coefficients is deduced when the phase difference data of overlapping area contain noise randomly. The matrix T which can be used to evaluate the impact of high-orders Legendre polynomial terms on the outcomes of the low-order terms due to mode aliasing is proposed, and the magnitude of impact can be estimated by calculating the F norm of the T. In addition, the relationship between ratio shear, sampling points, terms of polynomials and noise propagation coefficients, and the relationship between ratio shear, sampling points and norms of the T matrix are both analyzed, respectively. Those research results can provide an optimization design way for radial shearing interferometry system with the theoretical reference and instruction.

  13. On multiple orthogonal polynomials for discrete Meixner measures

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

    Sorokin, Vladimir N

    2010-12-07

    The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.

  14. Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

    DTIC Science & Technology

    2001-09-11

    Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

  15. 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.

  16. Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

    Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

    2011-04-15

    Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

  17. 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…

  18. 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.

  19. Approximating smooth functions using algebraic-trigonometric polynomials

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

    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 4/3polynomials which the author has introduced andmore » investigated previously. Bibliography: 13 titles.« less

  20. The Protein Kinase SmSnRK2.6 Positively Regulates Phenolic Acid Biosynthesis in Salvia miltiorrhiza by Interacting with SmAREB1

    PubMed Central

    Jia, Yanyan; Bai, Zhenqing; Pei, Tianlin; Ding, Kai; Liang, Zongsuo; Gong, Yuehua

    2017-01-01

    Subclass III members of the sucrose non-fermenting-1-related protein kinase 2 (SnRK2) play essential roles in both the abscisic acid signaling and abiotic stress responses of plants by phosphorylating the downstream ABA-responsive element (ABRE)-binding proteins (AREB/ABFs). This comprehensive study investigated the function of new candidate genes, namely SmSnRK2.3, SmSnRK2.6, and SmAREB1, with a view to breeding novel varieties of Salvia miltiorrhiza with improved stress tolerance stresses and more content of bioactive ingredients. Exogenous ABA strongly induced the expression of these genes. PlantCARE predicted several hormones and stress response cis-elements in their promoters. SmSnRK2.6 and SmAREB1 showed the highest expression levels in the leaves of S. miltiorrhiza seedlings, while SmSnRK2.3 exhibited a steady expression in their roots, stems, and leaves. A subcellular localization assay revealed that both SmSnRK2.3 and SmSnRK2.6 were located in the cell membrane, cytoplasm, and nucleus, whereas SmAREB1 was exclusive to the nucleus. Overexpressing SmSnRK2.3 did not significantly promote the accumulation of rosmarinic acid (RA) and salvianolic acid B (Sal B) in the transgenic S. miltiorrhiza hairy roots. However, overexpressing SmSnRK2.6 and SmAREB1 increased the contents of RA and Sal B, and regulated the expression levels of structural genes participating in the phenolic acid-branched and side-branched pathways, including SmPAL1, SmC4H, Sm4CL1, SmTAT, SmHPPR, SmRAS, SmCHS, SmCCR, SmCOMT, and SmHPPD. Furthermore, SmSnRK2.3 and SmSnRK2.6 interacted physically with SmAREB1. In summary, our results indicate that SmSnRK2.6 is involved in stress responses and can regulate structural gene transcripts to promote greater metabolic flux to the phenolic acid-branched pathway, via its interaction with SmAREB1, a transcription factor. In this way, SmSnRK2.6 contributes to the positive regulation of phenolic acids in S. miltiorrhiza hairy roots. PMID:28848585

  1. The Protein Kinase SmSnRK2.6 Positively Regulates Phenolic Acid Biosynthesis in Salvia miltiorrhiza by Interacting with SmAREB1.

    PubMed

    Jia, Yanyan; Bai, Zhenqing; Pei, Tianlin; Ding, Kai; Liang, Zongsuo; Gong, Yuehua

    2017-01-01

    Subclass III members of the sucrose non-fermenting-1-related protein kinase 2 (SnRK2) play essential roles in both the abscisic acid signaling and abiotic stress responses of plants by phosphorylating the downstream ABA-responsive element (ABRE)-binding proteins (AREB/ABFs). This comprehensive study investigated the function of new candidate genes, namely SmSnRK2.3 , SmSnRK2.6 , and SmAREB1 , with a view to breeding novel varieties of Salvia miltiorrhiza with improved stress tolerance stresses and more content of bioactive ingredients. Exogenous ABA strongly induced the expression of these genes. PlantCARE predicted several hormones and stress response cis -elements in their promoters. SmSnRK2.6 and SmAREB1 showed the highest expression levels in the leaves of S. miltiorrhiza seedlings, while SmSnRK2.3 exhibited a steady expression in their roots, stems, and leaves. A subcellular localization assay revealed that both SmSnRK2.3 and SmSnRK2.6 were located in the cell membrane, cytoplasm, and nucleus, whereas SmAREB1 was exclusive to the nucleus. Overexpressing SmSnRK2.3 did not significantly promote the accumulation of rosmarinic acid (RA) and salvianolic acid B (Sal B) in the transgenic S. miltiorrhiza hairy roots. However, overexpressing SmSnRK2.6 and SmAREB1 increased the contents of RA and Sal B, and regulated the expression levels of structural genes participating in the phenolic acid-branched and side-branched pathways, including SmPAL1 , SmC4H , Sm4CL1 , SmTAT , SmHPPR , SmRAS , SmCHS , SmCCR , SmCOMT , and SmHPPD . Furthermore, SmSnRK2.3 and SmSnRK2.6 interacted physically with SmAREB1. In summary, our results indicate that SmSnRK2.6 is involved in stress responses and can regulate structural gene transcripts to promote greater metabolic flux to the phenolic acid-branched pathway, via its interaction with SmAREB1 , a transcription factor. In this way, SmSnRK2.6 contributes to the positive regulation of phenolic acids in S. miltiorrhiza hairy roots.

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

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

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

    2014-10-01

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

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

    PubMed

    Kulkarni, Rishikesh; Rastogi, Pramod

    2018-02-01

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

  4. 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.

  5. Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

  6. 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.

  7. Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation

    PubMed Central

    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

  8. Direct calculation of modal parameters from matrix orthogonal polynomials

    NASA Astrophysics Data System (ADS)

    El-Kafafy, Mahmoud; Guillaume, Patrick

    2011-10-01

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

  9. STOREKEEPER RELATED1/G-Element Binding Protein (STKR1) Interacts with Protein Kinase SnRK1.

    PubMed

    Nietzsche, Madlen; Guerra, Tiziana; Alseekh, Saleh; Wiermer, Marcel; Sonnewald, Sophia; Fernie, Alisdair R; Börnke, Frederik

    2018-02-01

    Sucrose nonfermenting related kinase1 (SnRK1) is a conserved energy sensor kinase that regulates cellular adaptation to energy deficit in plants. Activation of SnRK1 leads to the down-regulation of ATP-consuming biosynthetic processes and the stimulation of energy-generating catabolic reactions by transcriptional reprogramming and posttranslational modifications. Although considerable progress has been made during the last years in understanding the SnRK1 signaling pathway, many of its components remain unidentified. Here, we show that the catalytic α-subunits KIN10 and KIN11 of the Arabidopsis ( Arabidopsis thaliana ) SnRK1 complex interact with the STOREKEEPER RELATED1/G-Element Binding Protein (STKR1) inside the plant cell nucleus. Overexpression of STKR1 in transgenic Arabidopsis plants led to reduced growth, a delay in flowering, and strongly attenuated senescence. Metabolite profiling revealed that the transgenic lines exhausted their carbohydrates during the dark period to a greater extent than the wild type and accumulated a range of amino acids. At the global transcriptome level, genes affected by STKR1 overexpression were broadly associated with systemic acquired resistance, and transgenic plants showed enhanced resistance toward a virulent strain of the biotrophic oomycete pathogen Hyaloperonospora arabidopsidis Noco2. We discuss a possible connection of STKR1 function, SnRK1 signaling, and plant immunity. © 2018 American Society of Plant Biologists. All Rights Reserved.

  10. On the derivatives of unimodular polynomials

    NASA Astrophysics Data System (ADS)

    Nevai, P.; Erdélyi, T.

    2016-04-01

    Let D be the open unit disk of the complex plane; its boundary, the unit circle of the complex plane, is denoted by \\partial D. Let \\mathscr P_n^c denote the set of all algebraic polynomials of degree at most n with complex coefficients. For λ ≥ 0, let {\\mathscr K}_n^λ \\stackrel{{def}}{=} \\biggl\\{P_n: P_n(z) = \\sumk=0^n{ak k^λ z^k}, ak \\in { C}, |a_k| = 1 \\biggr\\} \\subset {\\mathscr P}_n^c.The class \\mathscr K_n^0 is often called the collection of all (complex) unimodular polynomials of degree n. Given a sequence (\\varepsilon_n) of positive numbers tending to 0, we say that a sequence (P_n) of polynomials P_n\\in\\mathscr K_n^λ is \\{λ, (\\varepsilon_n)\\}-ultraflat if \\displaystyle (1-\\varepsilon_n)\\frac{nλ+1/2}{\\sqrt{2λ+1}}≤\\ve......a +1/2}}{\\sqrt{2λ +1}},\\qquad z \\in \\partial D,\\quad n\\in N_0.Although we do not know, in general, whether or not \\{λ, (\\varepsilon_n)\\}-ultraflat sequences of polynomials P_n\\in\\mathscr K_n^λ exist for each fixed λ>0, we make an effort to prove various interesting properties of them. These allow us to conclude that there are no sequences (P_n) of either conjugate, or plain, or skew reciprocal unimodular polynomials P_n\\in\\mathscr K_n^0 such that (Q_n) with Q_n(z)\\stackrel{{def}}{=} zP_n'(z)+1 is a \\{1,(\\varepsilon_n)\\}-ultraflat sequence of polynomials.Bibliography: 18 titles.

  11. 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.

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

    PubMed

    Hong, X; Harris, C J

    2000-01-01

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

  13. 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…

  14. Piecewise polynomial representations of genomic tracks.

    PubMed

    Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz

    2012-01-01

    Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.

  15. 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.

  16. Fatty acid composition modulates sensitivity of Legionella pneumophila to warnericin RK, an antimicrobial peptide.

    PubMed

    Verdon, Julien; Labanowski, Jérome; Sahr, Tobias; Ferreira, Thierry; Lacombe, Christian; Buchrieser, Carmen; Berjeaud, Jean-Marc; Héchard, Yann

    2011-04-01

    Warnericin RK is an antimicrobial peptide, produced by a Staphyloccocus warneri strain, described to be specifically active against Legionella, the pathogenic bacteria responsible for Legionnaires' disease. Warnericin RK is an amphiphilic alpha-helical peptide, which possesses a detergent-like mode of action. Two others peptides, δ-hemolysin I and II, produced by the same S. warneri strain, are highly similar to S. aureus δ-hemolysin and also display anti-Legionella activity. It has been recently reported that S. aureus δ-hemolysin activity on vesicles is likewise related to phospholipid acyl-chain structure, such as chain length and saturation. As staphylococcal δ-hemolysins were highly similar, we thus hypothesized that fatty acid composition of Legionella's membrane might influence the sensitivity of the bacteria to warnericin RK. Relationship between sensitivity to the peptide and fatty acid composition was then followed in various conditions. Cells in stationary phase, which were already described as less resistant than cells in exponential phase, displayed higher amounts of branched-chain fatty acids (BCFA) and short chain fatty acids. An adapted strain, able to grow at a concentration 33 fold higher than minimal inhibitory concentration of the wild type (i.e. 1μM), was isolated after repeated transfers of L. pneumophila in the presence of increased concentrations of warnericin RK. The amount of BCFA was significantly higher in the adapted strain than in the wild type strain. Also, a transcriptomic analysis of the wild type and adapted strains showed that two genes involved in fatty acid biosynthesis were repressed in the adapted strain. These genes encode enzymes involved in desaturation and elongation of fatty acids respectively. Their repression was in agreement with the decrease of unsaturated fatty acids and fatty acid chain length in the adapted strain. Conclusively, our results indicate that the increase of BCFA and the decrease of fatty acid

  17. 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…

  18. Minimal Unified Resolution to R_{K^{(*)}} and R(D^{(*)}) Anomalies with Lepton Mixing.

    PubMed

    Choudhury, Debajyoti; Kundu, Anirban; Mandal, Rusa; Sinha, Rahul

    2017-10-13

    It is a challenging task to explain, in terms of a simple and compelling new physics scenario, the intriguing discrepancies between the standard model expectations and the data for the neutral-current observables R_{K} and R_{K^{*}}, as well as the charged-current observables R(D) and R(D^{*}). We show that this can be achieved in an effective theory with only two unknown parameters. In addition, this class of models predicts some interesting signatures in the context of both B decays as well as high-energy collisions.

  19. Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion

    NASA Astrophysics Data System (ADS)

    Sánchez-Vizuet, Tonatiuh; Cerfon, Antoine J.

    2018-02-01

    We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo-spectral collocation on a grid defined by the zeros of a non-standard family of orthogonal polynomials called Maxwell polynomials. Taking a one-dimensional equation describing energy diffusion due to Fokker-Planck collisions with a Maxwell-Boltzmann background distribution as the test bench for the performance of the scheme, we find that Maxwell based discretizations outperform other commonly used schemes in most situations, often by orders of magnitude. This provides a strong motivation for their use in high-dimensional gyrokinetic simulations. However, we also show that Maxwell based schemes are subject to a non-modal time stepping instability in their most straightforward implementation, so that special care must be given to the discrete representation of the linear operators in order to benefit from the advantages provided by Maxwell polynomials.

  20. The Translated Dowling Polynomials and Numbers.

    PubMed

    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.

  1. Transcriptional regulation of SlPYL, SlPP2C, and SlSnRK2 gene families encoding ABA signal core components during tomato fruit development and drought stress.

    PubMed

    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.

  2. Degenerate r-Stirling Numbers and r-Bell Polynomials

    NASA Astrophysics Data System (ADS)

    Kim, T.; Yao, Y.; Kim, D. S.; Jang, G.-W.

    2018-01-01

    The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

  3. Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

    PubMed

    Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan

    2012-01-01

    Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. © 2012 Acoustical Society of America.

  4. Polynomial solutions of the Monge-Ampère equation

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

    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 ofmore » such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.« less

  5. Cloning and expression profiling of the PacSnRK2 and PacPP2C gene families during fruit development, ABA treatment, and dehydration stress in sweet cherry.

    PubMed

    Shen, Xinjie; Guo, Xiao; Zhao, Di; Zhang, Qiang; Jiang, Yuzhuang; Wang, Yantao; Peng, Xiang; Wei, Yan; Zhai, Zefeng; Zhao, Wei; Li, Tianhong

    2017-10-01

    Plant SNF1-related protein kinase 2 (SnRK2) and protein phosphatase 2C (PP2C) family members are core components of the ABA signal transduction pathway. SnRK2 and PP2C proteins have been suggested to play crucial roles in fruit ripening and improving plant tolerance to drought stress, but supporting genetic information has been lacking in sweet cherry (Prunus avium L.). Here, we cloned six full-length SnRK2 genes and three full-length PP2C genes from sweet cherry cv. Hong Deng. Quantitative PCR analysis revealed that PacSnRK2.2, PacSnRK2.3, PacSnRK2.6, and PacPP2C1-3 were negatively regulated in fruits in response to exogenous ABA treatment, PacSnRK2.4 and PacSnRK2.5 were upregulated, and PacSnRK2.1 expression was not affected. The ABA treatment also significantly promoted the accumulation of anthocyanins in sweet cherry fruit. The expression of all PacSnRK2 and PacPP2C genes was induced by dehydration stress, which also promoted the accumulation of drought stress signaling molecules in the sweet cherry fruits, including ABA, soluble sugars, and anthocyanin. Furthermore, a yeast two-hybrid analysis demonstrated that PacPP2C1 interacts with all six PacSnRK2s, while PacPP2C3 does not interact with PacSnRK2.5. PacPP2C2 does not interact with PacSnRK2.1 or PacSnRK2.4. These results indicate that PacSnRK2s and PacPP2Cs may play a variety of roles in the sweet cherry ABA signaling pathway and the fruit response to drought stress. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

  6. An rK28-Based Immunoenzymatic Assay for the Diagnosis of Canine Visceral Leishmaniasis in Latin America

    PubMed Central

    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.

    2016-01-01

    Direct observation of Leishmania parasites in tissue aspirates has shown low sensitivity for the detection of canine visceral leishmaniasis (VL). Therefore in the last quarter century immunoenzymatic tests have been developed to improve diagnosis. The purpose of this study was to develop a fast recombinant K28 antigen, naked-eye qualitative enzyme-linked immunosorbent assay (VL Ql-ELISA) and a quantitative version (VL Qt-ELISA), and to display it in a kit format, whose cutoff value (0.156) was selected as the most adequate one to differentiate reactive from nonreactive samples. Considering 167 cases and 300 controls, sensitivity was 91% for both assays and specificity was 100% and 98.7% in Ql-ELISA and Qt-ELISA, respectively. Positive predictive values were 100% and 97.4% for Ql-ELISA and Qt-ELISA, respectively, and negative predictive values were 95.2% for both ELISAs. Reagent stability, reliability studies, including periodic repetitions and retest of samples, cutoff selection, and comparison of rK28 ELISAs with rK39 immunochromatographic test, were the international criteria that supported the quality in both kits. The performance of both ELISA kits in this work confirmed their validity and emphasized their usefulness for low-to-medium complexity laboratories. PMID:27162270

  7. STOREKEEPER RELATED1/G-Element Binding Protein (STKR1) Interacts with Protein Kinase SnRK11[OPEN

    PubMed Central

    Nietzsche, Madlen; Guerra, Tiziana; Fernie, Alisdair R.

    2018-01-01

    Sucrose nonfermenting related kinase1 (SnRK1) is a conserved energy sensor kinase that regulates cellular adaptation to energy deficit in plants. Activation of SnRK1 leads to the down-regulation of ATP-consuming biosynthetic processes and the stimulation of energy-generating catabolic reactions by transcriptional reprogramming and posttranslational modifications. Although considerable progress has been made during the last years in understanding the SnRK1 signaling pathway, many of its components remain unidentified. Here, we show that the catalytic α-subunits KIN10 and KIN11 of the Arabidopsis (Arabidopsis thaliana) SnRK1 complex interact with the STOREKEEPER RELATED1/G-Element Binding Protein (STKR1) inside the plant cell nucleus. Overexpression of STKR1 in transgenic Arabidopsis plants led to reduced growth, a delay in flowering, and strongly attenuated senescence. Metabolite profiling revealed that the transgenic lines exhausted their carbohydrates during the dark period to a greater extent than the wild type and accumulated a range of amino acids. At the global transcriptome level, genes affected by STKR1 overexpression were broadly associated with systemic acquired resistance, and transgenic plants showed enhanced resistance toward a virulent strain of the biotrophic oomycete pathogen Hyaloperonospora arabidopsidis Noco2. We discuss a possible connection of STKR1 function, SnRK1 signaling, and plant immunity. PMID:29192025

  8. Ricci polynomial gravity

    NASA Astrophysics Data System (ADS)

    Hao, Xin; Zhao, Liu

    2017-12-01

    We study a novel class of higher-curvature gravity models in n spacetime dimensions which we call Ricci polynomial gravity. The action consists purely of a polynomial in Ricci curvature of order N . In the absence of the second-order terms in the action, the models are ghost free around the Minkowski vacuum. By appropriately choosing the coupling coefficients in front of each term in the action, it is shown that the models can have multiple vacua with different effective cosmological constants, and can be made free of ghost and scalar degrees of freedom around at least one of the maximally symmetric vacua for any n >2 and any N ≥4 . We also discuss some of the physical implications of the existence of multiple vacua in the contexts of black hole physics and cosmology.

  9. Imaging characteristics of Zernike and annular polynomial aberrations.

    PubMed

    Mahajan, Virendra N; Díaz, José Antonio

    2013-04-01

    The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

  10. Genetic parameters of legendre polynomials for first parity lactation curves.

    PubMed

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

    2000-11-01

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

  11. Conformal Galilei algebras, symmetric polynomials and singular vectors

    NASA Astrophysics Data System (ADS)

    Křižka, Libor; Somberg, Petr

    2018-01-01

    We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras cga_ℓ (d,C) with d=1 for any integer value ℓ \\in N. The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.

  12. Neck curve polynomials in neck rupture model

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

    Kurniadi, Rizal; Perkasa, Yudha S.; Waris, Abdul

    2012-06-06

    The Neck Rupture Model is a model that explains the scission process which has smallest radius in liquid drop at certain position. Old fashion of rupture position is determined randomly so that has been called as Random Neck Rupture Model (RNRM). The neck curve polynomials have been employed in the Neck Rupture Model for calculation the fission yield of neutron induced fission reaction of {sup 280}X{sub 90} with changing of order of polynomials as well as temperature. The neck curve polynomials approximation shows the important effects in shaping of fission yield curve.

  13. More on rotations as spin matrix polynomials

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

    Curtright, Thomas L.

    2015-09-15

    Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.

  14. A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE

    NASA Technical Reports Server (NTRS)

    Truong, T. K.

    1994-01-01

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

  15. Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos

    DTIC Science & Technology

    2002-07-25

    Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc., AMS... orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection...1) by generalized polynomial chaos expansion, where the uncertainties can be introduced through κ, f , or g, or some combinations. It is worth

  16. Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils.

    PubMed

    Mahajan, Virendra N

    2012-06-20

    In a recent paper, we considered the classical aberrations of an anamorphic optical imaging system with a rectangular pupil, representing the terms of a power series expansion of its aberration function. These aberrations are inherently separable in the Cartesian coordinates (x,y) of a point on the pupil. Accordingly, there is x-defocus and x-coma, y-defocus and y-coma, and so on. We showed that the aberration polynomials orthonormal over the pupil and representing balanced aberrations for such a system are represented by the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point; for example, L(l)(x)L(m)(y), where l and m are positive integers (including zero) and L(l)(x), for example, represents an orthonormal Legendre polynomial of degree l in x. The compound two-dimensional (2D) Legendre polynomials, like the classical aberrations, are thus also inherently separable in the Cartesian coordinates of the pupil point. Moreover, for every orthonormal polynomial L(l)(x)L(m)(y), there is a corresponding orthonormal polynomial L(l)(y)L(m)(x) obtained by interchanging x and y. These polynomials are different from the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil. In this paper, we show that the orthonormal aberration polynomials for an anamorphic system with a circular pupil, obtained by the Gram-Schmidt orthogonalization of the 2D Legendre polynomials, are not separable in the two coordinates. Moreover, for a given polynomial in x and y, there is no corresponding polynomial obtained by interchanging x and y. For example, there are polynomials representing x-defocus, balanced x-coma, and balanced x-spherical aberration, but no corresponding y-aberration polynomials. The missing y-aberration terms are contained in other polynomials. We emphasize that the Zernike circle polynomials, although orthogonal over a circular pupil, are not suitable for an anamorphic system as

  17. From sequences to polynomials and back, via operator orderings

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

    Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu

    2013-12-15

    Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

  18. Flat bases of invariant polynomials and P-matrices of E{sub 7} and E{sub 8}

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

    Talamini, Vittorino

    2010-02-15

    Let G be a compact group of linear transformations of a Euclidean space V. The G-invariant C{sup {infinity}} functions can be expressed as C{sup {infinity}} functions of a finite basic set of G-invariant homogeneous polynomials, sometimes called an integrity basis. The mathematical description of the orbit space V/G depends on the integrity basis too: it is realized through polynomial equations and inequalities expressing rank and positive semidefiniteness conditions of the P-matrix, a real symmetric matrix determined by the integrity basis. The choice of the basic set of G-invariant homogeneous polynomials forming an integrity basis is not unique, so it ismore » not unique the mathematical description of the orbit space too. If G is an irreducible finite reflection group, Saito et al. [Commun. Algebra 8, 373 (1980)] characterized some special basic sets of G-invariant homogeneous polynomials that they called flat. They also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection groups except of the two largest groups E{sub 7} and E{sub 8}. In this paper the flat basic sets of invariant homogeneous polynomials of E{sub 7} and E{sub 8} and the corresponding P-matrices are determined explicitly. Using the results here reported one is able to determine easily the P-matrices corresponding to any other integrity basis of E{sub 7} or E{sub 8}. From the P-matrices one may then write down the equations and inequalities defining the orbit spaces of E{sub 7} and E{sub 8} relatively to a flat basis or to any other integrity basis. The results here obtained may be employed concretely to study analytically the symmetry breaking in all theories where the symmetry group is one of the finite reflection groups E{sub 7} and E{sub 8} or one of the Lie groups E{sub 7} and E{sub 8} in their adjoint representations.« less

  19. A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

    NASA Astrophysics Data System (ADS)

    Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing

    2015-09-01

    The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the 'hypercube' polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the 'simplex' polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

  20. Mechanisms of regulation of SNF1/AMPK/SnRK1 protein kinases.

    PubMed

    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.

  1. Mechanisms of regulation of SNF1/AMPK/SnRK1 protein kinases

    PubMed Central

    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

  2. Inequalities for a polynomial and its derivative

    NASA Astrophysics Data System (ADS)

    Chanam, Barchand; Dewan, K. K.

