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Sample records for general linear matrix

  1. General linear matrix model, Minkowski spacetime and the Standard Model

    CERN Document Server

    Belyea, Chris

    2010-01-01

    The Hermitian matrix model with general linear symmetry is argued to decouple into a finite unitary matrix model that contains metastable multidimensional lattice configurations and a fermion determinant. The simplest metastable state is a Hermitian Weyl kinetic operator of either handedness on a 3+1 D lattice with general nonlocal interactions. The Hermiticity produces 16 effective Weyl fermions by species doubling, 8 left- and 8 right-handed. These are identified with a Standard Model generation. Only local non-anomalous gauge fields within the soup of general fluctuations can survive at long distances, and the degrees of freedom for gauge fields of an $SU(8)_L X SU(8)_R$ GUT are present. Standard Model gauge symmetries associate with particular species symmetries, for example change of QCD color associates with permutation of doubling status amongst space directions. Vierbein gravity is probably also generated. While fundamental Higgs fields are not possible, low fermion current masses can arise from chira...

  2. A Matrix Approach for General Higher Order Linear Recurrences

    Science.gov (United States)

    2011-01-01

    properties of linear recurrences (such as the well-known Fibonacci and Pell sequences ). In [2], Er defined k linear recurring sequences of order at...the nth term of the ith generalized order-k Fibonacci sequence . Communicated by Lee See Keong. Received: March 26, 2009; Revised: August 28, 2009...6], the author gave the generalized order-k Fibonacci and Pell (F-P) sequence as follows: For m ≥ 0, n > 0 and 1 ≤ i ≤ k uin = 2 muin−1 + u i n−2

  3. Estimation linear model using block generalized inverse of a matrix

    OpenAIRE

    Jasińska, Elżbieta; Preweda, Edward

    2013-01-01

    The work shows the principle of generalized linear model, point estimation, which can be used as a basis for determining the status of movements and deformations of engineering objects. The structural model can be put on any boundary conditions, for example, to ensure the continuity of the deformations. Estimation by the method of least squares was carried out taking into account the terms and conditions of the Gauss- Markov for quadratic forms stored using Lagrange function. The original sol...

  4. Linear connections on matrix geometries

    CERN Document Server

    Madore, J; Mourad, J; Madore, John; Masson, Thierry; Mourad, Jihad

    1994-01-01

    A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.

  5. Matrix algebra for linear models

    CERN Document Server

    Gruber, Marvin H J

    2013-01-01

    Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f

  6. Linearized supergravity from Matrix theory

    CERN Document Server

    Kabat, D; Kabat, Daniel; Taylor, Washington

    1998-01-01

    We show that the linearized supergravity potential between two objects arising from the exchange of quanta with zero longitudinal momentum is reproduced to all orders in 1/r by terms in the one-loop Matrix theory potential. The essential ingredient in the proof is the identification of the Matrix theory quantities corresponding to moments of the stress tensor and membrane current. We also point out that finite-N Matrix theory violates the Equivalence Principle.

  7. Introduction to general and generalized linear models

    CERN Document Server

    Madsen, Henrik

    2010-01-01

    IntroductionExamples of types of data Motivating examples A first view on the modelsThe Likelihood PrincipleIntroduction Point estimation theory The likelihood function The score function The information matrix Alternative parameterizations of the likelihood The maximum likelihood estimate (MLE) Distribution of the ML estimator Generalized loss-function and deviance Quadratic approximation of the log-likelihood Likelihood ratio tests Successive testing in hypothesis chains Dealing with nuisance parameters General Linear ModelsIntroduction The multivariate normal distribution General linear mod

  8. Multivariate covariance generalized linear models

    DEFF Research Database (Denmark)

    Bonat, W. H.; Jørgensen, Bent

    2016-01-01

    We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...... are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions...

  9. Matrix Superpotential Linear in Variable Parameter

    CERN Document Server

    Karadzhov, Yuri

    2011-01-01

    The paper presents the classification of matrix valued superpotentials corresponding to shape invariant systems of Schr\\"odinger equations. All inequivalent irreducible matrix superpotentials realized by matrices of arbitrary dimension with linear dependence on variable parameter are presented explicitly.

  10. Linear algebra and matrix analysis for statistics

    CERN Document Server

    Banerjee, Sudipto

    2014-01-01

    Matrices, Vectors, and Their OperationsBasic definitions and notations Matrix addition and scalar-matrix multiplication Matrix multiplication Partitioned matricesThe ""trace"" of a square matrix Some special matricesSystems of Linear EquationsIntroduction Gaussian elimination Gauss-Jordan elimination Elementary matrices Homogeneous linear systems The inverse of a matrixMore on Linear EquationsThe LU decompositionCrout's Algorithm LU decomposition with row interchanges The LDU and Cholesky factorizations Inverse of partitioned matrices The LDU decomposition for partitioned matricesThe Sherman-W

  11. Generalized Linear Covariance Analysis

    Science.gov (United States)

    Carpenter, James R.; Markley, F. Landis

    2014-01-01

    This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.

  12. THE GENERALIZED POLARIZATION SCATTERING MATRIX

    Science.gov (United States)

    the Least Square Best Estimate of the Generalized Polarization matrix from a set of measurements is then developed. It is shown that the Faraday...matrix data. It is then shown that the Least Square Best Estimate of the orientation angle of a symmetric target is also determinable from Faraday rotation contaminated short pulse monostatic polarization matrix data.

  13. Foundations of linear and generalized linear models

    CERN Document Server

    Agresti, Alan

    2015-01-01

    A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,

  14. Bayes linear covariance matrix adjustment

    CERN Document Server

    Wilkinson, Darren J

    1995-01-01

    In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be a...

  15. Matrix Tricks for Linear Statistical Models

    CERN Document Server

    Puntanen, Simo; Styan, George PH

    2011-01-01

    In teaching linear statistical models to first-year graduate students or to final-year undergraduate students there is no way to proceed smoothly without matrices and related concepts of linear algebra; their use is really essential. Our experience is that making some particular matrix tricks very familiar to students can substantially increase their insight into linear statistical models (and also multivariate statistical analysis). In matrix algebra, there are handy, sometimes even very simple "tricks" which simplify and clarify the treatment of a problem - both for the student and

  16. Generalized Cross-Gramian for Linear Systems

    DEFF Research Database (Denmark)

    Shaker, Hamid Reza

    2012-01-01

    The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross-gramian...... popular in several applications including model reduction, control configuration selection and sensitivity analysis. The ordinary cross-gramian which has been defined in the literature is the solution of a Sylvester equation. This Sylvester equation is not always solvable and therefore for some linear...... square symmetric systems, the ordinary cross-gramian does not exist. To cope with this problem, a new generalized cross-gramian is introduced in this paper. In contrast to the ordinary cross-gramian, the generalized cross-gramian can be easily obtained for general linear systems and therefore can be used...

  17. Generalized, Linear, and Mixed Models

    CERN Document Server

    McCulloch, Charles E; Neuhaus, John M

    2011-01-01

    An accessible and self-contained introduction to statistical models-now in a modernized new editionGeneralized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects.A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed m

  18. Speaker Adaptation with Transformation Matrix Linear Interpolation

    Institute of Scientific and Technical Information of China (English)

    XU Xiang-hua; ZHU Jie

    2004-01-01

    A transformation matrix linear interpolation (TMLI) approach for speaker adaptation is proposed. TMLI uses the transformation matrixes produced by MLLR from selected training speakers and the testing speaker. With only 3 adaptation sentences, the performance shows a 12.12% word error rate reduction. As the number of adaptation sentences increases, the performance saturates quickly. To improve the behavior of TMLI for large amounts of adaptation data, the TMLI+MAP method which combines TMLI with MAP technique is proposed. Experimental results show TMLI+MAP achieved better recognition accuracy than MAP and MLLR+MAP for both small and large amounts of adaptation data.

  19. An inversion algorithm for general tridiagonal matrix

    Institute of Scientific and Technical Information of China (English)

    Rui-sheng RAN; Ting-zhu HUANG; Xing-ping LIU; Tong-xiang GU

    2009-01-01

    An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established.The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.

  20. Linear $r$-matrix algebra for classical separable systems

    CERN Document Server

    Eilbeck, J C; Kuznetsov, V B; Tsiganov, A V; Kuznetsov, Vadim B.

    1994-01-01

    We consider a hierarchy of the natural type Hamiltonian systems of $n$ degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of $2\\times 2$ matrices for the whole hierarchy and construct the associated linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Using the method of variable separation we provide the integration of the systems in classical mechanics conctructing the separation equations and, hence, the explicit form of action variables. The quantisation problem is discussed with the help of the separation variables.

  1. Bayes linear covariance matrix adjustment for multivariate dynamic linear models

    CERN Document Server

    Wilkinson, Darren J

    2008-01-01

    A methodology is developed for the adjustment of the covariance matrices underlying a multivariate constant time series dynamic linear model. The covariance matrices are embedded in a distribution-free inner-product space of matrix objects which facilitates such adjustment. This approach helps to make the analysis simple, tractable and robust. To illustrate the methods, a simple model is developed for a time series representing sales of certain brands of a product from a cash-and-carry depot. The covariance structure underlying the model is revised, and the benefits of this revision on first order inferences are then examined.

  2. A Generalization of the Alias Matrix

    DEFF Research Database (Denmark)

    Kulahci, Murat; Bisgaard, S.

    2006-01-01

    The investigation of aliases or biases is important for the interpretation of the results from factorial experiments. For two-level fractional factorials this can be facilitated through their group structure. For more general arrays the alias matrix can be used. This tool is traditionally based...... on the assumption that the error structure is that associated with ordinary least squares. For situations where that is not the case, we provide in this article a generalization of the alias matrix applicable under the generalized least squares assumptions. We also show that for the special case of split plot error...... structure, the generalized alias matrix simplifies to the ordinary alias matrix....

  3. Positivity of Matrices with Generalized Matrix Functions

    Institute of Scientific and Technical Information of China (English)

    Fuzhen ZHANG

    2012-01-01

    Using an elementary fact on matrices we show by a unified approach the positivity of a partitioned positive semidefinite matrix with each square block replaced by a compound matrix,an elementary symmetric function or a generalized matrix function.In addition,we present a refined version of the Thompson determinant compression theorem.

  4. Generating Nice Linear Systems for Matrix Gaussian Elimination

    Science.gov (United States)

    Homewood, L. James

    2004-01-01

    In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

  5. Identification of matrix conditions that give rise to the linear coupling resonances

    Energy Technology Data Exchange (ETDEWEB)

    Gardner,C.J.

    2009-03-01

    General definitions of horizontal and vertical amplitudes for linear coupled motion are developed from the normal form of the one-turn matrix. This leads to the identification of conditions on the matrix that give rise to the linear coupling sum and difference resonances. The correspondence with the standard hamiltonian treatment of the resonances is discussed.

  6. QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS

    Institute of Scientific and Technical Information of China (English)

    Ai-guo Xiao; Shou-fu Li; Min Yang

    2001-01-01

    In this paper, we present some invariants and conservation laws of general linear methods applied to differential equation systems. We show that the quadratic invariants and symplecticity of the systems can be extended to general linear methods by a tensor product, and show that general linear methods with the matrix M=0 inherit in an extended sense the quadratic invariants possessed by the differential equation systems being integrated and preserve in an extended sense the symplectic structure of the phase space in the integration of Hamiltonian systems. These unify and extend existing relevant results on Runge-Kutta methods, linear multistep methods and one-leg methods. Finally, as special cases of general linear methods, we examine multistep Runge-Kutta methods, one-leg methods and linear two-step methods in detail.

  7. THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION BTXB=D ON LINEAR MANIFOLDS

    Institute of Scientific and Technical Information of China (English)

    邓远北; 胡锡炎; 张磊

    2003-01-01

    This paper discusses the solutions of the linear matrix equation BT X B=Don some linear manifolds.Some necessary and sufficient conditions for the existenceof the solution and the expression of the general solution are given.And also someoptimal approximation solutions are discussed.

  8. On the unitarity of linearized General Relativity coupled to matter

    CERN Document Server

    Atkins, Michael

    2010-01-01

    We consider the unitarity of the S-matrix for linearized General Relativity coupled to particle physics models. Taking renormalization group effects of the Planck mass into account, we find that the scale at which unitarity is violated is strongly dependent on the particle content of the theory. We find that the requirement that the S-matrix be unitary up to the scale at which quantum gravitational effects become strong implies a bound on the particle content of the model.

  9. General Randic matrix and general Randi'c energy

    Directory of Open Access Journals (Sweden)

    Ran Gu;

    2014-09-01

    Full Text Available Let $G$ be a simple graph with vertex set $V(G = {v_1, v_2,ldots , v_n}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2, cdots, n$. Inspired by the Randi'c matrix and the general Randi'c index of a graph, we introduce the concept of general Randi'c matrix $textbf{R}_alpha$ of $G$, which is defined by $(textbf{R}_alpha_{i,j}=(d_id_j^alpha$ if $v_i$ and $v_j$ are adjacent, and zero otherwise. Similarly, the general Randi'{c} eigenvalues are the eigenvalues of the general Randi'{c} matrix, the greatest general Randi'{c} eigenvalue is the general Randi'{c} spectral radius of $G$, and the general Randi'{c} energy is the sum of the absolute values of the general Randi'{c} eigenvalues. In this paper, we prove some properties of the general Randi'c matrix and obtain lower and upper bounds for general Randi'{c} energy, also, we get some lower bounds for general Randi'{c} spectral radius of a connected graph. Moreover, we give a new sharp upper bound for the general Randi'{c} energy when $alpha=-1/2$.[2mm] noindent{bf Keywords:} general Randi'c matrix, general Randi'c energy, eigenvalues, spectral radius.

  10. Homology stability for the general linear group

    NARCIS (Netherlands)

    Maazen, Hendrik

    1979-01-01

    This thesis studies the homology stability problem for general linear groups over Euclidean rings and over subrings of the field of rational numbers. Affine linear groups, acting on affine space rather than linear space, are also considered. In order to get stability results one establishes that cer

  11. Homology stability for the general linear group

    NARCIS (Netherlands)

    Maazen, Hendrik

    1979-01-01

    This thesis studies the homology stability problem for general linear groups over Euclidean rings and over subrings of the field of rational numbers. Affine linear groups, acting on affine space rather than linear space, are also considered. In order to get stability results one establishes that

  12. Adaptive quasi-likelihood estimate in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    CHEN Xia; CHEN Xiru

    2005-01-01

    This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.

  13. Multivariate generalized linear mixed models using R

    CERN Document Server

    Berridge, Damon Mark

    2011-01-01

    Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R. A Unified Framework for a Broad Class of Models The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model...

  14. Generalised Assignment Matrix Methodology in Linear Programming

    Science.gov (United States)

    Jerome, Lawrence

    2012-01-01

    Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

  15. Linear matrix differential equations of higher-order and applications

    Directory of Open Access Journals (Sweden)

    Mustapha Rachidi

    2008-07-01

    Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

  16. Iterative linear system solvers with approximate matrix-vector products

    NARCIS (Netherlands)

    Eshof, J. van den; Sleijpen, G.L.G.; Gijzen, M.B. van

    2003-01-01

    There are classes of linear problems for which a matrix-vector product is a time consuming operation because an expensive approximation method is required to compute it to a given accuracy. One important example is simulations in lattice QCD with Neuberger fermions where a matrix multiply

  17. Matrix preconditioning: a robust operation for optical linear algebra processors.

    Science.gov (United States)

    Ghosh, A; Paparao, P

    1987-07-15

    Analog electrooptical processors are best suited for applications demanding high computational throughput with tolerance for inaccuracies. Matrix preconditioning is one such application. Matrix preconditioning is a preprocessing step for reducing the condition number of a matrix and is used extensively with gradient algorithms for increasing the rate of convergence and improving the accuracy of the solution. In this paper, we describe a simple parallel algorithm for matrix preconditioning, which can be implemented efficiently on a pipelined optical linear algebra processor. From the results of our numerical experiments we show that the efficacy of the preconditioning algorithm is affected very little by the errors of the optical system.

  18. Generalized PID observer design for descriptor linear systems.

    Science.gov (United States)

    Wu, Ai-Guo; Duan, Guang-Ren; Fu, Yan-Ming

    2007-10-01

    A type of generalized proportional-integral-derivative observers is proposed for descriptor linear systems. Based on a general parametric solution to a type of generalized Sylvester matrix equations, a parametric design approach for such observers is established. The proposed approach provides parameterizations for all the observer gain matrices, gives the parametric expression for the corresponding left eigenvector matrix of the observer system matrix, realizes the elimination of impulsive behaviors, and guarantees the regularity of the observer system. The design method can offer all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances. In addition, a numerical example is employed to show the design procedure and illustrate the effect of the presented approach.

  19. Linear generalized synchronization of chaotic systems with uncertain parameters

    Institute of Scientific and Technical Information of China (English)

    Jia Zhen

    2008-01-01

    A more general form of projective synchronization,so called linear generalized synchronization(LGS)is proposed,which includes the generalized projective synchronization(GPS)and the hybrid projective synchronization(HPS)as its special cases.Based on the adaptive technique and Lyapunov stability theory,a general method for achieving the LGS between two chaotic or hyperchaotic systems with uncertain parameters in any scaling matrix is presented.Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.

  20. Large Margin Linear Discriminative Visualization by Matrix Relevance Learning

    NARCIS (Netherlands)

    Biehl, Michael; Bunte, Kerstin; Schleif, Frank-Michael; Schneider, Petra; Villmann, Thomas

    2012-01-01

    We suggest and investigate the use of Generalized Matrix Relevance Learning (GMLVQ) in the context of discriminative visualization. This prototype-based, supervised learning scheme parameterizes an adaptive distance measure in terms of a matrix of relevance factors. By means of a few benchmark

  1. Generalized multicritical one-matrix models

    CERN Document Server

    Ambjorn, J; Makeenko, Y

    2016-01-01

    We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series with a heavy tail, leading to a cut of the potential and its derivative at the real axis, and reduces to a polynomial at Kazakov's multicritical points. From the combinatorial point of view the generalized model allows polygons of arbitrary large degrees (or vertices of arbitrary large degree, when considering the dual graphs), and it is the weight assigned to these large order polygons which brings about the interpolation between the multicritical points in the one-matrix model.

  2. Generalized multicritical one-matrix models

    Science.gov (United States)

    Ambjørn, J.; Budd, T.; Makeenko, Y.

    2016-12-01

    We show that there exists a simple generalization of Kazakov's multicritical one-matrix model, which interpolates between the various multicritical points of the model. The associated multicritical potential takes the form of a power series with a heavy tail, leading to a cut of the potential and its derivative at the real axis, and reduces to a polynomial at Kazakov's multicritical points. From the combinatorial point of view the generalized model allows polygons of arbitrary large degrees (or vertices of arbitrary large degree, when considering the dual graphs), and it is the weight assigned to these large order polygons which brings about the interpolation between the multicritical points in the one-matrix model.

  3. Admissible Estimators in the General Multivariate Linear Model with Respect to Inequality Restricted Parameter Set

    Directory of Open Access Journals (Sweden)

    Liu Gang

    2009-01-01

    Full Text Available By using the methods of linear algebra and matrix inequality theory, we obtain the characterization of admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set. In the classes of homogeneous and general linear estimators, the necessary and suffcient conditions that the estimators of regression coeffcient function are admissible are established.

  4. Strong Linear Correlation Between Eigenvalues and Diagonal Matrix Elements

    CERN Document Server

    Shen, J J; Zhao, Y M; Yoshinaga, N

    2008-01-01

    We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of given shell model Hamiltonian without complicated iterations.

  5. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

    Science.gov (United States)

    El-Gebeily, M.; Yushau, B.

    2008-01-01

    In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

  6. Minimal solution of linear formed fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    Maryam Mosleh

    2012-10-01

    Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

  7. The linear model and hypothesis a general unifying theory

    CERN Document Server

    Seber, George

    2015-01-01

    This book provides a concise and integrated overview of hypothesis testing in four important subject areas, namely linear and nonlinear models, multivariate analysis, and large sample theory. The approach used is a geometrical one based on the concept of projections and their associated idempotent matrices, thus largely avoiding the need to involve matrix ranks. It is shown that all the hypotheses encountered are either linear or asymptotically linear, and that all the underlying models used are either exactly or asymptotically linear normal models. This equivalence can be used, for example, to extend the concept of orthogonality in the analysis of variance to other models, and to show that the asymptotic equivalence of the likelihood ratio, Wald, and Score (Lagrange Multiplier) hypothesis tests generally applies.

  8. General linear dynamics - quantum, classical or hybrid

    CERN Document Server

    Elze, H-T; Vallone, F

    2011-01-01

    We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. This is of practical as well as of foundational interest and no fully satisfactory solution of this problem has been established to date. Related aspects will be observed in a general linear ensemble theory, which comprises classical and quantum dynamics in the form of Liouville and von Neumann equations, respectively, as special cases. Considering the simplest object characterized by a two-dimensional state-space, we illustrate how quantum mechanics is special in several respects among possible linear generalizations.

  9. A note on combined generalized Sylvester matrix equations

    Institute of Scientific and Technical Information of China (English)

    Guangren DUAN

    2004-01-01

    The solution of two combined generalized Sylvester matrix equations is studied.It is first shown that the two combined generalized Sylvester matrix equations can be converted into a normal Sylvester matrix equation through extension,and then with the help of a result for solution to normal Sylvester matrix equations,the complete solution to the two combined generalized Sylvester matrix equations is derived.A demonstrative example shows the effect of the proposed approach.

  10. GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS

    Institute of Scientific and Technical Information of China (English)

    陈正新

    2014-01-01

    Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) 6= 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.

  11. Higher-order linear matrix descriptor differential equations of Apostol-Kolodner type

    Directory of Open Access Journals (Sweden)

    2009-02-01

    Full Text Available In this article, we study a class of linear rectangular matrix descriptor differential equations of higher-order whose coefficients are square constant matrices. Using the Weierstrass canonical form, the analytical formulas for the solution of this general class is analytically derived, for consistent and non-consistent initial conditions.

  12. Linearization of a Matrix Riccati Equation Associated to an Optimal Control Problem

    Directory of Open Access Journals (Sweden)

    Foued Zitouni

    2014-01-01

    Full Text Available The matrix Riccati equation that must be solved to obtain the solution to stochastic optimal control problems known as LQG homing is linearized for a class of processes. The results generalize a theorem proved by Whittle and the one-dimensional case already considered by the authors. A particular two-dimensional problem is solved explicitly.

  13. THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Zhen-yun Peng; Xi-yan Hu; Lei Zhang

    2004-01-01

    The necessary and sufficient conditions for the existence of and the expressions for bismmetric soutions of the matrix equation(Ⅰ)A1X1B1+A2X2B2+…AkXkBk=D,(Ⅱ)A1XB1+A2XB2+…+AkXBk=D and (Ⅲ)(A1XB1,A2XB2,…,AkXBK)=(D1,D2,…,Dk) are derived by using kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given.Numerical methods and numerical experiments of finding the nearest solutions are also provided.

  14. A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

    DEFF Research Database (Denmark)

    Harrod, Steven

    2009-01-01

    The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover......, it is consistent with the Arganbright Principles because the arrays and functions are clear in their operation and easily manipulated by the user....

  15. [General practice--linear thinking and complexity].

    Science.gov (United States)

    Stalder, H

    2006-09-27

    As physicians, we apply and teach linear thinking. This approach permits to dissect the patient's problem to the molecular level and has contributed enormously to the knowledge and progress of medicine. The linear approach is particularly useful in medical education, in quantitative research and helps to resolve simple problems. However, it risks to be rigid. Living beings (such as patients and physicians!) have to be considered as complex systems. A complex system cannot be dissected into its parts without losing its identity. It is dependent on its past and interactions with the outside are often followed by unpredictable reactions. The patient-centred approach in medicine permits the physician, a complex system himself, to integrate the patient's system and to adapt to his reality. It is particularly useful in general medicine.

  16. Using R In Generalized Linear Models

    Directory of Open Access Journals (Sweden)

    Mihaela Covrig

    2015-09-01

    Full Text Available This paper aims to approach the estimation of generalized linear models (GLM on the basis of the glm routine package in R. Particularly, regression models will be analyzed for those cases in which the explained variable follows a Poisson or a Negative Binomial distribution. The paper will briefly present the GLM methodology for count data, while the practical part will revolve around estimating and comparing models in which the response variable shows the number of claims in a portfolio of automobile insurance policies.

  17. Multivariate Generalized Linear Mixed Models Using R

    CERN Document Server

    Berridge, Damon M

    2011-01-01

    To provide researchers with the ability to analyze large and complex data sets using robust models, this book presents a unified framework for a broad class of models that can be applied using a dedicated R package (Sabre). The first five chapters cover the analysis of multilevel models using univariate generalized linear mixed models (GLMMs). The next few chapters extend to multivariate GLMMs and the last chapters address more specialized topics, such as parallel computing for large-scale analyses. Each chapter includes many real-world examples implemented using Sabre as well as exercises and

  18. New Criteria for Judging Generalized Strictly Diagonally Dominant Matrix

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jin-song

    2015-01-01

    Generalized strictly diagonally dominant matrices play a wide and important role in computational mathematics, mathematical physics, theory of dynamical systems, etc. But it is difficult to judge a matrix is or not generalized strictly diagonally dominant matrix. In this paper, by using the properties of α-chain diagonally dominant matrix, we obtain new criteria for judging generalized strictly diagonally dominant matrix, which enlarge the identification range.

  19. Multi linear formulation of differential geometry and matrix regularizations

    CERN Document Server

    Arnlind, Joakim; Huisken, Gerhard

    2010-01-01

    We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations. For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and a large class of explicit examples is provided. Furthermore, we illustrate the fact that techniques from differential geometry can carry over to matrix analogues by proving that a bound on the discrete Gauss curvature implies a bound on the eigenvalues of the discrete Laplace operator.

  20. Dense Subsemigroups of Matrix Semigroups and Semigroups of Linear Transformations

    Institute of Scientific and Technical Information of China (English)

    Yupaporn Kemprasit

    2002-01-01

    Let V be a vector space over a field F = (F, +, .), F* = F\\{0}, LF(V)the semigroup of all linear transformations of V into itself under composition, and Mn(F) the multiplicative full n × n matrix semigroup over F. In this paper, it is proved that the semigroup Mn(F) has a proper dense subsemigroup if and only if(F*, .) has an element of infinite order. Also, the semigroup LF(V) has a proper dense subsemigroup if and only if dimF V = ∞ or (F*, .) has an element of infinite order.

  1. H∞ /H2 model reduction through dilated linear matrix inequalities

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2012-01-01

    This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field...... not satisfactorily approximates the original system, an iterative algorithm based on dilated LMIs is proposed to significantly improve the approximation bound. The effectiveness of the method is accessed by numerical experiments. The method is also applied to the $H_2$ order reduction of a flexible wind turbine...

  2. Exact solution of some linear matrix equations using algebraic methods

    Science.gov (United States)

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  3. Linear spin-2 fields in most general backgrounds

    CERN Document Server

    Bernard, Laura; Schmidt-May, Angnis; von Strauss, Mikael

    2015-01-01

    We derive the full perturbative equations of motion for the most general background solutions in ghost-free bimetric theory in its metric formulation. Clever field redefinitions at the level of fluctuations enable us to circumvent the problem of varying a square-root matrix appearing in the theory. This greatly simplifies the expressions for the linear variation of the bimetric interaction terms. We show that these field redefinitions exist and are uniquely invertible if and only if the variation of the square-root matrix itself has a unique solution, which is a requirement for the linearised theory to be well-defined. As an application of our results we examine the constraint structure of ghost-free bimetric theory at the level of linear equations of motion for the first time. We identify a scalar combination of equations which is responsible for the absence of the Boulware-Deser ghost mode in the theory. The bimetric scalar constraint is in general not manifestly covariant in its nature. However, in the mas...

  4. OPERATOR AND MATRIX REPRESENTATION FOR THE GENERALIZED INVERSE A(2)T,S

    Institute of Scientific and Technical Information of China (English)

    陈永林

    2001-01-01

    This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(2)T,S and give some of their applications.

  5. The matricial relaxation of a linear matrix inequality

    CERN Document Server

    Helton, J William; McCullough, Scott

    2010-01-01

    Given linear matrix inequalities (LMIs) L_1 and L_2, it is natural to ask: (Q1) when does one dominate the other, that is, does L_1(X) PsD imply L_2(X) PsD? (Q2) when do they have the same solution set? Such questions can be NP-hard. This paper describes a natural relaxation of an LMI, based on substituting matrices for the variables x_j. With this relaxation, the domination questions (Q1) and (Q2) have elegant answers, indeed reduce to constructible semidefinite programs. Assume there is an X such that L_1(X) and L_2(X) are both PD, and suppose the positivity domain of L_1 is bounded. For our "matrix variable" relaxation a positive answer to (Q1) is equivalent to the existence of matrices V_j such that L_2(x)=V_1^* L_1(x) V_1 + ... + V_k^* L_1(x) V_k. As for (Q2) we show that, up to redundancy, L_1 and L_2 are unitarily equivalent. Such algebraic certificates are typically called Positivstellensaetze and the above are examples of such for linear polynomials. The paper goes on to derive a cleaner and more pow...

  6. Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

    DEFF Research Database (Denmark)

    Garde, Henrik

    2017-01-01

    Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity....... For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method...

  7. Generalized companion matrix for approximate GCD

    CERN Document Server

    Boito, Paola

    2011-01-01

    We study a variant of the univariate approximate GCD problem, where the coe?- cients of one polynomial f(x)are known exactly, whereas the coe?cients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.

  8. Generalized Quadratic Linearization of Machine Models

    OpenAIRE

    Parvathy Ayalur Krishnamoorthy; Kamaraj Vijayarajan; Devanathan Rajagopalan

    2011-01-01

    In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome th...

  9. Localized density matrix minimization and linear scaling algorithms

    CERN Document Server

    Lai, Rongjie

    2015-01-01

    We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\\ell_1$ regularization to the free energy of the quantum system. Based on the fact that the density matrix decays exponential away from the diagonal for insulating system or system at finite temperature, the proposed $\\ell_1$ regularized variational method provides a nice way to approximate the original quantum system. We provide theoretical analysis of the approximation behavior and also design convergence guaranteed numerical algorithms based on Bregman iteration. More importantly, the $\\ell_1$ regularized system naturally leads to localized density matrices with banded structure, which enables us to develop approximating algorithms to find the localized density matrices with computation cost linearly dependent on the problem size.

  10. General practice--linear thinking and complexity

    National Research Council Canada - National Science Library

    Stalder, H

    2006-01-01

    As physicians, we apply and teach linear thinking. This approach permits to dissect the patient's problem to the molecular level and has contributed enormously to the knowledge and progress of medicine...

  11. A block Hankel generalized confluent Vandermonde matrix

    NARCIS (Netherlands)

    Klein, A.; Spreij, P.

    2014-01-01

    Vandermonde matrices are well known. They have a number of interesting properties and play a role in (Lagrange) interpolation problems, partial fraction expansions, and finding solutions to linear ordinary differential equations, to mention just a few applications. Usually, one takes these matrices

  12. A block Hankel generalized confluent Vandermonde matrix

    NARCIS (Netherlands)

    Klein, A.; Spreij, P.

    2014-01-01

    Vandermonde matrices are well known. They have a number of interesting properties and play a role in (Lagrange) interpolation problems, partial fraction expansions, and finding solutions to linear ordinary differential equations, to mention just a few applications. Usually, one takes these matrices

  13. A Note on the Identifiability of Generalized Linear Mixed Models

    DEFF Research Database (Denmark)

    Labouriau, Rodrigo

    2014-01-01

    I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first and second order moments and some general mild regularity ...... conditions, and, therefore, is extensible to quasi-likelihood based generalized linear models. In particular, binomial and Poisson mixed models with dispersion parameter are identifiable when equipped with the standard parametrization......I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first and second order moments and some general mild regularity...

  14. Construction of extended exponential general linear methods 524 ...

    African Journals Online (AJOL)

    Construction of extended exponential general linear methods 524 for solving semi-linear problems. ... Journal Home > Vol 13, No 2 (2014) > ... This paper introduces a new approach for constructing higher order of EEGLM which have become ...

  15. Penalized maximum likelihood estimation for generalized linear point processes

    OpenAIRE

    2010-01-01

    A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space and give results on Gateaux differentiability of the log-likelihood. Of particular interest is when the intensity is expressed in terms of a linear filter parametrized by a Sobolev space. Using that the Sobolev spaces are reproducing kernel Hilbert spaces we...

  16. Abstract Acceleration of General Linear Loops

    OpenAIRE

    2014-01-01

    International audience; We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states iteratively, abstract acceleration captures the effect of the loop with a single, non-iterative transfer function applied to the initial states at the loop head. In contrast to previous acceleration techniques, our approach applies to a...

  17. High-Dimensional Random Matrices from the Classical Matrix Groups, and Generalized Hypergeometric Functions of Matrix Argument

    Directory of Open Access Journals (Sweden)

    Donald St. P. Richards

    2011-08-01

    Full Text Available Results from the theory of the generalized hypergeometric functions of matrix argument, and the related zonal polynomials, are used to develop a new approach to study the asymptotic distributions of linear functions of uniformly distributed random matrices from the classical compact matrix groups. In particular, we provide a new approach for proving the following result of D’Aristotile, Diaconis, and Newman: Let the random matrix Hn be uniformly distributed according to Haar measure on the group of n × n orthogonal matrices, and let An be a non-random n × n real matrix such that tr (A'nAn = 1. Then, as n→∞, √n tr AnHn converges in distribution to the standard normal distribution.

  18. The origin of linear scaling Fock matrix calculation with density prescreening

    Energy Technology Data Exchange (ETDEWEB)

    Mitin, Alexander V., E-mail: mitin@phys.chem.msu.ru [Chemistry Department, Moscow State University, Moscow, 119991 (Russian Federation)

    2015-12-31

    A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.

  19. Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT).

    Science.gov (United States)

    Pernal, Katarzyna; Giesbertz, Klaas J H

    2016-01-01

    Recent advances in reduced density matrix functional theory (RDMFT) and linear response time-dependent reduced density matrix functional theory (TD-RDMFT) are reviewed. In particular, we present various approaches to develop approximate density matrix functionals which have been employed in RDMFT. We discuss the properties and performance of most available density matrix functionals. Progress in the development of functionals has been paralleled by formulation of novel RDMFT-based methods for predicting properties of molecular systems and solids. We give an overview of these methods. The time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting practical and generally useful functionals which would work within the adiabatic approximation. In this chapter we concentrate on the formulation of TD-RDMFT response equations and various adiabatic approximations. None of the adiabatic approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals (PINOs). We focus on applications of the linear response formulations to two-electron systems, for which the (almost) exact functional is known.

  20. A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

    KAUST Repository

    Huang, Jianhua Z.

    2012-03-01

    Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome this and other challenges by embedding the covariance matrix of the observed data for each subject in a larger covariance matrix and employing the familiar EM algorithm to compute the maximum likelihood estimates of the parameters and their standard errors. We illustrate and assess the methodology using real data sets and simulations. © 2011 Elsevier B.V.

  1. Generalized S-matrix in Mixed Representations

    CERN Document Server

    Ishikawa, K; Ishikawa, Kenzo; Shimomura, Takashi

    2006-01-01

    A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring instruments where momenta and positions satisfy minimum uncertainty are studied with a use of minimum wave packets, coherent states. In the present work, we show general features of the generalized scattering amplitudes based on ${\\phi}^4$ theory. We give a proof of completeness of many body states, asymptotic behaviors in the large distance region, and factorization of the amplitudes. Despite of the non-orthogonal properties of wave packets, we found that the probability interpretation is verified. A differential probability depends upon the wave packet size but a total probability that is integrated in the final states is independent from the size of final state wave packet and becomes universal. Few body amplitudes are studied as examples.

  2. ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS

    Institute of Scientific and Technical Information of China (English)

    YUE LI; CHEN XIRU

    2005-01-01

    For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.

  3. Differentiable Kernels in Generalized Matrix Learning Vector Quantization

    NARCIS (Netherlands)

    Kästner, M.; Nebel, D.; Riedel, M.; Biehl, M.; Villmann, T.

    2013-01-01

    In the present paper we investigate the application of differentiable kernel for generalized matrix learning vector quantization as an alternative kernel-based classifier, which additionally provides classification dependent data visualization. We show that the concept of differentiable kernels allo

  4. A General Formulation for the Stiffness Matrix of Parallel Mechanisms

    CERN Document Server

    Quennouelle, Cyril

    2012-01-01

    Starting from the definition of a stiffness matrix, the authors present a new formulation of the Cartesian stiffness matrix of parallel mechanisms. The proposed formulation is more general than any other stiffness matrix found in the literature since it can take into account the stiffness of the passive joints, it can consider additional compliances in the joints or in the links and it remains valid for large displacements. Then, the validity, the conservative property, the positive definiteness and the relation with other formulations of stiffness matrices are discussed theoretically. Finally, a numerical example is given in order to illustrate the correctness of this matrix.

  5. Generalized Ultrametric Semilattices of Linear Signals

    Science.gov (United States)

    2014-01-23

    ultrametric semilattice with a totally ordered distance set is isomorphic to a space of that kind. It follows that the formal definition of...from the National Science Foundation (NSF awards \\#0720882 ( CSR -EHS: PRET), \\#0931843 (CPS: Large: ActionWebs), and \\#1035672 (CPS: Medium: Timing...distance set is isomorphic to a space of that kind. It follows that the formal definition of generalized ultrametric semilattices with totally ordered

  6. General Neutrino Mass Matrix Patterns and Its Underlying Family Symmetries

    CERN Document Server

    Damanik, Asan; Anggraita, Pramudita; Muslim,

    2014-01-01

    Baseon on current experimental results, such as neutrino oscillations and the neutrinoless double beta decays (i.e. data from Super Kamiokande, KamLAND, SNO, etc.), the neutrino mixing matrix can be adequately determined. Though there are still certain parameters that have possibility limits, but based on the current experimental results it is possible to construct a general form of neutrino mass matrix. Starting from this general form of the neutrino mass matrix we put certain conditions in the context of the seesaw mechanism model to determine the possible pattern of the neutrino mass matrix that has a texture zero. From the obtained neutrino mass matrix pattern, there are three class of patterns, where two of the class are known to be realized in literature by the underlying family symmetries of the $D_{4}$ and $A_{4}$ groups, the dihedral and tetrahedral symmetry groups.

  7. A framework for general sparse matrix-matrix multiplication on GPUs and heterogeneous processors

    DEFF Research Database (Denmark)

    Liu, Weifeng; Vinter, Brian

    2015-01-01

    General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM implementation has to handle...

  8. Generalized L1 penalized matrix factorization

    DEFF Research Database (Denmark)

    Rasmussen, Morten Arendt

    2017-01-01

    for constraining models to obey certain structural properties, including parameter sparsity and sparsity on pairwise differences between parameter estimates. The utility of this framework is used to modify principal component analysis, partial least squares, canonical correlation analysis, and multivariate......Traditionally, chemometric models consists of parameters found by solving a least squares criterion. However, these models can suffer from overfitting, as well as being hard to interpret because of the large number of active parameters. This work proposes the use of a generalized L1 norm penalty...... analysis of variance type of models applied to synthetic and chemical data. This work argues that L1 norm penalized models offers parsimony, robustness and predictive performance, and reveals a path for modifying unconstrained chemometric models through convex penalties....

  9. Generalized Multicarrier CDMA: Unification and Linear Equalization

    Directory of Open Access Journals (Sweden)

    Wang Zhengdao

    2005-01-01

    Full Text Available Relying on block-symbol spreading and judicious design of user codes, this paper builds on the generalized multicarrier (GMC quasisynchronous CDMA system that is capable of multiuser interference (MUI elimination and intersymbol interference (ISI suppression with guaranteed symbol recovery, regardless of the wireless frequency-selective channels. GMC-CDMA affords an all-digital unifying framework, which encompasses single-carrier and several multicarrier (MC CDMA systems. Besides the unifying framework, it is shown that GMC-CDMA offers flexibility both in full load (maximum number of users allowed by the available bandwidth and in reduced load settings. A novel blind channel estimation algorithm is also derived. Analytical evaluation and simulations illustrate the superior error performance and flexibility of uncoded GMC-CDMA over competing MC-CDMA alternatives especially in the presence of uplink multipath channels.

  10. Efficient matrix approach to optical wave propagation and Linear Canonical Transforms.

    Science.gov (United States)

    Shakir, Sami A; Fried, David L; Pease, Edwin A; Brennan, Terry J; Dolash, Thomas M

    2015-10-01

    The Fresnel diffraction integral form of optical wave propagation and the more general Linear Canonical Transforms (LCT) are cast into a matrix transformation form. Taking advantage of recent efficient matrix multiply algorithms, this approach promises an efficient computational and analytical tool that is competitive with FFT based methods but offers better behavior in terms of aliasing, transparent boundary condition, and flexibility in number of sampling points and computational window sizes of the input and output planes being independent. This flexibility makes the method significantly faster than FFT based propagators when only a single point, as in Strehl metrics, or a limited number of points, as in power-in-the-bucket metrics, are needed in the output observation plane.

  11. Robust root clustering for linear uncertain systems using generalized Lyapunov theory

    Science.gov (United States)

    Yedavalli, R. K.

    1993-01-01

    Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

  12. Robust root clustering for linear uncertain systems using generalized Lyapunov theory

    Science.gov (United States)

    Yedavalli, R. K.

    1993-01-01

    Consideration is given to the problem of matrix root clustering in subregions of a complex plane for linear state space models with real parameter uncertainty. The nominal matrix root clustering theory of Gutman & Jury (1981) using the generalized Liapunov equation is extended to the perturbed matrix case, and bounds are derived on the perturbation to maintain root clustering inside a given region. The theory makes it possible to obtain an explicit relationship between the parameters of the root clustering region and the uncertainty range of the parameter space.

  13. Solution Properties of Linear Descriptor (Singular Matrix Differential Systems of Higher Order with (Non- Consistent Initial Conditions

    Directory of Open Access Journals (Sweden)

    Athanasios A. Pantelous

    2010-01-01

    Full Text Available In some interesting applications in control and system theory, linear descriptor (singular matrix differential equations of higher order with time-invariant coefficients and (non- consistent initial conditions have been used. In this paper, we provide a study for the solution properties of a more general class of the Apostol-Kolodner-type equations with consistent and nonconsistent initial conditions.

  14. Matrix theory from generalized inverses to Jordan form

    CERN Document Server

    Piziak, Robert

    2007-01-01

    Each chapter ends with a list of references for further reading. Undoubtedly, these will be useful for anyone who wishes to pursue the topics deeper. … the book has many MATLAB examples and problems presented at appropriate places. … the book will become a widely used classroom text for a second course on linear algebra. It can be used profitably by graduate and advanced level undergraduate students. It can also serve as an intermediate course for more advanced texts in matrix theory. This is a lucidly written book by two authors who have made many contributions to linear and multilinear algebra.-K.C. Sivakumar, IMAGE, No. 47, Fall 2011Always mathematically constructive, this book helps readers delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.-L'enseignement Mathématique, January-June 2007, Vol. 53, No. 1-2.

  15. Some Properties of Complex Matrix-Variate Generalized Dirichlet Integrals

    Indian Academy of Sciences (India)

    Joy Jacob; Sebastian George; A M Mathai

    2005-08-01

    Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.

  16. Derivation of the state matrix for dynamic analysis of linear homogeneous media.

    Science.gov (United States)

    Parra Martinez, Juan Pablo; Dazel, Olivier; Göransson, Peter; Cuenca, Jacques

    2016-08-01

    A method to obtain the state matrix of an arbitrary linear homogeneous medium excited by a plane wave is proposed. The approach is based on projections on the eigenspace of the governing equations matrix. It is an alternative to manually obtaining a linearly independent set of equations by combining the governing equations. The resulting matrix has been validated against previously published derivations for an anisotropic poroelastic medium.

  17. Accurate low-rank matrix recovery from a small number of linear measurements

    CERN Document Server

    Candes, Emmanuel J

    2009-01-01

    We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the entries, and we wish to fill in the missing entries (this is the famous Netflix problem). When M is believed to have low rank, one would ideally try to recover M by finding the minimum-rank matrix that is consistent with the data; this is, however, problematic since this is a nonconvex problem that is, generally, intractable. Nuclear-norm minimization has been proposed as a tractable approach, and past papers have delved into the theoretical properties of nuclear-norm minimization algorithms, establishing conditions under which minimizing the nuclear norm yields the minimum rank solution. We review this spring of emerging literature and extend and refine previous theoretical results. Our focus is on providing error bounds when M is well approximated by a low-rank matrix, and ...

  18. Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

    Science.gov (United States)

    Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

    2016-07-12

    We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

  19. GENERALIZED MATRIXES OF GALOIS PROTOCOLS EXCHANGE ENCRYPTION KEYS

    Directory of Open Access Journals (Sweden)

    Anatoly Beletsky

    2016-03-01

    Full Text Available The methods of construction of matrix formation the secret protocols legalized subscribers of public communications networks encryption keys. Based key exchange protocols laid asymmetric cryptography algorithms. The solution involves the calculation of one-way functions and is based on the use of generalized Galois arrays of isomorphism relationship with forming elements, and depending on the selected irreducible polynomial generating matrix. A simple method for constructing generalized Galois matrix by the method of filling the diagonal. In order to eliminate the isomorphism of Galois arrays and their constituent elements, limiting the possibility of building one-way functions, Galois matrix subjected to similarity transformation carried out by means of permutation matrices. The variant of the organization of the algebraic attacks on encryption keys sharing protocols and discusses options for easing the consequences of an attack.

  20. Exact Computation of Parallel Robot's Generalized Inertia Matrix

    Institute of Scientific and Technical Information of China (English)

    ZHAO Yongjie; YANG Zhiyong; MEI Jiangping; HUANG Tian

    2005-01-01

    According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot's generalized inertia matrix is presented. Based on the matrix theory, the generalized inertia matrix of the parallel robot can be computed on the assumption that the robot is in these new hypothetical states respectively. The approach is demonstrated by the Delta robot as an example. Based on the principle of the virtual work, the inverse dynamics model of the robot is formulized after the kinematics analysis. Finally, a numerical example is given and the element distribution of the Delta robot's inertia matrix in the workspace is studied. The method has computational advantage of numerical accuracy for the Delta robot and can be parallelized easily.

  1. Parallel Multi Channel Convolution using General Matrix Multiplication

    OpenAIRE

    VASUDEVAN, ARAVIND; Anderson, Andrew; Gregg, David

    2017-01-01

    Convolutional neural networks (CNNs) have emerged as one of the most successful machine learning technologies for image and video processing. The most computationally intensive parts of CNNs are the convolutional layers, which convolve multi-channel images with multiple kernels. A common approach to implementing convolutional layers is to expand the image into a column matrix (im2col) and perform Multiple Channel Multiple Kernel (MCMK) convolution using an existing parallel General Matrix Mul...

  2. Generalized Linear Models with Applications in Engineering and the Sciences

    CERN Document Server

    Myers, Raymond H; Vining, G Geoffrey; Robinson, Timothy J

    2012-01-01

    Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities."-Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Ma

  3. Natural connections given by general linear and classical connections

    OpenAIRE

    Janyška, Josef

    2004-01-01

    We assume a vector bundle $p: E\\to M$ with a general linear connection $K$ and a classical linear connection $\\Lam$ on $M$. We prove that all classical linear connections on the total space $E$ naturally given by $(\\Lam, K)$ form a 15-parameter family. Further we prove that all connections on $J^1 E$ naturally given by $(\\Lam, K)$ form a 14-parameter family. Both families of connections are described geometrically.

  4. A New Method for Solving General Dual Fuzzy Linear Systems

    Directory of Open Access Journals (Sweden)

    M. Otadi

    2013-09-01

    Full Text Available . According to fuzzy arithmetic, general dual fuzzy linear system (GDFLS cannot be replaced by a fuzzy linear system (FLS. In this paper, we use new notation of fuzzy numbers and convert a GDFLS to two linear systems in crisp case, then we discuss complexity of the proposed method. Conditions for the existence of a unique fuzzy solution to n × n GDFLS are derived

  5. An Efficient GPU General Sparse Matrix-Matrix Multiplication for Irregular Data

    DEFF Research Database (Denmark)

    Liu, Weifeng; Vinter, Brian

    2014-01-01

    matrices. Recent work on GPU SpGEMM has demonstrated rather good both time and space complexity, but works best for fairly regular matrices. In this work we present a GPU SpGEMM algorithm that particularly focuses on the above three problems. Memory pre-allocation for the result matrix is organized......General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle extra...... irregularity from three aspects: (1) the number of the nonzero entries in the result sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the result sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input...

  6. Testing Parametric versus Semiparametric Modelling in Generalized Linear Models

    NARCIS (Netherlands)

    Härdle, W.K.; Mammen, E.; Müller, M.D.

    1996-01-01

    We consider a generalized partially linear model E(Y|X,T) = G{X'b + m(T)} where G is a known function, b is an unknown parameter vector, and m is an unknown function.The paper introduces a test statistic which allows to decide between a parametric and a semiparametric model: (i) m is linear, i.e. m(

  7. Minimal solution of general dual fuzzy linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of)], E-mail: abbasbandy@yahoo.com; Otadi, M.; Mosleh, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh (Iran, Islamic Republic of)

    2008-08-15

    Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered.

  8. Neural Generalized Predictive Control of a non-linear Process

    DEFF Research Database (Denmark)

    Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

    1998-01-01

    qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...

  9. Linear and nonlinear optical processing of polymer matrix nanocomposites

    Science.gov (United States)

    DeJournett, Travis J.; Han, Karen; Olasov, Lauren R.; Zeng, Fan W.; Lee, Brennan; Spicer, James B.

    2015-08-01

    This work focuses on the scalable synthesis and processing of nanostructures in polymer matrix nanocomposites (PMNCs) for applications that require photochemical functionality of these nanostructures. An in situ vapor deposition process using various metal and metal oxide precursors has been used to create a range of nanocomposites that display photochromic and photocatalytic behaviors. Under specific processing conditions, these composites consist of discrete nanoparticles distributed uniformly throughout the bulk of an optically transparent polymer matrix. Incorporating other chemical species as supplementary deposition agents in the synthesis process can modify these particles and produce complicated nanostructures with enhanced properties. In particular, work has been carried out to structure nanoparticles using laser irradiation. Starting with metallic or metal oxide nanoparticles in the polymer matrix, localized chemical vapor deposition in the near-particle environment has been carried out using laser irradiation to decompose chemical precursors leading to the formation of secondary structures surrounding the seed nanoparticles. Control of the spatial and temporal characteristics of the excitation source allows for synthesis of nanocomposites with a high degree of control over the location, composition and size of nanoparticles in the matrix and presents the opportunity to produce patterned materials with spatially varying properties.

  10. Linear generalized synchronization of continuous-time chaotic systems

    Energy Technology Data Exchange (ETDEWEB)

    Lu Junguo E-mail: jglu@sjtu.edu.cn; Xi Yugeng

    2003-08-01

    This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification.

  11. A general and simple method for obtaining R2 from generalized linear mixed‐effects models

    National Research Council Canada - National Science Library

    Nakagawa, Shinichi; Schielzeth, Holger; O'Hara, Robert B

    2013-01-01

    The use of both linear and generalized linear mixed‐effects models ( LMM s and GLMM s) has become popular not only in social and medical sciences, but also in biological sciences, especially in the field of ecology and evolution...