    2007-12-01

    Let , 1[less-than-or-equals, slant][mu][less-than-or-equals, slant]n, be a polynomial of degree n such that p(z)[not equal to]0 in z0, then for 0polynomial and its derivative, Math. Inequal. Appl. 2 (2) (1999) 203-205] proved Equality holds for the polynomial where n is a multiple of [mu]E In this paper, we obtain an improvement of the above inequality by involving some of the coefficients. As an application of our result, we further improve upon a result recently proved by Aziz and Shah [A. Aziz, W.M. Shah, Inequalities for a polynomial and its derivative, Math. Inequal. Appl. 7 (3) (2004) 379-391].

  3. Applications of polynomial optimization in financial risk investment

    NASA Astrophysics Data System (ADS)

    Zeng, Meilan; Fu, Hongwei

    2017-09-01

    Recently, polynomial optimization has many important applications in optimization, financial economics and eigenvalues of tensor, etc. This paper studies the applications of polynomial optimization in financial risk investment. We consider the standard mean-variance risk measurement model and the mean-variance risk measurement model with transaction costs. We use Lasserre's hierarchy of semidefinite programming (SDP) relaxations to solve the specific cases. The results show that polynomial optimization is effective for some financial optimization problems.

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

    NASA Astrophysics Data System (ADS)

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

    2016-01-01

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

  5. Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

    PubMed Central

    Santonja, F.; Chen-Charpentier, B.

    2012-01-01

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

  6. Optimal Chebyshev polynomials on ellipses in the complex plane

    NASA Technical Reports Server (NTRS)

    Fischer, Bernd; Freund, Roland

    1989-01-01

    The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

  7. Principal polynomial analysis.

    PubMed

    Laparra, Valero; Jiménez, Sandra; Tuia, Devis; Camps-Valls, Gustau; Malo, Jesus

    2014-11-01

    This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of maximal variance by means of curves, instead of straight lines. Contrarily to previous approaches, PPA reduces to performing simple univariate regressions, which makes it computationally feasible and robust. Moreover, PPA shows a number of interesting analytical properties. First, PPA is a volume-preserving map, which in turn guarantees the existence of the inverse. Second, such an inverse can be obtained in closed form. Invertibility is an important advantage over other learning methods, because it permits to understand the identified features in the input domain where the data has physical meaning. Moreover, it allows to evaluate the performance of dimensionality reduction in sensible (input-domain) units. Volume preservation also allows an easy computation of information theoretic quantities, such as the reduction in multi-information after the transform. Third, the analytical nature of PPA leads to a clear geometrical interpretation of the manifold: it allows the computation of Frenet-Serret frames (local features) and of generalized curvatures at any point of the space. And fourth, the analytical Jacobian allows the computation of the metric induced by the data, thus generalizing the Mahalanobis distance. These properties are demonstrated theoretically and illustrated experimentally. The performance of PPA is evaluated in dimensionality and redundancy reduction, in both synthetic and real datasets from the UCI repository.

  8. Universal Racah matrices and adjoint knot polynomials: Arborescent knots

    NASA Astrophysics Data System (ADS)

    Mironov, A.; Morozov, A.

    2016-04-01

    By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in particular unifies the HOMFLY (SUN) and Kauffman (SON) polynomials. For E8 the adjoint representation is also fundamental. We suggest to extend the universality from the dimensions to the Racah matrices and this immediately produces a unified description of the adjoint knot polynomials for all arborescent (double-fat) knots, including twist, 2-bridge and pretzel. Technically we develop together the universality and the "eigenvalue conjecture", which expresses the Racah and mixing matrices through the eigenvalues of the quantum R-matrix, and for dealing with the adjoint polynomials one has to extend it to the previously unknown 6 × 6 case. The adjoint polynomials do not distinguish between mutants and therefore are not very efficient in knot theory, however, universal polynomials in higher representations can probably be better in this respect.

  9. Late complications in patients with Björk-Shiley and St. Jude Medical heart valve replacement.

    PubMed

    Horstkotte, D; Körfer, R; Seipel, L; Bircks, W; Loogen, F

    1983-09-01

    Valve-related complications after Björk-Shiley mitral valve implantation (n = 475), aortic valve implantation (n = 424), or mitral-aortic valve implantation (n = 119) were compared with those after St. Jude Medical mitral valve replacement (n = 173), aortic valve replacement (n = 152), or mitral-aortic valve replacement (n = 69). All patients were placed on anticoagulant therapy with phenprocoumon early after operation. All patients had a comparable follow-up time of approximately 23 months, which showed that cumulative thromboembolic rates were significantly higher after St. Jude valve implantation than after Björk-Shiley valve implantation. Reoperations were necessary because of valve thrombosis (0.46%), perivalvular leakage (2.2%), or prosthetic valve endocarditis with perivalvular regurgitation (0.46%). One Björk-Shiley mitral valve prosthesis had to be replaced because of fracture of the outlet strut. Without significant intergroup differences, hemorrhage due to anticoagulant treatment was the most frequent complication. Thromboembolic complications were significantly more frequent after Björk-Shiley mitral, aortic, and double valve replacements than after St. Jude valve implantation. This may lead to consideration of changes in the prophylaxis of thrombus formations in the St. Jude valve, especially in aortic valve replacements, in patients with sinus rhythm.

  10. Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

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

    Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408; Roy, Pinaki, E-mail: pinaki@isical.ac.in

    We construct energy-dependent potentials for which the Schrödinger equations admit solutions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

  11. BAC-recombineering for studying plant gene regulation: developmental control and cellular localization of SnRK1 kinase subunits.

    PubMed

    Bitrián, Marta; Roodbarkelari, Farshad; Horváth, Mihály; Koncz, Csaba

    2011-03-01

    Recombineering, permitting precise modification of genes within bacterial artificial chromosomes (BACs) through homologous recombination mediated by lambda phage-encoded Red proteins, is a widely used powerful tool in mouse, Caenorhabditis and Drosophila genetics. As Agrobacterium-mediated transfer of large DNA inserts from binary BACs and TACs into plants occurs at low frequency, recombineering is so far seldom exploited in the analysis of plant gene functions. We have constructed binary plant transformation vectors, which are suitable for gap-repair cloning of genes from BACs using recombineering methods previously developed for other organisms. Here we show that recombineering facilitates PCR-based generation of precise translational fusions between coding sequences of fluorescent reporter and plant proteins using galK-based exchange recombination. The modified target genes alone or as part of a larger gene cluster can be transferred by high-frequency gap-repair into plant transformation vectors, stably maintained in Agrobacterium and transformed without alteration into plants. Versatile application of plant BAC-recombineering is illustrated by the analysis of developmental regulation and cellular localization of interacting AKIN10 catalytic and SNF4 activating subunits of Arabidopsis Snf1-related (SnRK1) protein kinase using in vivo imaging. To validate full functionality and in vivo interaction of tagged SnRK1 subunits, it is demonstrated that immunoprecipitated SNF4-YFP is bound to a kinase that phosphorylates SnRK1 candidate substrates, and that the GFP- and YFP-tagged kinase subunits co-immunoprecipitate with endogenous wild type AKIN10 and SNF4. © 2011 The Authors. The Plant Journal © 2011 Blackwell Publishing Ltd.

  12. SnRK1-triggered switch of bZIP63 dimerization mediates the low-energy response in plants

    PubMed Central

    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

  13. Radial integrals <r(k)>4f and nephelauxetic effect of Nd3+ in crystals.

    PubMed

    Petrov, D; Angelov, B

    2014-01-24

    The radial expectation values <r(k)>4f,k=2, 4, 6, for oxygen- or halogen- coordinated Nd(3+) ions in 25 crystals have been obtained from experimental Slater parameter shifts ΔFk=Fk (free ion) - Fk (crystal) by means of the dielectric screening model. The <r(k)>4f values found by this new approach are compatible with those computed by relativistic 4f wave functions. The nephelauxetic ratios βk in respect to the free ion Nd IV have been also determined and related to covalency and bonding parameters. Copyright © 2013 Elsevier B.V. All rights reserved.

  14. Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

    NASA Astrophysics Data System (ADS)

    Chen, Zhixiang; Fu, Bin

    This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a ΠΣΠ polynomial. We first prove that the first problem is #P-hard and then devise a O *(3 n s(n)) upper bound for this problem for any polynomial represented by an arithmetic circuit of size s(n). Later, this upper bound is improved to O *(2 n ) for ΠΣΠ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for ΠΣ polynomials. On the negative side, we prove that, even for ΠΣΠ polynomials with terms of degree ≤ 2, the first problem cannot be approximated at all for any approximation factor ≥ 1, nor "weakly approximated" in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time λ-approximation algorithm for ΠΣΠ polynomials with terms of degrees no more a constant λ ≥ 2. On the inapproximability side, we give a n (1 - ɛ)/2 lower bound, for any ɛ> 0, on the approximation factor for ΠΣΠ polynomials. When the degrees of the terms in these polynomials are constrained as ≤ 2, we prove a 1.0476 lower bound, assuming Pnot=NP; and a higher 1.0604 lower bound, assuming the Unique Games Conjecture.

  15. [Late complications following Björk-Shiley and St. Jude Medical heart valve replacement].

    PubMed

    Horstkotte, D; Körfer, R; Budde, T; Haerten, K; Schulte, H D; Bircks, W; Loogen, F

    1983-05-01

    Valve-related complications after Björk-Shiley mitral (n = 475), aortic (n = 424), or mitral-aortic implantation (n = 119) were compared to complications after St. Jude mitral (n = 173), aortic (n = 152), and St. Jude mitral and aortic (n = 63) replacements. The 1,018 consecutive patients with Björk-Shiley valves had been operated upon between 1974 and 1982, those with St. Jude valves between 1978 and 1982. All patients were placed on anticoagulant therapy with phenprocoumon early after operation and no significant intergroup differences in the effectiveness of the anticoagulant therapy were found. At a comparable follow-up time of approximately 23 months, 24 major thromboembolic episodes were observed after Björk-Shiley mitral (BSM) and 3 after St. Jude mitral valve implantation (SJM), corresponding to a thromboembolic rate of 2.82/100 patient years with BSM and 0.93/100 patient years with SJM. After aortic valve replacements, 1.93 events in 100 patient years occurred after Björk-Shiley aortic (BSA) and 0.73 after St. Jude aortic implantation (SJA). In patients with double valve replacements, these rates were 3.2 (BSM + BSA) and 0.88 (SJM + SJA), respectively. The cerebral vessels were involved in 52% and the arteries of the extremities in 22% of these major events. Six Björk-Shiley prostheses had to be replaced because of valve thrombosis. The overall incidence of severe hemorrhagic complications was 2.94/100 patient years in BSM and 1.79 in SJM. After aortic valve replacement, we found rates of 1.80/100 patient years (BSA) and 2.57/100 patient years (SJA), respectively. Intravascular hemolysis no longer seems to be a significant clinical problem. However, indications of red cell damage after heart valve replacement were significantly greater in patients with perivalvular leakage, valve thrombosis, or dysfunction than in those with normally functioning prostheses. Reoperations were necessary because of valve thrombosis (0.46%), perivalvular leakage (2

  16. Polynomial solution of quantum Grassmann matrices

    NASA Astrophysics Data System (ADS)

    Tierz, Miguel

    2017-05-01

    We study a model of quantum mechanical fermions with matrix-like index structure (with indices N and L) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with q-deformed orthogonal polynomials (Stieltjes-Wigert polynomials), for different values of L and arbitrary N. From the explicit evaluation of the thermal partition function, the energy levels and degeneracies are determined. For a given L, the number of states of different energy is quadratic in N, which implies an exponential degeneracy of the energy levels. We also show that at high-temperature we have a Gaussian matrix model, which implies a symmetry that swaps N and L, together with a Wick rotation of the spectral parameter. In this limit, we also write the partition function, for generic L and N, in terms of a single generalized Hermite polynomial.

  17. Transcriptional Regulation of Aggregatibacter actinomycetemcomitans lsrACDBFG and lsrRK Operons and Their Role in Biofilm Formation

    PubMed Central

    Torres-Escobar, Ascención; Juárez-Rodríguez, María Dolores; Lamont, Richard J.

    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

  18. Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission

    NASA Astrophysics Data System (ADS)

    Huang, Yuechen; Li, Haiyang

    2018-06-01

    This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method.

  19. Social Security Polynomials.

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    1992-01-01

    Demonstrates how the uniqueness and anonymity of a student's Social Security number can be utilized to create individualized polynomial equations that students can investigate using computers or graphing calculators. Students write reports of their efforts to find and classify all real roots of their equation. (MDH)

  20. Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. NBER Working Paper No. 20405

    ERIC Educational Resources Information Center

    Gelman, Andrew; Imbens, Guido

    2014-01-01

    It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

  1. Regulation of Bacteriocin Production and Cell Death by the VicRK Signaling System in Streptococcus mutans

    PubMed Central

    Senadheera, D. B.; Cordova, M.; Ayala, E. A.; Chávez de Paz, L. E.; Singh, K.; Downey, J. S.; Svensäter, G.; Goodman, S. D.

    2012-01-01

    The VicRK two-component signaling system modulates biofilm formation, genetic competence, and stress tolerance in Streptococcus mutans. We show here that the VicRK modulates bacteriocin production and cell viability, in part by direct modulation of competence-stimulating peptide (CSP) production in S. mutans. Global transcriptome and real-time transcriptional analysis of the VicK-deficient mutant (SmuvicK) revealed significant modulation of several bacteriocin-related loci, including nlmAB, nlmC, and nlmD (P < 0.001), suggesting a role for the VicRK in producing mutacins IV, V, and VI. Bacteriocin overlay assays revealed an altered ability of the vic mutants to kill related species. Since a well-conserved VicR binding site (TGTWAH-N5-TGTWAH) was identified within the comC coding region, we confirmed VicR binding to this sequence using DNA footprinting. Overexpression of the vic operon caused growth-phase-dependent repression of comC, comDE, and comX. In the vic mutants, transcription of nlmC/cipB encoding mutacin V, previously linked to CSP-dependent cell lysis, as well as expression of its putative immunity factor encoded by immB, were significantly affected relative to the wild type (P < 0.05). In contrast to previous reports that proposed a hyper-resistant phenotype for the VicK mutant in cell viability, the release of extracellular genomic DNA was significantly enhanced in SmuvicK (P < 0.05), likely as a result of increased autolysis compared with the parent. The drastic influence of VicRK on cell viability was also demonstrated using vic mutant biofilms. Taken together, we have identified a novel regulatory link between the VicRK and ComDE systems to modulate bacteriocin production and cell viability of S. mutans. PMID:22228735

  2. On a Family of Multivariate Modified Humbert Polynomials

    PubMed Central

    Aktaş, Rabia; Erkuş-Duman, Esra

    2013-01-01

    This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials. PMID:23935411

  3. Symmetric polynomials in information theory: Entropy and subentropy

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

    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 quantitymore » 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.« less

  4. Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

    NASA Astrophysics Data System (ADS)

    Burtyka, Filipp

    2018-01-01

    The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

  5. Nested polynomial trends for the improvement of Gaussian process-based predictors

    NASA Astrophysics Data System (ADS)

    Perrin, G.; Soize, C.; Marque-Pucheu, S.; Garnier, J.

    2017-10-01

    The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

  6. On the Waring problem for polynomial rings

    PubMed Central

    Fröberg, Ralf; Ottaviani, Giorgio; Shapiro, Boris

    2012-01-01

    In this note we discuss an analog of the classical Waring problem for . Namely, we show that a general homogeneous polynomial of degree divisible by k≥2 can be represented as a sum of at most kn k-th powers of homogeneous polynomials in . Noticeably, kn coincides with the number obtained by naive dimension count. PMID:22460787

  7. Dual exponential polynomials and linear differential equations

    NASA Astrophysics Data System (ADS)

    Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

    2018-01-01

    We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

  8. Planar harmonic polynomials of type B

    NASA Astrophysics Data System (ADS)

    Dunkl, Charles F.

    1999-11-01

    The hyperoctahedral group acting on icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>N is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators {Ti:1icons/Journals/Common/leq" ALT="leq" ALIGN="TOP"/> iicons/Journals/Common/leq" ALT="leq" ALIGN="TOP"/> N}. These operators are analogous to partial derivative operators. This paper finds all the polynomials h on icons/Journals/Common/BbbR" ALT="BbbR" ALIGN="TOP"/>N which are harmonic, icons/Journals/Common/Delta" ALT="Delta" ALIGN="TOP"/>Bh = 0 and annihilated by Ti for i>2, where the Laplacian 0305-4470/32/46/308/img1" ALT="(sum). They are given explicitly in terms of a novel basis of polynomials, defined by generating functions. The harmonic polynomials can be used to find wavefunctions for the quantum many-body spin Calogero model.

  9. Georeferencing CAMS data: Polynomial rectification and beyond

    NASA Astrophysics Data System (ADS)

    Yang, Xinghe

    The Calibrated Airborne Multispectral Scanner (CAMS) is a sensor used in the commercial remote sensing program at NASA Stennis Space Center. In geographic applications of the CAMS data, accurate geometric rectification is essential for the analysis of the remotely sensed data and for the integration of the data into Geographic Information Systems (GIS). The commonly used rectification techniques such as the polynomial transformation and ortho rectification have been very successful in the field of remote sensing and GIS for most remote sensing data such as Landsat imagery, SPOT imagery and aerial photos. However, due to the geometric nature of the airborne line scanner which has high spatial frequency distortions, the polynomial model and the ortho rectification technique in current commercial software packages such as Erdas Imagine are not adequate for obtaining sufficient geometric accuracy. In this research, the geometric nature, especially the major distortions, of the CAMS data has been described. An analytical step-by-step geometric preprocessing has been utilized to deal with the potential high frequency distortions of the CAMS data. A generic sensor-independent photogrammetric model has been developed for the ortho-rectification of the CAMS data. Three generalized kernel classes and directional elliptical basis have been formulated into a rectification model of summation of multisurface functions, which is a significant extension to the traditional radial basis functions. The preprocessing mechanism has been fully incorporated into the polynomial, the triangle-based finite element analysis as well as the summation of multisurface functions. While the multisurface functions and the finite element analysis have the characteristics of localization, piecewise logic has been applied to the polynomial and photogrammetric methods, which can produce significant accuracy improvement over the global approach. A software module has been implemented with full

  10. Comparison Between Polynomial, Euler Beta-Function and Expo-Rational B-Spline Bases

    NASA Astrophysics Data System (ADS)

    Kristoffersen, Arnt R.; Dechevsky, Lubomir T.; Laksa˚, Arne; Bang, Børre

    2011-12-01

    Euler Beta-function B-splines (BFBS) are the practically most important instance of generalized expo-rational B-splines (GERBS) which are not true expo-rational B-splines (ERBS). BFBS do not enjoy the full range of the superproperties of ERBS but, while ERBS are special functions computable by a very rapidly converging yet approximate numerical quadrature algorithms, BFBS are explicitly computable piecewise polynomial (for integer multiplicities), similar to classical Schoenberg B-splines. In the present communication we define, compute and visualize for the first time all possible BFBS of degree up to 3 which provide Hermite interpolation in three consecutive knots of multiplicity up to 3, i.e., the function is being interpolated together with its derivatives of order up to 2. We compare the BFBS obtained for different degrees and multiplicities among themselves and versus the classical Schoenberg polynomial B-splines and the true ERBS for the considered knots. The results of the graphical comparison are discussed from analytical point of view. For the numerical computation and visualization of the new B-splines we have used Maple 12.

  11. 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.

  12. Polynomial Supertree Methods Revisited

    PubMed Central

    Brinkmeyer, Malte; Griebel, Thasso; Böcker, Sebastian

    2011-01-01

    Supertree methods allow to reconstruct large phylogenetic trees by combining smaller trees with overlapping leaf sets into one, more comprehensive supertree. The most commonly used supertree method, matrix representation with parsimony (MRP), produces accurate supertrees but is rather slow due to the underlying hard optimization problem. In this paper, we present an extensive simulation study comparing the performance of MRP and the polynomial supertree methods MinCut Supertree, Modified MinCut Supertree, Build-with-distances, PhySIC, PhySIC_IST, and super distance matrix. We consider both quality and resolution of the reconstructed supertrees. Our findings illustrate the tradeoff between accuracy and running time in supertree construction, as well as the pros and cons of voting- and veto-based supertree approaches. Based on our results, we make some general suggestions for supertree methods yet to come. PMID:22229028

  13. Fast Minimum Variance Beamforming Based on Legendre Polynomials.

    PubMed

    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.

  14. SnRK1 is differentially regulated in the cotyledon and embryo axe of bean (Phaseolus vulgaris L) seeds.

    PubMed

    Coello, Patricia; Martínez-Barajas, Eleazar

    2014-07-01

    SnRK1 activity is developmentally regulated in bean seeds and exhibits a transient increase with the highest value at 20 days after anthesis (DAA), which coincides with the beginning of protein and starch accumulation. The catalytic subunit of SnRK1 shows a consistent decrease throughout the seed development period. However, by 15 DAA a significant proportion of the catalytic subunit appears phosphorylated. The increase in activity and phosphorylation of the catalytic subunit coincides with a decrease in hexoses. However, SnRK1 activity is differentially regulated in the cotyledon and embryo axe, where a larger proportion of the catalytic subunit is phosphorylated. SnRK1 obtained from endosperm extract is inhibited by T6P and to a lesser extent by ADPG and UDPG, whereas the enzyme isolated from embryo is virtually insensitive to T6P but exhibits some inhibition by ADPG and UDPG. In cotyledon extracts, the effects of T6P and ADPG on SnRK1 activity are additive, whereas in embryo extract, T6P inhibits the enzyme only when ADPG is present. After fractionation on Sephacryl-S300, SnRK1 activity obtained from cotyledon extracts is detected as a single peak associated with a molecular weight of 250 kDa whereas that obtained form embryo axe extracts detected as 2 peaks associated with molecular weight of 250 and 180 kDa. In both cases, the catalytic subunit exhibits a wide distribution but is concentrated in the fractions with the highest activity. To analyse the composition of the complex, cotyledon and embryo extracts were treated with a reversible crosslinker (DSP). DSP induced the formation of complexes with molecular weights of 97 and 180 kDa in the cotyledon and embryo extracts, respectively. Since all the phosphorylated catalytic subunit is present in the complexes induced by DSP, it appears that the phosphorylation favors its interaction with other proteins. Copyright © 2014 Elsevier Masson SAS. All rights reserved.

  15. Fast beampattern evaluation by polynomial rooting

    NASA Astrophysics Data System (ADS)

    Häcker, P.; Uhlich, S.; Yang, B.

    2011-07-01

    Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.

  16. [Minor strut fracture of the Björk-Shiley mitral valve].

    PubMed

    Sugita, T; Yasuda, R; Watarida, S; Onoe, M; Tabata, R; Mori, A

    1990-06-01

    In May, 1982, a 49-year-old man underwent mitral valve replacement (MVR) in our hospital with a 31 mm Björk-Shiley prosthesis for mitral regurgitation. He had been doing well until his episode of palpitation and dyspnea of sudden onset, and was transferred to our ICU with severe cardiogenic shock in Aug, 1986. Chest X-ray film revealed pulmonary edema and breakage of the valve with migration of the disc and the minor strut of the prosthesis. He was operated upon 5 hours after the onset of his complaints. The minor strut was removed from the left upper pulmonary vein and mitral valve re-replacement was done with a 29 mm Björk-Shiley Monostrut valve. The disc which had dislocated into the abdominal aorta was also recovered on the twenty-third post operative day. His postoperative course was uneventful. Immediate diagnosis and subsequent re-operation is absolute indication for rescue from acute cardiac failure due to mechanical failure of any prosthetic valve.

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

    PubMed

    Zhang, Huaguang; Xie, Xiangpeng; Tong, Shaocheng

    2011-10-01

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

  18. 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

  19. Polynomial interpolation and sums of powers of integers

    NASA Astrophysics Data System (ADS)

    Cereceda, José Luis

    2017-02-01

    In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, Pk(n) and Qk(n), such that Pk(n) = Qk(n) = fk(n) for n = 1, 2,… , k, where fk(1), fk(2),… , fk(k) are k arbitrarily chosen (real or complex) values. Then, we focus on the case that fk(n) is given by the sum of powers of the first n positive integers Sk(n) = 1k + 2k + ṡṡṡ + nk, and show that Sk(n) admits the polynomial representations Sk(n) = Pk(n) and Sk(n) = Qk(n) for all n = 1, 2,… , and k ≥ 1, where the first representation involves the Eulerian numbers, and the second one the Stirling numbers of the second kind. Finally, we consider yet another polynomial formula for Sk(n) alternative to the well-known formula of Bernoulli.