  12. Thermodynamic bounds and general properties of optimal efficiency and power in linear responses.

    Science.gov (United States)

    Jiang, Jian-Hua

    2014-10-01

    We study the optimal exergy efficiency and power for thermodynamic systems with an Onsager-type "current-force" relationship describing the linear response to external influences. We derive, in analytic forms, the maximum efficiency and optimal efficiency for maximum power for a thermodynamic machine described by a N×N symmetric Onsager matrix with arbitrary integer N. The figure of merit is expressed in terms of the largest eigenvalue of the "coupling matrix" which is solely determined by the Onsager matrix. Some simple but general relationships between the power and efficiency at the conditions for (i) maximum efficiency and (ii) optimal efficiency for maximum power are obtained. We show how the second law of thermodynamics bounds the optimal efficiency and the Onsager matrix and relate those bounds together. The maximum power theorem (Jacobi's Law) is generalized to all thermodynamic machines with a symmetric Onsager matrix in the linear-response regime. We also discuss systems with an asymmetric Onsager matrix (such as systems under magnetic field) for a particular situation and we show that the reversible limit of efficiency can be reached at finite output power. Cooperative effects are found to improve the figure of merit significantly in systems with multiply cross-correlated responses. Application to example systems demonstrates that the theory is helpful in guiding the search for high performance materials and structures in energy researches.

  13. Penalized maximum likelihood estimation for generalized linear point processes

    DEFF Research Database (Denmark)

    Hansen, Niels Richard

    2010-01-01

    A generalized linear point process is specified in terms of an intensity that depends upon a linear predictor process through a fixed non-linear function. We present a framework where the linear predictor is parametrized by a Banach space and give results on Gateaux differentiability of the log-likelihood....... Of particular interest is when the intensity is expressed in terms of a linear filter parametrized by a Sobolev space. Using that the Sobolev spaces are reproducing kernel Hilbert spaces we derive results on the representation of the penalized maximum likelihood estimator in a special case and the gradient...... of the negative log-likelihood in general. The latter is used to develop a descent algorithm in the Sobolev space. We conclude the paper by extensions to multivariate and additive model specifications. The methods are implemented in the R-package ppstat....

  14. Student Transfer Guide General Education Articulation Matrix, 1998-99.

    Science.gov (United States)

    Louisiana State Board of Regents, Baton Rouge.

    This guide represents Louisiana public higher education's initial effort to improve the transfer process by making the process of transfer and evaluation of credit more easily understandable. A student transfer guide, this document includes a matrix of forty General Education college credit courses which (with few exceptions) can transfer between…

  15. Linear response theory for the density matrix renormalization group: efficient algorithms for strongly correlated excited states.

    Science.gov (United States)

    Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic

    2014-01-14

    Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.

  16. Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states

    Science.gov (United States)

    Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic

    2014-01-01

    Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.

  17. Noether's theory of generalized linear nonholonomic mechanical systems

    Institute of Scientific and Technical Information of China (English)

    Dong Wen-Shan; Huang Bao-Xin; Fang Jian-Hui

    2011-01-01

    By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether's theorem and the Noether's inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.

  18. Controllability of Linear Systems on Generalized Heisenberg Groups

    OpenAIRE

    Dath, Mouhamadou; Jouan, Philippe

    2015-01-01

    This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems, and more precise controllability criteria are stated for them.

  19. McDonald Generalized Linear Failure Rate Distribution

    Directory of Open Access Journals (Sweden)

    Ibrahim Elbatal

    2014-10-01

    Full Text Available We introduce in this paper a new six-parameters generalized version of the generalized linear failure rate (GLFR distribution which is called McDonald Generalized Linear failure rate (McGLFR distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing, and upside down bathtub-and bathtub shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. Some structural properties of the new distribution are studied. Moreover we discuss maximum likelihood estimation of the unknown parameters of the new model.

  20. General Linear Models: An Integrated Approach to Statistics

    Directory of Open Access Journals (Sweden)

    Andrew Faulkner

    2008-09-01

    Full Text Available Generally, in psychology, the various statistical analyses are taught independently from each other. As a consequence, students struggle to learn new statistical analyses, in contexts that differ from their textbooks. This paper gives a short introduction to the general linear model (GLM, in which it is showed that ANOVA (one-way, factorial, repeated measure and analysis of covariance is simply a multiple correlation/regression analysis (MCRA. Generalizations to other cases, such as multivariate and nonlinear analysis, are also discussed. It can easily be shown that every popular linear analysis can be derived from understanding MCRA.

  1. Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

    Institute of Scientific and Technical Information of China (English)

    Guangren DUAN; Yunli WU

    2006-01-01

    A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

  2. Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

    DEFF Research Database (Denmark)

    Adegas, Fabiano Daher; Stoustrup, Jakob

    2015-01-01

    the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems...

  3. Extensions of linear-quadratic control, optimization and matrix theory

    CERN Document Server

    Jacobson, David H

    1977-01-01

    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  4. Topological, smooth and holomorphic classifications of nonautonomous linear differential systems and projective matrix Riccati equations

    CERN Document Server

    Gorbuzov, V N

    2011-01-01

    The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and projective matrix Riccati equations.

  5. Invertible Linear Maps on the General Linear Lie Algebras Preserving Solvability

    Institute of Scientific and Technical Information of China (English)

    CHEN ZHENG-XIN; CHEN QIONG

    2012-01-01

    Let Mn be the algebra of all n × n complex matrices and gl(n,C) be the general linear Lie algebra,where n ≥ 2.An invertible linear map ?:gl(n,C) →gl(n,C) preserves solvability in both directions if both ? and ?-1 map every solvable Lie subalgebra of gl(n,C) to some solvable Lie subalgebra.In this paper we classify the invertible linear maps preserving solvability on gl(n,C) in both directions.As a sequence,such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.

  6. General Linear Models: An Integrated Approach to Statistics

    OpenAIRE

    Andrew Faulkner; Sylvain Chartier

    2008-01-01

    Generally, in psychology, the various statistical analyses are taught independently from each other. As a consequence, students struggle to learn new statistical analyses, in contexts that differ from their textbooks. This paper gives a short introduction to the general linear model (GLM), in which it is showed that ANOVA (one-way, factorial, repeated measure and analysis of covariance) is simply a multiple correlation/regression analysis (MCRA). Generalizations to other cases, such as multiv...

  7. Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

    Directory of Open Access Journals (Sweden)

    Hua-Feng He

    2014-01-01

    class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.

  8. New linear codes from matrix-product codes with polynomial units

    DEFF Research Database (Denmark)

    Hernando, Fernando; Ruano Benito, Diego

    2010-01-01

    A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.......A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented....

  9. Derivatives of eigenvalues and eigenvectors of a general complex matrix

    Science.gov (United States)

    Murthy, Durbha V.; Haftka, Raphael T.

    1988-01-01

    A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

  10. Extending the linear model with R generalized linear, mixed effects and nonparametric regression models

    CERN Document Server

    Faraway, Julian J

    2005-01-01

    Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway''s critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies. Following in those footsteps, Extending the Linear Model with R surveys the techniques that grow from the regression model, presenting three extensions to that framework: generalized linear models (GLMs), mixed effect models, and nonparametric regression models. The author''s treatment is thoroughly modern and covers topics that include GLM diagnostics, generalized linear mixed models, trees, and even the use of neural networks in statistics. To demonstrate the interplay of theory and practice, throughout the book the author weaves the use of the R software environment to analyze the data of real examples, providing all of the R commands necessary to reproduce the analyses. All of the ...

  11. Testing for one Generalized Linear Single Order Parameter

    DEFF Research Database (Denmark)

    Ellegaard, Niels Langager; Christensen, Tage Emil; Dyre, Jeppe

    work the order parameter may be chosen to have a non-exponential relaxation. The model predictions contradict the general consensus of the properties of viscous liquids in two ways: (i) The model predicts that following a linear isobaric temperature step, the normalized volume and entalpy relaxation...... functions are identical. This assumption conflicts with some (but not all) reports, utilizing the Tool-Narayanaswamy formalism to extrapolate from non-linear measurements to the linear regime. (ii) The model predicts that the theoretical "linear Prigogine-Defay" ratio is one. This ratio has never been...... responses or extrapolate from measurements of a glassy state away from equilibrium. Starting from a master equation description of inherent dynamics, we calculate the complex thermodynamic response functions. We device a way of testing for the generalized single order parameter model by measuring 3 complex...

  12. Estimation and variable selection for generalized additive partial linear models

    KAUST Repository

    Wang, Li

    2011-08-01

    We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.

  13. ON DETERMINATION OF THE IMPULSIVESOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    This note contains three main results.Firstly,a complete solution of the Linear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented that takes into account both the non-zero initial conditions of the pseudo state and the nonzero initial conditions of the input.Secondly,in order to characterise the dynamics of the LNHMDEs correctly,some important concepts such as the state,slow state (smooth state) and fast state (impulsive state) are generalized to the LNHMDE case and the solution of the LNHMDEs is separated into the smooth (slow) response and the fast (implusive) response.As a third result,a new characterization of the impulsive free initial conditions of the LNHMDEs is given.

  14. A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments

    Directory of Open Access Journals (Sweden)

    Ayşe Betül Koç

    2014-01-01

    Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.

  15. Dynamic generalized linear models for monitoring endemic diseases

    DEFF Research Database (Denmark)

    Lopes Antunes, Ana Carolina; Jensen, Dan Børge; Halasa, T.

    The objective was to use a Dynamic Generalized Linear Model (DGLM) based on abinomial distribution with a linear trend, for monitoring the PRRS (Porcine Reproductive and Respiratory Syndrome sero-prevalence in Danish swine herds. The DGLM was described and its performance for monitoring control...... in sero-prevalence. Based on this, it was possible to detect variations in the growth model component. This study is a proof-of-concept, demonstrating the use of DGLMs for monitoring endemic diseases. In addition, the principles stated might be useful in general research on monitoring and surveillance...

  16. Generalized model of double random phase encoding based on linear algebra

    Science.gov (United States)

    Nakano, Kazuya; Takeda, Masafumi; Suzuki, Hiroyuki; Yamaguchi, Masahiro

    2013-01-01

    We propose a generalized model for double random phase encoding (DRPE) based on linear algebra. We defined the DRPE procedure in six steps. The first three steps form an encryption procedure, while the later three steps make up a decryption procedure. We noted that the first (mapping) and second (transform) steps can be generalized. As an example of this generalization, we used 3D mapping and a transform matrix, which is a combination of a discrete cosine transform and two permutation matrices. Finally, we investigated the sensitivity of the proposed model to errors in the decryption key.

  17. Fuzzy attitude control of solar sail via linear matrix inequalities

    Science.gov (United States)

    Baculi, Joshua; Ayoubi, Mohammad A.

    2017-09-01

    This study presents a fuzzy tracking controller based on the Takagi-Sugeno (T-S) fuzzy model of the solar sail. First, the T-S fuzzy model is constructed by linearizing the existing nonlinear equations of motion of the solar sail. Then, the T-S fuzzy model is used to derive the state feedback controller gains for the Twin Parallel Distributed Compensation (TPDC) technique. The TPDC tracks and stabilizes the attitude of the solar sail to any desired state in the presence of parameter uncertainties and external disturbances while satisfying actuator constraints. The performance of the TPDC is compared to a PID controller that is tuned using the Ziegler-Nichols method. Numerical simulation shows the TPDC outperforms the PID controller when stabilizing the solar sail to a desired state.

  18. Exactly Recovering Low-Rank Matrix in Linear Time via $l_1$ Filter

    CERN Document Server

    Liu, Risheng; Su, Zhixun

    2011-01-01

    Recovering a low rank matrix from corrupted data, which is known as Robust PCA, has attracted considerable interests in recent years. This problem can be exactly solved by a combined nuclear norm and $l_1$ norm minimization. However, due to the computational burden of SVD inherent with the nuclear norm minimization, traditional methods suffer from high computational complexity, especially for large scale datasets. In this paper, inspired by digital filtering idea in image processing, we propose a novel algorithm, named $l_1$ Filter, for solving Robust PCA with linear cost. The $l_1$ Filter is defined by a seed, which is a exactly recovered small submatrix of the underlying low rank matrix. By solving some $l_1$ minimization problems in parallel, the full low rank matrix can be exactly recovered from corrupted observations with linear cost. Both theoretical analysis and experimental results exhibit that our method is an efficient way to exactly recovering low rank matrix in linear time.

  19. Generalized linear mixed models modern concepts, methods and applications

    CERN Document Server

    Stroup, Walter W

    2012-01-01

    PART I The Big PictureModeling BasicsWhat Is a Model?Two Model Forms: Model Equation and Probability DistributionTypes of Model EffectsWriting Models in Matrix FormSummary: Essential Elements for a Complete Statement of the ModelDesign MattersIntroductory Ideas for Translating Design and Objectives into ModelsDescribing ""Data Architecture"" to Facilitate Model SpecificationFrom Plot Plan to Linear PredictorDistribution MattersMore Complex Example: Multiple Factors with Different Units of ReplicationSetting the StageGoals for Inference with Models: OverviewBasic Tools of InferenceIssue I: Data

  20. On Optimal Backward Perturbation Analysis for the Linear System with Skew Circulant Coefficient Matrix

    Science.gov (United States)

    Jiang, Zhaolin; Shen, Nuo; Zhou, Jianwei

    2013-01-01

    We first give the style spectral decomposition of a special skew circulant matrix C and then get the style decomposition of arbitrary skew circulant matrix by making use of the Kronecker products between the elements of first row in skew circulant and the special skew circulant C. Besides that, we obtain the singular value of skew circulant matrix as well. Finally, we deal with the optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix on the base of its style spectral decomposition. PMID:24369488

  1. Global synchronization of Chua's chaotic delay network by using linear matrix inequality

    Institute of Scientific and Technical Information of China (English)

    Li Zhi; Shi Song-Jiao

    2004-01-01

    Global synchronization of Chua's chaotic dynamical networks with coupling delays is investigated in this paper.Unlike other approaches, where only local results were obtained, the network is found to be not linearized in this paper.Instead, the global synchronization is obtained by using the linear matrix inequality theory. Moreover, some quite simple linear-state-error feedback controllers for global synchronization are derived, which can be easily constructed based on the minimum eigenvalue of the coupling matrix. A simulation of Chua's chaotic network with global coupling delays in nodes is finally given, which is used to verify the theoretical results of the proposed global synchronization scheme.

  2. Linear matrix inequalities for analysis and control of linear vector second-order systems

    Energy Technology Data Exchange (ETDEWEB)

    Adegas, Fabiano D. [Aalborg Univ. (Denmark); Stoustrup, Jakob [Aalborg Univ. (Denmark)

    2014-10-06

    Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form.

  3. Consensus of Continuous-Time Multiagent Systems with General Linear Dynamics and Nonuniform Sampling

    Directory of Open Access Journals (Sweden)

    Yanping Gao

    2013-01-01

    Full Text Available This paper studies the consensus problem of multiple agents with general linear continuous-time dynamics. It is assumed that the information transmission among agents is intermittent; namely, each agent can only obtain the information of other agents at some discrete times, where the discrete time intervals may not be equal. Some sufficient conditions for consensus in the cases of state feedback and static output feedback are established, and it is shown that if the controller gain and the upper bound of discrete time intervals satisfy certain linear matrix inequality, then consensus can be reached. Simulations are performed to validate the theoretical results.

  4. H∞ filtering of Markov jump linear systems with general transition probabilities and output quantization.

    Science.gov (United States)

    Shen, Mouquan; Park, Ju H

    2016-07-01

    This paper addresses the H∞ filtering of continuous Markov jump linear systems with general transition probabilities and output quantization. S-procedure is employed to handle the adverse influence of the quantization and a new approach is developed to conquer the nonlinearity induced by uncertain and unknown transition probabilities. Then, sufficient conditions are presented to ensure the filtering error system to be stochastically stable with the prescribed performance requirement. Without specified structure imposed on introduced slack variables, a flexible filter design method is established in terms of linear matrix inequalities. The effectiveness of the proposed method is validated by a numerical example.

  5. The Optimal Linear Combination of Multiple Predictors Under the Generalized Linear Models.

    Science.gov (United States)

    Jin, Hua; Lu, Ying

    2009-11-15

    Multiple alternative diagnostic tests for one disease are commonly available to clinicians. It's important to use all the good diagnostic predictors simultaneously to establish a new predictor with higher statistical utility. Under the generalized linear model for binary outcomes, the linear combination of multiple predictors in the link function is proved optimal in the sense that the area under the receiver operating characteristic (ROC) curve of this combination is the largest among all possible linear combination. The result was applied to analysis of the data from the Study of Osteoporotic Fractures (SOF) with comparison to Su and Liu's approach.

  6. Thurstonian models for sensory discrimination tests as generalized linear models

    DEFF Research Database (Denmark)

    Brockhoff, Per B.; Christensen, Rune Haubo Bojesen

    2010-01-01

    Sensory discrimination tests such as the triangle, duo-trio, 2-AFC and 3-AFC tests produce binary data and the Thurstonian decision rule links the underlying sensory difference 6 to the observed number of correct responses. In this paper it is shown how each of these four situations can be viewed...... as a so-called generalized linear model. The underlying sensory difference 6 becomes directly a parameter of the statistical model and the estimate d' and it's standard error becomes the "usual" output of the statistical analysis. The d' for the monadic A-NOT A method is shown to appear as a standard...... linear contrast in a generalized linear model using the probit link function. All methods developed in the paper are implemented in our free R-package sensR (http://www.cran.r-project.org/package=sensR/). This includes the basic power and sample size calculations for these four discrimination tests...

  7. A random effects generalized linear model for reliability compositive evaluation

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments. The relevant algorithms are also provided. Simulation results manifest the soundness and effectiveness of the proposed model.

  8. RF Circuit linearity optimization using a general weak nonlinearity model

    NARCIS (Netherlands)

    Cheng, W.; Oude Alink, M.S.; Annema, Anne J.; Croon, Jeroen A.; Nauta, Bram

    2012-01-01

    This paper focuses on optimizing the linearity in known RF circuits, by exploring the circuit design space that is usually available in today’s deep submicron CMOS technologies. Instead of using brute force numerical optimizers we apply a generalized weak nonlinearity model that only involves AC

  9. The General Linear Model as Structural Equation Modeling

    Science.gov (United States)

    Graham, James M.

    2008-01-01

    Statistical procedures based on the general linear model (GLM) share much in common with one another, both conceptually and practically. The use of structural equation modeling path diagrams as tools for teaching the GLM as a body of connected statistical procedures is presented. A heuristic data set is used to demonstrate a variety of univariate…

  10. Applying the General Linear Model to Repeated Measures Problems.

    Science.gov (United States)

    Pohlmann, John T.; McShane, Michael G.

    The purpose of this paper is to demonstrate the use of the general linear model (GLM) in problems with repeated measures on a dependent variable. Such problems include pretest-posttest designs, multitrial designs, and groups by trials designs. For each of these designs, a GLM analysis is demonstrated wherein full models are formed and restrictions…

  11. A random effects generalized linear model for reliability compositive evaluation

    Institute of Scientific and Technical Information of China (English)

    ZHAO Hui; YU Dan

    2009-01-01

    This paper first proposes a random effects generalized linear model to evaluate the storage life of one kind of high reliable and small sample-sized products by combining multi-sources information of products coming from the same population but stored at different environments.The relevant algorithms are also provided.Simulation results manifest the soundness and effectiveness of the proposed model.

  12. 2-norm error bounds and estimates for Lanczos approximations to linear systems and rational matrix functions

    CERN Document Server

    Frommer, A; Lippert, Th; Rittich, H

    2012-01-01

    The Lanczos process constructs a sequence of orthonormal vectors v_m spanning a nested sequence of Krylov subspaces generated by a hermitian matrix A and some starting vector b. In this paper we show how to cheaply recover a secondary Lanczos process, starting at an arbitrary Lanczos vector v_m and how to use this secondary process to efficiently obtain computable error estimates and error bounds for the Lanczos approximations to a solution of a linear system Ax = b as well as, more generally, for the Lanczos approximations to the action of a rational matrix function on a vector. Our approach uses the relation between the Lanczos process and quadrature as developed by Golub and Meurant. It is different from methods known so far because of its use of the secondary Lanczos process. With our approach, it is now in particular possible to efficiently obtain upper bounds for the error in the 2-norm, provided a lower bound on the smallest eigenvalue of A is known. This holds for the error of the cg iterates as well ...

  13. On absolute stability of Lur'e control systems with multiple non-linearities using linear matrix inequalities

    Institute of Scientific and Technical Information of China (English)

    Min WU; Yong HE; Jinhua SHE

    2004-01-01

    Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability ofLur' e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method.

  14. Iterative linearized density matrix propagation for modeling coherent excitation energy transfer in photosynthetic light harvesting.

    Science.gov (United States)

    Huo, P; Coker, D F

    2010-11-14

    Rather than incoherent hopping between chromophores, experimental evidence suggests that the excitation energy transfer in some biological light harvesting systems initially occurs coherently, and involves coherent superposition states in which excitation spreads over multiple chromophores separated by several nanometers. Treating such delocalized coherent superposition states in the presence of decoherence and dissipation arising from coupling to an environment is a significant challenge for conventional theoretical tools that either use a perturbative approach or make the Markovian approximation. In this paper, we extend the recently developed iterative linearized density matrix (ILDM) propagation scheme [E. R. Dunkel et al., J. Chem. Phys. 129, 114106 (2008)] to study coherent excitation energy transfer in a model of the Fenna-Matthews-Olsen light harvesting complex from green sulfur bacteria. This approach is nonperturbative and uses a discrete path integral description employing a short time approximation to the density matrix propagator that accounts for interference between forward and backward paths of the quantum excitonic system while linearizing the phase in the difference between the forward and backward paths of the environmental degrees of freedom resulting in a classical-like treatment of these variables. The approach avoids making the Markovian approximation and we demonstrate that it successfully describes the coherent beating of the site populations on different chromophores and gives good agreement with other methods that have been developed recently for going beyond the usual approximations, thus providing a new reliable theoretical tool to study coherent exciton transfer in light harvesting systems. We conclude with a discussion of decoherence in independent bilinearly coupled harmonic chromophore baths. The ILDM propagation approach in principle can be applied to more general descriptions of the environment.

  15. A new heuristic algorithm for general integer linear programming problems

    Institute of Scientific and Technical Information of China (English)

    GAO Pei-wang; CAI Ying

    2006-01-01

    A new heuristic algorithm is proposed for solving general integer linear programming problems.In the algorithm,the objective function hyperplane is used as a cutting plane,and then by introducing a special set of assistant sets,an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane.A simple numerical example shows that the algorithm is efficient for some problems,and therefore,of practical interest.

  16. Regularization Paths for Generalized Linear Models via Coordinate Descent

    Directory of Open Access Journals (Sweden)

    Jerome Friedman

    2010-02-01

    Full Text Available We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, two-class logistic regression, and multi- nomial regression problems while the penalties include ℓ1 (the lasso, ℓ2 (ridge regression and mixtures of the two (the elastic net. The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

  17. Computing generalized inverses using LU factorization of matrix product

    CERN Document Server

    Stanimirović,; Tasić,; B, M; 10.1080/00207160701582077

    2011-01-01

    An algorithm for computing {2, 3}, {2, 4}, {1, 2, 3}, {1, 2, 4} -inverses and the Moore-Penrose inverse of a given rational matrix A is established. Classes A(2, 3)s and A(2, 4)s are characterized in terms of matrix products (R*A)+R* and T*(AT*)+, where R and T are rational matrices with appropriate dimensions and corresponding rank. The proposed algorithm is based on these general representations and the Cholesky factorization of symmetric positive matrices. The algorithm is implemented in programming languages MATHEMATICA and DELPHI, and illustrated via examples. Numerical results of the algorithm, corresponding to the Moore-Penrose inverse, are compared with corresponding results obtained by several known methods for computing the Moore-Penrose inverse.

  18. The left invariant metric in the general linear group

    CERN Document Server

    Andruchow, Esteban; Recht, Lazaro; Varela, Alejandro

    2011-01-01

    Left invariant metrics induced by the p-norms of the trace in the matrix algebra are studied on the general lineal group. By means of the Euler-Lagrange equations, existence and uniqueness of extremal paths for the length functional are established, and regularity properties of these extremal paths are obtained. Minimizing paths in the group are shown to have a velocity with constant singular values and multiplicity. In several special cases, these geodesic paths are computed explicitly. In particular the Riemannian geodesics, corresponding to the case p=2, are characterized as the product of two one-parameter groups. It is also shown that geodesics are one-parameter groups if and only if the initial velocity is a normal matrix. These results are further extended to the context of compact operators with p-summable spectrum, where a differential equation for the spectral projections of the velocity vector of an extremal path is obtained.

  19. Linear models in matrix form a hands-on approach for the behavioral sciences

    CERN Document Server

    Brown, Jonathon D

    2014-01-01

    This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum ...

  20. Generalized non-linear strength theory and transformed stress space

    Institute of Scientific and Technical Information of China (English)

    YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo

    2004-01-01

    Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.

  1. General expression for linear and nonlinear time series models

    Institute of Scientific and Technical Information of China (English)

    Ren HUANG; Feiyun XU; Ruwen CHEN

    2009-01-01

    The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.

  2. Computation of Optimal Monotonicity Preserving General Linear Methods

    KAUST Repository

    Ketcheson, David I.

    2009-07-01

    Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.

  3. On the Generalized Inverse Matrix%浅谈广义逆矩阵

    Institute of Scientific and Technical Information of China (English)

    周海青

    2012-01-01

    文章介绍莫尔一潘鲁斯(Moore-Penrose)广义逆矩阵的概念及其与实际背景的联系.文章中定理1和定理2说明条件Ⅰ与相容线性方程组的基本解的广义逆矩阵的联系,定理3说明条件Ⅰ和Ⅳ与相容线性方程组的最小模解的广义逆矩阵的联系.%The article introduces the concept of Moore-Peniose's generalized inverse matrix and its relation with the actual background. Theorem 1 and Theorem 2 in this article illustrate the relation between Conditions 1 and generalized inverse matrix of the fundamental solution of compatible linear equation.Theorem 3 illustrates Condition I and Condition IV's relation with generalized inverse matrix of the minimal model solution of compatible linear equation.

  4. A Non-Gaussian Spatial Generalized Linear Latent Variable Model

    KAUST Repository

    Irincheeva, Irina

    2012-08-03

    We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents. © 2012 International Biometric Society.