  20. Combinatorial theory of Macdonald polynomials I: proof of Haglund's formula.

    PubMed

    Haglund, J; Haiman, M; Loehr, N

    2005-02-22

    Haglund recently proposed a combinatorial interpretation of the modified Macdonald polynomials H(mu). We give a combinatorial proof of this conjecture, which establishes the existence and integrality of H(mu). As corollaries, we obtain the cocharge formula of Lascoux and Schutzenberger for Hall-Littlewood polynomials, a formula of Sahi and Knop for Jack's symmetric functions, a generalization of this result to the integral Macdonald polynomials J(mu), a formula for H(mu) in terms of Lascoux-Leclerc-Thibon polynomials, and combinatorial expressions for the Kostka-Macdonald coefficients K(lambda,mu) when mu is a two-column shape.

  1. Higher order derivatives of R-Jacobi polynomials

    NASA Astrophysics Data System (ADS)

    Das, Sourav; Swaminathan, A.

    2016-06-01

    In this work, the R-Jacobi polynomials defined on the nonnegative real axis related to F-distribution are considered. Using their Sturm-Liouville system higher order derivatives are constructed. Orthogonality property of these higher ordered R-Jacobi polynomials are obtained besides their normal form, self-adjoint form and hypergeometric representation. Interesting results on the Interpolation formula and Gaussian quadrature formulae are obtained with numerical examples.

  2. Torus Knot Polynomials and Susy Wilson Loops

    NASA Astrophysics Data System (ADS)

    Giasemidis, Georgios; Tierz, Miguel

    2014-12-01

    We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of ( n, m) torus knots, and present a number of equivalent expressions, all related by Heine's transformations. Using this result, the symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang-Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang-Mills theory, which is known to give averages of Wilson loops in = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones-Rosso representation in terms of q-harmonic oscillators.

  3. M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori.

    PubMed

    Kwun, Young Chel; Munir, Mobeen; Nazeer, Waqas; Rafique, Shazia; Min Kang, Shin

    2017-08-18

    V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical properties of the material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of V-Phylenic nanotubes and nanotori. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

  4. The Fixed-Links Model in Combination with the Polynomial Function as a Tool for Investigating Choice Reaction Time Data

    ERIC Educational Resources Information Center

    Schweizer, Karl

    2006-01-01

    A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

  5. Identities associated with Milne-Thomson type polynomials and special numbers.

    PubMed

    Simsek, Yilmaz; Cakic, Nenad

    2018-01-01

    The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p -adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

  6. Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

    PubMed

    Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

    2012-01-01

    Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

  7. On direct theorems for best polynomial approximation

    NASA Astrophysics Data System (ADS)

    Auad, A. A.; AbdulJabbar, R. S.

    2018-05-01

    This paper is to obtain similarity for the best approximation degree of functions, which are unbounded in L p,α (A = [0,1]), which called weighted space by algebraic polynomials. {E}nH{(f)}p,α and the best approximation degree in the same space on the interval [0,2π] by trigonometric polynomials {E}nT{(f)}p,α of direct wellknown theorems in forms the average modules.

  8. Yellow fever vaccine: comparison of the neurovirulence of new 17D-204 Stamaril™ seed lots and RK 168-73 strain.

    PubMed

    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. Copyright © 2013 The International Alliance for Biological Standardization. Published by Elsevier Ltd. All rights reserved.

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

    PubMed

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

    2009-04-01

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

  10. 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.

  11. Maximal aggregation of polynomial dynamical systems

    PubMed Central

    Cardelli, Luca; Tschaikowski, Max

    2017-01-01

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

  12. Eye aberration analysis with Zernike polynomials

    NASA Astrophysics Data System (ADS)

    Molebny, Vasyl V.; Chyzh, Igor H.; Sokurenko, Vyacheslav M.; Pallikaris, Ioannis G.; Naoumidis, Leonidas P.

    1998-06-01

    New horizons for accurate photorefractive sight correction, afforded by novel flying spot technologies, require adequate measurements of photorefractive properties of an eye. Proposed techniques of eye refraction mapping present results of measurements for finite number of points of eye aperture, requiring to approximate these data by 3D surface. A technique of wave front approximation with Zernike polynomials is described, using optimization of the number of polynomial coefficients. Criterion of optimization is the nearest proximity of the resulted continuous surface to the values calculated for given discrete points. Methodology includes statistical evaluation of minimal root mean square deviation (RMSD) of transverse aberrations, in particular, varying consecutively the values of maximal coefficient indices of Zernike polynomials, recalculating the coefficients, and computing the value of RMSD. Optimization is finished at minimal value of RMSD. Formulas are given for computing ametropia, size of the spot of light on retina, caused by spherical aberration, coma, and astigmatism. Results are illustrated by experimental data, that could be of interest for other applications, where detailed evaluation of eye parameters is needed.

  13. 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…

  14. 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.

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

    NASA Astrophysics Data System (ADS)

    Lei, Hanlun; Xu, Bo; Circi, Christian

    2018-05-01

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

  16. On the coefficients of differentiated expansions of ultraspherical polynomials

    NASA Technical Reports Server (NTRS)

    Karageorghis, Andreas; Phillips, Timothy N.

    1989-01-01

    A formula expressing the coefficients of an expression of ultraspherical polynomials which has been differentiated an arbitrary number of times in terms of the coefficients of the original expansion is proved. The particular examples of Chebyshev and Legendre polynomials are considered.

  17. Mapping Landslides in Lunar Impact Craters Using Chebyshev Polynomials and Dem's

    NASA Astrophysics Data System (ADS)

    Yordanov, V.; Scaioni, M.; Brunetti, M. T.; Melis, M. T.; Zinzi, A.; Giommi, P.

    2016-06-01

    Geological slope failure processes have been observed on the Moon surface for decades, nevertheless a detailed and exhaustive lunar landslide inventory has not been produced yet. For a preliminary survey, WAC images and DEM maps from LROC at 100 m/pixels have been exploited in combination with the criteria applied by Brunetti et al. (2015) to detect the landslides. These criteria are based on the visual analysis of optical images to recognize mass wasting features. In the literature, Chebyshev polynomials have been applied to interpolate crater cross-sections in order to obtain a parametric characterization useful for classification into different morphological shapes. Here a new implementation of Chebyshev polynomial approximation is proposed, taking into account some statistical testing of the results obtained during Least-squares estimation. The presence of landslides in lunar craters is then investigated by analyzing the absolute values off odd coefficients of estimated Chebyshev polynomials. A case study on the Cassini A crater has demonstrated the key-points of the proposed methodology and outlined the required future development to carry out.

  18. Improved multivariate polynomial factoring algorithm

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

    Wang, P.S.

    1978-10-01

    A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described. The new algorithm has improved strategies for dealing with the known problems of the original algorithm, namely, the leading coefficient problem, the bad-zero problem and the occurrence of extraneous factors. It has an algorithm for correctly predetermining leading coefficients of the factors. A new and efficient p-adic algorithm named EEZ is described. Bascially it is a linearly convergent variable-by-variable parallel construction. The improved algorithm is generally faster and requires less store then the original algorithm. Machine examples with comparative timingmore » are included.« less

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

    NASA Astrophysics Data System (ADS)

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

    2017-07-01

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

  20. LecRK-V, an L-type lectin receptor kinase in Haynaldia villosa, plays positive role in resistance to wheat powdery mildew.

    PubMed

    Wang, Zongkuan; Cheng, Jiangyue; Fan, Anqi; Zhao, Jia; Yu, Zhongyu; Li, Yingbo; Zhang, Heng; Xiao, Jin; Muhammad, Faheem; Wang, Haiyan; Cao, Aizhong; Xing, Liping; Wang, Xiue

    2018-01-01

    Plant sense potential microbial pathogen using pattern recognition receptors (PRRs) to recognize pathogen-associated molecular patterns (PAMPs). The Lectin receptor-like kinase genes (LecRKs) are involved in various cellular processes mediated by signal transduction pathways. In the present study, an L-type lectin receptor kinase gene LecRK-V was cloned from Haynaldia villosa, a diploid wheat relative which is highly resistant to powdery mildew. The expression of LecRK-V was rapidly up-regulated by Bgt inoculation and chitin treatment. Its transcript level was higher in the leaves than in roots, culms, spikes and callus. Single-cell transient overexpression of LecRK-V led to decreased haustorium index in wheat variety Yangmai158, which is powdery mildew susceptible. Stable transformation LecRK-V into Yangmai158 significantly enhanced the powdery mildew resistance at both seedling and adult stages. At seedling stage, the transgenic line was highly resistance to 18 of the tested 23 Bgt isolates, hypersensitive responses (HR) were observed for 22 Bgt isolates, and more ROS at the Bgt infection sites was accumulated. These indicated that LecRK-V confers broad-spectrum resistance to powdery mildew, and ROS and SA pathways contribute to the enhanced powdery mildew resistance in wheat. © 2017 The Authors. Plant Biotechnology Journal published by Society for Experimental Biology and The Association of Applied Biologists and John Wiley & Sons Ltd.

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

    PubMed

    Zhao, Chunyu; Burge, James H

    2007-12-24

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

  2. Polynomial asymptotes of the second kind

    NASA Astrophysics Data System (ADS)

    Dobbs, David E.

    2011-03-01

    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 conics. Prerequisites include the division algorithm for polynomials with coefficients in the field of real numbers and elementary facts about limits from calculus. This note could be used as enrichment material in courses ranging from Calculus to Real Analysis to Abstract Algebra.

  3. Acute aortic regurgitation secondary to disk embolization of a Björk-Shiley prosthetic aortic valve.

    PubMed

    Grande, Robert D; Katz, William E

    2011-03-01

    Having passed the 30th anniversary of the first implantation of a Björk-Shiley convexo-concave tilting mechanical valve, recognition of the life-threatening complication of strut fracture is not widespread. The authors report the case of a 48-year-old man with acute-onset chest pain and dyspnea found to have strut fracture and disk embolization of a 26-year-old Björk-Shiley prosthetic aortic valve. The value of echocardiography in the diagnosis of this condition is discussed. Copyright © 2010 American Society of Echocardiography. Published by Mosby, Inc. All rights reserved.

  4. Quantization of gauge fields, graph polynomials and graph homology

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

    Kreimer, Dirk, E-mail: kreimer@physik.hu-berlin.de; 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.more » -- 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.« less

  5. 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.

  6. Polynomial equations for science orbits around Europa

    NASA Astrophysics Data System (ADS)

    Cinelli, Marco; Circi, Christian; Ortore, Emiliano

    2015-07-01

    In this paper, the design of science orbits for the observation of a celestial body has been carried out using polynomial equations. The effects related to the main zonal harmonics of the celestial body and the perturbation deriving from the presence of a third celestial body have been taken into account. The third body describes a circular and equatorial orbit with respect to the primary body and, for its disturbing potential, an expansion in Legendre polynomials up to the second order has been considered. These polynomial equations allow the determination of science orbits around Jupiter's satellite Europa, where the third body gravitational attraction represents one of the main forces influencing the motion of an orbiting probe. Thus, the retrieved relationships have been applied to this moon and periodic sun-synchronous and multi-sun-synchronous orbits have been determined. Finally, numerical simulations have been carried out to validate the analytical results.

  7. Novel quadrilateral elements based on explicit Hermite polynomials for bending of Kirchhoff-Love plates

    NASA Astrophysics Data System (ADS)

    Beheshti, Alireza

    2018-03-01

    The contribution addresses the finite element analysis of bending of plates given the Kirchhoff-Love model. To analyze the static deformation of plates with different loadings and geometries, the principle of virtual work is used to extract the weak form. Following deriving the strain field, stresses and resultants may be obtained. For constructing four-node quadrilateral plate elements, the Hermite polynomials defined with respect to the variables in the parent space are applied explicitly. Based on the approximated field of displacement, the stiffness matrix and the load vector in the finite element method are obtained. To demonstrate the performance of the subparametric 4-node plate elements, some known, classical examples in structural mechanics are solved and there are comparisons with the analytical solutions available in the literature.

  8. Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

    NASA Astrophysics Data System (ADS)

    Malik, Pradeep; Swaminathan, A.

    2010-11-01

    In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

  9. Placing Intelligence into an Evolutionary Framework or How "g" Fits into the "r-K" Matrix of Life-History Traits Including Longevity

    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…

  10. 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.

  11. Asymptotic formulae for the zeros of orthogonal polynomials

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

    Badkov, V M

    2012-09-30

    Let p{sub n}(t) be an algebraic polynomial that is orthonormal with weight p(t) on the interval [-1, 1]. When p(t) is a perturbation (in certain limits) of the Chebyshev weight of the first kind, the zeros of the polynomial p{sub n}( cos {tau}) and the differences between pairs of (not necessarily consecutive) zeros are shown to satisfy asymptotic formulae as n{yields}{infinity}, which hold uniformly with respect to the indices of the zeros. Similar results are also obtained for perturbations of the Chebyshev weight of the second kind. First, some preliminary results on the asymptotic behaviour of the difference between twomore » zeros of an orthogonal trigonometric polynomial, which are needed, are established. Bibliography: 15 titles.« less

  12. Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

    NASA Astrophysics Data System (ADS)

    Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong

    2018-04-01

    We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

  13. The Björk-Shiley 70 degree convexo-concave prosthesis strut fracture problem (present state of information).

    PubMed

    Ostermeyer, J; Horstkotte, D; Bennett, J; Huysmans, H; Lindblom, D; Olin, C; Orinius, E; Semb, G

    1987-04-01

    Between June 1980 and June 1983 4028 Björk-Shiley 70 degree convexo-concave prosthetic heart valves were distributed and implanted in Australia, Canada, Europe and South Africa. As of March 1986, a total of 52 outlet strut fractures (1.29%; 70% CL: 1.1%-1.5%) have been reported from 29 implant institutions in 12 countries. The majority (82.7%) occurred in Europe. Intervals between implantation and fracture were 13 days to 45.3 months (mean: 18.4 months; 70% CL: 16.6 months-20.1 months). The mortality rate after strut fracture was 78.7% (70% CL: 72.5%-84.9%). Upon stratification of the fracture by valve sizes and types it becomes evident that 75% (70% CL: 68.8%-81.2%) of all fractures are related to the sizes 29 mm to 33 mm (which virtually represent the same valve size) and predominantly to mitral valves (p less than 0.01). The large valves again have been stratified into two subsets, namely those fabricated from flanges originally machined as Björk-Shiley 60 degree convexo-concave valves (group I) and later produced valves machined initially to 70 degree specifications (group II). In group I the fracture rate was 5.2% (70% CL: 4.2%-6.2%) versus 1.6% (70% CL: 1.1%-2.1%) in group II (p less than 0.01), which identifies the group I 29 mm-33 mm Björk-Shiley 70 degree convexo-concave valves as the highest risk group for strut fracture. The rates are based upon all available information as of March 16, 1986.(ABSTRACT TRUNCATED AT 250 WORDS)

  14. 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.

  15. 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.

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

    NASA Astrophysics Data System (ADS)

    Recchioni, Maria Cristina

    2001-12-01

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

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

    PubMed

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

    2017-06-26

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

  18. Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials

    NASA Astrophysics Data System (ADS)

    Odake, Satoru; Sasaki, Ryu

    2017-04-01

    As the fourth stage of the project multi-indexed orthogonal polynomials, we present the multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials in the framework of ‘discrete quantum mechanics’ with real shifts defined on the semi-infinite lattice in one dimension. They are obtained, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier, from the quantum mechanical systems corresponding to the original orthogonal polynomials by multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of virtual state vectors. The virtual state vectors are the solutions of the matrix Schrödinger equation on all the lattice points having negative energies and infinite norm. This is in good contrast to the (q-)Racah systems defined on a finite lattice, in which the ‘virtual state’ vectors satisfy the matrix Schrödinger equation except for one of the two boundary points.

  19. Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials

    PubMed Central

    Corteel, Sylvie; Williams, Lauren K.

    2010-01-01

    We introduce some combinatorial objects called staircase tableaux, which have cardinality 4nn !, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities α and γ, and they may exit and enter at the right with probabilities β and δ. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials. PMID:20348417

  20. Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials.

    PubMed

    Corteel, Sylvie; Williams, Lauren K

    2010-04-13

    We introduce some combinatorial objects called staircase tableaux, which have cardinality 4(n)n!, and connect them to both the asymmetric exclusion process (ASEP) and Askey-Wilson polynomials. The ASEP is a model from statistical mechanics introduced in the late 1960s, which describes a system of interacting particles hopping left and right on a one-dimensional lattice of n sites with open boundaries. It has been cited as a model for traffic flow and translation in protein synthesis. In its most general form, particles may enter and exit at the left with probabilities alpha and gamma, and they may exit and enter at the right with probabilities beta and delta. In the bulk, the probability of hopping left is q times the probability of hopping right. Our first result is a formula for the stationary distribution of the ASEP with all parameters general, in terms of staircase tableaux. Our second result is a formula for the moments of (the weight function of) Askey-Wilson polynomials, also in terms of staircase tableaux. Since the 1980s there has been a great deal of work giving combinatorial formulas for moments of classical orthogonal polynomials (e.g. Hermite, Charlier, Laguerre); among these polynomials, the Askey-Wilson polynomials are the most important, because they are at the top of the hierarchy of classical orthogonal polynomials.

  1. New separated polynomial solutions to the Zernike system on the unit disk and interbasis expansion.

    PubMed

    Pogosyan, George S; Wolf, Kurt Bernardo; Yakhno, Alexander

    2017-10-01

    The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the unit disk to classify wavefront aberrations in circular pupils is shown to have a set of new orthonormal solution bases involving Legendre and Gegenbauer polynomials in nonorthogonal coordinates, close to Cartesian ones. We find the overlaps between the original Zernike basis and a representative of the new set, which turn out to be Clebsch-Gordan coefficients.

  2. Comparative evaluation of immunochromatographic dipstick test (ICT) rk39, soluble antigen ELISA and IFAT for the sero-diagnosis of visceral leishmaniasis in Morocco.

    PubMed

    Mniouil, Meryem; Fellah, Hajiba; Amarir, Fatima; Sadak, Abderrahim; Et-Touys, Abdeslam; Bakri, Youssef; Moustachi, Aziza; Tassou, Fatima Zahraa; Hida, Mostapha; Lyagoubi, Mohamed; Adlaoui, El Bachir; Rhajaoui, Mohamed; Sebti, Faiza

    2018-06-01

    A rapid, sensitive and specific tool for detection of Leishmania infantum infection in Humans would be highly desirable, because it would allow control interventions in endemic areas of visceral leishmaniasis. This study was carried out at the Reference National Laboratory of Leishmaniasis (RNLL) in National Institute of Hygiene (NIH) Morocco, in order to evaluate the diagnostic potential of immunochromatographic dipstick test (ICT) rk39 in Moroccan suspected VL patients. A total of 49 admitted patients with strong clinical suspicion of VL and 40 healthy controls were investigated for the performance of the ICT rk39. Bone marrow smears were examined for microscopic detection of Leishmania amastigotes obtained from the admitted patients. Only PCR and smear positive cases were considered as gold standard as well as confirmed cases of VL. Out of 49 suspected patients, twenty four (48.9%) were found PCR and smear-positive and twenty three (46.9%) were positive for ICT rk39. Voluntary healthy controls, which included twenty persons from the endemic zone and twenty from non-endemic zone of VL, were found all negative for the strip test. The sensitivity in sera was 75% by ELISA and 87.5% by IFAT, compared with 95.8% for ICT rk39. Specificity was 95.8%, with both tests ELISA and IFAT, and 100% by ICT rk39 respectively. Present study findings again reinforce that the ICT rk39 is a simple, reliable and easy-to-perform non-invasive diagnostic tool for visceral leishmaniasis in the endemic area of Morocco. Copyright © 2018 Elsevier B.V. All rights reserved.

  3. Ectopic expression of vaccinia virus E3 and K3 cannot rescue ectromelia virus replication in rabbit RK13 cells.

    PubMed

    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.

  4. Molecular cloning and comparative analysis of a PR-1-RK hybrid gene from Triticum urartu, the A-genome progenitor of hexaploid wheat

    USDA-ARS?s Scientific Manuscript database

    Wheat genomes encode pathogenesis-related protein 1 (PR-1)/receptor-like kinase (RK) hybrid proteins as first reported for hexaploid wheat. To date, no PR-1-RK-like proteins have been identified in the diploid wild wheat Triticum urartu, the A-genome progenitor of hexaploid wheat. Here we report the...

  5. Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform

    PubMed Central

    Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

    2018-01-01

    Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm. PMID:29438317

  6. Polynomial Phase Estimation Based on Adaptive Short-Time Fourier Transform.

    PubMed

    Jing, Fulong; Zhang, Chunjie; Si, Weijian; Wang, Yu; Jiao, Shuhong

    2018-02-13

    Polynomial phase signals (PPSs) have numerous applications in many fields including radar, sonar, geophysics, and radio communication systems. Therefore, estimation of PPS coefficients is very important. In this paper, a novel approach for PPS parameters estimation based on adaptive short-time Fourier transform (ASTFT), called the PPS-ASTFT estimator, is proposed. Using the PPS-ASTFT estimator, both one-dimensional and multi-dimensional searches and error propagation problems, which widely exist in PPSs field, are avoided. In the proposed algorithm, the instantaneous frequency (IF) is estimated by S-transform (ST), which can preserve information on signal phase and provide a variable resolution similar to the wavelet transform (WT). The width of the ASTFT analysis window is equal to the local stationary length, which is measured by the instantaneous frequency gradient (IFG). The IFG is calculated by the principal component analysis (PCA), which is robust to the noise. Moreover, to improve estimation accuracy, a refinement strategy is presented to estimate signal parameters. Since the PPS-ASTFT avoids parameter search, the proposed algorithm can be computed in a reasonable amount of time. The estimation performance, computational cost, and implementation of the PPS-ASTFT are also analyzed. The conducted numerical simulations support our theoretical results and demonstrate an excellent statistical performance of the proposed algorithm.

  7. Control of magnetic bearing systems via the Chebyshev polynomial-based unified model (CPBUM) neural network.

    PubMed

    Jeng, J T; Lee, T T

    2000-01-01

    A Chebyshev polynomial-based unified model (CPBUM) neural network is introduced and applied to control a magnetic bearing systems. First, we show that the CPBUM neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional feedforward/recurrent neural network. It turns out that the CPBUM neural network is more suitable in the design of controller than the conventional feedforward/recurrent neural network. Second, we propose the inverse system method, based on the CPBUM neural networks, to control a magnetic bearing system. The proposed controller has two structures; namely, off-line and on-line learning structures. We derive a new learning algorithm for each proposed structure. The experimental results show that the proposed neural network architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

  8. Effect of amino acid substitution in the staphylococcal peptides warnericin RK and PSMα on their anti-Legionella and hemolytic activities.

    PubMed

    Marchand, Adrienne; Augenstreich, Jacques; Loiseau, Clémence; Verdon, Julien; Lecomte, Sophie; Berjeaud, Jean-Marc

    2015-07-01

    Warnericin RK from Staphylococcus warneri and PSMα from Staphylococcus epidermidis are anti-Legionella peptides which were differently classified in a previous study according to their mode of action. Indeed, warnericin RK is highly hemolytic with a bactericidal mode of action, whereas PSMα is poorly hemolytic with a bacteriostatic mode of action toward L. pneumophila. In order to find anti-Legionella peptides which are not hemolytic, a collection of peptides varying in sequence from warnericin RK to PSMα were designed and synthesized, and their anti-Legionella activities, in terms of growth inhibition, permeabilization, and bactericidal effect, as well as their hemolytic activities, were measured and compared. The results showed that some residues, at position 14 for both peptides for instance, were of major importance for bactericidal and hemolytic activities.

  9. Orthogonal Polynomials Associated with Complementary Chain Sequences

    NASA Astrophysics Data System (ADS)

    Behera, Kiran Kumar; Sri Ranga, A.; Swaminathan, A.

    2016-07-01

    Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.

  10. 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.

  11. Role of the parCBA Operon of the Broad-Host-Range Plasmid RK2 in Stable Plasmid Maintenance

    PubMed Central

    Easter, Carla L.; Schwab, Helmut; Helinski, Donald R.

    1998-01-01

    The par region of the stably maintained broad-host-range plasmid RK2 is organized as two divergent operons, parCBA and parDE, and a cis-acting site. parDE encodes a postsegregational killing system, and parCBA encodes a resolvase (ParA), a nuclease (ParB), and a protein of unknown function (ParC). The present study was undertaken to further delineate the role of the parCBA region in the stable maintenance of RK2 by first introducing precise deletions in the three genes and then assessing the abilities of the different constructs to stabilize RK2 in three strains of Escherichia coli and two strains of Pseudomonas aeruginosa. The intact parCBA operon was effective in stabilizing a conjugation-defective RK2 derivative in E. coli MC1061K and RR1 but was relatively ineffective in E. coli MV10Δlac. In the two strains in which the parCBA operon was effective, deletions in parB, parC, or both parB and parC caused an approximately twofold reduction in the stabilizing ability of the operon, while a deletion in the parA gene resulted in a much greater loss of parCBA activity. For P. aeruginosa PAO1161Rifr, the parCBA operon provided little if any plasmid stability, but for P. aeruginosa PAC452Rifr, the RK2 plasmid was stabilized to a substantial extent by parCBA. With this latter strain, parA and res alone were sufficient for stabilization. The cer resolvase system of plasmid ColE1 and the loxP/Cre system of plasmid P1 were tested in comparison with the parCBA operon. We found that, not unlike what was previously observed with MC1061K, cer failed to stabilize the RK2 plasmid with par deletions in strain MV10Δlac, but this multimer resolution system was effective in stabilizing the plasmid in strain RR1. The loxP/Cre system, on the other hand, was very effective in stabilizing the plasmid in all three E. coli strains. These observations indicate that the parA gene, along with its res site, exhibits a significant level of plasmid stabilization in the absence of the parC and

  12. On polynomial selection for the general number field sieve

    NASA Astrophysics Data System (ADS)

    Kleinjung, Thorsten

    2006-12-01

    The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

  13. Calculators and Polynomial Evaluation.

    ERIC Educational Resources Information Center

    Weaver, J. F.