  5. Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

    CERN Document Server

    Gottwald, Fabian; Ivanov, Sergei D; Kühn, Oliver

    2015-01-01

    Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation (GLE), which can be rigorously derived by means of a linear projection (LP) technique. Within this framework a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here we discuss that this task is most naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importa...

  6. Practical likelihood analysis for spatial generalized linear mixed models

    DEFF Research Database (Denmark)

    Bonat, W. H.; Ribeiro, Paulo Justiniano

    2016-01-01

    We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. The Rhizoctonia root rot and the Rongelap are, respectiv......We investigate an algorithm for maximum likelihood estimation of spatial generalized linear mixed models based on the Laplace approximation. We compare our algorithm with a set of alternative approaches for two datasets from the literature. The Rhizoctonia root rot and the Rongelap are...... of Laplace approximation include the computation of the maximized log-likelihood value, which can be used for model selection and tests, and the possibility to obtain realistic confidence intervals for model parameters based on profile likelihoods. The Laplace approximation also avoids the tuning...

  7. The decoupling of second-order linear systems with a singular mass matrix

    Science.gov (United States)

    Kawano, Daniel T.; Morzfeld, Matthias; Ma, Fai

    2013-12-01

    It was demonstrated in earlier work that a nondefective, linear dynamical system with an invertible mass matrix in free or forced motion may be decoupled in the configuration space by a real and isospectral transformation. We extend this work by developing a procedure for decoupling a linear dynamical system with a singular mass matrix in the configuration space, transforming the original differential-algebraic system into decoupled sets of real, independent, first- and second-order differential equations. Numerical examples are provided to illustrate the application of the decoupling procedure.

  8. Neural Generalized Predictive Control of a non-linear Process

    DEFF Research Database (Denmark)

    Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole

    1998-01-01

    The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....

  9. Conditional likelihood inference in generalized linear mixed models.

    OpenAIRE

    Sartori, Nicola; Severini , T.A

    2002-01-01

    Consider a generalized linear model with a canonical link function, containing both fixed and random effects. In this paper, we consider inference about the fixed effects based on a conditional likelihood function. It is shown that this conditional likelihood function is valid for any distribution of the random effects and, hence, the resulting inferences about the fixed effects are insensitive to misspecification of the random effects distribution. Inferences based on the conditional likelih...

  10. A general theory of linear cosmological perturbations: bimetric theories

    CERN Document Server

    Lagos, Macarena

    2016-01-01

    We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.

  11. Credibility analysis of risk classes by generalized linear model

    Science.gov (United States)

    Erdemir, Ovgucan Karadag; Sucu, Meral

    2016-06-01

    In this paper generalized linear model (GLM) and credibility theory which are frequently used in nonlife insurance pricing are combined for reliability analysis. Using full credibility standard, GLM is associated with limited fluctuation credibility approach. Comparison criteria such as asymptotic variance and credibility probability are used to analyze the credibility of risk classes. An application is performed by using one-year claim frequency data of a Turkish insurance company and results of credible risk classes are interpreted.

  12. Electromagnetic axial anomaly in a generalized linear sigma model

    Science.gov (United States)

    Fariborz, Amir H.; Jora, Renata

    2017-06-01

    We construct the electromagnetic anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four-quark content. We compute in the leading order of this framework the decays into two photons of six pseudoscalars: π0(137 ), π0(1300 ), η (547 ), η (958 ), η (1295 ) and η (1760 ). Our results agree well with the available experimental data.

  13. Nonmonotonic Recursive Polynomial Expansions for Linear Scaling Calculation of the Density Matrix.

    Science.gov (United States)

    Rubensson, Emanuel H

    2011-05-10

    As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this letter, there is room for improvements. The key is to allow for nonmonotonicity in the recursive polynomial expansion. On the basis of this idea, new purification schemes are proposed that require only half the number of matrix-matrix multiplications compared to previous schemes. The speedup is essentially independent of the location of the chemical potential and increases with decreasing band gap.

  14. Residuals analysis of the generalized linear models for longitudinal data.

    Science.gov (United States)

    Chang, Y C

    2000-05-30

    The generalized estimation equation (GEE) method, one of the generalized linear models for longitudinal data, has been used widely in medical research. However, the related sensitivity analysis problem has not been explored intensively. One of the possible reasons for this was due to the correlated structure within the same subject. We showed that the conventional residuals plots for model diagnosis in longitudinal data could mislead a researcher into trusting the fitted model. A non-parametric method, named the Wald-Wolfowitz run test, was proposed to check the residuals plots both quantitatively and graphically. The rationale proposedin this paper is well illustrated with two real clinical studies in Taiwan.

  15. Bringing about matrix sparsity in linear-scaling electronic structure calculations.

    Science.gov (United States)

    Rubensson, Emanuel H; Rudberg, Elias

    2011-05-01

    The performance of linear-scaling electronic structure calculations depends critically on matrix sparsity. This article gives an overview of different strategies for removal of small matrix elements, with emphasis on schemes that allow for rigorous control of errors. In particular, a novel scheme is proposed that has significantly smaller computational overhead compared with the Euclidean norm-based truncation scheme of Rubensson et al. (J Comput Chem 2009, 30, 974) while still achieving the desired asymptotic behavior required for linear scaling. Small matrix elements are removed while ensuring that the Euclidean norm of the error matrix stays below a desired value, so that the resulting error in the occupied subspace can be controlled. The efficiency of the new scheme is investigated in benchmark calculations for water clusters including up to 6523 water molecules. Furthermore, the foundation of matrix sparsity is investigated. This includes a study of the decay of matrix element magnitude with distance between basis function centers for different molecular systems and different methods. The studied methods include Hartree–Fock and density functional theory using both pure and hybrid functionals. The relation between band gap and decay properties of the density matrix is also discussed.

  16. Comparative Study of Algorithms for Automated Generalization of Linear Objects

    Science.gov (United States)

    Azimjon, S.; Gupta, P. K.; Sukhmani, R. S. G. S.

    2014-11-01

    Automated generalization, rooted from conventional cartography, has become an increasing concern in both geographic information system (GIS) and mapping fields. All geographic phenomenon and the processes are bound to the scale, as it is impossible for human being to observe the Earth and the processes in it without decreasing its scale. To get optimal results, cartographers and map-making agencies develop set of rules and constraints, however these rules are under consideration and topic for many researches up until recent days. Reducing map generating time and giving objectivity is possible by developing automated map generalization algorithms (McMaster and Shea, 1988). Modification of the scale traditionally is a manual process, which requires knowledge of the expert cartographer, and it depends on the experience of the user, which makes the process very subjective as every user may generate different map with same requirements. However, automating generalization based on the cartographic rules and constrains can give consistent result. Also, developing automated system for map generation is the demand of this rapid changing world. The research that we have conveyed considers only generalization of the roads, as it is one of the indispensable parts of a map. Dehradun city, Uttarakhand state of India was selected as a study area. The study carried out comparative study of the generalization software sets, operations and algorithms available currently, also considers advantages and drawbacks of the existing software used worldwide. Research concludes with the development of road network generalization tool and with the final generalized road map of the study area, which explores the use of open source python programming language and attempts to compare different road network generalization algorithms. Thus, the paper discusses the alternative solutions for automated generalization of linear objects using GIS-technologies. Research made on automated of road network

  17. Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

    Science.gov (United States)

    Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D.; Kühn, Oliver

    2015-06-01

    Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.

  18. Parametrizing linear generalized Langevin dynamics from explicit molecular dynamics simulations

    Energy Technology Data Exchange (ETDEWEB)

    Gottwald, Fabian; Karsten, Sven; Ivanov, Sergei D., E-mail: sergei.ivanov@uni-rostock.de; Kühn, Oliver [Institute of Physics, Rostock University, Universitätsplatz 3, 18055 Rostock (Germany)

    2015-06-28

    Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into a few important degrees of freedom which are treated most accurately and others which constitute a thermal bath. Particular attention in this respect attracts the linear generalized Langevin equation, which can be rigorously derived by means of a linear projection technique. Within this framework, a complicated interaction with the bath can be reduced to a single memory kernel. This memory kernel in turn is parametrized for a particular system studied, usually by means of time-domain methods based on explicit molecular dynamics data. Here, we discuss that this task is more naturally achieved in frequency domain and develop a Fourier-based parametrization method that outperforms its time-domain analogues. Very surprisingly, the widely used rigid bond method turns out to be inappropriate in general. Importantly, we show that the rigid bond approach leads to a systematic overestimation of relaxation times, unless the system under study consists of a harmonic bath bi-linearly coupled to the relevant degrees of freedom.

  19. Global stabilization of linear periodically time-varying switched systems via matrix inequalities

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this paper, we address the stabilization problem for linear periodically time-varying switched systems.Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.

  20. Formulating robust linear regression estimation as a one-class LDA criterion: discriminative hat matrix.

    Science.gov (United States)

    Dufrenois, F; Noyer, J C

    2013-02-01

    Linear discriminant analysis, such as Fisher's criterion, is a statistical learning tool traditionally devoted to separating a training dataset into two or even several classes by the way of linear decision boundaries. In this paper, we show that this tool can formalize the robust linear regression problem as a robust estimator will do. More precisely, we develop a one-class Fischer's criterion in which the maximization provides both the regression parameters and the separation of the data in two classes: typical data and atypical data or outliers. This new criterion is built on the statistical properties of the subspace decomposition of the hat matrix. From this angle, we improve the discriminative properties of the hat matrix which is traditionally used as outlier diagnostic measure in linear regression. Naturally, we call this new approach discriminative hat matrix. The proposed algorithm is fully nonsupervised and needs only the initialization of one parameter. Synthetic and real datasets are used to study the performance both in terms of regression and classification of the proposed approach. We also illustrate its potential application to image recognition and fundamental matrix estimation in computer vision.

  1. STRONGLY CONSISTENT ESTIMATION FOR A MULTIVARIATE LINEAR RELATIONSHIP MODEL WITH ESTIMATED COVARIANCES MATRIX

    Institute of Scientific and Technical Information of China (English)

    Yee LEUNG; WU Kefa; DONG Tianxin

    2001-01-01

    In this paper, a multivariate linear functional relationship model, where the covariance matrix of the observational errors is not restricted, is considered. The parameter estimation of this model is discussed. The estimators are shown to be a strongly consistent estimation under some mild conditions on the incidental parameters.

  2. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

    CERN Document Server

    Li, Deng-Feng

    2016-01-01

    This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

  3. Confidence Intervals of Variance Functions in Generalized Linear Model

    Institute of Scientific and Technical Information of China (English)

    Yong Zhou; Dao-ji Li

    2006-01-01

    In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models (GLMs), when designs are fixed points and random variables respectively. Bias-corrected confidence bands are proposed for the (conditional) variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the (conditional) variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparametric autoregressive times series model with heteroscedastic conditional variance.

  4. Comparison between Unknown Input Estimation of a System Using Projection Operator Approach and Generalized Matrix Inverse Method

    Directory of Open Access Journals (Sweden)

    Ashis De

    2014-01-01

    Full Text Available In this paper a detailed comparison between the estimation results of unknown inputs of a linear time invariant system using projection operator approach and using the method of generalized matrix inverse have been discussed. The full order observer constructed using projection operator approach has been extended and implemented for this purpose.

  5. Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

    CERN Document Server

    Chung, Moses; Davidson, Ronald C; Groening, Lars; Xiao, Chen

    2016-01-01

    In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution, formulated on the basis of the single-particle Courant-Snyder (CS) invariants, has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. The new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. The corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed des...

  6. A Graphical User Interface to Generalized Linear Models in MATLAB

    Directory of Open Access Journals (Sweden)

    Peter Dunn

    1999-07-01

    Full Text Available Generalized linear models unite a wide variety of statistical models in a common theoretical framework. This paper discusses GLMLAB-software that enables such models to be fitted in the popular mathematical package MATLAB. It provides a graphical user interface to the powerful MATLAB computational engine to produce a program that is easy to use but with many features, including offsets, prior weights and user-defined distributions and link functions. MATLAB's graphical capacities are also utilized in providing a number of simple residual diagnostic plots.

  7. Synthesis of linear regression coefficients by recovering the within-study covariance matrix from summary statistics.

    Science.gov (United States)

    Yoneoka, Daisuke; Henmi, Masayuki

    2017-06-01

    Recently, the number of regression models has dramatically increased in several academic fields. However, within the context of meta-analysis, synthesis methods for such models have not been developed in a commensurate trend. One of the difficulties hindering the development is the disparity in sets of covariates among literature models. If the sets of covariates differ across models, interpretation of coefficients will differ, thereby making it difficult to synthesize them. Moreover, previous synthesis methods for regression models, such as multivariate meta-analysis, often have problems because covariance matrix of coefficients (i.e. within-study correlations) or individual patient data are not necessarily available. This study, therefore, proposes a brief explanation regarding a method to synthesize linear regression models under different covariate sets by using a generalized least squares method involving bias correction terms. Especially, we also propose an approach to recover (at most) threecorrelations of covariates, which is required for the calculation of the bias term without individual patient data. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

  8. A parallel algorithm for the eigenvalues and eigenvectors for a general complex matrix

    Science.gov (United States)

    Shroff, Gautam

    1989-01-01

    A new parallel Jacobi-like algorithm is developed for computing the eigenvalues of a general complex matrix. Most parallel methods for this parallel typically display only linear convergence. Sequential norm-reducing algorithms also exit and they display quadratic convergence in most cases. The new algorithm is a parallel form of the norm-reducing algorithm due to Eberlein. It is proven that the asymptotic convergence rate of this algorithm is quadratic. Numerical experiments are presented which demonstrate the quadratic convergence of the algorithm and certain situations where the convergence is slow are also identified. The algorithm promises to be very competitive on a variety of parallel architectures.

  9. A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence

    Directory of Open Access Journals (Sweden)

    Aynur Yalçiner

    2013-01-01

    Full Text Available We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.

  10. Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems

    Directory of Open Access Journals (Sweden)

    Xinbo Zhang

    2014-01-01

    Full Text Available A polymorphic uncertain linear programming (PULP model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.

  11. Generalized space and linear momentum operators in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Costa, Bruno G. da, E-mail: bruno.costa@ifsertao-pe.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Sertão Pernambucano, Campus Petrolina, BR 407, km 08, 56314-520 Petrolina, Pernambuco (Brazil); Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil); Borges, Ernesto P., E-mail: ernesto@ufba.br [Instituto de Física, Universidade Federal da Bahia, R. Barão de Jeremoabo s/n, 40170-115 Salvador, Bahia (Brazil)

    2014-06-15

    We propose a modification of a recently introduced generalized translation operator, by including a q-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator p{sup ^}{sub q}, and its canonically conjugate deformed position operator x{sup ^}{sub q}. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual q-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.

  12. Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems

    Directory of Open Access Journals (Sweden)

    Cui-Xia Li

    2014-01-01

    Full Text Available Based on the modified Hermitian and skew-Hermitian splitting (MHSS and preconditioned MHSS (PMHSS methods, a generalized preconditioned MHSS (GPMHSS method for a class of complex symmetric linear systems is presented. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From a practical point of view, we have analyzed and implemented inexact GPMHSS (IGPMHSS iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments are reported to confirm the efficiency of the proposed methods.

  13. Generalized Ghost Dark Energy with Non-Linear Interaction

    CERN Document Server

    Ebrahimi, E; Mehrabi, A; Movahed, S M S

    2016-01-01

    In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...

  14. FUNDAMENTAL MATRIX OF LINEAR CONTINUOUS SYSTEM IN THE PROBLEM OF ESTIMATING ITS TRANSPORT DELAY

    Directory of Open Access Journals (Sweden)

    N. A. Dudarenko

    2014-09-01

    Full Text Available The paper deals with the problem of quantitative estimation for transport delay of linear continuous systems. The main result is received by means of fundamental matrix of linear differential equations solutions specified in the normal Cauchy form for the cases of SISO and MIMO systems. Fundamental matrix has the dual property. It means that the weight function of the system can be formed as a free motion of systems. Last one is generated by the vector of initial system conditions, which coincides with the matrix input of the system being researched. Thus, using the properties of the system- solving for fundamental matrix has given the possibility to solve the problem of estimating transport linear continuous system delay without the use of derivation procedure in hardware environment and without formation of exogenous Dirac delta function. The paper is illustrated by examples. The obtained results make it possible to solve the problem of modeling the pure delay links using consecutive chain of aperiodic links of the first order with the equal time constants. Modeling results have proved the correctness of obtained computations. Knowledge of transport delay can be used when configuring multi- component technological complexes and in the diagnosis of their possible functional degeneration.

  15. General quantum constraints on detector noise in continuous linear measurements

    Science.gov (United States)

    Miao, Haixing

    2017-01-01

    In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum noise of the detector, arising from quantum fluctuations in the detector input and output. It determines how fast we acquire information about the system and also influences the system evolution in terms of measurement backaction. We therefore often categorize it as the so-called imprecision noise and quantum backaction noise. There is a general Heisenberg-like uncertainty relation that constrains the magnitude of and the correlation between these two types of quantum noise. The main result of this paper is to show that, when the detector becomes ideal, i.e., at the quantum limit with minimum uncertainty, not only does the uncertainty relation takes the equal sign as expected, but also there are two new equalities. This general result is illustrated by using the typical cavity QED setup with the system being either a qubit or a mechanical oscillator. Particularly, the dispersive readout of a qubit state, and the measurement of mechanical motional sideband asymmetry are considered.

  16. A New General Linear Convolution Model for fMRI Data Process

    Institute of Scientific and Technical Information of China (English)

    YUAN Hong; CHEN Hua-fu; YAO De-zhong

    2005-01-01

    General linear model (GLM) is the most popular method for functional magnetic resource imaging (fMRI) data analysis. However, its theory is imperfect. The key of this model is how to constitute the design-matrix to model the interesting effects better and separate noises better. For the purpose of detecting brain function activation, according to the principle of GLM, a new convolution model is presented by a new dynamic function convolving with design-matrix, which combining with t-test can be used to detect brain active signal. The fMRI imaging result of visual stimulus experiment indicates that brain activities mainly concentrate among vland v2 areas of visual cortex, and also verified the validity of this technique.

  17. Bayesian Subset Modeling for High-Dimensional Generalized Linear Models

    KAUST Repository

    Liang, Faming

    2013-06-01

    This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of sure screening and consistency with the existing sure independence screening (SIS) and iterative sure independence screening (ISIS) procedures. However, since the proposed procedure makes use of joint information from all predictors, it generally outperforms SIS and ISIS in real applications. This article also makes extensive comparisons of BSR with the popular penalized likelihood methods, including Lasso, elastic net, SIS, and ISIS. The numerical results indicate that BSR can generally outperform the penalized likelihood methods. The models selected by BSR tend to be sparser and, more importantly, of higher prediction ability. In addition, the performance of the penalized likelihood methods tends to deteriorate as the number of predictors increases, while this is not significant for BSR. Supplementary materials for this article are available online. © 2013 American Statistical Association.

  18. A new family of gauges in linearized general relativity

    Science.gov (United States)

    Esposito, Giampiero; Stornaiolo, Cosimo

    2000-05-01

    For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations. Thus, starting from the de Donder gauge, which is not conformally invariant but is the gravitational counterpart of the Lorenz gauge, one can consider, led by formal analogy, a new family of gauges in general relativity, which involve fifth-order covariant derivatives of metric perturbations. The admissibility of such gauges in the classical theory is first proven in the cases of linearized theory about flat Euclidean space or flat Minkowski spacetime. In the former, the general solution of the equation for the fulfillment of the gauge condition after infinitesimal diffeomorphisms involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter, one needs instead the kernel of powers of the wave operator, and a contour integral. The analysis is also used to put restrictions on the dimensionless parameter occurring in the DeWitt supermetric, while the proof of admissibility is generalized to a suitable class of curved Riemannian backgrounds. Eventually, a non-local construction of the tensor field is obtained which makes it possible to achieve conformal invariance of the above gauges.

  19. Advanced topics in linear algebra weaving matrix problems through the Weyr form

    CERN Document Server

    O'Meara, Kevin; Vinsonhaler, Charles

    2011-01-01

    The Weyr matrix canonical form is a largely unknown cousin of the Jordan canonical form. Discovered by Eduard Weyr in 1885, the Weyr form outperforms the Jordan form in a number of mathematical situations, yet it remains somewhat of a mystery, even to many who are skilled in linear algebra. Written in an engaging style, this book presents various advanced topics in linear algebra linked through the Weyr form. Kevin O'Meara, John Clark, and Charles Vinsonhaler develop the Weyr form from scratch and include an algorithm for computing it. A fascinating duality exists between the Weyr form and the

  20. Extraction of linear anisotropic parameters using optical coherence tomography and hybrid Mueller matrix formalism.

    Science.gov (United States)

    Liao, Chia-Chi; Lo, Yu-Lung

    2015-04-20

    A method is proposed for extracting the linear birefringence (LB) and linear dichroism (LD) properties of an anisotropic optical sample using reflection-mode optical coherence tomography (OCT) and a hybrid Mueller matrix formalism. To ensure the accuracy of the extracted parameter values, a method is proposed for calibrating and compensating the polarization distortion effect induced by the beam splitters in the OCT system using a composite quarter-waveplate / half-waveplate / quarter-waveplate structure. The validity of the proposed method is confirmed by extracting the LB and LD properties of a quarter-wave plate and a defective polarizer. To the best of the authors' knowledge, the method proposed in this study represents the first reported attempt to utilize an inverse Mueller matrix formalism and a reflection-mode OCT structure to extract the LB and LD parameters of optically anisotropic samples.

  1. Batched Triangular Dense Linear Algebra Kernels for Very Small Matrix Sizes on GPUs

    KAUST Repository

    Charara, Ali

    2017-03-06

    Batched dense linear algebra kernels are becoming ubiquitous in scientific applications, ranging from tensor contractions in deep learning to data compression in hierarchical low-rank matrix approximation. Within a single API call, these kernels are capable of simultaneously launching up to thousands of similar matrix computations, removing the expensive overhead of multiple API calls while increasing the occupancy of the underlying hardware. A challenge is that for the existing hardware landscape (x86, GPUs, etc.), only a subset of the required batched operations is implemented by the vendors, with limited support for very small problem sizes. We describe the design and performance of a new class of batched triangular dense linear algebra kernels on very small data sizes using single and multiple GPUs. By deploying two-sided recursive formulations, stressing the register usage, maintaining data locality, reducing threads synchronization and fusing successive kernel calls, the new batched kernels outperform existing state-of-the-art implementations.

  2. Explicit estimating equations for semiparametric generalized linear latent variable models

    KAUST Repository

    Ma, Yanyuan

    2010-07-05

    We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.

  3. Modeling local item dependence with the hierarchical generalized linear model.

    Science.gov (United States)

    Jiao, Hong; Wang, Shudong; Kamata, Akihito

    2005-01-01

    Local item dependence (LID) can emerge when the test items are nested within common stimuli or item groups. This study proposes a three-level hierarchical generalized linear model (HGLM) to model LID when LID is due to such contextual effects. The proposed three-level HGLM was examined by analyzing simulated data sets and was compared with the Rasch-equivalent two-level HGLM that ignores such a nested structure of test items. The results demonstrated that the proposed model could capture LID and estimate its magnitude. Also, the two-level HGLM resulted in larger mean absolute differences between the true and the estimated item difficulties than those from the proposed three-level HGLM. Furthermore, it was demonstrated that the proposed three-level HGLM estimated the ability distribution variance unaffected by the LID magnitude, while the two-level HGLM with no LID consideration increasingly underestimated the ability variance as the LID magnitude increased.

  4. dglars: An R Package to Estimate Sparse Generalized Linear Models

    Directory of Open Access Journals (Sweden)

    Luigi Augugliaro

    2014-09-01

    Full Text Available dglars is a publicly available R package that implements the method proposed in Augugliaro, Mineo, and Wit (2013, developed to study the sparse structure of a generalized linear model. This method, called dgLARS, is based on a differential geometrical extension of the least angle regression method proposed in Efron, Hastie, Johnstone, and Tibshirani (2004. The core of the dglars package consists of two algorithms implemented in Fortran 90 to efficiently compute the solution curve: a predictor-corrector algorithm, proposed in Augugliaro et al. (2013, and a cyclic coordinate descent algorithm, proposed in Augugliaro, Mineo, and Wit (2012. The latter algorithm, as shown here, is significantly faster than the predictor-corrector algorithm. For comparison purposes, we have implemented both algorithms.

  5. Analysis of Robust Quasi-deviances for Generalized Linear Models

    Directory of Open Access Journals (Sweden)

    Eva Cantoni

    2004-04-01

    Full Text Available Generalized linear models (McCullagh and Nelder 1989 are a popular technique for modeling a large variety of continuous and discrete data. They assume that the response variables Yi , for i = 1, . . . , n, come from a distribution belonging to the exponential family, such that E[Yi ] = ?i and V[Yi ] = V (?i , and that ?i = g(?i = xiT?, where ? ? IR p is the vector of parameters, xi ? IR p, and g(. is the link function. The non-robustness of the maximum likelihood and the maximum quasi-likelihood estimators has been studied extensively in the literature. For model selection, the classical analysis-of-deviance approach shares the same bad robustness properties. To cope with this, Cantoni and Ronchetti (2001 propose a robust approach based on robust quasi-deviance functions for estimation and variable selection. We refer to that paper for a deeper discussion and the review of the literature.

  6. Mixed Task and Data Parallel Executions in General Linear Methods

    Directory of Open Access Journals (Sweden)

    Thomas Rauber

    2007-01-01

    Full Text Available On many parallel target platforms it can be advantageous to implement parallel applications as a collection of multiprocessor tasks that are concurrently executed and are internally implemented with fine-grain SPMD parallelism. A class of applications which can benefit from this programming style are methods for solving systems of ordinary differential equations. Many recent solvers have been designed with an additional potential of method parallelism, but the actual effectiveness of mixed task and data parallelism depends on the specific communication and computation requirements imposed by the equation to be solved. In this paper we study mixed task and data parallel implementations for general linear methods realized using a library for multiprocessor task programming. Experiments on a number of different platforms show good efficiency results.

  7. Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation.