    The intent of this paper is to suggest and illustrate how electronic hand-held calculators, especially non-programmable ones with limited data-storage capacity, can be used to advantage by students in one particular aspect of work with polynomial functions. The basic mathematical background upon which calculator application is built is summarized.…

  14. Cloning of Gossypium hirsutum Sucrose Non-Fermenting 1-Related Protein Kinase 2 Gene (GhSnRK2) and Its Overexpression in Transgenic Arabidopsis Escalates Drought and Low Temperature Tolerance

    PubMed Central

    Bello, Babatunde; Zhang, Xueyan; Liu, Chuanliang; Yang, Zhaoen; Yang, Zuoren; Wang, Qianhua; Zhao, Ge; Li, Fuguang

    2014-01-01

    The molecular mechanisms of stress tolerance and the use of modern genetics approaches for the improvement of drought stress tolerance have been major focuses of plant molecular biologists. In the present study, we cloned the Gossypium hirsutum sucrose non-fermenting 1-related protein kinase 2 (GhSnRK2) gene and investigated its functions in transgenic Arabidopsis. We further elucidated the function of this gene in transgenic cotton using virus-induced gene silencing (VIGS) techniques. We hypothesized that GhSnRK2 participates in the stress signaling pathway and elucidated its role in enhancing stress tolerance in plants via various stress-related pathways and stress-responsive genes. We determined that the subcellular localization of the GhSnRK2-green fluorescent protein (GFP) was localized in the nuclei and cytoplasm. In contrast to wild-type plants, transgenic plants overexpressing GhSnRK2 exhibited increased tolerance to drought, cold, abscisic acid and salt stresses, suggesting that GhSnRK2 acts as a positive regulator in response to cold and drought stresses. Plants overexpressing GhSnRK2 displayed evidence of reduced water loss, turgor regulation, elevated relative water content, biomass, and proline accumulation. qRT-PCR analysis of GhSnRK2 expression suggested that this gene may function in diverse tissues. Under normal and stress conditions, the expression levels of stress-inducible genes, such as AtRD29A, AtRD29B, AtP5CS1, AtABI3, AtCBF1, and AtABI5, were increased in the GhSnRK2-overexpressing plants compared to the wild-type plants. GhSnRK2 gene silencing alleviated drought tolerance in cotton plants, indicating that VIGS technique can certainly be used as an effective means to examine gene function by knocking down the expression of distinctly expressed genes. The results of this study suggested that the GhSnRK2 gene, when incorporated into Arabidopsis, functions in positive responses to drought stress and in low temperature tolerance. PMID:25393623

  15. Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions

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

    Lüchow, Arne, E-mail: luechow@rwth-aachen.de; Jülich Aachen Research Alliance; Sturm, Alexander

    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 fewmore » 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.« less

  16. Roots of polynomials by ratio of successive derivatives

    NASA Technical Reports Server (NTRS)

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

    1972-01-01

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

  17. 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…

  18. Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

    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.

  19. A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

    NASA Astrophysics Data System (ADS)

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

    2001-08-01

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

  20. Accurate Estimation of Solvation Free Energy Using Polynomial Fitting Techniques

    PubMed Central

    Shyu, Conrad; Ytreberg, F. Marty

    2010-01-01

    This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem 30: 2297–2304, 2009). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant λ values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software. PMID:20623657

  1. Bayes Node Energy Polynomial Distribution to Improve Routing in Wireless Sensor Network

    PubMed Central

    Palanisamy, Thirumoorthy; Krishnasamy, Karthikeyan N.

    2015-01-01

    Wireless Sensor Network monitor and control the physical world via large number of small, low-priced sensor nodes. Existing method on Wireless Sensor Network (WSN) presented sensed data communication through continuous data collection resulting in higher delay and energy consumption. To conquer the routing issue and reduce energy drain rate, Bayes Node Energy and Polynomial Distribution (BNEPD) technique is introduced with energy aware routing in the wireless sensor network. The Bayes Node Energy Distribution initially distributes the sensor nodes that detect an object of similar event (i.e., temperature, pressure, flow) into specific regions with the application of Bayes rule. The object detection of similar events is accomplished based on the bayes probabilities and is sent to the sink node resulting in minimizing the energy consumption. Next, the Polynomial Regression Function is applied to the target object of similar events considered for different sensors are combined. They are based on the minimum and maximum value of object events and are transferred to the sink node. Finally, the Poly Distribute algorithm effectively distributes the sensor nodes. The energy efficient routing path for each sensor nodes are created by data aggregation at the sink based on polynomial regression function which reduces the energy drain rate with minimum communication overhead. Experimental performance is evaluated using Dodgers Loop Sensor Data Set from UCI repository. Simulation results show that the proposed distribution algorithm significantly reduce the node energy drain rate and ensure fairness among different users reducing the communication overhead. PMID:26426701

  2. Bayes Node Energy Polynomial Distribution to Improve Routing in Wireless Sensor Network.

    PubMed

    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.

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

    PubMed

    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.

  4. Evaluation of more general integrals involving universal associated Legendre polynomials

    NASA Astrophysics Data System (ADS)

    You, Yuan; Chen, Chang-Yuan; Tahir, Farida; Dong, Shi-Hai

    2017-05-01

    We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. We present a popular integral formula which includes universal associated Legendre polynomials and we also evaluate some important integrals involving the product of two universal associated Legendre polynomials Pl' m'(x ) , Pk' n'(x ) and x2 a(1-x2 ) -p -1, xb(1±x2 ) -p, and xc(1-x2 ) -p(1±x ) -1, where l'≠k' and m'≠n'. Their selection rules are also mentioned.

  5. Robust stability of fractional order polynomials with complicated uncertainty structure

    PubMed Central

    Şenol, Bilal; Pekař, Libor

    2017-01-01

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

  6. On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

    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.

  7. Polynomials to model the growth of young bulls in performance tests.

    PubMed

    Scalez, D C B; Fragomeni, B O; Passafaro, T L; Pereira, I G; Toral, F L B

    2014-03-01

    The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.

  8. 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…

  9. Transfer matrix computation of critical polynomials for two-dimensional Potts models

    DOE PAGES

    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 increasingmore » 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.« less

  10. Radiographic detection of single-leg fracture in Björk-Shiley Convexo-Concave prosthetic valves: a phantom model study.

    PubMed

    Gilchrist, I C; Cardella, J F; Fox, P S; Pae, W E; el-Ghamry Sabe, A A; Landis, J R; Localio, A R; Kunselman, A R; Hopper, K D

    1997-02-01

    Cineradiography can identify patients with single-leg fractured Björk-Shiley Convexo-Concave valves, although little is known about the sensitivity and specificity of this technique. We evaluated three normal and six (0 microm gap) single-leg fractured Björk-Shiley valves that were placed in a working phantom model. Valves were randomly imaged a total of 33 times and duplicated into a 120-valve series with a 1:9 ratio of abnormal/normal valves. Six reviewers independently graded each valve and demonstrated markedly different rates of identifying the fractured valves. Average sensitivity at the grade that clinically results in valve explanation was 47%. Among the normal valves, a correct identification was made 96% (range 91% to 99%) of the time. Present radiographic technology may have significant difficulty in identifying true single-leg fracture in Björk-Shiley valves with limb separations that are common among clinically explanted valves.

  11. Polynomial chaos expansion with random and fuzzy variables

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  12. Polynomial algebra of discrete models in systems biology.

    PubMed

    Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

    2010-07-01

    An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

  13. Arabidopsis Duodecuple Mutant of PYL ABA Receptors Reveals PYL Repression of ABA-Independent SnRK2 Activity.

    PubMed

    Zhao, Yang; Zhang, Zhengjing; Gao, Jinghui; Wang, Pengcheng; Hu, Tao; Wang, Zegang; Hou, Yueh-Ju; Wan, Yizhen; Liu, Wenshan; Xie, Shaojun; Lu, Tianjiao; Xue, Liang; Liu, Yajie; Macho, Alberto P; Tao, W Andy; Bressan, Ray A; Zhu, Jian-Kang

    2018-06-12

    Abscisic acid (ABA) is an important phytohormone controlling responses to abiotic stresses and is sensed by proteins from the PYR/PYL/RCAR family. To explore the genetic contribution of PYLs toward ABA-dependent and ABA-independent processes, we generated and characterized high-order Arabidopsis mutants with mutations in the PYL family. We obtained a pyl quattuordecuple mutant and found that it was severely impaired in growth and failed to produce seeds. Thus, we carried out a detailed characterization of a pyl duodecuple mutant, pyr1pyl1/2/3/4/5/7/8/9/10/11/12. The duodecuple mutant was extremely insensitive to ABA effects on seed germination, seedling growth, stomatal closure, leaf senescence, and gene expression. The activation of SnRK2 protein kinases by ABA was blocked in the duodecuple mutant, but, unexpectedly, osmotic stress activation of SnRK2s was enhanced. Our results demonstrate an important role of basal ABA signaling in growth, senescence, and abscission and reveal that PYLs antagonize ABA-independent activation of SnRK2s by osmotic stress. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

  14. High degree interpolation polynomial in Newton form

    NASA Technical Reports Server (NTRS)

    Tal-Ezer, Hillel

    1988-01-01

    Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.

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

    NASA Astrophysics Data System (ADS)

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

    2017-10-01

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

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

    PubMed Central

    Ding, A. Adam; Wu, Hulin

    2015-01-01

    We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093

  17. Mathematics of Zernike polynomials: a review.

    PubMed

    McAlinden, Colm; McCartney, Mark; Moore, Jonathan

    2011-11-01

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

  18. Simulation of aspheric tolerance with polynomial fitting

    NASA Astrophysics Data System (ADS)

    Li, Jing; Cen, Zhaofeng; Li, Xiaotong

    2018-01-01

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

  19. Enhancing sparsity of Hermite polynomial expansions by iterative rotations

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

    Yang, Xiu; Lei, Huan; Baker, Nathan A.

    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.

  20. Adaptive-Mesh-Refinement for hyperbolic systems of conservation laws based on a posteriori stabilized high order polynomial reconstructions

    NASA Astrophysics Data System (ADS)

    Semplice, Matteo; Loubère, Raphaël

    2018-02-01

    In this paper we propose a third order accurate finite volume scheme based on a posteriori limiting of polynomial reconstructions within an Adaptive-Mesh-Refinement (AMR) simulation code for hydrodynamics equations in 2D. The a posteriori limiting is based on the detection of problematic cells on a so-called candidate solution computed at each stage of a third order Runge-Kutta scheme. Such detection may include different properties, derived from physics, such as positivity, from numerics, such as a non-oscillatory behavior, or from computer requirements such as the absence of NaN's. Troubled cell values are discarded and re-computed starting again from the previous time-step using a more dissipative scheme but only locally, close to these cells. By locally decrementing the degree of the polynomial reconstructions from 2 to 0 we switch from a third-order to a first-order accurate but more stable scheme. The entropy indicator sensor is used to refine/coarsen the mesh. This sensor is also employed in an a posteriori manner because if some refinement is needed at the end of a time step, then the current time-step is recomputed with the refined mesh, but only locally, close to the new cells. We show on a large set of numerical tests that this a posteriori limiting procedure coupled with the entropy-based AMR technology can maintain not only optimal accuracy on smooth flows but also stability on discontinuous profiles such as shock waves, contacts, interfaces, etc. Moreover numerical evidences show that this approach is at least comparable in terms of accuracy and cost to a more classical CWENO approach within the same AMR context.

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

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2003-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2013-04-01

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

  3. a Unified Matrix Polynomial Approach to Modal Identification

    NASA Astrophysics Data System (ADS)

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

    1998-04-01

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

  4. Hermite polynomials and quasi-classical asymptotics

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

    Ali, S. Twareque, E-mail: twareque.ali@concordia.ca; Engliš, Miroslav, E-mail: englis@math.cas.cz

    2014-04-15

    We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.

  5. Polynomial sequences for bond percolation critical thresholds

    DOE PAGES

    Scullard, Christian R.

    2011-09-22

    In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4, 6, 12) and (3 4, 6) using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. 03021), implemented as a branching process of lattices. I find the estimates for the bond percolation thresholds, pc(4, 6, 12) = 0.69377849... and p c(3 4, 6) = 0.43437077..., compared with Parviainen’s numerical results of p c = 0.69373383... and p c = 0.43430621... . These deviations are of the order 10 -5, as is standard for this method. Deriving thresholds in this way for a given latticemore » leads to a polynomial with integer coefficients, the root in [0, 1] of which gives the estimate for the bond threshold and I show how the method can be refined, leading to a series of higher order polynomials making predictions that likely converge to the exact answer. Finally, I discuss how this fact hints that for certain graphs, such as the kagome lattice, the exact bond threshold may not be the root of any polynomial with integer coefficients.« less

  6. The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

    PubMed

    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.

  7. Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes

    DOE PAGES

    Zlotnikov, Michael

    2016-08-24

    We develop a polynomial reduction procedure that transforms any gauge fixed CHY amplitude integrand for n scattering particles into a σ-moduli multivariate polynomial of what we call the standard form. We show that a standard form polynomial must have a specific ladder type monomial structure, which has finite size at any n, with highest multivariate degree given by (n – 3)(n – 4)/2. This set of monomials spans a complete basis for polynomials with rational coefficients in kinematic data on the support of scattering equations. Subsequently, at tree and one-loop level, we employ the global residue theorem to derive amore » prescription that evaluates any CHY amplitude by means of collecting simple residues at infinity only. Furthermore, the prescription is then applied explicitly to some tree and one-loop amplitude examples.« less

  8. Recurrence relations for orthogonal polynomials for PDEs in polar and cylindrical geometries.

    PubMed

    Richardson, Megan; Lambers, James V

    2016-01-01

    This paper introduces two families of orthogonal polynomials on the interval (-1,1), with weight function [Formula: see text]. The first family satisfies the boundary condition [Formula: see text], and the second one satisfies the boundary conditions [Formula: see text]. These boundary conditions arise naturally from PDEs defined on a disk with Dirichlet boundary conditions and the requirement of regularity in Cartesian coordinates. The families of orthogonal polynomials are obtained by orthogonalizing short linear combinations of Legendre polynomials that satisfy the same boundary conditions. Then, the three-term recurrence relations are derived. Finally, it is shown that from these recurrence relations, one can efficiently compute the corresponding recurrences for generalized Jacobi polynomials that satisfy the same boundary conditions.

  9. Using high-order polynomial basis in 3-D EM forward modeling based on volume integral equation method

    NASA Astrophysics Data System (ADS)

    Kruglyakov, Mikhail; Kuvshinov, Alexey

    2018-05-01

    3-D interpretation of electromagnetic (EM) data of different origin and scale becomes a common practice worldwide. However, 3-D EM numerical simulations (modeling)—a key part of any 3-D EM data analysis—with realistic levels of complexity, accuracy and spatial detail still remains challenging from the computational point of view. We present a novel, efficient 3-D numerical solver based on a volume integral equation (IE) method. The efficiency is achieved by using a high-order polynomial (HOP) basis instead of the zero-order (piecewise constant) basis that is invoked in all routinely used IE-based solvers. We demonstrate that usage of the HOP basis allows us to decrease substantially the number of unknowns (preserving the same accuracy), with corresponding speed increase and memory saving.

  10. Direct discriminant locality preserving projection with Hammerstein polynomial expansion.

    PubMed

    Chen, Xi; Zhang, Jiashu; Li, Defang

    2012-12-01

    Discriminant locality preserving projection (DLPP) is a linear approach that encodes discriminant information into the objective of locality preserving projection and improves its classification ability. To enhance the nonlinear description ability of DLPP, we can optimize the objective function of DLPP in reproducing kernel Hilbert space to form a kernel-based discriminant locality preserving projection (KDLPP). However, KDLPP suffers the following problems: 1) larger computational burden; 2) no explicit mapping functions in KDLPP, which results in more computational burden when projecting a new sample into the low-dimensional subspace; and 3) KDLPP cannot obtain optimal discriminant vectors, which exceedingly optimize the objective of DLPP. To overcome the weaknesses of KDLPP, in this paper, a direct discriminant locality preserving projection with Hammerstein polynomial expansion (HPDDLPP) is proposed. The proposed HPDDLPP directly implements the objective of DLPP in high-dimensional second-order Hammerstein polynomial space without matrix inverse, which extracts the optimal discriminant vectors for DLPP without larger computational burden. Compared with some other related classical methods, experimental results for face and palmprint recognition problems indicate the effectiveness of the proposed HPDDLPP.

  11. Hydrogel Film-Immobilized Lactobacillus brevis RK03 for γ-Aminobutyric Acid Production

    PubMed Central

    Hsueh, Yi-Huang; Liaw, Wen-Chang; Kuo, Jen-Min; Deng, Chi-Shin

    2017-01-01

    Hydrogels of 2-hydroxyethyl methacrylate/polyethylene glycol diacrylate (HEMA/PEGDA) have been extensively studied for their use in biomedical and pharmaceutical applications owing to their nontoxic and highly hydrophilic characteristics. Recently, cells immobilized by HEMA/PEGDA hydrogels have also been studied for enhanced production in fermentation. Hydrogel films of HEMA/PEGDA copolymer were generated by Ultraviolet (UV)-initiated photopolymerization. The hydrogel films were used to immobilize viable Lactobacillus brevis RK03 cells for the bioconversion of monosodium glutamate (MSG) to γ-aminobutyric acid (GABA). The mechanical properties and fermentation yields of the L. brevis RK03 cells immobilized on polyacrylate hydrogel films with different monomeric formulations were investigated. Fermentation was carried out in 75 mL de Man, Rogosa and Sharpe (MRS) medium containing various concentrations of MSG. We found that HEMA (93%)/PEGDA (3%) hydrogels (sample H) maximized GABA production. The conversion rate of MSG to GABA reached a maximum value of 98.4% after 240 h. Bioconversion activity gradually declined after 420 h to 83.8% after five cycles of semi-continuous fermentation. Our results suggest that HEMA (93%)/PEGDA (3%) hydrogels have great potential for use in GABA production via semi-continuous fermentation. PMID:29099794

  12. The neighbourhood polynomial of some families of dendrimers

    NASA Astrophysics Data System (ADS)

    Nazri Husin, Mohamad; Hasni, Roslan

    2018-04-01

    The neighbourhood polynomial N(G,x) is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph and it is defined as (G,x)={\\sum }U\\in N(G){x}|U|, where N(G) is neighbourhood complex of a graph, whose vertices of the graph and faces are subsets of vertices that have a common neighbour. A dendrimers is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, we compute this polynomial for some families of dendrimer.

  13. Newly developed PPAR-alpha agonist (R)-K-13675 inhibits the secretion of inflammatory markers without affecting cell proliferation or tube formation.

    PubMed

    Kitajima, Ken; Miura, Shin-Ichiro; Mastuo, Yoshino; Uehara, Yoshinari; Saku, Keijiro

    2009-03-01

    Peroxisome proliferator-activated receptor-alpha (PPAR-alpha) is a key regulator of lipid and glucose metabolism and has been implicated in inflammation. The vascular effects of activator for PPARs, particularly PPAR-alpha, on vascular cells remain to be fully elucidated. Therefore, we analyzed the hypothesis that newly developed (R)-K-13675 decreases the secretion of inflammatory markers without affecting cell proliferation or tube formation. Human coronary endothelial cells (HCECs) were maintained in different doses of (R)-K-13675 under serum starvation. After 20h, the levels of monocyte chemoattractant protein-1 (MCP-1), regulated on activation, normal T expressed and secreted (RANTES), interleukin-6 (IL-6) and interferon-gamma (INF-gamma) secreted in the medium and nuclear factor kappa B (NFkappaB) in cell lysate were analyzed using enzyme-linked immunosorbent assays (ELISA). Upon treatment with (R)-K-13675 at 0, 10, 20, 50 and 100nM, with the inflammatory markers at 0nM as 100 (arbitrary units), MCP-1 levels were significantly suppressed (94+/-9, 88+/-2, 80+/-5 and 74+/-11, respectively). RANTES, IL-6 and INF-gamma levels were also significantly suppressed (RANTES: 92+/-2, 74+/-9, 64+/-7 and 60+/-2, respectively, IL-6: 97+/-2, 89+/-10, 82+/-1 and 66+/-7, respectively, INF-gamma: 98+/-7, 94+/-3, 76+/-8 and 64+/-8, respectively). NFkappaB levels were also decreased to 91+/-5, 90+/-5, 84+/-7 and 82+/-8, respectively. In addition, (R)-K-13675 did not affect HCEC proliferation or tube formation at up to 100nM. Thus, (R)-K-13675 was associated with the inhibition of inflammatory responses without affecting cell proliferation or angiogenesis, and subsequently may induce an anti-atherosclerotic effect.

  14. Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

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

    Huan, Xun; Safta, Cosmin; Sargsyan, Khachik

    Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quanti cation analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several com- pressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers of l1 ls, SpaRSA, CGIST, FPC AS, and ADMM, we develop techniques to mitigate over tting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendationsmore » on parameter settings for these tech- niques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-cross flow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy and computational tradeoffs between polynomial bases of different degrees, and practi- cability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.« less

  15. Uncertainty Quantification in CO 2 Sequestration Using Surrogate Models from Polynomial Chaos Expansion

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

    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 amore » 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.« less

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

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

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

    2013-12-15

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

  17. 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.

  18. Generalized clustering conditions of Jack polynomials at negative Jack parameter {alpha}

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

    Bernevig, B. Andrei; Department of Physics, Princeton University, Princeton, New Jersey 08544; Haldane, F. D. M.

    We present several conjectures on the behavior and clustering properties of Jack polynomials at a negative parameter {alpha}=-(k+1/r-1), with partitions that violate the (k,r,N)- admissibility rule of [Feigin et al. [Int. Math. Res. Notices 23, 1223 (2002)]. We find that the ''highest weight'' Jack polynomials of specific partitions represent the minimum degree polynomials in N variables that vanish when s distinct clusters of k+1 particles are formed, where s and k are positive integers. Explicit counting formulas are conjectured. The generalized clustering conditions are useful in a forthcoming description of fractional quantum Hall quasiparticles.

  19. Information entropy of Gegenbauer polynomials and Gaussian quadrature

    NASA Astrophysics Data System (ADS)

    Sánchez-Ruiz, Jorge

    2003-05-01

    In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.

  20. Enhancement of radiosensitizing effect of the nitroimidazole derivative RK28 on the proliferation of MethA tumor cells in combined use with diethyldithiocarbamate

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

    Mashiba, Harukazu; Matsunaga, Keiko; Hata, Kazuo

    1991-01-01

    The radiosensitizing effect of the nitroimidazole derivative RK28 and diethyldithiocarbamate (DDC), which is an inhibitor of superoxide dismutase activity, was examined in vitro by using Meth A tumor cells. The radiosensitizing effect of 0.5 mM RK28 was observed in both of 10 Gy and 15 Gy irradiated groups. The addition of 5 {times} 10{sup {minus}7} M DDC also enhanced the radiation-induced proliferation inhibition. Marked enhancement of the anti-proliferative effect was observed in combined use of 0.2 mM or 0.5 mM RK28 with 2 {times} 10 M or 5 {times} 10{sup {minus}7} M DDC. These results suggest that enhanced oxygen effectmore » could be expected through combined use of the ionizing irradiation with both of these agents.« less

  1. 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…

  2. Fast template matching with polynomials.

    PubMed

    Omachi, Shinichiro; Omachi, Masako

    2007-08-01

    Template matching is widely used for many applications in image and signal processing. This paper proposes a novel template matching algorithm, called algebraic template matching. Given a template and an input image, algebraic template matching efficiently calculates similarities between the template and the partial images of the input image, for various widths and heights. The partial image most similar to the template image is detected from the input image for any location, width, and height. In the proposed algorithm, a polynomial that approximates the template image is used to match the input image instead of the template image. The proposed algorithm is effective especially when the width and height of the template image differ from the partial image to be matched. An algorithm using the Legendre polynomial is proposed for efficient approximation of the template image. This algorithm not only reduces computational costs, but also improves the quality of the approximated image. It is shown theoretically and experimentally that the computational cost of the proposed algorithm is much smaller than the existing methods.

  3. Low-Complexity Polynomial Channel Estimation in Large-Scale MIMO With Arbitrary Statistics

    NASA Astrophysics Data System (ADS)

    Shariati, Nafiseh; Bjornson, Emil; Bengtsson, Mats; Debbah, Merouane

    2014-10-01

    This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact that computational complexity is one of the main challenges in such systems, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced for arbitrary channel and interference statistics. While the conventional minimum mean square error (MMSE) estimator has cubic complexity in the dimension of the covariance matrices, due to an inversion operation, our proposed estimators significantly reduce this to square complexity by approximating the inverse by a L-degree matrix polynomial. The coefficients of the polynomial are optimized to minimize the mean square error (MSE) of the estimate. We show numerically that near-optimal MSEs are achieved with low polynomial degrees. We also derive the exact computational complexity of the proposed estimators, in terms of the floating-point operations (FLOPs), by which we prove that the proposed estimators outperform the conventional estimators in large-scale MIMO systems of practical dimensions while providing a reasonable MSEs. Moreover, we show that L needs not scale with the system dimensions to maintain a certain normalized MSE. By analyzing different interference scenarios, we observe that the relative MSE loss of using the low-complexity PEACH estimators is smaller in realistic scenarios with pilot contamination. On the other hand, PEACH estimators are not well suited for noise-limited scenarios with high pilot power; therefore, we also introduce the low-complexity diagonalized estimator that performs well in this regime. Finally, we ...

  4. 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.

  5. Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

    PubMed

    Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

    2016-01-01

    Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

  6. 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.

  7. On the coefficients of integrated expansions of Bessel polynomials

    NASA Astrophysics Data System (ADS)

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

    2006-03-01

    A new formula expressing explicitly the integrals of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another new explicit formula relating the Bessel coefficients of an expansion for infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is also established. An application of these formulae for solving ordinary differential equations with varying coefficients is discussed.

  8. 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.

  9. The SnRK2-APC/CTE regulatory module mediates the antagonistic action of gibberellic acid and abscisic acid pathways

    PubMed Central

    Lin, Qibing; Wu, Fuqing; Sheng, Peike; Zhang, Zhe; Zhang, Xin; Guo, Xiuping; Wang, Jiulin; Cheng, Zhijun; Wang, Jie; Wang, Haiyang; Wan, Jianmin

    2015-01-01

    Abscisic acid (ABA) and gibberellic acid (GA) antagonistically regulate many developmental processes and responses to biotic or abiotic stresses in higher plants. However, the molecular mechanism underlying this antagonism is still poorly understood. Here, we show that loss-of-function mutation in rice Tiller Enhancer (TE), an activator of the APC/CTE complex, causes hypersensitivity and hyposensitivity to ABA and GA, respectively. We find that TE physically interacts with ABA receptor OsPYL/RCARs and promotes their degradation by the proteasome. Genetic analysis also shows OsPYL/RCARs act downstream of TE in mediating ABA responses. Conversely, ABA inhibits APC/CTE activity by phosphorylating TE through activating the SNF1-related protein kinases (SnRK2s), which may interrupt the interaction between TE and OsPYL/RCARs and subsequently stabilize OsPYL/RCARs. In contrast, GA can reduce the level of SnRK2s and may promote APC/CTE-mediated degradation of OsPYL/RCARs. Thus, we propose that the SnRK2-APC/CTE regulatory module represents a regulatory hub underlying the antagonistic action of GA and ABA in plants. PMID:26272249

  10. Generating the patterns of variation with GeoGebra: the case of polynomial approximations

    NASA Astrophysics Data System (ADS)

    Attorps, Iiris; Björk, Kjell; Radic, Mirko

    2016-01-01

    In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students' learning opportunities in the study group compared with the control group.

  11. Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

    NASA Astrophysics Data System (ADS)

    Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco

    2018-05-01

    In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.

  12. An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

    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.

  13. Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

    NASA Astrophysics Data System (ADS)

    Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

    2017-08-01

    Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

  14. Design of reinforced areas of concrete column using quadratic polynomials

    NASA Astrophysics Data System (ADS)

    Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

    2017-11-01

    Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

  15. A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

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

    Vignat, C.; Lamberti, P. W.

    2009-10-15

    Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positivemore » curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.« less

  16. 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.)

  17. Polynomial approximation of the Lense-Thirring rigid precession frequency

    NASA Astrophysics Data System (ADS)

    De Falco, Vittorio; Motta, Sara

    2018-05-01

    We propose a polynomial approximation of the global Lense-Thirring rigid precession frequency to study low-frequency quasi-periodic oscillations around spinning black holes. This high-performing approximation allows to determine the expected frequencies of a precessing thick accretion disc with fixed inner radius and variable outer radius around a black hole with given mass and spin. We discuss the accuracy and the applicability regions of our polynomial approximation, showing that the computational times are reduced by a factor of ≈70 in the range of minutes.

  18. A combinatorial model for the Macdonald polynomials.

    PubMed

    Haglund, J

    2004-11-16

    We introduce a polynomial C(mu)[Z; q, t], depending on a set of variables Z = z(1), z(2),..., a partition mu, and two extra parameters q, t. The definition of C(mu) involves a pair of statistics (maj(sigma, mu), inv(sigma, mu)) on words sigma of positive integers, and the coefficients of the z(i) are manifestly in N[q,t]. We conjecture that C(mu)[Z; q, t] is none other than the modified Macdonald polynomial H(mu)[Z; q, t]. We further introduce a general family of polynomials F(T)[Z; q, S], where T is an arbitrary set of squares in the first quadrant of the xy plane, and S is an arbitrary subset of T. The coefficients of the F(T)[Z; q, S] are in N[q], and C(mu)[Z; q, t] is a sum of certain F(T)[Z; q, S] times nonnegative powers of t. We prove F(T)[Z; q, S] is symmetric in the z(i) and satisfies other properties consistent with the conjecture. We also show how the coefficient of a monomial in F(T)[Z; q, S] can be expressed recursively. maple calculations indicate the F(T)[Z; q, S] are Schur-positive, and we present a combinatorial conjecture for their Schur coefficients when the set T is a partition with at most three columns.

  19. Zernike expansion of derivatives and Laplacians of the Zernike circle polynomials.

    PubMed

    Janssen, A J E M

    2014-07-01

    The partial derivatives and Laplacians of the Zernike circle polynomials occur in various places in the literature on computational optics. In a number of cases, the expansion of these derivatives and Laplacians in the circle polynomials are required. For the first-order partial derivatives, analytic results are scattered in the literature. Results start as early as 1942 in Nijboer's thesis and continue until present day, with some emphasis on recursive computation schemes. A brief historic account of these results is given in the present paper. By choosing the unnormalized version of the circle polynomials, with exponential rather than trigonometric azimuthal dependence, and by a proper combination of the two partial derivatives, a concise form of the expressions emerges. This form is appropriate for the formulation and solution of a model wavefront sensing problem of reconstructing a wavefront on the level of its expansion coefficients from (measurements of the expansion coefficients of) the partial derivatives. It turns out that the least-squares estimation problem arising here decouples per azimuthal order m, and per m the generalized inverse solution assumes a concise analytic form so that singular value decompositions are avoided. The preferred version of the circle polynomials, with proper combination of the partial derivatives, also leads to a concise analytic result for the Zernike expansion of the Laplacian of the circle polynomials. From these expansions, the properties of the Laplacian as a mapping from the space of circle polynomials of maximal degree N, as required in the study of the Neumann problem associated with the transport-of-intensity equation, can be read off within a single glance. Furthermore, the inverse of the Laplacian on this space is shown to have a concise analytic form.

  20. Modeling of noise pollution and estimated human exposure around İstanbul Atatürk Airport in Turkey.

    PubMed

    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. © 2013.

  1. Kinetic study of Escherichia coli BPPTCC-EgRK2 to produce recombinant cellulase for ethanol production from oil palm empty fruit bunch

    NASA Astrophysics Data System (ADS)

    Limoes, S.; Rahman, S. F.; Setyahadi, S.; Gozan, M.

    2018-03-01

    Oil Palm Empty Fruit Bunch (OPEFB) is an abundant biomass resource in Indonesia, which contains 46,77% (w/w) of cellulose. The high cellulose content of OPEFB can be used as a substrate for bacteria cultivation to produce cellulase. By using OPEFB as an alternative substrate, the production cost of cellulase in industrial scale can be suppressed. However, currently there are no available research that simulate a cellulase production plant design. Prior to simulating the cellulase plant design, kinetic studies of bacteria used in cultivation are needed to create an accurate simulation. In this research, kinetic studies of E. coli BPPTCC-EgRK2 growth were examined with the Monod approach to get the Monod constant (Ks) and maximum specific growth rate (μmax). This study found that E. coli BPPTCC-EgRK2 have μmax and Ks of 1.581 and 0.0709 respectively. BPPTCC-EgRK2 produced intracellular cellulase, thus gave linear correlation between cell concentration and cellulase production.

  2. Polynomial elimination theory and non-linear stability analysis for the Euler equations

    NASA Technical Reports Server (NTRS)

    Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

    1986-01-01

    Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

  3. Trade off between variable and fixed size normalization in orthogonal polynomials based iris recognition system.

    PubMed

    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.

  4. Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

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

    Degroote, M.; Henderson, T. M.; Zhao, J.

    We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

  5. 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.

  6. Minimal Polynomial Method for Estimating Parameters of Signals Received by an Antenna Array

    NASA Astrophysics Data System (ADS)

    Ermolaev, V. T.; Flaksman, A. G.; Elokhin, A. V.; Kuptsov, V. V.

    2018-01-01

    The effectiveness of the projection minimal polynomial method for solving the problem of determining the number of sources of signals acting on an antenna array (AA) with an arbitrary configuration and their angular directions has been studied. The method proposes estimating the degree of the minimal polynomial of the correlation matrix (CM) of the input process in the AA on the basis of a statistically validated root-mean-square criterion. Special attention is paid to the case of the ultrashort sample of the input process when the number of samples is considerably smaller than the number of AA elements, which is important for multielement AAs. It is shown that the proposed method is more effective in this case than methods based on the AIC (Akaike's Information Criterion) or minimum description length (MDL) criterion.

  7. A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or 6 - j Symbols.

    DTIC Science & Technology

    1978-03-01

    Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966. [11] D. Stanton, Some basic hypergeometric polynomials arising from... Some bas ic hypergeometr ic an a logues of the classical orthogonal polynomials and applications , to appear. [3] C. de Boor and G. H. Golub , The...Report #1833 A SET OF ORTHOGONAL POLYNOMIALS THAT GENERALIZE THE RACAR COEFFICIENTS OR 6 — j SYMBOLS Richard Askey and James Wilson •

  8. 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.

  9. Functional analysis of duplicated Symbiosis Receptor Kinase (SymRK) genes during nodulation and mycorrhizal infection in soybean (Glycine max).

    PubMed

    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. Copyright © 2015 Elsevier GmbH. All rights reserved.

  10. Improved One-Way Hash Chain and Revocation Polynomial-Based Self-Healing Group Key Distribution Schemes in Resource-Constrained Wireless Networks

    PubMed Central

    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

  11. An Accurate Projector Calibration Method Based on Polynomial Distortion Representation

    PubMed Central

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

    2015-01-01

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

  12. Lifting q-difference operators for Askey-Wilson polynomials and their weight function

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

    Atakishiyeva, M. K.; Atakishiyev, N. M., E-mail: natig_atakishiyev@hotmail.com

    2011-06-15

    We determine an explicit form of a q-difference operator that transforms the continuous q-Hermite polynomials H{sub n}(x | q) of Rogers into the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q) on the top level in the Askey q-scheme. This operator represents a special convolution-type product of four one-parameter q-difference operators of the form {epsilon}{sub q}(c{sub q}D{sub q}) (where c{sub q} are some constants), defined as Exton's q-exponential function {epsilon}{sub q}(z) in terms of the Askey-Wilson divided q-difference operator D{sub q}. We also determine another q-difference operator that lifts the orthogonality weight function for the continuous q-Hermite polynomialsH{submore » n}(x | q) up to the weight function, associated with the Askey-Wilson polynomials p{sub n}(x; a, b, c, d | q).« less

  13. 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.

  14. Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

    NASA Astrophysics Data System (ADS)

    Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

    2018-05-01

    A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

  15. Intraoperative echocardiography of a dislodged Björk-Shiley mitral valve disc.

    PubMed

    Tanaka, M; Abe, T; Takeuchi, E; Watanabe, T; Tamaki, S

    1991-02-01

    The successful management of a patient who suffered an outlet strut fracture of a Björk-Shiley 60-degree convexo-concave mitral valve prosthesis is reported. Emergency operation was life-saving. Preoperative echocardiography assisted in making a prompt diagnosis, and intraoperative echocardiography allowed the detection and removal of the dislodged disc from the left ventricle at the time of the operation. The role of intraoperative echocardiography in the diagnosis of prosthetic strut fracture is emphasized.

  16. New realisation of Preisach model using adaptive polynomial approximation

    NASA Astrophysics Data System (ADS)

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

    2012-09-01

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

  17. Kostant polynomials and the cohomology ring for G/B

    PubMed Central

    Billey, Sara C.

    1997-01-01

    The Schubert calculus for G/B can be completely determined by a certain matrix related to the Kostant polynomials introduced in section 5 of Bernstein, Gelfand, and Gelfand [Bernstein, I., Gelfand, I. & Gelfand, S. (1973) Russ. Math. Surv. 28, 1–26]. The polynomials are defined by vanishing properties on the orbit of a regular point under the action of the Weyl group. For each element w in the Weyl group the polynomials also have nonzero values on the orbit points corresponding to elements which are larger in the Bruhat order than w. The main theorem given here is an explicit formula for these values. The matrix of orbit values can be used to determine the cup product for the cohomology ring for G/B, using only linear algebra or as described by Lascoux and Schützenberger [Lascoux, A. & Schützenberger, M.-P. (1982) C. R. Seances Acad. Sci. Ser. A 294, 447–450]. Complete proofs of all the theorems will appear in a forthcoming paper. PMID:11038536

  18. Matrix of moments of the Legendre polynomials and its application to problems of electrostatics

    NASA Astrophysics Data System (ADS)

    Savchenko, A. O.

    2017-01-01

    In this work, properties of the matrix of moments of the Legendre polynomials are presented and proven. In particular, the explicit form of the elements of the matrix inverse to the matrix of moments is found and theorems of the linear combination and orthogonality are proven. On the basis of these properties, the total charge and the dipole moment of a conducting ball in a nonuniform electric field, the charge distribution over the surface of the conducting ball, its multipole moments, and the force acting on a conducting ball situated on the axis of a nonuniform axisymmetric electric field are determined. All assertions are formulated in theorems, the proofs of which are based on the properties of the matrix of moments of the Legendre polynomials.

  19. Rate-distortion optimized tree-structured compression algorithms for piecewise polynomial images.

    PubMed

    Shukla, Rahul; Dragotti, Pier Luigi; Do, Minh N; Vetterli, Martin

    2005-03-01

    This paper presents novel coding algorithms based on tree-structured segmentation, which achieve the correct asymptotic rate-distortion (R-D) behavior for a simple class of signals, known as piecewise polynomials, by using an R-D based prune and join scheme. For the one-dimensional case, our scheme is based on binary-tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly to achieve the correct exponentially decaying R-D behavior (D(R) - c(o)2(-c1R)), thus improving over classic wavelet schemes. We also prove that the computational complexity of the scheme is of O(N log N). We then show the extension of this scheme to the two-dimensional case using a quadtree. This quadtree-coding scheme also achieves an exponentially decaying R-D behavior, for the polygonal image model composed of a white polygon-shaped object against a uniform black background, with low computational cost of O(N log N). Again, the key is an R-D optimized prune and join strategy. Finally, we conclude with numerical results, which show that the proposed quadtree-coding scheme outperforms JPEG2000 by about 1 dB for real images, like cameraman, at low rates of around 0.15 bpp.

  20. 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).

  1. Characterization of a Potential Probiotic Lactobacillus brevis RK03 and Efficient Production of γ-Aminobutyric Acid in Batch Fermentation.

    PubMed

    Wu, Chien-Hui; Hsueh, Yi-Huang; Kuo, Jen-Min; Liu, Si-Jia

    2018-01-04

    Lactic acid bacteria were isolated from fish and evaluated for their γ-aminobutyric acid (GABA)-producing abilities. Out of thirty-two isolates, Lactobacillus brevis RK03 showed the highest GABA production ability. The effects of various fermentation parameters including initial glutamic acid level, culture temperature, initial pH, and incubation time on GABA production were investigated via a singleparameter optimization strategy. For industrial large-scale production, a low-cost GABA producing medium (GM) broth was developed for fermentation with L. brevis RK03. We found that an optimized GM broth recipe of 1% glucose; 2.5% yeast extract; 2 ppm each of CaCO₃, MnSO₄, and Tween 80; and 10 μM pyridoxal phosphate (PLP) resulted in a maximum GABA yield of 62,523 mg/L after 88 h following the addition of 650 mM monosodium glutamate (MSG), for a conversion rate of 93.28%. Our data provide a practical approach for the highly efficient and economic production of GABA. In addition, L. brevis RK03 is highly resistant to gastric acid and bovine bile salt. Thus, the discovery of Lactobacillus strains with the ability to synthesize GABA may offer new opportunities in the design of improved health-promoting functional foods.

  2. Characterization of a Potential Probiotic Lactobacillus brevis RK03 and Efficient Production of γ-Aminobutyric Acid in Batch Fermentation

    PubMed Central

    Hsueh, Yi-Huang; Kuo, Jen-Min; Liu, Si-Jia

    2018-01-01

    Lactic acid bacteria were isolated from fish and evaluated for their γ-aminobutyric acid (GABA)-producing abilities. Out of thirty-two isolates, Lactobacillus brevis RK03 showed the highest GABA production ability. The effects of various fermentation parameters including initial glutamic acid level, culture temperature, initial pH, and incubation time on GABA production were investigated via a singleparameter optimization strategy. For industrial large-scale production, a low-cost GABA producing medium (GM) broth was developed for fermentation with L. brevis RK03. We found that an optimized GM broth recipe of 1% glucose; 2.5% yeast extract; 2 ppm each of CaCO3, MnSO4, and Tween 80; and 10 μM pyridoxal phosphate (PLP) resulted in a maximum GABA yield of 62,523 mg/L after 88 h following the addition of 650 mM monosodium glutamate (MSG), for a conversion rate of 93.28%. Our data provide a practical approach for the highly efficient and economic production of GABA. In addition, L. brevis RK03 is highly resistant to gastric acid and bovine bile salt. Thus, the discovery of Lactobacillus strains with the ability to synthesize GABA may offer new opportunities in the design of improved health-promoting functional foods. PMID:29300336

  3. Interpolation Hermite Polynomials For Finite Element Method

    NASA Astrophysics Data System (ADS)

    Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

    2018-02-01

    We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

  4. New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

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

    Marquette, Ian; Quesne, Christiane

    2013-04-15

    In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequencesmore » of EOP.« less

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

    PubMed

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

    2014-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2004-01-01

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

  7. Antimicrobial profile of Arthrobacter kerguelensis VL-RK_09 isolated from Mango orchards.

    PubMed

    Munaganti, Rajesh Kumar; Muvva, Vijayalakshmi; Konda, Saidulu; Naragani, Krishna; Mangamuri, Usha Kiranmayi; Dorigondla, Kumar Reddy; Akkewar, Dattatray M

    An actinobacterial strain VL-RK_09 having potential antimicrobial activities was isolated from a mango orchard in Krishna District, Andhra Pradesh (India) and was identified as Arthrobacter kerguelensis. The strain A. kerguelensis VL-RK_09 exhibited a broad spectrum of in vitro antimicrobial activity against bacteria and fungi. Production of bioactive metabolites by the strain was the highest in modified yeast extract malt extract dextrose broth, as compared to other media tested. Lactose (1%) and peptone (0.5%) were found to be the most suitable carbon and nitrogen sources, respectively, for the optimum production of the bioactive metabolites. The maximum production of the bioactive metabolites was detected in the culture medium with an initial pH of 7, in which the strain was incubated for five days at 30°C under shaking conditions. Screening of secondary metabolites obtained from the culture broth led to the isolation of a compound active against a wide variety of Gram-positive and negative bacteria and fungi. The structure of the first active fraction was elucidated using Fourier transform infrared spectroscopy, electrospray ionization mass spectrometry, 1 H and 13 C nuclear magnetic resonance spectroscopy. The compound was identified as S,S-dipropyl carbonodithioate. This study is the first report of the occurrence of this compound in the genus Arthrobacter. Copyright © 2016 Sociedade Brasileira de Microbiologia. Published by Elsevier Editora Ltda. All rights reserved.

  8. Colored knot polynomials for arbitrary pretzel knots and links

    DOE PAGES

    Galakhov, D.; Melnikov, D.; Mironov, A.; ...

    2015-04-01

    A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)-parametric family of pretzel knots and links. The answer for the Jones and HOMFLY is fully and explicitly expressed through the Racah matrix of Uq(SU N), and looks related to a modular transformation of toric conformal block. Knot polynomials are among the hottest topics in modern theory. They are supposed to summarize nicely representation theory of quantum algebras and modular properties of conformal blocks. The result reported in the present letter, provides a spectacular illustration and support to this general expectation.

  9. Two-component system VicRK regulates functions associated with establishment of Streptococcus sanguinis in biofilms.

    PubMed

    Moraes, Julianna J; Stipp, Rafael N; Harth-Chu, Erika N; Camargo, Tarsila M; Höfling, José F; Mattos-Graner, Renata O

    2014-12-01

    Streptococcus sanguinis is a commensal pioneer colonizer of teeth and an opportunistic pathogen of infectious endocarditis. The establishment of S. sanguinis in host sites likely requires dynamic fitting of the cell wall in response to local stimuli. In this study, we investigated the two-component system (TCS) VicRK in S. sanguinis (VicRKSs), which regulates genes of cell wall biogenesis, biofilm formation, and virulence in opportunistic pathogens. A vicK knockout mutant obtained from strain SK36 (SKvic) showed slight reductions in aerobic growth and resistance to oxidative stress but an impaired ability to form biofilms, a phenotype restored in the complemented mutant. The biofilm-defective phenotype was associated with reduced amounts of extracellular DNA during aerobic growth, with reduced production of H2O2, a metabolic product associated with DNA release, and with inhibitory capacity of S. sanguinis competitor species. No changes in autolysis or cell surface hydrophobicity were detected in SKvic. Reverse transcription-quantitative PCR (RT-qPCR), electrophoretic mobility shift assays (EMSA), and promoter sequence analyses revealed that VicR directly regulates genes encoding murein hydrolases (SSA_0094, cwdP, and gbpB) and spxB, which encodes pyruvate oxidase for H2O2 production. Genes previously associated with spxB expression (spxR, ccpA, ackA, and tpK) were not transcriptionally affected in SKvic. RT-qPCR analyses of S. sanguinis biofilm cells further showed upregulation of VicRK targets (spxB, gbpB, and SSA_0094) and other genes for biofilm formation (gtfP and comE) compared to expression in planktonic cells. This study provides evidence that VicRKSs regulates functions crucial for S. sanguinis establishment in biofilms and identifies novel VicRK targets potentially involved in hydrolytic activities of the cell wall required for these functions. Copyright © 2014, American Society for Microbiology. All Rights Reserved.

  10. Two-Component System VicRK Regulates Functions Associated with Establishment of Streptococcus sanguinis in Biofilms

    PubMed Central

    Moraes, Julianna J.; Stipp, Rafael N.; Harth-Chu, Erika N.; Camargo, Tarsila M.; Höfling, José F.

    2014-01-01

    Streptococcus sanguinis is a commensal pioneer colonizer of teeth and an opportunistic pathogen of infectious endocarditis. The establishment of S. sanguinis in host sites likely requires dynamic fitting of the cell wall in response to local stimuli. In this study, we investigated the two-component system (TCS) VicRK in S. sanguinis (VicRKSs), which regulates genes of cell wall biogenesis, biofilm formation, and virulence in opportunistic pathogens. A vicK knockout mutant obtained from strain SK36 (SKvic) showed slight reductions in aerobic growth and resistance to oxidative stress but an impaired ability to form biofilms, a phenotype restored in the complemented mutant. The biofilm-defective phenotype was associated with reduced amounts of extracellular DNA during aerobic growth, with reduced production of H2O2, a metabolic product associated with DNA release, and with inhibitory capacity of S. sanguinis competitor species. No changes in autolysis or cell surface hydrophobicity were detected in SKvic. Reverse transcription-quantitative PCR (RT-qPCR), electrophoretic mobility shift assays (EMSA), and promoter sequence analyses revealed that VicR directly regulates genes encoding murein hydrolases (SSA_0094, cwdP, and gbpB) and spxB, which encodes pyruvate oxidase for H2O2 production. Genes previously associated with spxB expression (spxR, ccpA, ackA, and tpK) were not transcriptionally affected in SKvic. RT-qPCR analyses of S. sanguinis biofilm cells further showed upregulation of VicRK targets (spxB, gbpB, and SSA_0094) and other genes for biofilm formation (gtfP and comE) compared to expression in planktonic cells. This study provides evidence that VicRKSs regulates functions crucial for S. sanguinis establishment in biofilms and identifies novel VicRK targets potentially involved in hydrolytic activities of the cell wall required for these functions. PMID:25183732

  11. 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…

  12. Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

    PubMed Central

    Chen, Andrew; Chen, Chiachung

    2013-01-01

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

  13. Digital SAR processing using a fast polynomial transform

    NASA Technical Reports Server (NTRS)

    Butman, S.; Lipes, R.; Rubin, A.; Truong, T. K.