    Science.gov (United States)

    Huo, Pengfei; Coker, David F

    2012-12-14

    Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.

  8. Multireference linearized Coupled Cluster theory for strongly correlated systems using Matrix Product States

    OpenAIRE

    Sharma, Sandeep; Alavi, Ali

    2015-01-01

    We propose a multireference linearized coupled cluster theory using matrix product states (MPS-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles (MRCISD), for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries, to highly multireference systems such as the chromium dimer and lattice models such as period...

  9. Extending Local Canonical Correlation Analysis to Handle General Linear Contrasts for fMRI Data

    Directory of Open Access Journals (Sweden)

    Mingwu Jin

    2012-01-01

    Full Text Available Local canonical correlation analysis (CCA is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM, a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

  10. A unified approach to fixed-order controller design via linear matrix inequalities

    Directory of Open Access Journals (Sweden)

    Iwasaki T.

    1995-01-01

    Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 𝒬 -stabilization as a robust stabilization problem, and robust L ∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type B G C + ( B G C T + Q < 0 for the unknown matrix G . Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X ∈ 𝒞 1 and X − 1 ∈ 𝒞 2 where 𝒞 1 and 𝒞 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

  11. Efficient linear-scaling calculation of response properties: density matrix-based Laplace-transformed coupled-perturbed self-consistent field theory.

    Science.gov (United States)

    Beer, Matthias; Ochsenfeld, Christian

    2008-06-14

    A density matrix-based Laplace reformulation of coupled-perturbed self-consistent field (CPSCF) theory is presented. It allows a direct, instead of iterative, solution for the integral-independent part of the density matrix-based CPSCF (D-CPSCF) equations [J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 127, 054103 (2007)]. In this way, the matrix-multiplication overhead compared to molecular orbital-based solutions is reduced to a minimum, while at the same time, the linear-scaling behavior of D-CPSCF theory is preserved. The present Laplace-based equation solver is expected to be of general applicability.

  12. Nonlinear hidden symmetries in General Relativity and String Theory: a matrix generalization of the Ernst potentials

    CERN Document Server

    Barbosa-Cendejas, Nandinii; Kanakoglou, Konstantinos; Paschalis, Joannis E

    2011-01-01

    In this paper we recall a simple formulation of the stationary electrovacuum theory in terms of the famous complex Ernst potentials, a pair of functions which allows one to generate new exact solutions from known ones by means of the so-called nonlinear hidden symmetries of Lie-Backlund type. This formalism turned out to be very useful to perform a complete classification of all 4D solutions which present two spacetime symmetries or possess two Killing vectors. Curiously enough, the Ernst formalism can be extended and applied to stationary General Relativity as well as the effective heterotic string theory reduced down to three spatial dimensions by means of a (real) matrix generalization of the Ernst potentials. Thus, in this theory one can also make use of nonlinear matrix hidden symmetries in order to generate new exact solutions from seed ones. Due to the explicit independence of the matrix Ernst potential formalism of the original theory (prior to dimensional reduction) on the dimension D, in the case wh...

  13. A New Family of Gauges in Linearized General Relativity

    CERN Document Server

    Esposito, G; Esposito, Giampiero; Stornaiolo, Cosimo

    2000-01-01

    For vacuum Maxwell theory in four dimensions, a supplementary condition exists (due to Eastwood and Singer) which is invariant under conformal rescalings of the metric, in agreement with the conformal symmetry of the Maxwell equations. Thus, starting from the de Donder gauge, which is not conformally invariant but is the gravitational counterpart of the Lorenz gauge, one can consider, led by formal analogy, a new family of gauges in general relativity, which involve fifth-order covariant derivatives of metric perturbations. The admissibility of such gauges in the classical theory is here proven in the cases of linearized theory about flat Euclidean space or flat Minkowski space-time. In the former, the general solution of the equation for the fulfillment of the gauge condition after infinitesimal diffeomorphisms involves a 3-harmonic function and an inverse Fourier transform. In the latter, one needs instead the kernel of powers of the wave operator, and a contour integral. The analysis is also used to put re...

  14. Generalized linear models with coarsened covariates: a practical Bayesian approach.

    Science.gov (United States)

    Johnson, Timothy R; Wiest, Michelle M

    2014-06-01

    Coarsened covariates are a common and sometimes unavoidable phenomenon encountered in statistical modeling. Covariates are coarsened when their values or categories have been grouped. This may be done to protect privacy or to simplify data collection or analysis when researchers are not aware of their drawbacks. Analyses with coarsened covariates based on ad hoc methods can compromise the validity of inferences. One valid method for accounting for a coarsened covariate is to use a marginal likelihood derived by summing or integrating over the unknown realizations of the covariate. However, algorithms for estimation based on this approach can be tedious to program and can be computationally expensive. These are significant obstacles to their use in practice. To overcome these limitations, we show that when expressed as a Bayesian probability model, a generalized linear model with a coarsened covariate can be posed as a tractable missing data problem where the missing data are due to censoring. We also show that this model is amenable to widely available general-purpose software for simulation-based inference for Bayesian probability models, providing researchers a very practical approach for dealing with coarsened covariates.

  15. The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

    Science.gov (United States)

    Pang, Haotian; Liu, Han; Vanderbei, Robert

    2014-02-01

    We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

  16. Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

    Science.gov (United States)

    Mukhopadhyay, S.; Ramasesha, S.

    2009-08-01

    We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting π electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

  17. Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method.

    Science.gov (United States)

    Mukhopadhyay, S; Ramasesha, S

    2009-08-21

    We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

  18. An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

    Directory of Open Access Journals (Sweden)

    P. Bumroongsri

    2014-01-01

    Full Text Available An offline model predictive control (MPC algorithm for linear parameter varying (LPV systems is presented. The main contribution is to develop an offline MPC algorithm for LPV systems that can deal with both time-varying scheduling parameter and persistent disturbance. The norm-bounding technique is used to derive an offline MPC algorithm based on the parameter-dependent state feedback control law and the parameter-dependent Lyapunov functions. The online computational time is reduced by solving offline the linear matrix inequality (LMI optimization problems to find the sequences of explicit state feedback control laws. At each sampling instant, a parameter-dependent state feedback control law is computed by linear interpolation between the precomputed state feedback control laws. The algorithm is illustrated with two examples. The results show that robust stability can be ensured in the presence of both time-varying scheduling parameter and persistent disturbance.

  19. Adaptive Error Estimation in Linearized Ocean General Circulation Models

    Science.gov (United States)

    Chechelnitsky, Michael Y.

    1999-01-01

    Data assimilation methods are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. This study addresses the problem of estimating model and measurement error statistics from observations. We start by testing innovation based methods of adaptive error estimation with low-dimensional models in the North Pacific (5-60 deg N, 132-252 deg E) to TOPEX/POSEIDON (TIP) sea level anomaly data, acoustic tomography data from the ATOC project, and the MIT General Circulation Model (GCM). A reduced state linear model that describes large scale internal (baroclinic) error dynamics is used. The methods are shown to be sensitive to the initial guess for the error statistics and the type of observations. A new off-line approach is developed, the covariance matching approach (CMA), where covariance matrices of model-data residuals are "matched" to their theoretical expectations using familiar least squares methods. This method uses observations directly instead of the innovations sequence and is shown to be related to the MT method and the method of Fu et al. (1993). Twin experiments using the same linearized MIT GCM suggest that altimetric data are ill-suited to the estimation of internal GCM errors, but that such estimates can in theory be obtained using acoustic data. The CMA is then applied to T/P sea level anomaly data and a linearization of a global GFDL GCM which uses two vertical modes. We show that the CMA method can be used with a global model and a global data set, and that the estimates of the error statistics are robust. We show that the fraction of the GCM-T/P residual variance explained by the model error is larger than that derived in Fukumori et al.(1999) with the method of Fu et al.(1993). Most of the model error is explained by the barotropic mode. However, we find that impact of the change in the error statistics on the data assimilation estimates is very small. This is explained by the large

  20. Generalized linear longitudinal mixed models with linear covariance structure and multiplicative random effects

    DEFF Research Database (Denmark)

    Holst, René; Jørgensen, Bent

    2015-01-01

    The paper proposes a versatile class of multiplicative generalized linear longitudinal mixed models (GLLMM) with additive dispersion components, based on explicit modelling of the covariance structure. The class incorporates a longitudinal structure into the random effects models and retains...... a marginal as well as a conditional interpretation. The estimation procedure is based on a computationally efficient quasi-score method for the regression parameters combined with a REML-like bias-corrected Pearson estimating function for the dispersion and correlation parameters. This avoids...... the multidimensional integral of the conventional GLMM likelihood and allows an extension of the robust empirical sandwich estimator for use with both association and regression parameters. The method is applied to a set of otholit data, used for age determination of fish....

  1. A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

    Science.gov (United States)

    Yedavalli, R. K.

    1992-01-01

    The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

  2. A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

    Science.gov (United States)

    Yedavalli, R. K.

    1992-01-01

    The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

  3. THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS(AX=B,XC=D)

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this article, the generalized reflexive solution of matrix equations (AX =B, XC = D) is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.

  4. The linearized inversion of the generalized interferometric multiple imaging

    KAUST Repository

    Aldawood, Ali

    2016-09-06

    The generalized interferometric multiple imaging (GIMI) procedure can be used to image duplex waves and other higher order internal multiples. Imaging duplex waves could help illuminate subsurface zones that are not easily illuminated by primaries such as vertical and nearly vertical fault planes, and salt flanks. To image first-order internal multiple, the GIMI framework consists of three datuming steps, followed by applying the zero-lag cross-correlation imaging condition. However, the standard GIMI procedure yields migrated images that suffer from low spatial resolution, migration artifacts, and cross-talk noise. To alleviate these problems, we propose a least-squares GIMI framework in which we formulate the first two steps as a linearized inversion problem when imaging first-order internal multiples. Tests on synthetic datasets demonstrate the ability to localize subsurface scatterers in their true positions, and delineate a vertical fault plane using the proposed method. We, also, demonstrate the robustness of the proposed framework when imaging the scatterers or the vertical fault plane with erroneous migration velocities.

  5. Bayesian inference for generalized linear models for spiking neurons

    Directory of Open Access Journals (Sweden)

    Sebastian Gerwinn

    2010-05-01

    Full Text Available Generalized Linear Models (GLMs are commonly used statistical methods for modelling the relationship between neural population activity and presented stimuli. When the dimension of the parameter space is large, strong regularization has to be used in order to fit GLMs to datasets of realistic size without overfitting. By imposing properly chosen priors over parameters, Bayesian inference provides an effective and principled approach for achieving regularization. Here we show how the posterior distribution over model parameters of GLMs can be approximated by a Gaussian using the Expectation Propagation algorithm. In this way, we obtain an estimate of the posterior mean and posterior covariance, allowing us to calculate Bayesian confidence intervals that characterize the uncertainty about the optimal solution. From the posterior we also obtain a different point estimate, namely the posterior mean as opposed to the commonly used maximum a posteriori estimate. We systematically compare the different inference techniques on simulated as well as on multi-electrode recordings of retinal ganglion cells, and explore the effects of the chosen prior and the performance measure used. We find that good performance can be achieved by choosing an Laplace prior together with the posterior mean estimate.

  6. Generalized Functional Linear Models With Semiparametric Single-Index Interactions

    KAUST Repository

    Li, Yehua

    2010-06-01

    We introduce a new class of functional generalized linear models, where the response is a scalar and some of the covariates are functional. We assume that the response depends on multiple covariates, a finite number of latent features in the functional predictor, and interaction between the two. To achieve parsimony, the interaction between the multiple covariates and the functional predictor is modeled semiparametrically with a single-index structure. We propose a two step estimation procedure based on local estimating equations, and investigate two situations: (a) when the basis functions are pre-determined, e.g., Fourier or wavelet basis functions and the functional features of interest are known; and (b) when the basis functions are data driven, such as with functional principal components. Asymptotic properties are developed. Notably, we show that when the functional features are data driven, the parameter estimates have an increased asymptotic variance, due to the estimation error of the basis functions. Our methods are illustrated with a simulation study and applied to an empirical data set, where a previously unknown interaction is detected. Technical proofs of our theoretical results are provided in the online supplemental materials.

  7. Multivariate statistical modelling based on generalized linear models

    CERN Document Server

    Fahrmeir, Ludwig

    1994-01-01

    This book is concerned with the use of generalized linear models for univariate and multivariate regression analysis. Its emphasis is to provide a detailed introductory survey of the subject based on the analysis of real data drawn from a variety of subjects including the biological sciences, economics, and the social sciences. Where possible, technical details and proofs are deferred to an appendix in order to provide an accessible account for non-experts. Topics covered include: models for multi-categorical responses, model checking, time series and longitudinal data, random effects models, and state-space models. Throughout, the authors have taken great pains to discuss the underlying theoretical ideas in ways that relate well to the data at hand. As a result, numerous researchers whose work relies on the use of these models will find this an invaluable account to have on their desks. "The basic aim of the authors is to bring together and review a large part of recent advances in statistical modelling of m...

  8. Generalized linear model for estimation of missing daily rainfall data

    Science.gov (United States)

    Rahman, Nurul Aishah; Deni, Sayang Mohd; Ramli, Norazan Mohamed

    2017-04-01

    The analysis of rainfall data with no missingness is vital in various applications including climatological, hydrological and meteorological study. The issue of missing data is a serious concern since it could introduce bias and lead to misleading conclusions. In this study, five imputation methods including simple arithmetic average, normal ratio method, inverse distance weighting method, correlation coefficient weighting method and geographical coordinate were used to estimate the missing data. However, these imputation methods ignored the seasonality in rainfall dataset which could give more reliable estimation. Thus this study is aimed to estimate the missingness in daily rainfall data by using generalized linear model with gamma and Fourier series as the link function and smoothing technique, respectively. Forty years daily rainfall data for the period from 1975 until 2014 which consists of seven stations at Kelantan region were selected for the analysis. The findings indicated that the imputation methods could provide more accurate estimation values based on the least mean absolute error, root mean squared error and coefficient of variation root mean squared error when seasonality in the dataset are considered.

  9. A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

    Directory of Open Access Journals (Sweden)

    Min Sun

    2014-01-01

    Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

  10. An all-optical matrix multiplication scheme with non-linear material based switching system

    Institute of Scientific and Technical Information of China (English)

    Archan Kumar Das; Sourangshu Mukhopadhyay

    2005-01-01

    Optics is a potential candidate in information, data, and image processing. In all-optical data and information processing, optics has been used as information carrying signal because of its inherent advantages of parallelism. Several optical methods are proposed in support of the above processing. In many algebraic,arithmetic, and image processing schemes fundamental logic and memory operations are conducted exploring all-optical devices. In this communication we report an all-optical matrix multiplication operation with non-linear material based switching circuit.

  11. Hardware Efficient Approximative Matrix Inversion for Linear Pre-Coding in Massive MIMO

    OpenAIRE

    Prabhu, Hemanth; Edfors, Ove; Rodrigues, Joachim; Liu, Liang; Rusek, Fredrik

    2014-01-01

    This paper describes a hardware efficient linear pre-coder for Massive MIMO Base Stations (BSs) comprising a very large number of antennas, say, in the order of 100s, serving multiple users simultaneously. To avoid hardware demanding direct matrix inversions required for the Zero-Forcing (ZF) pre-coder, we use low complexity Neumann series based approximations. Furthermore, we propose a method to speed-up the convergence of the Neumann series by using tri-diagonal pre-condition matrices, whic...

  12. Parameter identification of fractional order linear system based on Haar wavelet operational matrix.

    Science.gov (United States)

    Li, Yuanlu; Meng, Xiao; Zheng, Bochao; Ding, Yaqing

    2015-11-01

    Fractional order systems can be more adequate for the description of dynamical systems than integer order models, however, how to obtain fractional order models are still actively exploring. In this paper, an identification method for fractional order linear system was proposed. This is a method based on input-output data in time domain. The input and output signals are represented by Haar wavelet, and then fractional order systems described by fractional order differential equations are transformed into fractional order integral equations. Taking use of the Haar wavelet operational matrix of the fractional order integration, the fractional order linear system can easily be converted into a system of algebraic equation. Finally, the parameters of the fractional order system are determined by minimizing the errors between the output of the real system and that of the identified system. Numerical simulations, involving integral and fractional order systems, confirm the efficiency of the above methodology.

  13. TCSC controller design based on output feedback control with linear matrix inequality

    Energy Technology Data Exchange (ETDEWEB)

    Ishimaru, Masachika; Shirai, Goro [Hosei University, Tokyo (Japan). Dept. of Electrical Engineering; Niioka, Satoru; Yokoyama, Ryuichi [Tokyo Metropolitan University (Japan). Dept. of Electrical Engineering

    2000-07-01

    The authors aim at designing the fast responsible and robust stabilizing controller. Recently, many researches propose robust stabilizing compensators based on H{sub {infinity}} control theory. Especiady, the LMI (Linear Matrix Inequality) solving efficient convex problems is very effective. LMI is based on a linear function composed by matrices, and it is expansion of conventional H{sub {infinity}} control. In addition to the LMI approach, authors pay attention to the output-feedback control for stabilizing a system using observable output values. This paper presents a stabilizing control using measurable values by using the output-feedback method. In order to discuss the advantage of the proposed method, 3-machine 9-bus system is used. Moreover, this system is applied TCSC (Thyristor Controlled Series Capacitor) controllers, and H{sub {infinity}} control based on the LMI is proposed for the design method of TCSC controllers to attain the robust stability. (author)

  14. Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix.

    Science.gov (United States)

    Wang, Haokun; Zhao, Jun; Xu, Zuhua; Shao, Zhijiang

    2015-07-01

    The problem of joint input and state estimation for linear stochastic systems with a rank-deficient direct feedthrough matrix is discussed in this paper. Results from previous studies only solve the state estimation problem; globally optimal estimation of the unknown input is not provided. Based on linear minimum-variance unbiased estimation, a five-step recursive filter with global optimality is proposed to estimate both the unknown input and the state. The relationship between the proposed filter and the existing results is addressed. We show that the unbiased input estimation does not require any new information or additional constraints. Both the state and the unknown input can be estimated under the same unbiasedness condition. Global optimalities of both the state estimator and the unknown input estimator are proven in the minimum-variance unbiased sense.

  15. Solving the generalized Sylvester matrix equation AV+BW=VF via Kronecker map

    Institute of Scientific and Technical Information of China (English)

    Aiguo WU; Siming ZHAO; Guangren DUAN

    2008-01-01

    This note considers the solution to the generalized Sylvester matrix equation AV+BW=VF with F being an arbitrary matrix,where V and W are the matrices to be determined.With the help of the Kronecker map,an explicit parametric solution to this matrix equation is established.The proposed solution possesses a very simple and neat form,and allows the matrix F to be undetermined.

  16. Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

    Directory of Open Access Journals (Sweden)

    Yingxin Guo

    2011-01-01

    Full Text Available By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential system U′=A(xU+B(tV, V′=C(xU−A∗(tV, where A(t, B(t, and C(t are (n×n-matrices, and B, C are Hermitian. These results are sharper than some previous results.

  17. LINEAR GENERAL EQUILIBRIUM MODEL OF ENERGY DEMAND AND CO2 EMISSIONS GENERATED BY THE ANDALUSIAN PRODUCTIVE SYSTEM

    Directory of Open Access Journals (Sweden)

    Manuel Alejandro Cardenete

    2012-01-01

    Full Text Available In this study we apply a multiplier decomposition methodology of a linear general equilibrium model based on the regional social accounting matrix to the Andalusian economy. The aim of this methodology is to separate the size of the different effects in terms of energy expenditure and total emissions generated by the whole productive system to satisfy the final demand of each branch of the Andalusian economy and the direct emissions generated to produce energy for each subsystem.

  18. Dynamic Average Consensus and Consensusability of General Linear Multiagent Systems with Random Packet Dropout

    Directory of Open Access Journals (Sweden)

    Wen-Min Zhou

    2013-01-01

    Full Text Available This paper is concerned with the consensus problem of general linear discrete-time multiagent systems (MASs with random packet dropout that happens during information exchange between agents. The packet dropout phenomenon is characterized as being a Bernoulli random process. A distributed consensus protocol with weighted graph is proposed to address the packet dropout phenomenon. Through introducing a new disagreement vector, a new framework is established to solve the consensus problem. Based on the control theory, the perturbation argument, and the matrix theory, the necessary and sufficient condition for MASs to reach mean-square consensus is derived in terms of stability of an array of low-dimensional matrices. Moreover, mean-square consensusable conditions with regard to network topology and agent dynamic structure are also provided. Finally, the effectiveness of the theoretical results is demonstrated through an illustrative example.

  19. General expressions for R1ρ relaxation for N-site chemical exchange and the special case of linear chains

    Science.gov (United States)

    Koss, Hans; Rance, Mark; Palmer, Arthur G.

    2017-01-01

    Exploration of dynamic processes in proteins and nucleic acids by spin-locking NMR experiments has been facilitated by the development of theoretical expressions for the R1ρ relaxation rate constant covering a variety of kinetic situations. Herein, we present a generalized approximation to the chemical exchange, Rex, component of R1ρ for arbitrary kinetic schemes, assuming the presence of a dominant major site population, derived from the negative reciprocal trace of the inverse Bloch-McConnell evolution matrix. This approximation is equivalent to first-order truncation of the characteristic polynomial derived from the Bloch-McConnell evolution matrix. For three- and four-site chemical exchange, the first-order approximations are sufficient to distinguish different kinetic schemes. We also introduce an approach to calculate R1ρ for linear N-site schemes, using the matrix determinant lemma to reduce the corresponding 3N × 3N Bloch-McConnell evolution matrix to a 3 × 3 matrix. The first- and second order-expansions of the determinant of this 3 × 3 matrix are closely related to previously derived equations for two-site exchange. The second-order approximations for linear N-site schemes can be used to obtain more accurate approximations for non-linear N-site schemes, such as triangular three-site or star four-site topologies. The expressions presented herein provide powerful means for the estimation of Rex contributions for both low (CEST-limit) and high (R1ρ-limit) radiofrequency field strengths, provided that the population of one state is dominant. The general nature of the new expressions allows for consideration of complex kinetic situations in the analysis of NMR spin relaxation data.

  20. NGPG-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    丛玉豪

    2001-01-01

    The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations. After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGPG-stable if and only if it is A-stable.

  1. Robust linear equation dwell time model compatible with large scale discrete surface error matrix.

    Science.gov (United States)

    Dong, Zhichao; Cheng, Haobo; Tam, Hon-Yuen

    2015-04-01

    The linear equation dwell time model can translate the 2D convolution process of material removal during subaperture polishing into a more intuitional expression, and may provide relatively fast and reliable results. However, the accurate solution of this ill-posed equation is not so easy, and its practicability for a large scale surface error matrix is still limited. This study first solves this ill-posed equation by Tikhonov regularization and the least square QR decomposition (LSQR) method, and automatically determines an optional interval and a typical value for the damped factor of regularization, which are dependent on the peak removal rate of tool influence functions. Then, a constrained LSQR method is presented to increase the robustness of the damped factor, which can provide more consistent dwell time maps than traditional LSQR. Finally, a matrix segmentation and stitching method is used to cope with large scale surface error matrices. Using these proposed methods, the linear equation model becomes more reliable and efficient in practical engineering.

  2. Linear Spectral Analysis of Plume Emissions Using an Optical Matrix Processor

    Science.gov (United States)

    Gary, C. K.

    1992-01-01

    Plume spectrometry provides a means to monitor the health of a burning rocket engine, and optical matrix processors provide a means to analyze the plume spectra in real time. By observing the spectrum of the exhaust plume of a rocket engine, researchers have detected anomalous behavior of the engine and have even determined the failure of some equipment before it would normally have been noticed. The spectrum of the plume is analyzed by isolating information in the spectrum about the various materials present to estimate what materials are being burned in the engine. Scientists at the Marshall Space Flight Center (MSFC) have implemented a high resolution spectrometer to discriminate the spectral peaks of the many species present in the plume. Researchers at the Stennis Space Center Demonstration Testbed Facility (DTF) have implemented a high resolution spectrometer observing a 1200-lb. thrust engine. At this facility, known concentrations of contaminants can be introduced into the burn, allowing for the confirmation of diagnostic algorithms. While the high resolution of the measured spectra has allowed greatly increased insight into the functioning of the engine, the large data flows generated limit the ability to perform real-time processing. The use of an optical matrix processor and the linear analysis technique described below may allow for the detailed real-time analysis of the engine's health. A small optical matrix processor can perform the required mathematical analysis both quicker and with less energy than a large electronic computer dedicated to the same spectral analysis routine.

  3. Student Transfer Guide and General Education Articulation Matrix, 1999-2000.

    Science.gov (United States)

    Louisiana State Board of Regents, Baton Rouge.

    The Louisiana State Board of Regents' 1999-2000 Student Transfer Guide and General Education Articulation Matrix represents Louisiana public higher education's ongoing effort to improve the transfer process. The courses in this guide's matrix are typically referred to as "general education" or "core curriculum" courses. Students should note that…

  4. General formulation of process noise matrix for track fitting with Kalman filter

    CERN Document Server

    Bhattacharya, Kolahal; Mondal, Naba K

    2015-01-01

    In the context of track fitting problems by a Kalman filter, the general functional forms of the elements of the random noise matrix are derived for tracking through thick layers of materials and magnetic fields. This work generalizes the form of the random noise matrix obtained by Mankel[1].

  5. MGMRES: A generalization of GMRES for solving large sparse nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Young, D.M.; Chen, J.Y. [Univ. of Texas, Austin, TX (United States)

    1994-12-31

    The authors are concerned with the solution of the linear system (1): Au = b, where A is a real square nonsingular matrix which is large, sparse and non-symmetric. They consider the use of Krylov subspace methods. They first choose an initial approximation u{sup (0)} to the solution {bar u} = A{sup {minus}1}B of (1). They also choose an auxiliary matrix Z which is nonsingular. For n = 1,2,{hor_ellipsis} they determine u{sup (n)} such that u{sup (n)} {minus} u{sup (0)}{epsilon}K{sub n}(r{sup (0)},A) where K{sub n}(r{sup (0)},A) is the (Krylov) subspace spanned by the Krylov vectors r{sup (0)}, Ar{sup (0)}, {hor_ellipsis}, A{sup n{minus}1}r{sup 0} and where r{sup (0)} = b{minus}Au{sup (0)}. If ZA is SPD they also require that (u{sup (n)}{minus}{bar u}, ZA(u{sup (n)}{minus}{bar u})) be minimized. If, on the other hand, ZA is not SPD, then they require that the Galerkin condition, (Zr{sup n}, v) = 0, be satisfied for all v{epsilon}K{sub n}(r{sup (0)}, A) where r{sup n} = b{minus}Au{sup (n)}. In this paper the authors consider a generalization of GMRES. This generalized method, which they refer to as `MGMRES`, is very similar to GMRES except that they let Z = A{sup T}Y where Y is a nonsingular matrix which is symmetric by not necessarily SPD.

  6. TWO ITERATION METHODS FOR SOLVING LINEAR ALGEBRAIC SYSTEMS WITH LOW ORDER MATRIX A AND HIGH ORDER MATRIX B: Y = (A B)Y + Ф

    Institute of Scientific and Technical Information of China (English)

    Shuang-suo Zhao; Zhang-hua Luo; Guo-feng Zhang

    2000-01-01

    This paper presents optimum an one-parameter iteration (OOPI) method and a multi-parameter iteration direct (MPID) method for efficiently solving linear algebraic systems with low order matrix A and high order matrix B: Y = (A B)Y +Ф. On parallel computers (also on serial computer) the former will be efficient, even very efficient under certain conditions, the latter will be universally very efficient.

  7. A generalization of the MDS method by mixed integer linear and nonlinear mathematical models

    Directory of Open Access Journals (Sweden)

    Sadegh Niroomand

    2014-09-01

    Full Text Available The Multi-Dimensional Scaling (MDS method is used in statistics to detect hidden interrelations among multi-dimensional data and it has a wide range of applications. The method’s input is a matrix that describes the similarity/dissimilarity among objects of unknown dimension. The objects are generally reconstructed as points of a lower dimensional space to reveal the geometric configuration of the objects. The original MDS method uses Euclidean distance, for measuring both the distance of the reconstructed points and the bias of the reconstructed distances from the original similarity values. In this paper, these distances are distinguished, and distances other than Euclidean are also used, generalizing the MDS method. Two different distances may be used for the two different purposes. Therefore the instances of the generalized MDS model are denoted as  model, where the first distance is the type of distance of the reconstructed points and the second one measures the bias of the reconstructed distances and the similarity values. In the case of   and   distances mixed-integer programming models are provided. The computational experiences show that the generalized model can catch the key properties of the original configuration, if any exist. Keywords: Multivariate Analysis; Multi-Dimensional Scaling; Optimization; Mixed Integer Linear Programming; Statistics.

  8. Taylor series approximation of semi-blind best linear unbiased channel estimates for the general linear model

    OpenAIRE

    Pladdy, Christopher; Nerayanuru, Sreenivasa M.; Fimoff, Mark; Özen, Serdar; Zoltowski, Michael

    2004-01-01

    We present a low complexity approximate method for semi-blind best linear unbiased estimation (BLUE) of a channel impulse response vector (CIR) for a communication system, which utilizes a periodically transmitted training sequence, within a continuous stream of information symbols. The algorithm achieves slightly degraded results at a much lower complexity than directly computing the BLUE CIR estimate. In addition, the inverse matrix required to invert the weighted normal equations to solve ...

  9. GENERALIZED RICCATI TRANSFORMATION AND OSCILLATION FOR LINEAR DIFFERENTIAL EQUATIONS WITH DAMPING

    Institute of Scientific and Technical Information of China (English)

    ZhengZhaowen; LiuJingzhao

    2005-01-01

    Using generalized Riccati transformation, some new oscillation criteria for damped linear differential equations are established. These results improve and generalize some known oscillation criteria due to A.Wintner [8], I.V.Kamenev [10] for the undamped linear differential equations, and Sobol [3], J.S.W.Wong [1] for the damped linear differential equations.

  10. Generalized (,,-Pairs for Uncertain Linear Infinite-Dimensional Systems

    Directory of Open Access Journals (Sweden)

    Naohisa Otsuka

    2009-01-01

    Full Text Available We introduce the concept of generalized (,,-pairs which is related to generalized (,-invariant subspaces and generalized (,-invariant subspaces for infinite-dimensional systems. As an application the parameter-insensitive disturbance-rejection problem with dynamic compensator is formulated and its solvability conditions are presented. Further, an illustrative example is also examined.

  11. Connections between Generalizing and Justifying: Students' Reasoning with Linear Relationships

    Science.gov (United States)

    Ellis, Amy B.

    2007-01-01

    Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…

  12. Generalized Derivations of Formal Triangular Matrix Rings%形式三角矩阵环的广义导子

    Institute of Scientific and Technical Information of China (English)

    谢乐平

    2011-01-01

    利用代数方法,得到了形式三角矩阵环Tri(A,M,B)的广义导子可以由环A,B的广义导子和(A,B)-双模M的广义拟线性映射表示的结论,同时由此结论推得形式三角矩阵环Tri(A,M,B)的导子的结构.%Generalized derivations of the formal triangular matrix ring Tri(A, M, B) are obtained by generalized derivations of A,B and a generalized fitting-linear mapping of M by using algebraic method. Using this result, the structure form of the derivations of the formal triangular'matrix ring Tri(A, M, B) is obtained.

  13. Equivalent Linearization of Polymer Matrix Composite Infill Wall Subjected to Seismic Ground Motions

    Directory of Open Access Journals (Sweden)

    BuSeog Ju

    2013-10-01

    Full Text Available Polymer Matrix Composite (PMC material was introduced as a new conceptual infill construction for seismic retrofitting. A proposed PMC-infilled system was composed of two basic structural components: inner PMC-infilled sandwich and outer FRP damping panels designed toconstrain the energy-dissipating layers. These two components along with the steel frame were intended for providing the desired stiffness and damping following different drift values. The observed behavior of the proposed PMC-infilled system was evaluated experimentally based on the stiffness, the mode of failure and the energy dissipation outputs. In this study, a piece-wise linear dynamic analysis for a proposed PMC-infilled frame was performed according to the previous research, for the assessment of their effectiveness and the responses under the simulated earthquake loading. Upon comparing the results of undamped (without PMC panel and damped (with PMC panel structures, numerical results showed that structural damping with passive interface damping layer could significantly enhance the seismic response. Furthermore, the numerical simulation response showed that the response of theequivalent linearized model produces more conservative results, in comparison to the response of piece-wise linear model.

  14. Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

    Science.gov (United States)

    Wawro, Megan Jean

    2011-01-01

    In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

  15. S-AMP: Approximate Message Passing for General Matrix Ensembles

    DEFF Research Database (Denmark)

    Cakmak, Burak; Winther, Ole; Fleury, Bernard H.

    2014-01-01

    We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends...

  16. Effect of linear sorption on solute transport in a coupled fracture-matrix system with sinusoidal fracture geometry

    Directory of Open Access Journals (Sweden)

    N.Natarajan

    2010-10-01

    Full Text Available Modeling of solute transport through fractured rock is an important component of in many disciplines especially groundwater contamination and nuclear waste disposal. Several studies have been conducted on single rock fracture using parallel plate model and recently solute and thermal transport has been numerically modeled in the sinusoidal fracture matrix coupled system. The effect of linear sorption has been studied on the same. Results suggest the high matrix porosity and matrix diffusion coefficient enhance the sorption process and reduce the matrix diffusion of solutes. The velocity of the fluid reduces with increment in fracture aperture.

  17. Generalized ray-transfer matrix for an optical element having an arbitrary wavefront aberration.

    Science.gov (United States)

    Jeong, Tae Moon; Ko, Do-Kyeong; Lee, Jongmin

    2005-11-15

    A generalized ray-transfer matrix for describing the action of an optical element having an arbitrary wavefront aberration is obtained. In this generalized ray-transfer matrix, the action of the aberrated optical element is represented by the product of radial ray-transfer matrices and tangential ray-transfer matrices. The refraction angle of an incident ray is calculated from the gradient of the wavefront aberration at the point of incidence, and the radial and tangential ray-transfer matrices directly use the gradient as a matrix component. To show the validity of the generalized ray-transfer matrix, intercept heights from a spot diagram are calculated with the generalized ray-transfer matrix and compared with those calculated with commercial ray-tracing software.

  18. A General Linear Method for Equating with Small Samples

    Science.gov (United States)

    Albano, Anthony D.

    2015-01-01

    Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

  19. PYESSENCE: Generalized Coupled Quintessence Linear Perturbation Python Code

    Science.gov (United States)

    Leithes, Alexander

    2016-09-01

    PYESSENCE evolves linearly perturbed coupled quintessence models with multiple (cold dark matter) CDM fluid species and multiple DE (dark energy) scalar fields, and can be used to generate quantities such as the growth factor of large scale structure for any coupled quintessence model with an arbitrary number of fields and fluids and arbitrary couplings.

  20. Computing a logarithm of a unitary matrix with general spectrum

    CERN Document Server

    Loring, Terry A

    2012-01-01

    In theory, a unitary matrix U has a skew-hermitian logarithm H. In a computing environment one expects only to know U^*U \\approx I and might wish to compute H with e^H \\approx U and H^*= -H. This is relatively easy to accomplish using the Schur decomposition. Reasonable error bounds are derived. In cases where the norm of U^*U-I is somewhat large we discuss the utility of pre-processing with Newton's method of approximating the polar decomposition. In the case of U being J-skew-symmetric, one can insist that H be J-skew-symmetric and skew-Hermitian.

  1. Linearizability of Nonlinear Third-Order Ordinary Differential Equations by Using a Generalized Linearizing Transformation

    OpenAIRE

    Thailert, E.; Suksern, S.

    2014-01-01

    We discuss the linearization problem of third-order ordinary differential equation under the generalized linearizing transformation. We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation. We also illustrate how to construct the generalized linearizing transformation. Some examples of linearizable equation are provided to demonstrate our procedure.

  2. Local field enhancement at the core of cylindrical nanoinclusions embedded in a linear dielectric host matrix

    Directory of Open Access Journals (Sweden)

    Y.A. Abbo

    2016-09-01

    Full Text Available In this paper we have discussed theoretical concepts and presented numerical results of local field enhancement at the core of different assemblages of metal/dielectric cylindrical nanoinclusions embedded in a linear dielectric host matrix. The obtained results show that for a composite with metal coated inclusions there exist two peak values of the enhancement factor at two different resonant frequencies. The existence of the second maxima becomes more important for a larger volume fraction of the metal part of the inclusion. For dielectric coated metal core inclusions and pure metal inclusions there is only one resonant frequency and one peak value of the enhancement factor. The enhancement of an electromagnetic wave is promising for the existence of nonlinear optical phenomena such as optical bistability which is important in optical communication and in optical computing such as optical switch and memory elements.

  3. Observer design for matrix second order linear systems with uncertain disturbance input-a parametric approach

    Institute of Scientific and Technical Information of China (English)

    Wu Yunli; Li Zhibin; Duan Guangren

    2006-01-01

    A simple parametric approach to design a full-order observer for matrix second-order linear systems with uncertain disturbance input in the matrixsecond-order framework is proposed. The basic idea is to minimize the H2 norm of the transfer function from disturbance to estimation error using the design degrees of freedom provided by a parametric approach in the observer design. Besides the design parameters, the eigenvalues of the closed-loop system are also optimized within desired regions on the left-half of the complex plane. Using the proposed approach, additional specifications can be easily achieved. A spring-mass system is using to show the effect of the proposed approaches.

  4. Static Output-Feedback Control for Vehicle Suspensions: A Single-Step Linear Matrix Inequality Approach

    Directory of Open Access Journals (Sweden)

    Josep Rubió-Massegú

    2013-01-01

    Full Text Available In this paper, a new strategy to design static output-feedback controllers for a class of vehicle suspension systems is presented. A theoretical background on recent advances in output-feedback control is first provided, which makes possible an effective synthesis of static output-feedback controllers by solving a single linear matrix inequality optimization problem. Next, a simplified model of a quarter-car suspension system is proposed, taking the ride comfort, suspension stroke, road holding ability, and control effort as the main performance criteria in the vehicle suspension design. The new approach is then used to design a static output-feedback H∞ controller that only uses the suspension deflection and the sprung mass velocity as feedback information. Numerical simulations indicate that, despite the restricted feedback information, this static output-feedback H∞ controller exhibits an excellent behavior in terms of both frequency and time responses, when compared with the corresponding state-feedback H∞ controller.

  5. Linear matrix inequality approach for synchronization control of fuzzy cellular neural networks with mixed time delays

    Institute of Scientific and Technical Information of China (English)

    P. Balasubramaniam; M. Kalpana; R. Rakkiyappan

    2012-01-01

    Fuzzy cellular neural networks (FCNNs) are special kinds of cellular neural networks (CNNs).Each cell in an FCNN contains fuzzy operating abilities.The entire network is governed by cellular computing laws.The design of FCNNs is based on fuzzy local rules.In this paper,a linear matrix inequality (LMI) approach for synchronization control of FCNNs with mixed delays is investigated.Mixed delays include discrete time-varying delays and unbounded distributed delays.A dynamic control scheme is proposed to achieve the synchronization between a drive network and a response network.By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term and the free-weighting matrices method an improved delay-dependent stability criterion is derived in terms of LMIs.The controller can be easily obtained by solving the derived LMIs.A numerical example and its simulations are presented to illustrate the effectiveness of the proposed method.

  6. Maximum Likelihood in a Generalized Linear Finite Mixture Model by Using the EM Algorithm

    NARCIS (Netherlands)

    Jansen, R.C.

    A generalized linear finite mixture model and an EM algorithm to fit the model to data are described. By this approach the finite mixture model is embedded within the general framework of generalized linear models (GLMs). Implementation of the proposed EM algorithm can be readily done in statistical

  7. Generalized linear IgA dermatosis with palmar involvement

    OpenAIRE

    Norris, Ivy N; Haeberle, M Tye; Callen, Jeffrey P.; Malone, Janine C

    2015-01-01

    Linear IgA bullous dermatosis (LABD) is a sub-epidermal blistering disorder characterized by deposition of IgA along the basement membrane zone (BMZ) as detected by immunofluorescence microscopy. The diagnosis is made by clinicopathologic correlation with immunofluorescence confirmation. Differentiation from other bullous dermatoses is important because therapeutic measures differ. Prompt initiation of the appropriate therapies can have a major impact on outcomes. We present three cases with ...

  8. A Low Complexity Subspace-Based DOA Estimation Algorithm with Uniform Linear Array Correlation Matrix Subsampling

    Directory of Open Access Journals (Sweden)

    Do-Sik Yoo

    2015-01-01

    Full Text Available We propose a low complexity subspace-based direction-of-arrival (DOA estimation algorithm employing a direct signal space construction method (DSPCM by subsampling the autocorrelation matrix of a uniform linear array (ULA. Three major contributions of this paper are as follows. First of all, we introduce the method of autocorrelation matrix subsampling which enables us to employ a low complexity algorithm based on a ULA without computationally complex eigenvalue decomposition or singular-value decomposition. Secondly, we introduce a signal vector separation method to improve the distinguishability among signal vectors, which can greatly improve the performance, particularly, in low signal-to-noise ratio (SNR regime. Thirdly, we provide a root finding (RF method in addition to a spectral search (SS method as the angle finding scheme. Through simulations, we illustrate that the performance of the proposed scheme is reasonably close to computationally much more expensive MUSIC- (MUltiple SIgnal Classification- based algorithms. Finally, we illustrate that the computational complexity of the proposed scheme is reduced, in comparison with those of MUSIC-based schemes, by a factor of O(N2/K, where K is the number of sources and N is the number of antenna elements.

  9. Scalable Linear Visual Feature Learning via Online Parallel Nonnegative Matrix Factorization.

    Science.gov (United States)

    Zhao, Xueyi; Li, Xi; Zhang, Zhongfei; Shen, Chunhua; Zhuang, Yueting; Gao, Lixin; Li, Xuelong

    2016-12-01

    Visual feature learning, which aims to construct an effective feature representation for visual data, has a wide range of applications in computer vision. It is often posed as a problem of nonnegative matrix factorization (NMF), which constructs a linear representation for the data. Although NMF is typically parallelized for efficiency, traditional parallelization methods suffer from either an expensive computation or a high runtime memory usage. To alleviate this problem, we propose a parallel NMF method called alternating least square block decomposition (ALSD), which efficiently solves a set of conditionally independent optimization subproblems based on a highly parallelized fine-grained grid-based blockwise matrix decomposition. By assigning each block optimization subproblem to an individual computing node, ALSD can be effectively implemented in a MapReduce-based Hadoop framework. In order to cope with dynamically varying visual data, we further present an incremental version of ALSD, which is able to incrementally update the NMF solution with a low computational cost. Experimental results demonstrate the efficiency and scalability of the proposed methods as well as their applications to image clustering and image retrieval.

  10. Generalizing a categorization of students' interpretations of linear kinematics graphs

    Science.gov (United States)

    Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

    2016-06-01

    We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.

  11. On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X’β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞.

  12. On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    ZHANG SanGuo; LIAO Yuan

    2008-01-01

    In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE)concerning the quasi-likelihood equation ∑ni=1 Xi(yi-μ(X1iβ)) =0 for univariate generalized linear model E(y|X) =μ(X1β). Given uncorrelated residuals{ei=Yi-μ(X1iβ0), 1≤i≤n}and other conditions, we prove that (β)n-β0=Op(λ--1/2n)holds, where (β)n is a root of the above equation,β0 is the true value of parameter β and λ-n denotes the smallest eigenvalue of the matrix Sn=Σni=1 XiX1i. We also show that the convergence rate above is sharp, provided independent nonasymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas(1976)for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is S-1n→0, as the sample size n→∞.

  13. Generalized linear IgA dermatosis with palmar involvement.

    Science.gov (United States)

    Norris, Ivy N; Haeberle, M Tye; Callen, Jeffrey P; Malone, Janine C

    2015-09-17

    Linear IgA bullous dermatosis (LABD) is a sub-epidermal blistering disorder characterized by deposition of IgA along the basement membrane zone (BMZ) as detected by immunofluorescence microscopy. The diagnosis is made by clinicopathologic correlation with immunofluorescence confirmation. Differentiation from other bullous dermatoses is important because therapeutic measures differ. Prompt initiation of the appropriate therapies can have a major impact on outcomes. We present three cases with prominent palmar involvement to alert the clinician of this potential physical exam finding and to consider LABD in the right context.

  14. The Schur algorithm for generalized Schur functions III : J-unitary matrix polynomials on the circle

    NARCIS (Netherlands)

    Alpay, Daniel; Azizov, Tomas; Dijksma, Aad; Langer, Heinz

    2003-01-01

    The main result is that for J = ((1)(0) (0)(-1)) every J-unitary 2 x 2-matrix polynomial on the unit circle is an essentially unique product of elementary J-unitary 2 x 2-matrix polynomials which are either of degree 1 or 2k. This is shown by means of the generalized Schur transformation introduced

  15. Analytical solution of linear ordinary differential equations by differential transfer matrix method

    Directory of Open Access Journals (Sweden)

    Sina Khorasani

    2003-08-01

    Full Text Available We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the $n$th-order differential equation to a system of $n$ linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method.

  16. A general algorithm for computing distance transforms in linear time

    NARCIS (Netherlands)

    Meijster, A.; Roerdink, J.B.T.M.; Hesselink, W.H.; Goutsias, J; Vincent, L; Bloomberg, DS

    2000-01-01

    A new general algorithm fur computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the com

  17. A general algorithm for computing distance transforms in linear time

    NARCIS (Netherlands)

    Meijster, A.; Roerdink, J.B.T.M.; Hesselink, W.H.; Goutsias, J; Vincent, L; Bloomberg, DS

    2000-01-01

    A new general algorithm fur computing distance transforms of digital images is presented. The algorithm consists of two phases. Both phases consist of two scans, a forward and a backward scan. The first phase scans the image column-wise, while the second phase scans the image row-wise. Since the

  18. General formalism for partial spatial coherence in reflection Mueller matrix polarimetry.

    Science.gov (United States)

    Ossikovski, Razvigor; Hingerl, Kurt

    2016-09-01

    Starting from the first principles, we derive the expressions governing partially coherent Mueller matrix reflection polarimetry on spatially inhomogeneous samples. These are reported both in their general form and in the practically important specific form for two juxtaposed media.

  19. The general RF tuning for IH-DTL linear accelerators

    Science.gov (United States)

    Lu, Y. R.; Ratzinger, U.; Schlitt, B.; Tiede, R.

    2007-11-01

    The RF tuning is the most important research for achieving the resonant frequency and the flatness of electric field distributions along the axis of RF accelerating structures. The six different tuning concepts and that impacts on the longitudinal field distributions have been discussed in detail combining the RF tuning process of a 1:2 modeled 20.85 MV compact IH-DTL cavity, which was designed to accelerate proton, helium, oxygen or C 4+ from 400 keV/ u to 7 MeV/u and used as the linear injector of 430 MeV/ u synchrotron [Y.R. Lu, S. Minaev, U. Ratzinger, B. Schlitt, R.Tiede, The Compact 20MV IH-DTL for the Heidelberg Therapy Facility, in: Proceedings of the LINAC Conference, Luebeck, Germany, 2004 [1]; Y.R. Lu, Frankfurt University Dissertation, 2005. [2

  20. ON THE GENERALIZED INVERSE NEVILLE-TYPE MATRIX-VALUED RATIONAL INTERPOLANTS

    Institute of Scientific and Technical Information of China (English)

    Zhibing Chen

    2003-01-01

    A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7,9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

  1. Transfer matrix computation of generalized critical polynomials in percolation

    Science.gov (United States)

    Scullard, Christian R.; Lykke Jacobsen, Jesper

    2012-12-01

    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 PB(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 PB(p) was defined by a contraction-deletion identity, similar to that satisfied by the Tutte polynomial. Here, we give an alternative probabilistic definition of PB(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 pc(4, 82) = 0.676 803 329…, pc(kagome) = 0.524 404 998…, pc(3, 122) = 0.740 420 798…, comparable to the best simulation results. We also show that the alternative definition of PB(p) can be applied to study site percolation problems. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

  2. The ε-Algorithm and η-Algorithm for Generalized Inverse Rectangular Matrix Pade Approximants

    Institute of Scientific and Technical Information of China (English)

    1999-01-01

    An axiomatic definition for the generalized inverse matrix Pade approximation (GMPA) is introduced. The matrix rational approximants are of the form of the matrix-valued numerator and the scalar denominator. By means of generalized inverse for matrices, the ε-algorithm for the computation of GMPA is established. The well-known Wynn identity for GMPA is proved on the basis of ε-algorithm. The η-algorithm is defined in a similar way. The equivalence relation between ε-algorithm and η-algorithm is proposed. Some common examples and a numerical example are given to illustrate the methods in this paper.

  3. The general RF tuning for IH-DTL linear accelerators

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Y.R. [Key State Laboratory of Nuclear Physics and Technology, Peking University (China)], E-mail: yrlu@pku.edu.cn; Ratzinger, U. [Institute of Applied Physics, Frankfurt University (Germany); Schlitt, B. [Gesellschaft fuer Schwerionenforschung, mbH, Darmstadt (Germany); Tiede, R. [Institute of Applied Physics, Frankfurt University (Germany)

    2007-11-21

    The RF tuning is the most important research for achieving the resonant frequency and the flatness of electric field distributions along the axis of RF accelerating structures. The six different tuning concepts and that impacts on the longitudinal field distributions have been discussed in detail combining the RF tuning process of a 1:2 modeled 20.85 MV compact IH-DTL cavity, which was designed to accelerate proton, helium, oxygen or C{sup 4+} from 400 keV/u to 7 MeV/u and used as the linear injector of 430 MeV/u synchrotron [Y.R. Lu, S. Minaev, U. Ratzinger, B. Schlitt, R.Tiede, The Compact 20MV IH-DTL for the Heidelberg Therapy Facility, in: Proceedings of the LINAC Conference, Luebeck, Germany, 2004 ; Y.R. Lu, Frankfurt University Dissertation, 2005. ] in Heidelberg Heavy Ion Cancer Therapy (HICAT). Some of tuning concepts are also suitable and effective for the tuning of RFQ and/or other RF accelerating structures. Finally good field flatness in IH-DTL cavity has been realized successfully. The experience got from the model cavity tuning benefits real power cavity tuning, which is only needed to be tuned by the plungers. The cavity had a beam commissioning successfully for the initial beam acceleration at the end of 2006.

  4. Transferability of regional permafrost disturbance susceptibility modelling using generalized linear and generalized additive models

    Science.gov (United States)

    Rudy, Ashley C. A.; Lamoureux, Scott F.; Treitz, Paul; van Ewijk, Karin Y.

    2016-07-01

    To effectively assess and mitigate risk of permafrost disturbance, disturbance-prone areas can be predicted through the application of susceptibility models. In this study we developed regional susceptibility models for permafrost disturbances using a field disturbance inventory to test the transferability of the model to a broader region in the Canadian High Arctic. Resulting maps of susceptibility were then used to explore the effect of terrain variables on the occurrence of disturbances within this region. To account for a large range of landscape characteristics, the model was calibrated using two locations: Sabine Peninsula, Melville Island, NU, and Fosheim Peninsula, Ellesmere Island, NU. Spatial patterns of disturbance were predicted with a generalized linear model (GLM) and generalized additive model (GAM), each calibrated using disturbed and randomized undisturbed locations from both locations and GIS-derived terrain predictor variables including slope, potential incoming solar radiation, wetness index, topographic position index, elevation, and distance to water. Each model was validated for the Sabine and Fosheim Peninsulas using independent data sets while the transferability of the model to an independent site was assessed at Cape Bounty, Melville Island, NU. The regional GLM and GAM validated well for both calibration sites (Sabine and Fosheim) with the area under the receiver operating curves (AUROC) > 0.79. Both models were applied directly to Cape Bounty without calibration and validated equally with AUROC's of 0.76; however, each model predicted disturbed and undisturbed samples differently. Additionally, the sensitivity of the transferred model was assessed using data sets with different sample sizes. Results indicated that models based on larger sample sizes transferred more consistently and captured the variability within the terrain attributes in the respective study areas. Terrain attributes associated with the initiation of disturbances were

  5. Solution and applications of a class of general linear variational inequalities

    Institute of Scientific and Technical Information of China (English)

    何炳生

    1996-01-01

    Many problems in mathematical programming can be described as a general linear variational inequality of the following form: find a vector u*, such thatSome iterative methods for solving a class of general linear variational inequalities have been presented. It is pointed out that the methods can be used to solve some practical extended programming problems.