    1981-01-01

    A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network.

  14. Quadratic polynomial interpolation on triangular domain

    NASA Astrophysics Data System (ADS)

    Li, Ying; Zhang, Congcong; Yu, Qian

    2018-04-01

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

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

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

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

    2014-02-15

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

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

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

    Karagiannis, Georgios; Lin, Guang

    2014-02-15

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

  17. Minimizing Higgs potentials via numerical polynomial homotopy continuation

    NASA Astrophysics Data System (ADS)

    Maniatis, M.; Mehta, D.

    2012-08-01

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

  18. Pan Sharpening Quality Investigation of Turkish In-Operation Remote Sensing Satellites: Applications with Rasat and GÖKTÜRK-2 Images

    NASA Astrophysics Data System (ADS)

    Ozendi, Mustafa; Topan, Hüseyin; Cam, Ali; Bayık, Çağlar

    2016-10-01

    Recently two optical remote sensing satellites, RASAT and GÖKTÜRK-2, launched successfully by the Republic of Turkey. RASAT has 7.5 m panchromatic, and 15 m visible bands whereas GÖKTÜRK-2 has 2.5 m panchromatic and 5 m VNIR (Visible and Near Infrared) bands. These bands with various resolutions can be fused by pan-sharpening methods which is an important application area of optical remote sensing imagery. So that, the high geometric resolution of panchromatic band and the high spectral resolution of VNIR bands can be merged. In the literature there are many pan-sharpening methods. However, there is not a standard framework for quality investigation of pan-sharpened imagery. The aim of this study is to investigate pan-sharpening performance of RASAT and GÖKTÜRK-2 images. For this purpose, pan-sharpened images are generated using most popular pan-sharpening methods IHS, Brovey and PCA at first. This procedure is followed by quantitative evaluation of pan-sharpened images using Correlation Coefficient (CC), Root Mean Square Error (RMSE), Relative Average Spectral Error (RASE), Spectral Angle Mapper (SAM) and Erreur Relative Globale Adimensionnelle de Synthése (ERGAS) metrics. For generation of pan-sharpened images and computation of metrics SharpQ tool is used which is developed with MATLAB computing language. According to metrics, PCA derived pan-sharpened image is the most similar one to multispectral image for RASAT, and Brovey derived pan-sharpened image is the most similar one to multispectral image for GÖKTÜRK-2. Finally, pan-sharpened images are evaluated qualitatively in terms of object availability and completeness for various land covers (such as urban, forest and flat areas) by a group of operators who are experienced in remote sensing imagery.

  19. 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

  20. On method of solving third-order ordinary differential equations directly using Bernstein polynomials

    NASA Astrophysics Data System (ADS)

    Khataybeh, S. N.; Hashim, I.

    2018-04-01

    In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

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

    NASA Astrophysics Data System (ADS)

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

    2004-08-01

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

  2. Polynomial chaos representation of databases on manifolds

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

    Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

    2017-04-15

    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. Themore » 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.« less

  3. 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.

  4. Image distortion analysis using polynomial series expansion.

    PubMed

    Baggenstoss, Paul M

    2004-11-01

    In this paper, we derive a technique for analysis of local distortions which affect data in real-world applications. In the paper, we focus on image data, specifically handwritten characters. Given a reference image and a distorted copy of it, the method is able to efficiently determine the rotations, translations, scaling, and any other distortions that have been applied. Because the method is robust, it is also able to estimate distortions for two unrelated images, thus determining the distortions that would be required to cause the two images to resemble each other. The approach is based on a polynomial series expansion using matrix powers of linear transformation matrices. The technique has applications in pattern recognition in the presence of distortions.

  5. [Late outlet strut fracture of an aortic Björk-Shiley and embolization of the prosthetic disc].

    PubMed

    Brochet, E; Bougis de Brux, M A; Assayag, P; Benacin, Y; Gamerman, G; Guerot, C; Valère, P E

    1988-09-01

    A new case of late fracture of an outlet strut in a convexo-concave Björk-Shiley valve is reported. The fracture occurred 6 years after aortic implantation of the valve and was responsible for aorto-iliac embolization by the prosthetic disc and death of the patient from cardiogenic shock. This not uncommon complication of the Björk-Shiley valve prosthesis is usually ascribed to the relative fragility of its outlet strut welded to the metallic ring and subjected to strong pressures. Although most cases were observed within the first two years of prosthetic valve insertion, and mainly with valves manufactured in 1981 and 1982, our case and a few others demonstrate the possibility of late rupture. Cardiologists must be aware of this possible complication, since in some favourable cases it can be diagnosed at an early stage and the patient's life can be saved by an emergency operation.

  6. Some Curious Properties and Loci Problems Associated with Cubics and Other Polynomials

    ERIC Educational Resources Information Center

    de Alwis, Amal

    2012-01-01

    The article begins with a well-known property regarding tangent lines to a cubic polynomial that has distinct, real zeros. We were then able to generalize this property to any polynomial with distinct, real zeros. We also considered a certain family of cubics with two fixed zeros and one variable zero, and explored the loci of centroids of…

  7. Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

    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.

  8. Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils.

    PubMed

    Mahajan, Virendra N

    2010-12-20

    The classical aberrations of an anamorphic optical imaging system, representing the terms of a power-series expansion of its aberration function, are separable in the Cartesian coordinates of a point on its pupil. We discuss the balancing of a classical aberration of a certain order with one or more such aberrations of lower order to minimize its variance across a rectangular pupil of such a system. We show that the balanced aberrations are the products of two Legendre polynomials, one for each of the two Cartesian coordinates of the pupil point. The compound Legendre polynomials are orthogonal across a rectangular pupil and, like the classical aberrations, are inherently separable in the Cartesian coordinates of the pupil point. They are different from the balanced aberrations and the corresponding orthogonal polynomials for a system with rotational symmetry but a rectangular pupil.

  9. Derivatives of random matrix characteristic polynomials with applications to elliptic curves

    NASA Astrophysics Data System (ADS)

    Snaith, N. C.

    2005-12-01

    The value distribution of derivatives of characteristic polynomials of matrices from SO(N) is calculated at the point 1, the symmetry point on the unit circle of the eigenvalues of these matrices. We consider subsets of matrices from SO(N) that are constrained to have at least n eigenvalues equal to 1 and investigate the first non-zero derivative of the characteristic polynomial at that point. The connection between the values of random matrix characteristic polynomials and values of L-functions in families has been well established. The motivation for this work is the expectation that through this connection with L-functions derived from families of elliptic curves, and using the Birch and Swinnerton-Dyer conjecture to relate values of the L-functions to the rank of elliptic curves, random matrix theory will be useful in probing important questions concerning these ranks.

  10. Fitting by Orthonormal Polynomials of Silver Nanoparticles Spectroscopic Data

    NASA Astrophysics Data System (ADS)

    Bogdanova, Nina; Koleva, Mihaela

    2018-02-01

    Our original Orthonormal Polynomial Expansion Method (OPEM) in one-dimensional version is applied for first time to describe the silver nanoparticles (NPs) spectroscopic data. The weights for approximation include experimental errors in variables. In this way we construct orthonormal polynomial expansion for approximating the curve on a non equidistant point grid. The corridors of given data and criteria define the optimal behavior of searched curve. The most important subinterval of spectra data is investigated, where the minimum (surface plasmon resonance absorption) is looking for. This study describes the Ag nanoparticles produced by laser approach in a ZnO medium forming a AgNPs/ZnO nanocomposite heterostructure.

  11. The polynomial form of the scattering equations is an H -basis

    NASA Astrophysics Data System (ADS)

    Bosma, Jorrit; Søgaard, Mads; Zhang, Yang

    2016-08-01

    We prove that the polynomial form of the scattering equations is a Macaulay H -basis. We demonstrate that this H -basis facilitates integrand reduction and global residue computations in a way very similar to using a Gröbner basis, but circumvents the heavy computation of the latter. As an example, we apply the H -basis to prove the conjecture that the dual basis of the polynomial scattering equations must contain one constant term.

  12. Measuring the levels of noise at the İstanbul Atatürk Airport and comparisons with model simulations.

    PubMed

    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. Crown Copyright © 2013. All rights reserved.

  13. Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

    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.

  14. Optimal approximation of harmonic growth clusters by orthogonal polynomials

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

    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.

  15. Source/sink interactions underpin crop yield: the case for trehalose 6-phosphate/SnRK1 in improvement of wheat

    PubMed Central

    Lawlor, David W.; Paul, Matthew J.

    2014-01-01

    Considerable interest has been evoked by the analysis of the regulatory pathway in carbohydrate metabolism and cell growth involving the non-reducing disaccharide trehalose (TRE). TRE is at small concentrations in mesophytes such as Arabidopsis thaliana and Triticum aestivum, excluding a role in osmoregulation once suggested for it. Studies of TRE metabolism, and genetic modification of it, have shown a very wide and more important role of the pathway in regulation of many processes in development, growth, and photosynthesis. It has now been established that rather than TRE, it is trehalose 6-phosphate (T6P) which has such profound effects. T6P is the intermediary in TRE synthesis formed from glucose-6-phosphate and UDP-glucose, derived from sucrose, by the action of trehalose phosphate synthase. The concentration of T6P is determined both by the rate of synthesis, which depends on the sucrose concentration, and also by the rate of breakdown by trehalose-6-phosphate phosphatase which produces TRE. Changing T6P concentrations by genetically modifying the enzymes of synthesis and breakdown has altered photosynthesis, sugar metabolism, growth, and development which affect responses to, and recovery from, environmental factors. Many of the effects of T6P on metabolism and growth occur via the interaction of T6P with the SnRK1 protein kinase system. T6P inhibits the activity of SnRK1, which de-represses genes encoding proteins involved in anabolism. Consequently, a large concentration of sucrose increases T6P and thereby inhibits SnRK1, so stimulating growth of cells and their metabolic activity. The T6P/SnRK1 mechanism offers an important new view of how the distribution of assimilates to organs, such as developing grains in cereal plants, is achieved. This review briefly summarizes the factors determining, and limiting, yield of wheat (particularly mass/grain which is highly conserved) and considers how T6P/SnRK1 might function to determine grain yield and might be

  16. A general method for computing Tutte polynomials of self-similar graphs

    NASA Astrophysics Data System (ADS)

    Gong, Helin; Jin, Xian'an

    2017-10-01

    Self-similar graphs were widely studied in both combinatorics and statistical physics. Motivated by the construction of the well-known 3-dimensional Sierpiński gasket graphs, in this paper we introduce a family of recursively constructed self-similar graphs whose inner duals are of the self-similar property. By combining the dual property of the Tutte polynomial and the subgraph-decomposition trick, we show that the Tutte polynomial of this family of graphs can be computed in an iterative way and in particular the exact expression of the formula of the number of their spanning trees is derived. Furthermore, we show our method is a general one that is easily extended to compute Tutte polynomials for other families of self-similar graphs such as Farey graphs, 2-dimensional Sierpiński gasket graphs, Hanoi graphs, modified Koch graphs, Apollonian graphs, pseudofractal scale-free web, fractal scale-free network, etc.

  17. Explicit bounds for the positive root of classes of polynomials with applications

    NASA Astrophysics Data System (ADS)

    Herzberger, Jürgen

    2003-03-01

    We consider a certain type of polynomial equations for which there exists--according to Descartes' rule of signs--only one simple positive root. These equations are occurring in Numerical Analysis when calculating or estimating the R-order or Q-order of convergence of certain iterative processes with an error-recursion of special form. On the other hand, these polynomial equations are very common as defining equations for the effective rate of return for certain cashflows like bonds or annuities in finance. The effective rate of interest i* for those cashflows is i*=q*-1, where q* is the unique positive root of such polynomial. We construct bounds for i* for a special problem concerning an ordinary simple annuity which is obtained by changing the conditions of such an annuity with given data applying the German rule (Preisangabeverordnung or short PAngV). Moreover, we consider a number of results for such polynomial roots in Numerical Analysis showing that by a simple variable transformation we can derive several formulas out of earlier results by applying this transformation. The same is possible in finance in order to generalize results to more complicated cashflows.

  18. Equations on knot polynomials and 3d/5d duality

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

    Mironov, A.; Morozov, A.; ITEP, Moscow

    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. Themore » 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.« less

  19. 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.

  20. Elective removal of convexo-concave Björk-Shiley valves.

    PubMed

    Rajesh, P B; Smith, G H; Lawford, P V; Black, M M

    1994-08-01

    Replacement has been an accepted method for treating advanced cardiac valvular disease for more than 25 years. However, the perfect prosthesis has yet to be developed, judging by the number of devices available. A prosthesis that initially appears promising may cause problems in due course, and indeed some devices have been modified or withdrawn from clinical use. A notable example of a prosthetic valve that has give problems is the Björk-Shiley convexo-concave prosthesis, some models of which have undergone mechanical failure due to strut fracture. We report the elective removal of such a valve and the subsequent examination of the prosthesis. The results of this examination suggest that a policy of elective removal is justified.

  1. Digital SAR processing using a fast polynomial transform

    NASA Technical Reports Server (NTRS)

    Truong, T. K.; Lipes, R. G.; Butman, S. A.; Reed, I. S.; Rubin, A. L.

    1984-01-01

    A new digital processing algorithm based on the fast polynomial transform is developed for producing images from Synthetic Aperture Radar data. This algorithm enables the computation of the two dimensional cyclic correlation of the raw echo data with the impulse response of a point target, thereby reducing distortions inherent in one dimensional transforms. This SAR processing technique was evaluated on a general-purpose computer and an actual Seasat SAR image was produced. However, regular production runs will require a dedicated facility. It is expected that such a new SAR processing algorithm could provide the basis for a real-time SAR correlator implementation in the Deep Space Network. Previously announced in STAR as N82-11295

  2. A polynomial chaos expansion based molecular dynamics study for probabilistic strength analysis of nano-twinned copper

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2017-03-01

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

  4. Strut fracture and disc embolization of a Björk-Shiley mitral valve prosthesis: localization of embolized disc by computerized axial tomography.

    PubMed

    Larrieu, A J; Puglia, E; Allen, P

    1982-08-01

    The case of a patient who survived strut fracture and embolization of a Björk-Shiley mitral prosthetic disc is presented. Prompt surgical treatment was directly responsible for survival. In addition, computerized axial tomography of the abdomen aided in localizing and retrieving the embolized disc, which was lodged at the origin of the superior mesenteric artery. A review of similar case reports from the literature supports our conclusions that the development of acute heart failure and absent or muffled prosthetic heart sounds in a patient with a Björk-Shiley prosthetic heart valve inserted prior to 1978 should raise the possibility of valve dysfunction and lead to early reoperation.

  5. 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)

  6. New graph polynomials in parametric QED Feynman integrals

    NASA Astrophysics Data System (ADS)

    Golz, Marcel

    2017-10-01

    In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by the fact that their parametric integrand is much larger and more involved. It is, moreover, only implicitly given as the result of certain differential operators applied to the scalar integrand exp(-ΦΓ /ΨΓ) , where ΨΓ and ΦΓ are the Kirchhoff and Symanzik polynomials of the Feynman graph Γ. In the case of quantum electrodynamics we find that the full parametric integrand inherits a rich combinatorial structure from ΨΓ and ΦΓ. In the end, it can be expressed explicitly as a sum over products of new types of graph polynomials which have a combinatoric interpretation via simple cycle subgraphs of Γ.

  7. Parameterized LMI Based Diagonal Dominance Compensator Study for Polynomial Linear Parameter Varying System

    NASA Astrophysics Data System (ADS)

    Han, Xiaobao; Li, Huacong; Jia, Qiusheng

    2017-12-01

    For dynamic decoupling of polynomial linear parameter varying(PLPV) system, a robust dominance pre-compensator design method is given. The parameterized precompensator design problem is converted into an optimal problem constrained with parameterized linear matrix inequalities(PLMI) by using the conception of parameterized Lyapunov function(PLF). To solve the PLMI constrained optimal problem, the precompensator design problem is reduced into a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a new constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator is achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation on a turbofan engine PLPV model.

  8. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems

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

    Li, Jun; Jiang, Bin; Guo, Hua, E-mail: hguo@unm.edu

    2013-11-28

    A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resultingmore » in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.« less

  9. Dynamic Harmony Search with Polynomial Mutation Algorithm for Valve-Point Economic Load Dispatch

    PubMed Central

    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

  10. Dynamic Harmony Search with Polynomial Mutation Algorithm for Valve-Point Economic Load Dispatch.

    PubMed

    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.

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

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

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

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

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

    DOE PAGES

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

    2017-06-22

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

  13. Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

    PubMed Central

    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

  14. Air Pollution Caused By Aircrafts in LTO-number-Record Breaking Year 2016 at Istanbul Atatürk Airport

    NASA Astrophysics Data System (ADS)

    Sen, Orhan; Durmus, Onur

    2017-04-01

    2016 was a record breaking year in terms of LTO numbers at Istanbul Atatürk Airport. The days with maximum LTO (Landing- Take-off) numbers coincides with the beginning or end of national festival days. In this study, air pollutant (HC, NOx, CO, SO2) quantities that are released as a result of LTO activities taking place at Atatürk Airport in 10-months-period of the year 2016 when LTO numbers reached peak point and emission quantities resulting from aircrafts on the days when maximum LTO numbers happened on a daily basis have been calculated with Tier 2 method. In Tier 2 method emission less than 935m (3000ft) of atmosphere during LTO activities related to airplane type without making domestic or international distinction and free from landing/ take-off point play an important role. This approach is used in calculating emissions that are being released to the atmosphere during LTO activities which have a maximum effect on air pollution by taking into account the fuel consumption of each airplane type and with the help of determined emission coefficients. As a result of the calculations between 01.01.2016 and 25.10.2016 at Istanbul Atatürk Airport, 186.986 LTO cycle took place by passenger and cargo aircrafts. And 209.984 tones fuel were consumed. As a result of this fuel consumption 187,2 tones hydrocarbon (HC), 3263,9 tones nitrogen oxide (NOx), 1626,5 tones carbon monoxide (CO) and 210 tones sulphur dioxide (SO2) emission were released as air pollutants. Keyword: LTO, Air pollution, Aircraft

  15. Pre-Service Social Studies Teachers' Viewpoints about Atatürk as Founding and Transformational Leader

    ERIC Educational Resources Information Center

    Dönmez, Cengiz; Uslu, Salih; Hamarat, Ercenk

    2017-01-01

    The aim of the current study is to identify the opinions of pre-service social studies teachers about Atatürk as a founding and transformational leader. The sample of the study comprises 180 pre-service teachers in the social studies teaching department of an education faculty in a public university. The data have been collected through an…

  16. 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.

  17. On Using Homogeneous Polynomials To Design Anisotropic Yield Functions With Tension/Compression Symmetry/Assymetry

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

    Soare, S.; Cazacu, O.; Yoon, J. W.

    With few exceptions, non-quadratic homogeneous polynomials have received little attention as possible candidates for yield functions. One reason might be that not every such polynomial is a convex function. In this paper we show that homogeneous polynomials can be used to develop powerful anisotropic yield criteria, and that imposing simple constraints on the identification process leads, aposteriori, to the desired convexity property. It is shown that combinations of such polynomials allow for modeling yielding properties of metallic materials with any crystal structure, i.e. both cubic and hexagonal which display strength differential effects. Extensions of the proposed criteria to 3D stressmore » states are also presented. We apply these criteria to the description of the aluminum alloy AA2090T3. We prove that a sixth order orthotropic homogeneous polynomial is capable of a satisfactory description of this alloy. Next, applications to the deep drawing of a cylindrical cup are presented. The newly proposed criteria were implemented as UMAT subroutines into the commercial FE code ABAQUS. We were able to predict six ears on the AA2090T3 cup's profile. Finally, we show that a tension/compression asymmetry in yielding can have an important effect on the earing profile.« less

  18. On Using Homogeneous Polynomials To Design Anisotropic Yield Functions With Tension/Compression Symmetry/Assymetry

    NASA Astrophysics Data System (ADS)

    Soare, S.; Yoon, J. W.; Cazacu, O.

    2007-05-01

    With few exceptions, non-quadratic homogeneous polynomials have received little attention as possible candidates for yield functions. One reason might be that not every such polynomial is a convex function. In this paper we show that homogeneous polynomials can be used to develop powerful anisotropic yield criteria, and that imposing simple constraints on the identification process leads, aposteriori, to the desired convexity property. It is shown that combinations of such polynomials allow for modeling yielding properties of metallic materials with any crystal structure, i.e. both cubic and hexagonal which display strength differential effects. Extensions of the proposed criteria to 3D stress states are also presented. We apply these criteria to the description of the aluminum alloy AA2090T3. We prove that a sixth order orthotropic homogeneous polynomial is capable of a satisfactory description of this alloy. Next, applications to the deep drawing of a cylindrical cup are presented. The newly proposed criteria were implemented as UMAT subroutines into the commercial FE code ABAQUS. We were able to predict six ears on the AA2090T3 cup's profile. Finally, we show that a tension/compression asymmetry in yielding can have an important effect on the earing profile.

  19. Modeling Source Water TOC Using Hydroclimate Variables and Local Polynomial Regression.

    PubMed

    Samson, Carleigh C; Rajagopalan, Balaji; Summers, R Scott

    2016-04-19

    To control disinfection byproduct (DBP) formation in drinking water, an understanding of the source water total organic carbon (TOC) concentration variability can be critical. Previously, TOC concentrations in water treatment plant source waters have been modeled using streamflow data. However, the lack of streamflow data or unimpaired flow scenarios makes it difficult to model TOC. In addition, TOC variability under climate change further exacerbates the problem. Here we proposed a modeling approach based on local polynomial regression that uses climate, e.g. temperature, and land surface, e.g., soil moisture, variables as predictors of TOC concentration, obviating the need for streamflow. The local polynomial approach has the ability to capture non-Gaussian and nonlinear features that might be present in the relationships. The utility of the methodology is demonstrated using source water quality and climate data in three case study locations with surface source waters including river and reservoir sources. The models show good predictive skill in general at these locations, with lower skills at locations with the most anthropogenic influences in their streams. Source water TOC predictive models can provide water treatment utilities important information for making treatment decisions for DBP regulation compliance under future climate scenarios.

  20. Optimization of L(+)-Lactic Acid Fermentation Without Neutralisation of Rhizopus Oryzae Mutant RK02 by Low-Energy Ion Implantation

    NASA Astrophysics Data System (ADS)

    Li, Wen; Wang, Tao; Yang, Yingge; Liu, Dan; Fan, Yonghong; Wang, Dongmei; Yang, Qian; Yao, Jianming; Zheng, Zhiming; Yu, Zengliang

    2008-04-01

    In order to get an industrial strain which can yield a high concentration of lactic acid for ISPR (in situ product removal), the original strain Rhizopus oryzae RE3303 was mutated by low-energy ion beam implantation. A mutant RK02 was screened, and the factors such as the substrate concentration, nitrogen source concentration, inoculum size, seed age, aeration and temperature that affect the production of lactic acid were studied in detail. Under optimal conditions, the maximum concentration of L(+)-lactic acid reached 34.85 g/L after 30 h shake-flask cultivation without adding any neutralisation (5% Glucose added), which was a 146% increase in lactic acid production after ion implantation compared with the original strain. It was also shown that RK02 can be used in ISPR to reduce the number of times of separation.

  1. A Polynomial-Based Nonlinear Least Squares Optimized Preconditioner for Continuous and Discontinuous Element-Based Discretizations of the Euler Equations

    DTIC Science & Technology

    2014-01-01

    system (here using left- preconditioning ) (KÃ)x = Kb̃, (3.1) where K is a low-order polynomial in à given by K = s(Ã) = m∑ i=0 kià i, (3.2) and has a... system with a complex spectrum, region E in the complex plane must be some convex form (e.g., an ellipse or polygon) that approximately encloses the...preconditioners with p = 2 and p = 20 on the spectrum of the preconditioned system matrices Kà and KH̃ for both CG Schur-complement form and DG form cases

  2. New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae

    NASA Astrophysics Data System (ADS)

    Abd-Elhameed, W. M.

    2017-07-01

    In this paper, a new formula relating Jacobi polynomials of arbitrary parameters with the squares of certain fractional Jacobi functions is derived. The derived formula is expressed in terms of a certain terminating hypergeometric function of the type _4F3(1) . With the aid of some standard reduction formulae such as Pfaff-Saalschütz's and Watson's identities, the derived formula can be reduced in simple forms which are free of any hypergeometric functions for certain choices of the involved parameters of the Jacobi polynomials and the Jacobi functions. Some other simplified formulae are obtained via employing some computer algebra algorithms such as the algorithms of Zeilberger, Petkovsek and van Hoeij. Some connection formulae between some Jacobi polynomials are deduced. From these connection formulae, some other linearization formulae of Chebyshev polynomials are obtained. As an application to some of the introduced formulae, a numerical algorithm for solving nonlinear Riccati differential equation is presented and implemented by applying a suitable spectral method.