  6. The generalization of some trellis properties of linear codes to group codes

    Institute of Scientific and Technical Information of China (English)

    KAN HaiBin; LI XueFei; SHEN Hong

    2009-01-01

    In this paper, we discuss some trellis properties for codes over a finite Abelian group, which are the generalization of the corresponding trellis properties for linear codes over a field. Also, we also inves-tigate difficulties when we try to generalize a property of a tail-biting trellis for a linear code over a field to a group code.

  7. Rayleigh-type Surface Quasimodes in General Linear Elasticity

    CERN Document Server

    Hansen, Sönke

    2010-01-01

    Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic in general, with traction-free boundary. Assuming a global variant of a condition of Barnett and Lothe, the construction is reduced to an eigenvalue problem for a selfadjoint scalar first order pseudo-differential operator on the boundary. The principal and the subprincipal symbol of this operator are computed. The formula for the subprincipal symbol seems to be new even in the isotropic case.

  8. A General Robust Linear Transceiver Design for Multi-Hop Amplify-and-Forward MIMO Relaying Systems

    Science.gov (United States)

    Xing, Chengwen; Ma, Shaodan; Fei, Zesong; Wu, Yik-Chung; Poor, H. Vincent

    2013-03-01

    In this paper, linear transceiver design for multi-hop amplify-and-forward (AF) multiple-input multiple-out (MIMO) relaying systems with Gaussian distributed channel estimation errors is investigated. Commonly used transceiver design criteria including weighted mean-square-error (MSE) minimization, capacity maximization, worst-MSE/MAX-MSE minimization and weighted sum-rate maximization, are considered and unified into a single matrix-variate optimization problem. A general robust design algorithm is proposed to solve the unified problem. Specifically, by exploiting majorization theory and properties of matrix-variate functions, the optimal structure of the robust transceiver is derived when either the covariance matrix of channel estimation errors seen from the transmitter side or the corresponding covariance matrix seen from the receiver side is proportional to an identity matrix. Based on the optimal structure, the original transceiver design problems are reduced to much simpler problems with only scalar variables whose solutions are readily obtained by iterative water-filling algorithm. A number of existing transceiver design algorithms are found to be special cases of the proposed solution. The differences between our work and the existing related work are also discussed in detail. The performance advantages of the proposed robust designs are demonstrated by simulation results.

  9. Bayesian generalized linear mixed modeling of Tuberculosis using informative priors.

    Science.gov (United States)

    Ojo, Oluwatobi Blessing; Lougue, Siaka; Woldegerima, Woldegebriel Assefa

    2017-01-01

    TB is rated as one of the world's deadliest diseases and South Africa ranks 9th out of the 22 countries with hardest hit of TB. Although many pieces of research have been carried out on this subject, this paper steps further by inculcating past knowledge into the model, using Bayesian approach with informative prior. Bayesian statistics approach is getting popular in data analyses. But, most applications of Bayesian inference technique are limited to situations of non-informative prior, where there is no solid external information about the distribution of the parameter of interest. The main aim of this study is to profile people living with TB in South Africa. In this paper, identical regression models are fitted for classical and Bayesian approach both with non-informative and informative prior, using South Africa General Household Survey (GHS) data for the year 2014. For the Bayesian model with informative prior, South Africa General Household Survey dataset for the year 2011 to 2013 are used to set up priors for the model 2014.

  10. Optimal control of large space structures via generalized inverse matrix

    Science.gov (United States)

    Nguyen, Charles C.; Fang, Xiaowen

    1987-01-01

    Independent Modal Space Control (IMSC) is a control scheme that decouples the space structure into n independent second-order subsystems according to n controlled modes and controls each mode independently. It is well-known that the IMSC eliminates control and observation spillover caused when the conventional coupled modal control scheme is employed. The independent control of each mode requires that the number of actuators be equal to the number of modelled modes, which is very high for a faithful modeling of large space structures. A control scheme is proposed that allows one to use a reduced number of actuators to control all modeled modes suboptimally. In particular, the method of generalized inverse matrices is employed to implement the actuators such that the eigenvalues of the closed-loop system are as closed as possible to those specified by the optimal IMSC. Computer simulation of the proposed control scheme on a simply supported beam is given.

  11. Item Response Theory Using Hierarchical Generalized Linear Models

    Directory of Open Access Journals (Sweden)

    Hamdollah Ravand

    2015-03-01

    Full Text Available Multilevel models (MLMs are flexible in that they can be employed to obtain item and person parameters, test for differential item functioning (DIF and capture both local item and person dependence. Papers on the MLM analysis of item response data have focused mostly on theoretical issues where applications have been add-ons to simulation studies with a methodological focus. Although the methodological direction was necessary as a first step to show how MLMs can be utilized and extended to model item response data, the emphasis needs to be shifted towards providing evidence on how applications of MLMs in educational testing can provide the benefits that have been promised. The present study uses foreign language reading comprehension data to illustrate application of hierarchical generalized models to estimate person and item parameters, differential item functioning (DIF, and local person dependence in a three-level model.

  12. Multireference linearized Coupled Cluster theory for strongly correlated systems using Matrix Product States

    CERN Document Server

    Sharma, Sandeep

    2015-01-01

    We propose a multireference linearized coupled cluster theory using matrix product states (MPS-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles (MRCISD), for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries, to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual DMRG algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens u...

  13. Two-Link Flexible Manipulator Control Using Sliding Mode Control Based Linear Matrix Inequality

    Science.gov (United States)

    Zulfatman; Marzuki, Mohammad; Alif Mardiyah, Nur

    2017-04-01

    Two-link flexible manipulator is a manipulator robot which at least one of its arms is made of lightweight material and not rigid. Flexible robot manipulator has some advantages over the rigid robot manipulator, such as lighter, requires less power and costs, and to result greater payload. However, suitable control algorithm to maintain the two-link flexible robot manipulator in accurate positioning is very challenging. In this study, sliding mode control (SMC) was employed as robust control algorithm due to its insensitivity on the system parameter variations and the presence of disturbances when the system states are sliding on a sliding surface. SMC algorithm was combined with linear matrix inequality (LMI), which aims to reduce the effects of chattering coming from the oscillation of the state during sliding on the sliding surface. Stability of the control algorithm is guaranteed by Lyapunov function candidate. Based on simulation works, SMC based LMI resulted in better performance improvements despite the disturbances with significant chattering reduction. This was evident from the decline of the sum of squared tracking error (SSTE) and the sum of squared of control input (SSCI) indexes respectively 25.4% and 19.4%.

  14. The neurochemical mobile with non-linear interaction matrix: an exploratory computational model.

    Science.gov (United States)

    Qi, Z; Fieni, D; Tretter, F; Voit, E O

    2013-05-01

    Several years ago, the "neurochemical mobile" was introduced as a visual tool for explaining the different balances between neurotransmitters in the brain and their role in mental disorders. Here we complement this concept with a non-linear computational systems model representing the direct and indirect interactions between neurotransmitters, as they have been described in the "neurochemical interaction matrix." The model is constructed within the framework of biochemical systems theory, which facilitates the mapping of numerically ill-characterized systems into a mathematical and computational construct that permits a variety of analyses. Simulations show how short- and long-term perturbations in any of the neurotransmitters migrate through the entire system, thereby affecting the balances within the mobile. In cases of short-term alterations, transients are of particular interest, whereas long-term changes shed light on persistently altered, allostatic states, which in mental diseases and sleep disorders could be due to a combination of unfavorable factors, resulting from a specific genetic predisposition, epigenetic effects, disease, or the repeated use of drugs, such as opioids and amphetamines.

  15. Linearized texture of three-dimensional extracellular matrix is mandatory for bladder cancer cell invasion

    Science.gov (United States)

    Alfano, Massimo; Nebuloni, Manuela; Allevi, Raffaele; Zerbi, Pietro; Longhi, Erika; Lucianò, Roberta; Locatelli, Irene; Pecoraro, Angela; Indrieri, Marco; Speziali, Chantal; Doglioni, Claudio; Milani, Paolo; Montorsi, Francesco; Salonia, Andrea

    2016-01-01

    In the fields of biomaterials and tissue engineering simulating the native microenvironment is of utmost importance. As a major component of the microenvironment, the extracellular matrix (ECM) contributes to tissue homeostasis, whereas modifications of native features are associated with pathological conditions. Furthermore, three-dimensional (3D) geometry is an important feature of synthetic scaffolds favoring cell stemness, maintenance and differentiation. We analyzed the 3D structure, geometrical measurements and anisotropy of the ECM isolated from (i) human bladder mucosa (basal lamina and lamina propria) and muscularis propria; and, (ii) bladder carcinoma (BC). Next, binding and invasion of bladder metastatic cell line was observed on synthetic scaffold recapitulating anisotropy of tumoral ECM, but not on scaffold with disorganized texture typical of non-neoplastic lamina propria. This study provided information regarding the ultrastructure and geometry of healthy human bladder and BC ECMs. Likewise, using synthetic scaffolds we identified linearization of the texture as a mandatory feature for BC cell invasion. Integrating microstructure and geometry with biochemical and mechanical factors could support the development of an innovative synthetic bladder substitute or a tumoral scaffold predictive of chemotherapy outcomes. PMID:27779205

  16. Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution

    Science.gov (United States)

    Han, Fang; Liu, Han

    2016-01-01

    Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson’s sample correlation matrix. Although Pearson’s sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall’s tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall’s tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall’s tau correlation matrix and the latent Pearson’s correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of “effective rank” in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a “sign subgaussian condition” which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition.

  17. Statistical analysis of latent generalized correlation matrix estimation in transelliptical distribution.

    Science.gov (United States)

    Han, Fang; Liu, Han

    2017-02-01

    Correlation matrix plays a key role in many multivariate methods (e.g., graphical model estimation and factor analysis). The current state-of-the-art in estimating large correlation matrices focuses on the use of Pearson's sample correlation matrix. Although Pearson's sample correlation matrix enjoys various good properties under Gaussian models, its not an effective estimator when facing heavy-tail distributions with possible outliers. As a robust alternative, Han and Liu (2013b) advocated the use of a transformed version of the Kendall's tau sample correlation matrix in estimating high dimensional latent generalized correlation matrix under the transelliptical distribution family (or elliptical copula). The transelliptical family assumes that after unspecified marginal monotone transformations, the data follow an elliptical distribution. In this paper, we study the theoretical properties of the Kendall's tau sample correlation matrix and its transformed version proposed in Han and Liu (2013b) for estimating the population Kendall's tau correlation matrix and the latent Pearson's correlation matrix under both spectral and restricted spectral norms. With regard to the spectral norm, we highlight the role of "effective rank" in quantifying the rate of convergence. With regard to the restricted spectral norm, we for the first time present a "sign subgaussian condition" which is sufficient to guarantee that the rank-based correlation matrix estimator attains the optimal rate of convergence. In both cases, we do not need any moment condition.

  18. An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

    Institute of Scientific and Technical Information of China (English)

    Shao Hai-Jian; Cai Guo-Liang; Wang Hao-Xiang

    2010-01-01

    In this study,a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional.This paper presents the comprehensive discussion of the approach and also extensive applications.

  19. The influence of fiber-matrix adhesion on the linear viscoelastic creep behavior of CF/PPS composites

    NARCIS (Netherlands)

    Motta Dias, M.H.; Jansen, K.M.B.; Luinge, H.; Nayak, K.; Bersee, H.E.N.

    2014-01-01

    The influence of fiber-matrix adhesion on the linear viscoelastic creep behavior of as received and surface modified carbon fiber (AR-CF and SM-CF, respectively) reinforced polyphenylene sulfide (PPS) composite materials was investigated. Short-term tensile creep tests were performed on ±45°

  20. The influence of fiber-matrix adhesion on the linear viscoelastic creep behavior of CF/PPS composites

    NARCIS (Netherlands)

    Motta Dias, M.H.; Jansen, K.M.B.; Luinge, H.; Nayak, K.; Bersee, H.E.N.

    2014-01-01

    The influence of fiber-matrix adhesion on the linear viscoelastic creep behavior of as received and surface modified carbon fiber (AR-CF and SM-CF, respectively) reinforced polyphenylene sulfide (PPS) composite materials was investigated. Short-term tensile creep tests were performed on ±45° specime

  1. Applications of Generalized Cascade Scattering Matrix on the Microwave Circuits and Antenna Arrays

    Directory of Open Access Journals (Sweden)

    Shun-Feng Cao

    2015-01-01

    Full Text Available The ideal lossless symmetrical reciprocal network (ILSRN is constructed and introduced to resolve the complex interconnections of two arbitrary microwave networks. By inserting the ILSRNs, the complex interconnections can be converted into the standard one-by-one case without changing the characteristics of the previous microwave networks. Based on the algorithm of the generalized cascade scattering matrix, a useful derivation on the excitation coefficients of antenna arrays is firstly proposed with consideration of the coupling effects. And then, the proposed techniques are applied on the microwave circuits and antenna arrays. Firstly, an improved magic-T is optimized, fabricated, and measured. Compared with the existing results, the prototype has a wider bandwidth, lower insertion loss, better return loss, isolation, and imbalances. Secondly, two typical linear waveguide slotted arrays are designed. Both the radiation patterns and scattering parameters at the input ports agree well with the desired goals. Finally, the feeding network of a two-element microstrip antenna array is optimized to decrease the mismatch at the input port, and a good impedance matching is successfully achieved.

  2. Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

    Institute of Scientific and Technical Information of China (English)

    Wu Yunli; Duan Guangren

    2006-01-01

    A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment.By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

  3. GENERAL FORMULA AND RECURRENCE FORMULA FOR RADIAL MATRIX ELEMENTS OF N-DIMENSIONAL ISOTROPIC HARMONIC OSCILLATOR

    Institute of Scientific and Technical Information of China (English)

    CHEN CHANG-YUAN

    2000-01-01

    In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.

  4. General approach for modeling partial coherence in spectroscopic Mueller matrix polarimetry.

    Science.gov (United States)

    Hingerl, Kurt; Ossikovski, Razvigor

    2016-01-15

    We present a general formalism for modeling partial coherence in spectroscopic Mueller matrix measurements of stratified media. The approach is based on the statistical definition of a Mueller matrix, as well as, on the fundamental representation of the measurement process as the convolution of the sample response with a specific instrumental function. The formalism is readily extended to describe other measurement imperfections occurring jointly with partial coherence and resulting in depolarizing experimental Mueller matrices.

  5. A generalization of random matrix theory and its application to statistical physics.

    Science.gov (United States)

    Wang, Duan; Zhang, Xin; Horvatic, Davor; Podobnik, Boris; Eugene Stanley, H

    2017-02-01

    To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.

  6. On the General Taylor Theorem and its Applications in Solving Non—linear Problems

    Institute of Scientific and Technical Information of China (English)

    ShiJunLIAO

    1997-01-01

    In this paper,we propose a general Taylor series and prove a general Taylor theorem and then simply give some applications of it in solving non-linear differential equations.The general Taylor series is a family of power series which contains the classical Taylor series in logic.Moreover,it can be valid in much larger regions.

  7. An efficient method for generalized linear multiplicative programming problem with multiplicative constraints

    OpenAIRE

    Zhao, Yingfeng; Liu, Sanyang

    2016-01-01

    We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of so...

  8. Best linear unbiased prediction of genomic breeding values using a trait-specific marker-derived relationship matrix.

    Directory of Open Access Journals (Sweden)

    Zhe Zhang

    Full Text Available BACKGROUND: With the availability of high density whole-genome single nucleotide polymorphism chips, genomic selection has become a promising method to estimate genetic merit with potentially high accuracy for animal, plant and aquaculture species of economic importance. With markers covering the entire genome, genetic merit of genotyped individuals can be predicted directly within the framework of mixed model equations, by using a matrix of relationships among individuals that is derived from the markers. Here we extend that approach by deriving a marker-based relationship matrix specifically for the trait of interest. METHODOLOGY/PRINCIPAL FINDINGS: In the framework of mixed model equations, a new best linear unbiased prediction (BLUP method including a trait-specific relationship matrix (TA was presented and termed TABLUP. The TA matrix was constructed on the basis of marker genotypes and their weights in relation to the trait of interest. A simulation study with 1,000 individuals as the training population and five successive generations as candidate population was carried out to validate the proposed method. The proposed TABLUP method outperformed the ridge regression BLUP (RRBLUP and BLUP with realized relationship matrix (GBLUP. It performed slightly worse than BayesB with an accuracy of 0.79 in the standard scenario. CONCLUSIONS/SIGNIFICANCE: The proposed TABLUP method is an improvement of the RRBLUP and GBLUP method. It might be equivalent to the BayesB method but it has additional benefits like the calculation of accuracies for individual breeding values. The results also showed that the TA-matrix performs better in predicting ability than the classical numerator relationship matrix and the realized relationship matrix which are derived solely from pedigree or markers without regard to the trait. This is because the TA-matrix not only accounts for the Mendelian sampling term, but also puts the greater emphasis on those markers that

  9. ORDER RESULTS OF GENERAL LINEAR METHODS FOR MULTIPLY STIFF SINGULAR PERTURBATION PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Si-qing Gan; Geng Sun

    2002-01-01

    In this paper we analyze the error behavior of general linear methods applied to some classes of one-parameter multiply stiff singularly perturbed problems. We obtain the global error estimate of algebraically and diagonally stable general linear methods. The main result of this paper can be viewed as an extension of that obtained by Xiao [13] for the case of Runge-Kutta methods.

  10. Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede

    2004-01-01

    This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...... matrix converter model. Regulated Order Extended Luenberger Observer (ROELO) is employed to bring better response in the whole speed operation range and a method to select the observer gain is presented. Experimental results are shown to illustrate the performance of the proposed system...

  11. (Anti-Hermitian Generalized (Anti-Hamiltonian Solution to a System of Matrix Equations

    Directory of Open Access Journals (Sweden)

    Juan Yu

    2014-01-01

    Full Text Available We mainly solve three problems. Firstly, by the decomposition of the (anti-Hermitian generalized (anti-Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-Hermitian generalized (anti-Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution min⁡X∈K⁡∥X^-X∥ is obtained, where K is the (anti-Hermitian generalized (anti-Hamiltonian solution set of the above system and X^ is the given matrix. Thirdly, the least squares (anti-Hermitian generalized (anti-Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-Hermitian generalized (anti-Hamiltonian solution and the corresponding numerical examples are presented.

  12. Speed-Sensorless DTC-SVM for Matrix Converter Drives With Simple Non-Linearity Compensation

    DEFF Research Database (Denmark)

    Lee, Kyo-Beum; Blaabjerg, Frede; Yoon, Tae-Woong

    2005-01-01

    This paper presents a new method to improve sensorless performance of matrix converter drives using a parameter estimation scheme. To improve low-speed sensorless performance, the non-Iinearities of a matrix converter drive such as commutation delays, turn-on and turn-off times of switching devic...

  13. On the generalized eigenvalue method for energies and matrix elements in lattice field theory

    CERN Document Server

    Blossier, Benoit; von Hippel, Georg; Mendes, Tereza; Sommer, Rainer

    2009-01-01

    We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as $\\exp(-(E_{N+1}-E_n) t)$. The gap $E_{N+1}-E_n$ can be made large by increasing the number $N$ of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order $1/m_b$ in HQET.

  14. Linear matrix inequality-based nonlinear adaptive robust control with application to unmanned aircraft systems

    Science.gov (United States)

    Kun, David William

    Unmanned aircraft systems (UASs) are gaining popularity in civil and commercial applications as their lightweight on-board computers become more powerful and affordable, their power storage devices improve, and the Federal Aviation Administration addresses the legal and safety concerns of integrating UASs in the national airspace. Consequently, many researchers are pursuing novel methods to control UASs in order to improve their capabilities, dependability, and safety assurance. The nonlinear control approach is a common choice as it offers several benefits for these highly nonlinear aerospace systems (e.g., the quadrotor). First, the controller design is physically intuitive and is derived from well known dynamic equations. Second, the final control law is valid in a larger region of operation, including far from the equilibrium states. And third, the procedure is largely methodical, requiring less expertise with gain tuning, which can be arduous for a novice engineer. Considering these facts, this thesis proposes a nonlinear controller design method that combines the advantages of adaptive robust control (ARC) with the powerful design tools of linear matrix inequalities (LMI). The ARC-LMI controller is designed with a discontinuous projection-based adaptation law, and guarantees a prescribed transient and steady state tracking performance for uncertain systems in the presence of matched disturbances. The norm of the tracking error is bounded by a known function that depends on the controller design parameters in a known form. Furthermore, the LMI-based part of the controller ensures the stability of the system while overcoming polytopic uncertainties, and minimizes the control effort. This can reduce the number of parameters that require adaptation, and helps to avoid control input saturation. These desirable characteristics make the ARC-LMI control algorithm well suited for the quadrotor UAS, which may have unknown parameters and may encounter external

  15. Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

    Institute of Scientific and Technical Information of China (English)

    Wu Wei; Cui Bao-Tong

    2007-01-01

    In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented.This class of chaotic neural networks covers several well-known neural network, such a Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

  16. 广义Fibonacci矩阵与Riordan矩阵%The Generalized Fibonacci Matrices and Riordan Matrix

    Institute of Scientific and Technical Information of China (English)

    洪小波; 黄中跃; 贾彦益

    2011-01-01

    利用Riordan矩阵理论研究了广义Fibonacci矩阵的性质,得到了广义Fibonacci矩阵的逆矩阵及一些包含Fibonacci数和Catalan数的组合恒等式.%The generalized Fibonacci matrices are studied by means of Riordan method. The inverse of the generalized Fibonacci matrix is derived,and some identities involving Fibonacci and Catalan numbers are also obtained.

  17. COMPUTING A NEAREST P-SYMMETRIC NONNEGATIVE DEFINITE MATRIX UNDER LINEAR RESTRICTION

    Institute of Scientific and Technical Information of China (English)

    Hua Dai

    2004-01-01

    Let P be an n × n symmetric orthogonal matrix. A real n × n matrix A is called P-symmetric nonnegative definite if A is symmetric nonnegative definite and (PA)T =PA. This paper is concerned with a kind of inverse problem for P-symmetric nonncgative definite matrices: Given a real n × n matrix A, real n × m matrices X and B, find an n × n P-symmetric nonnegative definite matrix A minimizing ‖A- A‖F subject to AX = B.Necessary and sufficient conditions are presented for the solvability of the problem. The expression of the solution to the problem is given. These results are applied to solve an inverse eigenvalue problem for P-symmetric nonnegative definite matrices.

  18. Univariate and multivariate general linear models theory and applications with SAS

    CERN Document Server

    Kim, Kevin

    2006-01-01

    Reviewing the theory of the general linear model (GLM) using a general framework, Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition presents analyses of simple and complex models, both univariate and multivariate, that employ data sets from a variety of disciplines, such as the social and behavioral sciences.With revised examples that include options available using SAS 9.0, this expanded edition divides theory from applications within each chapter. Following an overview of the GLM, the book introduces unrestricted GLMs to analyze multiple regr

  19. Predicting infectivity of Arbuscular Mycorrhizal fungi from soil variables using Generalized Additive Models and Generalized Linear Models

    Directory of Open Access Journals (Sweden)

    IRNANDA AIKO FIFI DJUUNA

    2010-07-01

    Full Text Available Djuuna IAF, Abbott LK, Van Niel K (2010 Predicting infectivity of Arbuscular Mycorrhizal fungi from soil variables using Generalized Additive Models and Generalized Linear Models. Biodiversitas 11: 145-150. The objective of this study was to predict the infectivity of arbuscular mycorrhizal fungi (AM fungi, from field soil based on soil properties and land use history using generalized additive models (GAMs and generalized linear models (GLMs. A total of 291 soil samples from a farm in Western Australia near Wickepin were collected and used in this study. Nine soil properties, including elevation, pH, EC, total C, total N, P, K, microbial biomass carbon, and soil texture, and land use history of the farm were used as independent variables, while the percentage of root length colonized (%RLC was used as the dependent variable. GAMs parameterized for the percent of root length colonized suggested skewed quadratic responses to soil pH and microbial biomass carbon; cubic responses to elevation and soil K; and linear responses to soil P, EC and total C. The strength of the relationship between percent root length colonized by AM fungi and environmental variables showed that only elevation, total C and microbial biomass carbon had strong relationships. In general, GAMs and GLMs models confirmed the strong relationship between infectivity of AM fungi (assessed in a glasshouse bioassay for soil collected in summer prior to the first rain of the season and soil properties.

  20. Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    YIN; Changming; ZHAO; Lincheng; WEI; Chengdong

    2006-01-01

    In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

  1. Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules.

    Science.gov (United States)

    Marrero-Ponce, Yovani; Martínez-Albelo, Eugenio R; Casañola-Martín, Gerardo M; Castillo-Garit, Juan A; Echevería-Díaz, Yunaimy; Zaldivar, Vicente Romero; Tygat, Jan; Borges, José E Rodriguez; García-Domenech, Ramón; Torrens, Francisco; Pérez-Giménez, Facundo

    2010-11-01

    Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E(k)) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES(k), is here proposed as a new molecular representation easily calculated from E(k). Then, the kth stochastic bond linear indices are calculated using ES(k) as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity

  2. Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach

    Energy Technology Data Exchange (ETDEWEB)

    Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)

    1993-08-28

    We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).