  3. Correlations of RMT characteristic polynomials and integrability: Hermitean matrices

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

    Osipov, Vladimir Al., E-mail: Vladimir.Osipov@uni-due.d; Kanzieper, Eugene, E-mail: Eugene.Kanzieper@hit.ac.i; Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100

    Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of {tau} functions, we (i) identify a zoo of hierarchical relations satisfied by {tau} functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasismore » is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.« less

  4. Scattering amplitudes from multivariate polynomial division

    NASA Astrophysics Data System (ADS)

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

    2012-11-01

    We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.

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

    PubMed Central

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

    2014-01-01

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

  6. Polynomial complexity despite the fermionic sign

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-06-01

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

  8. Optimization of Cubic Polynomial Functions without Calculus

    ERIC Educational Resources Information Center

    Taylor, Ronald D., Jr.; Hansen, Ryan

    2008-01-01

    In algebra and precalculus courses, students are often asked to find extreme values of polynomial functions in the context of solving an applied problem; but without the notion of derivative, something is lost. Either the functions are reduced to quadratics, since students know the formula for the vertex of a parabola, or solutions are…

  9. The hit problem for symmetric polynomials over the Steenrod algebra

    NASA Astrophysics Data System (ADS)

    Janfada, A. S.; Wood, R. M. W.

    2002-09-01

    We cite [18] for references to work on the hit problem for the polynomial algebra P(n) = [open face F]2[x1, ;…, xn] = [oplus B: plus sign in circle]d[gt-or-equal, slanted]0 Pd(n), viewed as a graded left module over the Steenrod algebra [script A] at the prime 2. The grading is by the homogeneous polynomials Pd(n) of degree d in the n variables x1, …, xn of grading 1. The present article investigates the hit problem for the [script A]-submodule of symmetric polynomials B(n) = P(n)[sum L: summation operator]n , where [sum L: summation operator]n denotes the symmetric group on n letters acting on the right of P(n). Among the main results is the symmetric version of the well-known Peterson conjecture. For a positive integer d, let [mu](d) denote the smallest value of k for which d = [sum L: summation operator]ki=1(2[lambda]i[minus sign]1), where [lambda]i [gt-or-equal, slanted] 0.

  10. A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

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

    Shao, Yan-Lin, E-mail: yanlin.shao@dnvgl.com; 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,more » 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.« less

  11. Protective effect of ginsenosides Rk3 and Rh4 on cisplatin-induced acute kidney injury in vitro and in vivo.

    PubMed

    Baek, Seung-Hoon; Shin, Byong-Kyu; Kim, Nam Jae; Chang, Sun-Young; Park, Jeong Hill

    2017-07-01

    Nephrotoxicity is the major side effect in cisplatin chemotherapy. Previously, we reported that the ginsenosides Rk3 and Rh4 reduced cisplatin toxicity on porcine renal proximal epithelial tubular cells (LLC-PK1). Here, we aimed to evaluate the protective effect of ginsenosides Rk3 and Rh4 on kidney function and elucidate their antioxidant effect using in vitro and in vivo models of cisplatin-induced acute renal failure. An enriched mixture of ginsenosides Rk3 and Rh4 (KG-KH; 49.3% and 43.1%, respectively) was purified from sun ginseng (heat processed Panax ginseng ). Cytotoxicity was induced by treatment of 20μM cisplatin to LLC-PK1 cells and rat model of acute renal failure was generated by single intraperitoneal injection of 5 mg/kg cisplatin. Protective effects were assessed by determining cell viability, reactive oxygen species generation, blood urea nitrogen, serum creatinine, antioxidant enzyme activity, and histopathological examination. The in vitro assay demonstrated that KG-KH (50 μg/mL) significantly increased cell viability (4.6-fold), superoxide dismutase activity (2.8-fold), and glutathione reductase activity (1.5-fold), but reduced reactive oxygen species generation (56%) compared to cisplatin control cells. KG-KH (6 mg/kg, per os ) also significantly inhibited renal edema (87% kidney index) and dysfunction (71.4% blood urea nitrogen, 67.4% creatinine) compared to cisplatin control rats. Of note, KG-KH significantly recovered the kidney levels of catalase (1.2-fold) and superoxide dismutase (1.5-fold). Considering the oxidative injury as an early trigger of cisplatin nephrotoxicity, our findings suggest that ginsenosides Rk3 and Rh4 protect the kidney from cisplatin-induced oxidative injury and help to recover renal function by restoring intrinsic antioxidant defenses.

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

    NASA Astrophysics Data System (ADS)

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

    2018-02-01

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

  13. Polynomial stability of a magneto-thermoelastic Mindlin-Timoshenko plate model

    NASA Astrophysics Data System (ADS)

    Ferreira, Marcio V.; Muñoz Rivera, Jaime E.

    2018-02-01

    In this paper, we consider the magneto-thermoelastic interactions in a two-dimensional Mindlin-Timoshenko plate. Our main result is concerned with the strong asymptotic stabilization of the model. In particular, we determine the rate of polynomial decay of the associated energy. In contrast with what was observed in other related articles, geometrical hypotheses on the plate configuration (such as radial symmetry) are not imposed in this study nor any kind of frictional damping mechanism. A suitable multiplier is instrumental in establishing the polynomial stability with the aid of a recent result due to Borichev and Tomilov (Math Ann 347(2):455-478, 2010).

  14. Introduction to Real Orthogonal Polynomials

    DTIC Science & Technology

    1992-06-01

    uses Green’s functions. As motivation , consider the Dirichlet problem for the unit circle in the plane, which involves finding a harmonic function u(r...xv ; a, b ; q) - TO [q-N ab+’q ; q, xq b. Orthogoy RMotion O0 (bq :q)x p.(q* ; a, b ; q) pg(q’ ; a, b ; q) (q "q), (aq)x (q ; q), (I -abq) (bq ; q... motivation and justi- fication for continued study of the intrinsic structure of orthogonal polynomials. 99 LIST OF REFERENCES 1. Deyer, W. M., ed., CRC

  15. SU-E-T-614: Derivation of Equations to Define Inflection Points and Its Analysis in Flattening Filter Free Photon Beams Based On the Principle of Polynomial function

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

    Muralidhar, K Raja; Komanduri, K

    2014-06-01

    Purpose: The objective of this work is to present a mechanism for calculating inflection points on profiles at various depths and field sizes and also a significant study on the percentage of doses at the inflection points for various field sizes and depths for 6XFFF and 10XFFF energy profiles. Methods: Graphical representation was done on Percentage of dose versus Inflection points. Also using the polynomial function, the authors formulated equations for calculating spot-on inflection point on the profiles for 6X FFF and 10X FFF energies for all field sizes and at various depths. Results: In a flattening filter free radiationmore » beam which is not like in Flattened beams, the dose at inflection point of the profile decreases as field size increases for 10XFFF. Whereas in 6XFFF, the dose at the inflection point initially increases up to 10x10cm2 and then decreases. The polynomial function was fitted for both FFF beams for all field sizes and depths. For small fields less than 5x5 cm2 the inflection point and FWHM are almost same and hence analysis can be done just like in FF beams. A change in 10% of dose can change the field width by 1mm. Conclusion: The present study, Derivative of equations based on the polynomial equation to define inflection point concept is precise and accurate way to derive the inflection point dose on any FFF beam profile at any depth with less than 1% accuracy. Corrections can be done in future studies based on the multiple number of machine data. Also a brief study was done to evaluate the inflection point positions with respect to dose in FFF energies for various field sizes and depths for 6XFFF and 10XFFF energy profiles.« less

  16. Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

    NASA Astrophysics Data System (ADS)

    Grobbelaar-Van Dalsen, Marié

    2015-02-01

    In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

  17. Advanced Stochastic Collocation Methods for Polynomial Chaos in RAVEN

    NASA Astrophysics Data System (ADS)

    Talbot, Paul W.

    As experiment complexity in fields such as nuclear engineering continually increases, so does the demand for robust computational methods to simulate them. In many simulations, input design parameters and intrinsic experiment properties are sources of uncertainty. Often small perturbations in uncertain parameters have significant impact on the experiment outcome. For instance, in nuclear fuel performance, small changes in fuel thermal conductivity can greatly affect maximum stress on the surrounding cladding. The difficulty quantifying input uncertainty impact in such systems has grown with the complexity of numerical models. Traditionally, uncertainty quantification has been approached using random sampling methods like Monte Carlo. For some models, the input parametric space and corresponding response output space is sufficiently explored with few low-cost calculations. For other models, it is computationally costly to obtain good understanding of the output space. To combat the expense of random sampling, this research explores the possibilities of using advanced methods in Stochastic Collocation for generalized Polynomial Chaos (SCgPC) as an alternative to traditional uncertainty quantification techniques such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) methods for applications in nuclear engineering. We consider traditional SCgPC construction strategies as well as truncated polynomial spaces using Total Degree and Hyperbolic Cross constructions. We also consider applying anisotropy (unequal treatment of different dimensions) to the polynomial space, and offer methods whereby optimal levels of anisotropy can be approximated. We contribute development to existing adaptive polynomial construction strategies. Finally, we consider High-Dimensional Model Reduction (HDMR) expansions, using SCgPC representations for the subspace terms, and contribute new adaptive methods to construct them. We apply these methods on a series of models of increasing

  18. Björk-Shiley strut fracture and disc escape: literature review and a method of disc retrieval.

    PubMed

    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.

  19. The Julia sets of basic uniCremer polynomials of arbitrary degree

    NASA Astrophysics Data System (ADS)

    Blokh, Alexander; Oversteegen, Lex

    Let P be a polynomial of degree d with a Cremer point p and no repelling or parabolic periodic bi-accessible points. We show that there are two types of such Julia sets J_P . The red dwarf J_P are nowhere connected im kleinen and such that the intersection of all impressions of external angles is a continuum containing p and the orbits of all critical images. The solar J_P are such that every angle with dense orbit has a degenerate impression disjoint from other impressions and J_P is connected im kleinen at its landing point. We study bi-accessible points and locally connected models of J_P and show that such sets J_P appear through polynomial-like maps for generic polynomials with Cremer points. Since known tools break down for d>2 (if d>2 , it is not known if there are small cycles near p , while if d=2 , this result is due to Yoccoz), we introduce wandering ray continua in J_P and provide a new application of Thurston laminations.

  20. An Exactly Solvable Spin Chain Related to Hahn Polynomials

    NASA Astrophysics Data System (ADS)

    Stoilova, Neli I.; van der Jeugt, Joris

    2011-03-01

    We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, it is shown that the single fermion eigenstates of the Hamiltonian can be computed in explicit form. The components of these eigenvectors turn out to be Hahn polynomials with parameters (α,β) and (α+1,β-1). The construction of the eigenvectors relies on two new difference equations for Hahn polynomials. The explicit knowledge of the eigenstates leads to a closed form expression for the correlation function of the spin chain. We also discuss some aspects of a q-extension of this model.

  1. The role of Tre6P and SnRK1 in maize early kernel development and events leading to stress-induced kernel abortion.

    PubMed

    Bledsoe, Samuel W; Henry, Clémence; Griffiths, Cara A; Paul, Matthew J; Feil, Regina; Lunn, John E; Stitt, Mark; Lagrimini, L Mark

    2017-04-12

    Drought stress during flowering is a major contributor to yield loss in maize. Genetic and biotechnological improvement in yield sustainability requires an understanding of the mechanisms underpinning yield loss. Sucrose starvation has been proposed as the cause for kernel abortion; however, potential targets for genetic improvement have not been identified. Field and greenhouse drought studies with maize are expensive and it can be difficult to reproduce results; therefore, an in vitro kernel culture method is presented as a proxy for drought stress occurring at the time of flowering in maize (3 days after pollination). This method is used to focus on the effects of drought on kernel metabolism, and the role of trehalose 6-phosphate (Tre6P) and the sucrose non-fermenting-1-related kinase (SnRK1) as potential regulators of this response. A precipitous drop in Tre6P is observed during the first two hours after removing the kernels from the plant, and the resulting changes in transcript abundance are indicative of an activation of SnRK1, and an immediate shift from anabolism to catabolism. Once Tre6P levels are depleted to below 1 nmol∙g -1 FW in the kernel, SnRK1 remained active throughout the 96 h experiment, regardless of the presence or absence of sucrose in the medium. Recovery on sucrose enriched medium results in the restoration of sucrose synthesis and glycolysis. Biosynthetic processes including the citric acid cycle and protein and starch synthesis are inhibited by excision, and do not recover even after the re-addition of sucrose. It is also observed that excision induces the transcription of the sugar transporters SUT1 and SWEET1, the sucrose hydrolyzing enzymes CELL WALL INVERTASE 2 (INCW2) and SUCROSE SYNTHASE 1 (SUSY1), the class II TREHALOSE PHOSPHATE SYNTHASES (TPS), TREHALASE (TRE), and TREHALOSE PHOSPHATE PHOSPHATASE (ZmTPPA.3), previously shown to enhance drought tolerance (Nuccio et al., Nat Biotechnol (October 2014):1-13, 2015). The impact

  2. Supersymmetric quantum mechanics: Engineered hierarchies of integrable potentials and related orthogonal polynomials

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

    Balondo Iyela, Daddy; Centre for Cosmology, Particle Physics and Phenomenology; Département de Physique, Université de Kinshasa

    2013-09-15

    Within the context of supersymmetric quantum mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy which should allow for its resolution. Specific classes of orthogonal polynomials characteristicmore » of such periodic hierarchies are thereby generated, while the methods of supersymmetric quantum mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper, these ideas are presented and solved explicitly for the cases N= 1 and N= 2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. In the context of dressing chains and deformed polynomial Heisenberg algebras, some partial results for N⩾ 3 also exist in the literature, which should be relevant to a complete study of the N⩾ 3 general periodic hierarchies.« less

  3. 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…

  4. Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere

    NASA Astrophysics Data System (ADS)

    Miller, W., Jr.; Li, Q.

    2015-04-01

    The Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere, HΨ = EΨ, with generic 3-parameter potential. Clearly, the polynomials are expansion coefficients for one eigenbasis of a symmetry operator L2 of H in terms of an eigenbasis of another symmetry operator L1, but the exact relationship appears not to have been made explicit. We work out the details of the expansion to show, explicitly, how the polynomials arise and how the principal properties of these functions: the measure, 3-term recurrence relation, 2nd order difference equation, duality of these relations, permutation symmetry, intertwining operators and an alternate derivation of Wilson functions - follow from the symmetry of this quantum system. This paper is an exercise to show that quantum mechancal concepts and recurrence relations for Gausian hypergeometrc functions alone suffice to explain these properties; we make no assumptions about the structure of Wilson polynomial/functions, but derive them from quantum principles. There is active interest in the relation between multivariable Wilson polynomials and the quantum superintegrable system on the n-sphere with generic potential, and these results should aid in the generalization. Contracting function space realizations of irreducible representations of this quadratic algebra to the other superintegrable systems one can obtain the full Askey scheme of orthogonal hypergeometric polynomials. All of these contractions of superintegrable systems with potential are uniquely induced by Wigner Lie algebra contractions of so(3, C) and e(2,C). All of the polynomials produced are interpretable as quantum expansion coefficients. It is important to extend this process to higher dimensions.

  5. A solver for General Unilateral Polynomial Matrix Equation with Second-Order Matrices Over Prime Finite Fields

    NASA Astrophysics Data System (ADS)

    Burtyka, Filipp

    2018-03-01

    The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.

  6. Growth Arrest by Trehalose-6-Phosphate: An Astonishing Case of Primary Metabolite Control over Growth by Way of the SnRK1 Signaling Pathway1[C][W][OA

    PubMed Central

    Delatte, Thierry L.; Sedijani, Prapti; Kondou, Youichi; Matsui, Minami; de Jong, Gerhardus J.; Somsen, Govert W.; Wiese-Klinkenberg, Anika; Primavesi, Lucia F.; Paul, Matthew J.; Schluepmann, Henriette

    2011-01-01

    The strong regulation of plant carbon allocation and growth by trehalose metabolism is important for our understanding of the mechanisms that determine growth and yield, with obvious applications in crop improvement. To gain further insight on the growth arrest by trehalose feeding, we first established that starch-deficient seedlings of the plastidic phosphoglucomutase1 mutant were similarly affected as the wild type on trehalose. Starch accumulation in the source cotyledons, therefore, did not cause starvation and consequent growth arrest in the growing zones. We then screened the FOX collection of Arabidopsis (Arabidopsis thaliana) expressing full-length cDNAs for seedling resistance to 100 mm trehalose. Three independent transgenic lines were identified with dominant segregation of the trehalose resistance trait that overexpress the bZIP11 (for basic region/leucine zipper motif) transcription factor. The resistance of these lines to trehalose could not be explained simply through enhanced trehalase activity or through inhibition of bZIP11 translation. Instead, trehalose-6-phosphate (T6P) accumulation was much increased in bZIP11-overexpressing lines, suggesting that these lines may be insensitive to the effects of T6P. T6P is known to inhibit the central stress-integrating kinase SnRK1 (KIN10) activity. We confirmed that this holds true in extracts from seedlings grown on trehalose, then showed that two independent transgenic lines overexpressing KIN10 were insensitive to trehalose. Moreover, the expression of marker genes known to be jointly controlled by SnRK1 activity and bZIP11 was consistent with low SnRK1 or bZIP11 activity in seedlings on trehalose. These results reveal an astonishing case of primary metabolite control over growth by way of the SnRK1 signaling pathway involving T6P, SnRK1, and bZIP11. PMID:21753116

  7. Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?

    NASA Astrophysics Data System (ADS)

    Anokhina, A.; Morozov, A.

    2018-04-01

    R-coloured knot polynomials for m-strand torus knots Torus [ m, n] are described by the Rosso-Jones formula, which is an example of evolution in n with Lyapunov exponents, labelled by Young diagrams from R ⊗ m . This means that they satisfy a finite-difference equation (recursion) of finite degree. For the gauge group SL( N ) only diagrams with no more than N lines can contribute and the recursion degree is reduced. We claim that these properties (evolution/recursion and reduction) persist for Khovanov-Rozansky (KR) polynomials, obtained by additional factorization modulo 1 + t, which is not yet adequately described in quantum field theory. Also preserved is some weakened version of differential expansion, which is responsible at least for a simple relation between reduced and unreduced Khovanov polynomials. However, in the KR case evolution is incompatible with the mirror symmetry under the change n -→ - n, what can signal about an ambiguity in the KR factorization even for torus knots.

  8. On Partial Fraction Decompositions by Repeated Polynomial Divisions

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2017-01-01

    We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

  9. 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.

  10. The two-component system VicRK regulates functions associated with Streptococcus mutans resistance to complement immunity.

    PubMed

    Alves, Livia A; Harth-Chu, Erika N; Palma, Thais H; Stipp, Rafael N; Mariano, Flávia S; Höfling, José F; Abranches, Jacqueline; Mattos-Graner, Renata O

    2017-10-01

    Streptococcus mutans, a dental caries pathogen, can promote systemic infections upon reaching the bloodstream. The two-component system (TCS) VicRK Sm of S. mutans regulates the synthesis of and interaction with sucrose-derived exopolysaccharides (EPS), processes associated with oral and systemic virulence. In this study, we investigated the mechanisms by which VicRK Sm affects S. mutans susceptibility to blood-mediated immunity. Compared with parent strain UA159, the vicK Sm isogenic mutant (UAvic) showed reduced susceptibility to deposition of C3b of complement, low binding to serum immunoglobulin G (IgG), and low frequency of C3b/IgG-mediated opsonophagocytosis by polymorphonuclear cells in a sucrose-independent way (P<.05). Reverse transcriptase quantitative polymerase chain reaction analysis comparing gene expression in UA159 and UAvic revealed that genes encoding putative peptidases of the complement (pepO and smu.399) were upregulated in UAvic in the presence of serum, although genes encoding murein hydrolases (SmaA and Smu.2146c) or metabolic/surface proteins involved in bacterial interactions with host components (enolase, GAPDH) were mostly affected in a serum-independent way. Among vicK Sm -downstream genes (smaA, smu.2146c, lysM, atlA, pepO, smu.399), only pepO and smu.399 were associated with UAvic phenotypes; deletion of both genes in UA159 significantly enhanced levels of C3b deposition and opsonophagocytosis (P<.05). Moreover, consistent with the fibronectin-binding function of PepO orthologues, UAvic showed increased binding to fibronectin. Reduced susceptibility to opsonophagocytosis was insufficient to enhance ex vivo persistence of UAvic in blood, which was associated with growth defects of this mutant under limited nutrient conditions. Our findings revealed that S. mutans employs mechanisms of complement evasion through peptidases, which are controlled by VicRK Sm. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

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

    NASA Astrophysics Data System (ADS)

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

    2018-01-01

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

  12. Application of the Polynomial-Based Least Squares and Total Least Squares Models for the Attenuated Total Reflection Fourier Transform Infrared Spectra of Binary Mixtures of Hydroxyl Compounds.

    PubMed

    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. © The Author(s) 2016.

  13. Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

    NASA Technical Reports Server (NTRS)

    Johnson, Duane

    1996-01-01

    Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

  14. Killings, duality and characteristic polynomials

    NASA Astrophysics Data System (ADS)

    Álvarez, Enrique; Borlaf, Javier; León, José H.

    1998-03-01

    In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the characteristic classes) can be explicitly computed for the dual model in terms of quantities pertaining to the original one and with the help of the canonical connection whose intrinsic characterization is given. Using our formalism the physically, and T-duality invariant, relevant result that top forms are zero when there is an isometry without fixed points is easily proved. © 1998

  15. Preliminary plant design of Escherichia coli BPPTCC-EgRK2 cell culture for recombinant cellulase production using Oil Palm Empty Fruit Bunch (OPEFB) as substrate

    NASA Astrophysics Data System (ADS)

    Surya, E. A.; Rahman, S. F.; Zulamraini, S.; Gozan, M.

    2018-03-01

    An economic analysis of recombinant cellulase production from E. coli BPPTCC Eg-RK2 was conducted to support the fulfilling of Indonesia’s energy roadmap for ethanol production. The plant use oil palm empty fruit bunch (OPEFB) as primary substrate in cellulase production, with the expected lifetime of 12 years. The plant is assumed to be built in Indonesia and will fulfill 1% of total market demand. The effect of different pretreatment process (alkaline, steam explosion, and sequential acid-alkaline) on the economic value was also studied. A simulation using SuperPro Designer was used to calculate the mass and energy balance based on the kinetic parameter of E. coli BPPTCC-EgRK2. Technology evaluation show that alkaline pretreatment gave the highest yield with no known inhibitors formed. The steam explosion show the lowest lignin and hemicellulose removal and known to form known fermentation inhibitors. The net present value of alkaline, steam explosion, and sequential acid-alkaline pretreatment were USD 7,118,000; - USD 73,411,000 and USD -114,013,000 respectively, which mean alkaline pretreatment is the only economically feasible pretreatment method for recombinant cellulase production.

  16. 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.

  17. Cubic Polynomials, Their Roots and the Perron-Frobenius Theorem

    ERIC Educational Resources Information Center

    Dealba, Luz Maria

    2002-01-01

    In this note several cubic polynomials and their roots are examined, in particular, how these roots move as some of the coefficients are modified. The results obtained are applied to eigenvalues of matrices. (Contains 8 figures and 1 footnote.)

  18. Quantized vortices in the ideal bose gas: a physical realization of random polynomials.

    PubMed

    Castin, Yvan; Hadzibabic, Zoran; Stock, Sabine; Dalibard, Jean; Stringari, Sandro

    2006-02-03

    We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.

  19. A major QTL corresponding to the Rk locus for resistance to root-knot nematodes in cowpea (Vigna unguiculata L. Walp.).

    PubMed

    Huynh, Bao-Lam; Matthews, William C; Ehlers, Jeffrey D; Lucas, Mitchell R; Santos, Jansen R P; Ndeve, Arsenio; Close, Timothy J; Roberts, Philip A

    2016-01-01

    Genome resolution of a major QTL associated with the Rk locus in cowpea for resistance to root-knot nematodes has significance for plant breeding programs and R gene characterization. Cowpea (Vigna unguiculata L. Walp.) is a susceptible host of root-knot nematodes (Meloidogyne spp.) (RKN), major plant-parasitic pests in global agriculture. To date, breeding for host resistance in cowpea has relied on phenotypic selection which requires time-consuming and expensive controlled infection assays. To facilitate marker-based selection, we aimed to identify and map quantitative trait loci (QTL) conferring the resistance trait. One recombinant inbred line (RIL) and two F2:3 populations, each derived from a cross between a susceptible and a resistant parent, were genotyped with genome-wide single nucleotide polymorphism (SNP) markers. The populations were screened in the field for root-galling symptoms and/or under growth-chamber conditions for nematode reproduction levels using M. incognita and M. javanica biotypes. One major QTL was mapped consistently on linkage group VuLG11 of each population. By genotyping additional cowpea lines and near-isogenic lines derived from conventional backcrossing, we confirmed that the detected QTL co-localized with the genome region associated with the Rk locus for RKN resistance that has been used in conventional breeding for many decades. This chromosomal location defined with flanking markers will be a valuable target in marker-assisted breeding and for positional cloning of genes controlling RKN resistance.

  20. On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations

    NASA Astrophysics Data System (ADS)

    Doha, E. H.

    2002-02-01

    An analytical formula expressing the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function is stated in a more compact form and proved in a simpler way than the formula suggested by Phillips and Karageorghis (27 (1990) 823). A new formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is given. The tensor product of ultraspherical polynomials is used to approximate a function of more than one variable. Formulae expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are described.

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

    NASA Astrophysics Data System (ADS)

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

    2017-02-01

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

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

    PubMed

    Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

    2015-10-16

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

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

    PubMed Central

    Li, Jing; Mahmoodi, Alireza; Joseph, Dileepan

    2015-01-01

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

  4. On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

    NASA Technical Reports Server (NTRS)

    Freund, Roland

    1988-01-01

    Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

  5. A comparison of polynomial approximations and artificial neural nets as response surfaces

    NASA Technical Reports Server (NTRS)

    Carpenter, William C.; Barthelemy, Jean-Francois M.

    1992-01-01

    Artificial neural nets and polynomial approximations were used to develop response surfaces for several test problems. Based on the number of functional evaluations required to build the approximations and the number of undetermined parameters associated with the approximations, the performance of the two types of approximations was found to be comparable. A rule of thumb is developed for determining the number of nodes to be used on a hidden layer of an artificial neural net, and the number of designs needed to train an approximation is discussed.

  6. Solving the Rational Polynomial Coefficients Based on L Curve

    NASA Astrophysics Data System (ADS)

    Zhou, G.; Li, X.; Yue, T.; Huang, W.; He, C.; Huang, Y.

    2018-05-01

    The rational polynomial coefficients (RPC) model is a generalized sensor model, which can achieve high approximation accuracy. And it is widely used in the field of photogrammetry and remote sensing. Least square method is usually used to determine the optimal parameter solution of the rational function model. However the distribution of control points is not uniform or the model is over-parameterized, which leads to the singularity of the coefficient matrix of the normal equation. So the normal equation becomes ill conditioned equation. The obtained solutions are extremely unstable and even wrong. The Tikhonov regularization can effectively improve and solve the ill conditioned equation. In this paper, we calculate pathological equations by regularization method, and determine the regularization parameters by L curve. The results of the experiments on aerial format photos show that the accuracy of the first-order RPC with the equal denominators has the highest accuracy. The high order RPC model is not necessary in the processing of dealing with frame images, as the RPC model and the projective model are almost the same. The result shows that the first-order RPC model is basically consistent with the strict sensor model of photogrammetry. Orthorectification results both the firstorder RPC model and Camera Model (ERDAS9.2 platform) are similar to each other, and the maximum residuals of X and Y are 0.8174 feet and 0.9272 feet respectively. This result shows that RPC model can be used in the aerial photographic compensation replacement sensor model.

  7. Explicit analytical expression for the condition number of polynomials in power form

    NASA Astrophysics Data System (ADS)

    Rack, Heinz-Joachim

    2017-07-01

    In his influential papers [1-3] W. Gautschi has defined and reshaped the condition number κ∞ of polynomials Pn of degree ≤ n which are represented in power form on a zero-symmetric interval [-ω, ω]. Basically, κ∞ is expressed as the product of two operator norms: an explicit factor times an implicit one (the l∞-norm of the coefficient vector of the n-th Chebyshev polynomial of the first kind relative to [-ω, ω]). We provide a new proof, economize the second factor and express it by an explicit analytical formula.

  8. Causality and a -theorem constraints on Ricci polynomial and Riemann cubic gravities

    NASA Astrophysics Data System (ADS)

    Li, Yue-Zhou; Lü, H.; Wu, Jun-Bao

    2018-01-01

    In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost-free, exhibiting an a -theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost-free and a -theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities.

  9. The sensitivity of catchment hypsometry and hypsometric properties to DEM resolution and polynomial order

    NASA Astrophysics Data System (ADS)

    Liffner, Joel W.; Hewa, Guna A.; Peel, Murray C.

    2018-05-01

    Derivation of the hypsometric curve of a catchment, and properties relating to that curve, requires both use of topographical data (commonly in the form of a Digital Elevation Model - DEM), and the estimation of a functional representation of that curve. An early investigation into catchment hypsometry concluded 3rd order polynomials sufficiently describe the hypsometric curve, without the consideration of higher order polynomials, or the sensitivity of hypsometric properties relating to the curve. Another study concluded the hypsometric integral (HI) is robust against changes in DEM resolution, a conclusion drawn from a very limited sample size. Conclusions from these earlier studies have resulted in the adoption of methods deemed to be "sufficient" in subsequent studies, in addition to assumptions that the robustness of the HI extends to other hypsometric properties. This study investigates and demonstrates the sensitivity of hypsometric properties to DEM resolution, DEM type and polynomial order through assessing differences in hypsometric properties derived from 417 catchments and sub-catchments within South Australia. The sensitivity of hypsometric properties across DEM types and polynomial orders is found to be significant, which suggests careful consideration of the methods chosen to derive catchment hypsometric information is required.

  10. 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.

  11. Filtrations on Springer fiber cohomology and Kostka polynomials

    NASA Astrophysics Data System (ADS)

    Bellamy, Gwyn; Schedler, Travis

    2018-03-01

    We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. In particular, this computes the grading on the zeroth Poisson homology of all classical finite W-algebras, as well as the filtration on the zeroth Hochschild homology of all quantum finite W-algebras, and we generalize to all homology degrees. As a consequence, we deduce a conjecture of Proudfoot on symplectic duality, relating in type A the Poisson homology of Slodowy slices to the intersection cohomology of nilpotent orbit closures. In the last section, we give an analogue of our main theorem in the setting of mirabolic D-modules.

  12. 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.

  13. Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

    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.

  14. Quadratic Polynomial Regression using Serial Observation Processing:Implementation within DART

    NASA Astrophysics Data System (ADS)

    Hodyss, D.; Anderson, J. L.; Collins, N.; Campbell, W. F.; Reinecke, P. A.

    2017-12-01

    Many Ensemble-Based Kalman ltering (EBKF) algorithms process the observations serially. Serial observation processing views the data assimilation process as an iterative sequence of scalar update equations. What is useful about this data assimilation algorithm is that it has very low memory requirements and does not need complex methods to perform the typical high-dimensional inverse calculation of many other algorithms. Recently, the push has been towards the prediction, and therefore the assimilation of observations, for regions and phenomena for which high-resolution is required and/or highly nonlinear physical processes are operating. For these situations, a basic hypothesis is that the use of the EBKF is sub-optimal and performance gains could be achieved by accounting for aspects of the non-Gaussianty. To this end, we develop here a new component of the Data Assimilation Research Testbed [DART] to allow for a wide-variety of users to test this hypothesis. This new version of DART allows one to run several variants of the EBKF as well as several variants of the quadratic polynomial lter using the same forecast model and observations. Dierences between the results of the two systems will then highlight the degree of non-Gaussianity in the system being examined. We will illustrate in this work the differences between the performance of linear versus quadratic polynomial regression in a hierarchy of models from Lorenz-63 to a simple general circulation model.

  15. Non-polynomial extensions of solvable potentials à la Abraham-Moses

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

    Odake, Satoru; Sasaki, Ryu; Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan

    2013-10-15

    Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Pöschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to themore » Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations.« less

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

    NASA Astrophysics Data System (ADS)

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

    2015-06-01

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

  17. 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.

  18. Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

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

    Lu, Fei; Department of Mathematics, University of California, Berkeley; Morzfeld, Matthias, E-mail: mmo@math.lbl.gov

    2015-02-01

    Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

  19. Successful treatment of a patient after sudden loss of the disc in a Björk-Shiley convexo-concave mitral prosthesis.

    PubMed

    Scalia, D; Giacomin, A; Da Col, U; Valfre, C

    1987-10-01

    The patient's survival after minor strut fracture and migration of a Björk-Shiley mitral prosthetic disc is presented. The operation was carried out in two stages: first emergency replacement of the mitral prosthesis and, later, elective removal of the dislocated disc.

  20. Polynomial-time algorithms for building a consensus MUL-tree.

    PubMed

    Cui, Yun; Jansson, Jesper; Sung, Wing-Kin

    2012-09-01

    A multi-labeled phylogenetic tree, or MUL-tree, is a generalization of a phylogenetic tree that allows each leaf label to be used many times. MUL-trees have applications in biogeography, the study of host-parasite cospeciation, gene evolution studies, and computer science. Here, we consider the problem of inferring a consensus MUL-tree that summarizes a given set of conflicting MUL-trees, and present the first polynomial-time algorithms for solving it. In particular, we give a straightforward, fast algorithm for building a strict consensus MUL-tree for any input set of MUL-trees with identical leaf label multisets, as well as a polynomial-time algorithm for building a majority rule consensus MUL-tree for the special case where every leaf label occurs at most twice. We also show that, although it is NP-hard to find a majority rule consensus MUL-tree in general, the variant that we call the singular majority rule consensus MUL-tree can be constructed efficiently whenever it exists.

  1. Polynomial modal analysis of slanted lamellar gratings.

    PubMed

    Granet, Gérard; Randriamihaja, Manjakavola Honore; Raniriharinosy, Karyl

    2017-06-01

    The problem of diffraction by slanted lamellar dielectric and metallic gratings in classical mounting is formulated as an eigenvalue eigenvector problem. The numerical solution is obtained by using the moment method with Legendre polynomials as expansion and test functions, which allows us to enforce in an exact manner the boundary conditions which determine the eigensolutions. Our method is successfully validated by comparison with other methods including in the case of highly slanted gratings.

  2. Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values

    NASA Astrophysics Data System (ADS)

    Van Assche, W.; Yáñez, R. J.; González-Férez, R.; Dehesa, Jesús S.

    2000-09-01

    The system of Gegenbauer or ultraspherical polynomials {Cnλ(x);n=0,1,…} is a classical family of polynomials orthogonal with respect to the weight function ωλ(x)=(1-x2)λ-1/2 on the support interval [-1,+1]. Integral functionals of Gegenbauer polynomials with integrand f(x)[Cnλ(x)]2ωλ(x), where f(x) is an arbitrary function which does not depend on n or λ, are considered in this paper. First, a general recursion formula for these functionals is obtained. Then, the explicit expression for some specific functionals of this type is found in a closed and compact form; namely, for the functionals with f(x) equal to (1-x)α(1+x)β, log(1-x2), and (1+x)log(1+x), which appear in numerous physico-mathematical problems. Finally, these functionals are used in the explicit evaluation of the momentum expectation values and of the D-dimensional hydrogenic atom with nuclear charge Z⩾1. The power expectation values are given by means of a terminating 5F4 hypergeometric function with unit argument, which is a considerable improvement with respect to Hey's expression (the only one existing up to now) which requires a double sum.

  3. Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model.

    PubMed

    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. Copyright © 2014 John Wiley & Sons, Ltd.

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

    NASA Astrophysics Data System (ADS)

    Karstens, William; Smith, David

    2013-03-01

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

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

    PubMed

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

    2014-08-01

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

  6. Suppressor of K+ transport growth defect 1 (SKD1) interacts with RING-type ubiquitin ligase and sucrose non-fermenting 1-related protein kinase (SnRK1) in the halophyte ice plant

    PubMed Central

    Chiang, Chih-Pin; Li, Chang-Hua; Jou, Yingtzy; Chen, Yu-Chan; Lin, Ya-Chung; Yang, Fang-Yu; Huang, Nu-Chuan; Yen, Hungchen Emilie

    2013-01-01

    SKD1 (suppressor of K+ transport growth defect 1) is an AAA-type ATPase that functions as a molecular motor. It was previously shown that SKD1 accumulates in epidermal bladder cells of the halophyte Mesembryanthemum crystallinum. SKD1 knock-down Arabidopsis mutants showed an imbalanced Na+/K+ ratio under salt stress. Two enzymes involved in protein post-translational modifications that physically interacted with McSKD1 were identified. McCPN1 (copine 1), a RING-type ubiquitin ligase, has an N-terminal myristoylation site that links to the plasma membrane, a central copine domain that interacts with McSKD1, and a C-terminal RING domain that catalyses protein ubiquitination. In vitro ubiquitination assay demonstrated that McCPN1 was capable of mediating ubiquitination of McSKD1. McSnRK1 (sucrose non-fermenting 1-related protein kinase) is a Ser/Thr protein kinase that contains an N-terminal STKc catalytic domain to phosphorylate McSKD1, and C-terminal UBA and KA1 domains to interact with McSKD1. The transcript and protein levels of McSnRK1 increased as NaCl concentrations increased. The formation of an SKD1–SnRK1–CPN1 ternary complex was demonstrated by yeast three-hybrid and bimolecular fluorescence complementation. It was found that McSKD1 preferentially interacts with McSnRK1 in the cytosol, and salt induced the re-distribution of McSKD1 and McSnRK1 towards the plasma membrane via the microtubule cytoskeleton and subsequently interacted with RING-type E3 McCPN1. The potential effects of ubiquitination and phosphorylation on McSKD1, such as changes in the ATPase activity and cellular localization, and how they relate to the functions of SKD1 in the maintenance of Na+/K+ homeostasis under salt stress, are discussed. PMID:23580756

  7. Suppressor of K+ transport growth defect 1 (SKD1) interacts with RING-type ubiquitin ligase and sucrose non-fermenting 1-related protein kinase (SnRK1) in the halophyte ice plant.

    PubMed

    Chiang, Chih-Pin; Li, Chang-Hua; Jou, Yingtzy; Chen, Yu-Chan; Lin, Ya-Chung; Yang, Fang-Yu; Huang, Nu-Chuan; Yen, Hungchen Emilie

    2013-05-01

    SKD1 (suppressor of K+ transport growth defect 1) is an AAA-type ATPase that functions as a molecular motor. It was previously shown that SKD1 accumulates in epidermal bladder cells of the halophyte Mesembryanthemum crystallinum. SKD1 knock-down Arabidopsis mutants showed an imbalanced Na+/K+ ratio under salt stress. Two enzymes involved in protein post-translational modifications that physically interacted with McSKD1 were identified. McCPN1 (copine 1), a RING-type ubiquitin ligase, has an N-terminal myristoylation site that links to the plasma membrane, a central copine domain that interacts with McSKD1, and a C-terminal RING domain that catalyses protein ubiquitination. In vitro ubiquitination assay demonstrated that McCPN1 was capable of mediating ubiquitination of McSKD1. McSnRK1 (sucrose non-fermenting 1-related protein kinase) is a Ser/Thr protein kinase that contains an N-terminal STKc catalytic domain to phosphorylate McSKD1, and C-terminal UBA and KA1 domains to interact with McSKD1. The transcript and protein levels of McSnRK1 increased as NaCl concentrations increased. The formation of an SKD1-SnRK1-CPN1 ternary complex was demonstrated by yeast three-hybrid and bimolecular fluorescence complementation. It was found that McSKD1 preferentially interacts with McSnRK1 in the cytosol, and salt induced the re-distribution of McSKD1 and McSnRK1 towards the plasma membrane via the microtubule cytoskeleton and subsequently interacted with RING-type E3 McCPN1. The potential effects of ubiquitination and phosphorylation on McSKD1, such as changes in the ATPase activity and cellular localization, and how they relate to the functions of SKD1 in the maintenance of Na+/K+ homeostasis under salt stress, are discussed.

  8. Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

    NASA Astrophysics Data System (ADS)

    Kent, Stephen M.

    2018-04-01

    If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey–Chrétien telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

  9. Non-axisymmetric Aberration Patterns from Wide-field Telescopes Using Spin-weighted Zernike Polynomials

    DOE PAGES

    Kent, Stephen M.

    2018-02-15

    If the optical system of a telescope is perturbed from rotational symmetry, the Zernike wavefront aberration coefficients describing that system can be expressed as a function of position in the focal plane using spin-weighted Zernike polynomials. Methodologies are presented to derive these polynomials to arbitrary order. This methodology is applied to aberration patterns produced by a misaligned Ritchey Chretian telescope and to distortion patterns at the focal plane of the DESI optical corrector, where it is shown to provide a more efficient description of distortion than conventional expansions.

  10. The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons

    NASA Astrophysics Data System (ADS)

    Iwao, Shinsuke; Nagai, Hidetomo

    2018-04-01

    This paper presents a study of the discrete Toda equation that was introduced in 1977. In this paper, it is proved that the determinantal solution of the discrete Toda equation, obtained via the Lax formalism, is naturally related to the dual Grothendieck polynomials, a K-theoretic generalization of the Schur polynomials. A tropical permanent solution to the ultradiscrete Toda equation is also derived. The proposed method gives a tropical algebraic representation of the static solitons. Lastly, a new cellular automaton realization of the ultradiscrete Toda equation is proposed.

  11. Estimating the spatial distribution of soil moisture based on Bayesian maximum entropy method with auxiliary data from remote sensing

    NASA Astrophysics Data System (ADS)

    Gao, Shengguo; Zhu, Zhongli; Liu, Shaomin; Jin, Rui; Yang, Guangchao; Tan, Lei

    2014-10-01

    Soil moisture (SM) plays a fundamental role in the land-atmosphere exchange process. Spatial estimation based on multi in situ (network) data is a critical way to understand the spatial structure and variation of land surface soil moisture. Theoretically, integrating densely sampled auxiliary data spatially correlated with soil moisture into the procedure of spatial estimation can improve its accuracy. In this study, we present a novel approach to estimate the spatial pattern of soil moisture by using the BME method based on wireless sensor network data and auxiliary information from ASTER (Terra) land surface temperature measurements. For comparison, three traditional geostatistic methods were also applied: ordinary kriging (OK), which used the wireless sensor network data only, regression kriging (RK) and ordinary co-kriging (Co-OK) which both integrated the ASTER land surface temperature as a covariate. In Co-OK, LST was linearly contained in the estimator, in RK, estimator is expressed as the sum of the regression estimate and the kriged estimate of the spatially correlated residual, but in BME, the ASTER land surface temperature was first retrieved as soil moisture based on the linear regression, then, the t-distributed prediction interval (PI) of soil moisture was estimated and used as soft data in probability form. The results indicate that all three methods provide reasonable estimations. Co-OK, RK and BME can provide a more accurate spatial estimation by integrating the auxiliary information Compared to OK. RK and BME shows more obvious improvement compared to Co-OK, and even BME can perform slightly better than RK. The inherent issue of spatial estimation (overestimation in the range of low values and underestimation in the range of high values) can also be further improved in both RK and BME. We can conclude that integrating auxiliary data into spatial estimation can indeed improve the accuracy, BME and RK take better advantage of the auxiliary

  12. Polynomial Size Formulations for the Distance and Capacity Constrained Vehicle Routing Problem

    NASA Astrophysics Data System (ADS)

    Kara, Imdat; Derya, Tusan

    2011-09-01

    The Distance and Capacity Constrained Vehicle Routing Problem (DCVRP) is an extension of the well known Traveling Salesman Problem (TSP). DCVRP arises in distribution and logistics problems. It would be beneficial to construct new formulations, which is the main motivation and contribution of this paper. We focused on two indexed integer programming formulations for DCVRP. One node based and one arc (flow) based formulation for DCVRP are presented. Both formulations have O(n2) binary variables and O(n2) constraints, i.e., the number of the decision variables and constraints grows with a polynomial function of the nodes of the underlying graph. It is shown that proposed arc based formulation produces better lower bound than the existing one (this refers to the Water's formulation in the paper). Finally, various problems from literature are solved with the node based and arc based formulations by using CPLEX 8.0. Preliminary computational analysis shows that, arc based formulation outperforms the node based formulation in terms of linear programming relaxation.

  13. Jack Polynomials as Fractional Quantum Hall States and the Betti Numbers of the ( k + 1)-Equals Ideal

    NASA Astrophysics Data System (ADS)

    Zamaere, Christine Berkesch; Griffeth, Stephen; Sam, Steven V.

    2014-08-01

    We show that for Jack parameter α = -( k + 1)/( r - 1), certain Jack polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in the case r = 2 identifies the span of the relevant Jack polynomials with the S n -invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type; we prove this for the ideal of the ( k + 1)-equals arrangement in the case when the number of coordinates n is at most 2 k + 1. In general, our conjecture predicts the graded S n -equivariant Betti numbers of the ideal of the ( k + 1)-equals arrangement with no restriction on the number of ambient dimensions.

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

    DOE PAGES

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

    2016-08-16

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

  15. HOMFLYPT polynomial is the best quantifier for topological cascades of vortex knots

    NASA Astrophysics Data System (ADS)

    Ricca, Renzo L.; Liu, Xin

    2018-02-01

    In this paper we derive and compare numerical sequences obtained by adapted polynomials such as HOMFLYPT, Jones and Alexander-Conway for the topological cascade of vortex torus knots and links that progressively untie by a single reconnection event at a time. Two cases are considered: the alternate sequence of knots and co-oriented links (with positive crossings) and the sequence of two-component links with oppositely oriented components (negative crossings). New recurrence equations are derived and sequences of numerical values are computed. In all cases the adapted HOMFLYPT polynomial proves to be the best quantifier for the topological cascade of torus knots and links.

  16. A polynomial-chaos-expansion-based building block approach for stochastic analysis of photonic circuits

    NASA Astrophysics Data System (ADS)

    Waqas, Abi; Melati, Daniele; Manfredi, Paolo; Grassi, Flavia; Melloni, Andrea

    2018-02-01

    The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.

  17. Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

    PubMed

    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.

  18. Characterization of thiol-based redox modifications of Brassica napusSNF1-related protein kinase 2.6-2C.

    PubMed

    Ma, Tianyi; Yoo, Mi-Jeong; Zhang, Tong; Liu, Lihong; Koh, Jin; Song, Wen-Yuan; Harmon, Alice C; Sha, Wei; Chen, Sixue

    2018-04-01

    Sucrose nonfermenting 1-related protein kinase 2.6 (SnRK2.6), also known as Open Stomata 1 (OST1) in Arabidopsis thaliana , plays a pivotal role in abscisic acid (ABA)-mediated stomatal closure. Four SnRK2.6 paralogs were identified in the Brassica napus genome in our previous work. Here we studied one of the paralogs, BnSnRK2.6-2C , which was transcriptionally induced by ABA in guard cells. Recombinant BnSnRK2.6-2C exhibited autophosphorylation activity and its phosphorylation sites were mapped. The autophosphorylation activity was inhibited by S-nitrosoglutathione (GSNO) and by oxidized glutathione (GSSG), and the inhibition was reversed by reductants. Using monobromobimane (mBBr) labeling, we demonstrated a dose-dependent modification of BnSnRK2.6-2C by GSNO. Furthermore, mass spectrometry analysis revealed previously uncharacterized thiol-based modifications including glutathionylation and sulfonic acid formation. Of the six cysteine residues in BnSnRK2.6-2C, C159 was found to have different types of thiol modifications, suggesting its high redox sensitivity and versatility. In addition, mBBr labeling on tyrosine residues was identified. Collectively, these data provide detailed biochemical characterization of redox-induced modifications and changes of the BnSnRK2.6-2C activity.

  19. Forward Behavioral Modeling of a Three-Way Amplitude Modulator-Based Transmitter Using an Augmented Memory Polynomial

    PubMed Central

    Chatrath, Jatin; Aziz, Mohsin; Helaoui, Mohamed

    2018-01-01

    Reconfigurable and multi-standard RF front-ends for wireless communication and sensor networks have gained importance as building blocks for the Internet of Things. Simpler and highly-efficient transmitter architectures, which can transmit better quality signals with reduced impairments, are an important step in this direction. In this regard, mixer-less transmitter architecture, namely, the three-way amplitude modulator-based transmitter, avoids the use of imperfect mixers and frequency up-converters, and their resulting distortions, leading to an improved signal quality. In this work, an augmented memory polynomial-based model for the behavioral modeling of such mixer-less transmitter architecture is proposed. Extensive simulations and measurements have been carried out in order to validate the accuracy of the proposed modeling strategy. The performance of the proposed model is evaluated using normalized mean square error (NMSE) for long-term evolution (LTE) signals. NMSE for a LTE signal of 1.4 MHz bandwidth with 100,000 samples for digital combining and analog combining are recorded as −36.41 dB and −36.9 dB, respectively. Similarly, for a 5 MHz signal the proposed models achieves −31.93 dB and −32.08 dB NMSE using digital and analog combining, respectively. For further validation of the proposed model, amplitude-to-amplitude (AM-AM), amplitude-to-phase (AM-PM), and the spectral response of the modeled and measured data are plotted, reasonably meeting the desired modeling criteria. PMID:29510501

  20. A Ramanujan-type measure for the Askey-Wilson polynomials

    NASA Technical Reports Server (NTRS)

    Atakishiyev, Natig M.

    1995-01-01

    A Ramanujan-type representation for the Askey-Wilson q-beta integral, admitting the transformation q to q(exp -1), is obtained. Orthogonality of the Askey-Wilson polynomials with respect to a measure, entering into this representation, is proved. A simple way of evaluating the Askey-Wilson q-beta integral is also given.

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