  3. General structure of democratic mass matrix of quark sector in E{sub 6} model

    Energy Technology Data Exchange (ETDEWEB)

    Ciftci, R., E-mail: rciftci@cern.ch [Ankara (Turkey); Çiftci, A. K., E-mail: abbas.kenan.ciftci@cern.ch [Ankara University, Ankara (Turkey)

    2016-03-25

    An extension of the Standard Model (SM) fermion sector, which is inspired by the E{sub 6} Grand Unified Theory (GUT) model, might be a good candidate to explain a number of unanswered questions in SM. Existence of the isosinglet quarks might explain great mass difference of bottom and top quarks. Also, democracy on mass matrix elements is a natural approach in SM. In this study, we have given general structure of Democratic Mass Matrix (DMM) of quark sector in E6 model.

  4. A new formulation to calculate general HFB matrix elements through Pfaffian

    CERN Document Server

    Mizusaki, Takahiro

    2012-01-01

    A new formula is presented for the calculation of matrix elements between multi-quasiparticle Hartree-Fock-Bogoliubov (HFB) states. The formula is expressed in terms of the Pfaffian, and is derived by using the Fermion coherent states with Grassmann numbers. It turns out that the formula corresponds to an extension of generalized Wick's theorem and simplifies the combinatorial complexity resulting from practical applications of generalized Wick's theorem by unifying the transition density and the transition pairing tensor in the HFB theory. The resultant formula is simpler and more compact than the traditional description of matrix elements of general many-body operators. In addition, through the derivation of our new formula, we found that the Pfaffian version of the Lewis Carroll formula corresponds to the relation conjectrured by Balian and Brezin for the HFB theory in 1969.

  5. GENERAL CENTRAL PATH AND THE LARGEST STEP GENERAL CENTRAL PATH FOLLOWING ALGORITHM FOR LINEAR PROGRAMMING

    Institute of Scientific and Technical Information of China (English)

    艾文宝; 张可村

    2001-01-01

    In this paper, we propose a general path following method, in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap. The algorithm maintains the O ( nL) ineration complexity. It enjoys quadratic convergence if the optimal vertex is nondegenerate.

  6. The Solution Structure and Error Estimation for The Generalized Linear Complementarity Problem

    Directory of Open Access Journals (Sweden)

    Tingfa Yan

    2014-07-01

    Full Text Available In this paper, we consider the generalized linear complementarity problem (GLCP. Firstly, we develop some equivalent reformulations of the problem under milder conditions, and then characterize the solution of the GLCP. Secondly, we also establish the global error estimation for the GLCP by weakening the assumption. These results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

  7. Bounded Real Lemma for Generalized Linear System with Finite Discrete Jumps

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    The strict bounded real lemma for linear system with finite discrete jumps was considered. Especially,the case where D matrices in the system are not assumed to be zero was dealt. Several versions of the bounded real lemma are presented in terms of solution to Riccati differential equations or inequalities with finite discrete jumps.Both the finite and infinite horizon cases are considered. These results generalize the existed bounded real lemma for linear systems.

  8. On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

    Institute of Scientific and Technical Information of China (English)

    Xiaojun YANG; Zhengxin WENG; Zuohua TIAN

    2004-01-01

    Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed,where uncertainty in initial conditions,terminal cost and extreme of the cost function are dealt with explicitly.Based on these results,a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.

  9. (Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations

    OpenAIRE

    Juan Yu; Qing-Wen Wang; Chang-Zhou Dong

    2014-01-01

    We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equations AX=B,XC=D are derived, respectively. Secondly, the optimal approximation solution min⁡X∈K⁡∥X^-X∥ is obtained, where K is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of t...

  10. Adaptive control of linear multivariable systems with high frequency gain matrix hurwitz

    Institute of Scientific and Technical Information of China (English)

    Ying ZHOU; Yuqiang WU; Shumin FEI

    2005-01-01

    A new adaptive control scheme is proposed for multivariable model reference adaptive control(MRAC) systems based on the nonlinear backstepping approach with vector form.The assumption on a priori knowledge of the high frequency gain matrix in existing results is relaxed and the new required condition for the high frequency gain matrix can be easily checked for certain plants so that the proposed method is widely applicable.This control scheme guarantees the global stability of the closed-loop systems and the tracking error can be arbitrary small.The simulation result for an application example shows the validity of the proposed nonlinear adaptive scheme.

  11. Parallelism in matrix computations

    CERN Document Server

    Gallopoulos, Efstratios; Sameh, Ahmed H

    2016-01-01

    This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of pa...

  12. Solutions to the generalized Sylvester matrix equations by a singular value decomposition

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper,solutions to the generalized Sylvester matrix equations AX-XF=BY and MXN-X=TY with A,M∈Rn×n,B,T∈Rn×n,F,N∈Rp×p and the matrices N,F being in companion form,are established by a singular value decomposition of a matrix with dimensions n×(n+pr).The algorithm proposed in this paper for the euqation AX-XF=BY does not require the controllability of matrix pair(A,B)andthe restriction that A,F do not have common eigenvalues.Since singular value decomposition is adopted,the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations,and can perform important functions in many design problems in control systems theory.

  13. Optimal explicit strong-stability-preserving general linear methods : complete results.

    Energy Technology Data Exchange (ETDEWEB)

    Constantinescu, E. M.; Sandu, A.; Mathematics and Computer Science; Virginia Polytechnic Inst. and State Univ.

    2009-03-03

    This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A global optimization strategy is used to find the most efficient schemes that have low storage requirements. Numerical results illustrate the theoretical findings.

  14. A generalized concordance correlation coefficient based on the variance components generalized linear mixed models for overdispersed count data.

    Science.gov (United States)

    Carrasco, Josep L

    2010-09-01

    The classical concordance correlation coefficient (CCC) to measure agreement among a set of observers assumes data to be distributed as normal and a linear relationship between the mean and the subject and observer effects. Here, the CCC is generalized to afford any distribution from the exponential family by means of the generalized linear mixed models (GLMMs) theory and applied to the case of overdispersed count data. An example of CD34+ cell count data is provided to show the applicability of the procedure. In the latter case, different CCCs are defined and applied to the data by changing the GLMM that fits the data. A simulation study is carried out to explore the behavior of the procedure with a small and moderate sample size.

  15. Analyticity of solutions of analytic non-linear general elliptic boundary value problems,and some results about linear problems

    Institute of Scientific and Technical Information of China (English)

    WANG Rouhuai

    2006-01-01

    The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.

  16. Odd and even sums of generalized Fibonacci numbers by matrix methods

    Science.gov (United States)

    Ho, C. K.; Chong, Chin-Yoon

    2014-06-01

    For integers A and B, and positive integers n, we define two generalized Fibonacci sequence {gn} and {hn}, respectively, by the recurrence relations gn+1 = Agn+gn-1 and hn+1 = hn+Bhn-1 where g0 = h0 = 0, g1 = h1 = 1. Using a matrix approach, we obtained the odd sum and even sum of the two sequences for all values of A and B.

  17. H{infinity} Filtering for Dynamic Compensation of Self-Powered Neutron Detectors - A Linear Matrix Inequality Based Method -

    Energy Technology Data Exchange (ETDEWEB)

    Park, M.G.; Kim, Y.H.; Cha, K.H.; Kim, M.K. [Korea Electric Power Research Institute, Taejon (Korea)

    1999-07-01

    A method is described to develop and H{infinity} filtering method for the dynamic compensation of self-powered neutron detectors normally used for fixed incore instruments. An H{infinity} norm of the filter transfer matrix is used as the optimization criteria in the worst-case estimation error sense. Filter modeling is performed for both continuous- and discrete-time models. The filter gains are optimized in the sense of noise attenuation level of H{infinity} setting. By introducing Bounded Real Lemma, the conventional algebraic Riccati inequalities are converted into Linear Matrix Inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The simulation results show that remarkable improvements are achieved in view of the filter response time and the filter design efficiency. (author). 15 refs., 4 figs., 3 tabs.

  18. Linear and nonlinear associations between general intelligence and personality in Project TALENT.

    Science.gov (United States)

    Major, Jason T; Johnson, Wendy; Deary, Ian J

    2014-04-01

    Research on the relations of personality traits to intelligence has primarily been concerned with linear associations. Yet, there are no a priori reasons why linear relations should be expected over nonlinear ones, which represent a much larger set of all possible associations. Using 2 techniques, quadratic and generalized additive models, we tested for linear and nonlinear associations of general intelligence (g) with 10 personality scales from Project TALENT (PT), a nationally representative sample of approximately 400,000 American high school students from 1960, divided into 4 grade samples (Flanagan et al., 1962). We departed from previous studies, including one with PT (Reeve, Meyer, & Bonaccio, 2006), by modeling latent quadratic effects directly, controlling the influence of the common factor in the personality scales, and assuming a direction of effect from g to personality. On the basis of the literature, we made 17 directional hypotheses for the linear and quadratic associations. Of these, 53% were supported in all 4 male grades and 58% in all 4 female grades. Quadratic associations explained substantive variance above and beyond linear effects (mean R² between 1.8% and 3.6%) for Sociability, Maturity, Vigor, and Leadership in males and Sociability, Maturity, and Tidiness in females; linear associations were predominant for other traits. We discuss how suited current theories of the personality-intelligence interface are to explain these associations, and how research on intellectually gifted samples may provide a unique way of understanding them. We conclude that nonlinear models can provide incremental detail regarding personality and intelligence associations.

  19. Interior-point algorithm based on general kernel function for monotone linear complementarity problem

    Institute of Scientific and Technical Information of China (English)

    LIU Yong; BAI Yan-qin

    2009-01-01

    A polynomial interior-point algorithm is presented for monotone linear complementarity problem (MLCP) based on:a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP.

  20. General linear methods and friends: Toward efficient solutions of multiphysics problems

    Science.gov (United States)

    Sandu, Adrian

    2017-07-01

    Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

  1. Dynamic stiffness matrix of a rectangular plate for the general case

    Science.gov (United States)

    Banerjee, J. R.; Papkov, S. O.; Liu, X.; Kennedy, D.

    2015-04-01

    The dynamic stiffness matrix of a rectangular plate for the most general case is developed by solving the bi-harmonic equation and finally casting the solution in terms of the force-displacement relationship of the freely vibrating plate. Essentially the frequency dependent dynamic stiffness matrix of the plate when all its sides are free is derived, making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions. Previous research on the dynamic stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported. This restriction is quite severe and made the general purpose application of the dynamic stiffness method impossible. The theory developed in this paper overcomes this long-lasting restriction. The research carried out here is basically fundamental in that the bi-harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense, leading to the development of the dynamic stiffness method. It is significant that the ingeniously sought solution presented in this paper is completely general, covering all possible cases of elastic deformations of the plate. The Wittrick-Williams algorithm is applied to the ensuing dynamic stiffness matrix to provide solutions for some representative problems. A carefully selected sample of mode shapes is also presented.

  2. Matrix Operations for Engineers and Scientists An Essential Guide in Linear Algebra

    CERN Document Server

    Jeffrey, Alan

    2010-01-01

    Engineers and scientists need to have an introduction to the basics of linear algebra in a context they understand. Computer algebra systems make the manipulation of matrices and the determination of their properties a simple matter, and in practical applications such software is often essential. However, using this tool when learning about matrices, without first gaining a proper understanding of the underlying theory, limits the ability to use matrices and to apply them to new problems. This book explains matrices in the detail required by engineering or science students, and it discusses linear systems of ordinary differential equations. These students require a straightforward introduction to linear algebra illustrated by applications to which they can relate. It caters of the needs of undergraduate engineers in all disciplines, and provides considerable detail where it is likely to be helpful. According to the author the best way to understand the theory of matrices is by working simple exercises designe...

  3. Basic Boundary Interpolation for Generalized Schur Functions and Factorization of Rational J-unitary Matrix Functions

    NARCIS (Netherlands)

    Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Wanjala, Gerald

    2006-01-01

    We define and solve a boundary interpolation problem for generalized Schur functions s(z) on the open unit disk D which have preassigned asymptotics when z from D tends nontangentially to a boundary point z1 ∈ T. The solutions are characterized via a fractional linear parametrization formula. We als

  4. A general non-linear optimization algorithm for lower bound limit analysis

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars

    2003-01-01

    The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...... load optimization problem. and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright (C) 2002 John Wiley Sons. Ltd....

  5. SELECTION OF THE LINEAR COMBINING VECTOR G OF THE GENERALIZED SELF-SHRINKING GENERATORS

    Institute of Scientific and Technical Information of China (English)

    Dong Lihua; Zeng Yong; Hu Yupu

    2006-01-01

    Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking (GSS) sequence is the selection of the linear combining vector G. Based on the calculation of the minimalpolynomial ofL GSS sequences and the comparison of their degrees, an algorithm for selecting the linear combining vector G is presented, which is simple to understand, to implement and to prove. By using this method,much more than 2L-1 linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.

  6. On the distribution of discounted loss reserves using generalized linear models

    NARCIS (Netherlands)

    Hoedemakers, T.; Beirlant, J.; Goovaerts, M.J.; Dhaene, J.

    2005-01-01

    Renshaw and Verrall [11] specified the generalized linear model (GLM) underlying the chain-ladder technique and suggested some other GLMs which might be useful in claims reserving. The purpose of this paper is to construct bounds for the discounted loss reserve within the framework of GLMs. Exact

  7. Large-Sample Theory for Generalized Linear Models with Non-natural Link and Random Variates

    Institute of Scientific and Technical Information of China (English)

    Jie-li Ding; Xi-ru Chen

    2006-01-01

    For generalized linear models (GLM), in the case that the regressors are stochastic and have different distributions and the observations of the responses may have different dimensionality, the asymptotic theory of the maximum likelihood estimate (MLE) of the parameters are studied under the assumption of a non-natural link function.

  8. Regression Is a Univariate General Linear Model Subsuming Other Parametric Methods as Special Cases.

    Science.gov (United States)

    Vidal, Sherry

    Although the concept of the general linear model (GLM) has existed since the 1960s, other univariate analyses such as the t-test and the analysis of variance models have remained popular. The GLM produces an equation that minimizes the mean differences of independent variables as they are related to a dependent variable. From a computer printout…

  9. Asymptotic Properties of the Maximum Likelihood Estimate in Generalized Linear Models with Stochastic Regressors

    Institute of Scientific and Technical Information of China (English)

    Jie Li DING; Xi Ru CHEN

    2006-01-01

    For generalized linear models (GLM), in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate (MLE)(β^)n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of(β^)n.

  10. The microcomputer scientific software series 2: general linear model--regression.

    Science.gov (United States)

    Harold M. Rauscher

    1983-01-01

    The general linear model regression (GLMR) program provides the microcomputer user with a sophisticated regression analysis capability. The output provides a regression ANOVA table, estimators of the regression model coefficients, their confidence intervals, confidence intervals around the predicted Y-values, residuals for plotting, a check for multicollinearity, a...

  11. Generalized Partially Linear Regression with Misclassified Data and an Application to Labour Market Transitions

    DEFF Research Database (Denmark)

    Dlugosz, Stephan; Mammen, Enno; Wilke, Ralf

    2017-01-01

    observations from Germany. It is shown that estimated marginal effects of a number of covariates are sizeably affected by misclassification and missing values in the analysis data. The proposed generalized partially linear regression extends existing models by allowing a misclassified discrete covariate...

  12. More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems

    Directory of Open Access Journals (Sweden)

    Jen-Yuan Chen

    2014-01-01

    Full Text Available Continuing from the works of Li et al. (2014, Li (2007, and Kincaid et al. (2000, we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.

  13. Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations

    Institute of Scientific and Technical Information of China (English)

    Davod Khojasteh Salkuyeh

    2007-01-01

    The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as preconditioners for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied. Some numerical experiments are given to show the efficiency of the new methods.

  14. ESTIMATION METHOD FOR SOLUTIONS TO GENERAL LINEAR SYSTEM OF VOLTERRAINTEGRAL INEQUALITIES INVOLVING ITERATED INTEGRAL FUNCTIONALS

    Institute of Scientific and Technical Information of China (English)

    MA Qinghua; YANG Enhao

    2000-01-01

    An estimation method for solutions to the general linear system of Volterratype integral inequalities containing several iterated integral functionals is obtained. This method is based on a result proved by the present second author in Journ. Math. Anal. Appl.(1984). A certain two-dimensional system of nonlinear ordinary differential equations is also discussed to demonstrate the usefulness of our method.

  15. Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    2004-01-01

    [1]McCullagh, P., Nelder, J. A., Generalized Linear Models, New York: Chapman and Hall, 1989.[2]Wedderbum, R. W. M., Quasi-likelihood functions, generalized linear models and Gauss-Newton method,Biometrika, 1974, 61:439-447.[3]Fahrmeir, L., Maximum likelihood estimation in misspecified generalized linear models, Statistics, 1990, 21:487-502.[4]Fahrmeir, L., Kaufmann, H., Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models, Ann. Statist., 1985, 13: 342-368.[5]Melder, J. A., Pregibon, D., An extended quasi-likelihood function, Biometrika, 1987, 74: 221-232.[6]Bennet, G., Probability inequalities for the sum of independent random variables, JASA, 1962, 57: 33-45.[7]Stout, W. F., Almost Sure Convergence, New York:Academic Press, 1974.[8]Petrov, V, V., Sums of Independent Random Variables, Berlin, New York: Springer-Verlag, 1975.

  16. General treatment of the non-linear Rsub(Xi) gauge condition

    Energy Technology Data Exchange (ETDEWEB)

    Girardi, G.; Malleville, C.; Sorba, P. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)

    1982-11-04

    It is shown that the non-linear Rsub(xi) gauge condition already introduced for the standard SU(2)xU(1) model can be generalized for any gauge model with the same type of simplification, namely the suppression of any coupling of the form: (massless gauge boson)x(massive gauge boson)x(unphysical Higgs).

  17. ON THE SOLVABILITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMICAL SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    Ai-guo Xiao

    2000-01-01

    The main purpose of the present paper is to examine the existence and local uniqueness of solutions of the implicit equations arising in the application of a weakly algebraically stable general linear methods to dissipative dynamical systems, and to extend the existing relevant results of Runge-Kutta methods by Humphries and Stuart(1994).

  18. A differential-geometric approach to generalized linear models with grouped predictors

    NARCIS (Netherlands)

    Augugliaro, Luigi; Mineo, Angelo M.; Wit, Ernst C.

    2016-01-01

    We propose an extension of the differential-geometric least angle regression method to perform sparse group inference in a generalized linear model. An efficient algorithm is proposed to compute the solution curve. The proposed group differential-geometric least angle regression method has important

  19. Multi-objective control of a full-car model using linear-matrix-inequalities and fixed-order optimisation

    Science.gov (United States)

    Türkay, Semiha; Akçay, Hüseyin

    2014-03-01

    This paper studies multi-objective control of a full-vehicle suspension excited by random road disturbances. The control problem is first formulated as a mixed ℋ2/ℋ∞ synthesis problem and an output-feedback solution is obtained by using linear-matrix-inequalities. Next, the multi-objective control problem is re-formulated as a non-convex and non-smooth optimisation problem with controller order restricted to be less than the vehicle model order. For a range of orders, controllers are synthesised by using the HIFOO toolbox. The efficacy of the presented procedures are demonstrated by several design examples.

  20. Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

    Institute of Scientific and Technical Information of China (English)

    S. Lakshmanan; P. Balasubramaniarn

    2011-01-01

    This paper studies the problem of linear matrix inequality(LMI)approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

  1. Linear Maps Preserving Idempotency of Products of Matrices on Upper Triangular Matrix Algebras

    Institute of Scientific and Technical Information of China (English)

    QI JING; JI GUO-XING

    2009-01-01

    . Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.

  2. Solving differential matrix Riccati equations by a piecewise-linearized method based on diagonal Padé approximants

    Science.gov (United States)

    Ibáñez, Javier; Hernández, Vicente

    2011-03-01

    Differential Matrix Riccati Equations (DMREs) appear in several branches of science such as applied physics and engineering. For example, these equations play a fundamental role in control theory, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a new method based on a theorem proved in this paper is described for solving DMREs by a piecewise-linearized approach. This method is applied for developing two block-oriented algorithms based on diagonal Padé approximants. MATLAB versions of the above algorithms are developed, comparing, under equal conditions, accuracy and computational costs with other piecewise-linearized algorithms implemented by the authors. Experimental results show the advantages of solving stiff or non-stiff DMREs by the implemented algorithms.

  3. Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements

    Energy Technology Data Exchange (ETDEWEB)

    Dong Shihai [Programa de IngenierIa Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, DF (Mexico); Chen Changyuan [Department of Physics, Yancheng Teachers College, Yancheng 224002 (China); Lozada-Cassou, M [Programa de Ingenieria Molecular, Instituto Mexicano del Petroleo, Lazaro Cardenas 152, 07730 Mexico, DF (Mexico)

    2005-07-14

    Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied.

  4. Strong consistency of maximum quasi-likelihood estimates in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    YiN; Changming; ZHAO; Lincheng

    2005-01-01

    In a generalized linear model with q × 1 responses, bounded and fixed p × qregressors Zi and general link function, under the most general assumption on the mini-mum eigenvalue of∑ni=1n ZiZ'i, the moment condition on responses as weak as possibleand other mild regular conditions, we prove that with probability one, the quasi-likelihoodequation has a solutionβn for all large sample size n, which converges to the true regres-sion parameterβo. This result is an essential improvement over the relevant results in literature.

  5. Generalized linear models with random effects unified analysis via H-likelihood

    CERN Document Server

    Lee, Youngjo; Pawitan, Yudi

    2006-01-01

    Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors.Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives. Complementing theory with examples, many of...

  6. Matrix elements for sum of power-law potentials in quantum mechanic using generalized hypergeometric functions

    Directory of Open Access Journals (Sweden)

    Ma'zoozeh E. Abu-Amra

    2008-04-01

    Full Text Available In this paper we derive close form for the matrix elements for $hat H=-Delta +V$, where $V$ is a pure power-law potential. We use trial functions of the form $$ psi _n(r= sqrt{{frac{2eta ^{gamma/2}(gamma _n} {n!Gamma(gamma }}} r^{gamma - 1/2} e^{-frac{sqrt{eta }}{2}r^q} _pF_1 ( -n,a_2,ldots ,a_p;gamma;sqrt {eta } r^q, $$ for $eta, q,gamma >0$ to obtain the matrix elements for $hat H$. These formulas are then optimized with respect to variational parameters $eta ,q$ and $gamma $ to obtain accurate upper bounds for the given nonsolvable eigenvalue problem in quantum mechanics. Moreover, we write the matrix elements in terms of the generalized hypergeomtric functions. These results are generalization of those found earlier in [2], [8-16] for power-law potentials. Applications and comparisons with earlier work are presented.

  7. Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

    Directory of Open Access Journals (Sweden)

    E. George Walters III

    2015-11-01

    Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

  8. An Algorithm for the calculation of non-isotropic collision integral matrix elements of the non-linear Boltzmann equation by the use of recurrence relations

    CERN Document Server

    Ender, I A; Flegontova, E Yu; Gerasimenko, A B

    2016-01-01

    An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.

  9. H{sub 2}/H{infinity} control of flexible structures through linear matrix inequalities with pole placement

    Energy Technology Data Exchange (ETDEWEB)

    Lopes, Jean C. [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil)

    2009-07-01

    The objective of this work is to apply the H2/H{infinity} control technique using linear matrix inequalities and pole placement constraints to the flexible structures control problem. The H2/H{infinity}control is a technique to design a controller with mixed features of the H2 and H{infinity} control formulations, such as, optimal dynamical performance and robust performance. The Linear Matrix Inequalities allow formulating the problem as a convex optimization problem, and additional constraints can be included such as the pole placement. The pole placement requirement comes from the necessity of adjusting the transient response of the plant and ensuring a specific behavior in terms of speed and damping responses. The mathematical model used for this study is related to a flexible beam, with an applied disturbance and an actuator in different positions. The state-space matrices of the structure were obtained using the finite element method with the Euler-Bernoulli formulation of beams. The results showed that the pole placement constraints can improve the performance of the controller H2/H{infinity}. The Matlab was used for the computational implementation. (author)

  10. Non-linear photoelectron effect contributes to the formation of negative matrix ions in UV-MALDI.

    Science.gov (United States)

    Alonso, E; Zenobi, R

    2016-07-20

    The mechanism of negative ion formation in matrix-assisted laser desorption/ionization (MALDI) is less well understood than that of positive ions: electron capture, disproportionation, and liberation of negatively charged sample molecules or clusters have been proposed to produce the initial anions in MALDI. Here, we propose that the non-linear photoelectric effect can explain the emission of electrons from the metallic target material. Moreover, electrons with sufficient kinetic energy (0-10 eV) could be responsible for the formation of initial negative ions. Gas-phase electron capture by neutral 2,5-dihydroxy benzoic acid (DHB) to yield M(-) is investigated on the basis of a coupled physical and chemical dynamics (CPCD) theory from the literature. A three-layer energy mass balance model is utilized to calculate the surface temperature of the matrix, which is used to determine the translational temperature, the number of desorbed matrix molecules per unit area, and the ion velocity. Calculations of dissociative attachment and autoionization rates of DHB are presented. It was found that both processes contribute significantly to the formation of [M - H](-) and [M - H2](-), although the predicted yield in the fluence range of 5-100 mJ cm(-2) is low, certainly less than that for positive ions M(+). This work represents the first proposal for a comprehensive theoretical description of negative ion formation in UV-MALDI.

  11. Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix

    Science.gov (United States)

    Han, Bin

    2003-06-01

    Tight wavelet frames and orthonormal wavelet bases with a general dilation matrix have applications in many areas. In this paper, for any d×d dilation matrix M, we demonstrate in a constructive way that we can construct compactly supported tight M-wavelet frames and orthonormal M-wavelet bases in of exponential decay, which are derived from compactly supported M-refinable functions, such that they can have both arbitrarily high smoothness and any preassigned order of vanishing moments. This paper improves several results in Battle (Comm. Math. Phys. 110 (1987) 601), Bownik (J. Fourier Anal. Appl. 7(2001) 489), Gröchenig and Ron (Proc. Amer. Math. Soc. 126 (1998) 1101), Lemarie (J. Math. Pures Appl. 67 (1988) 227), and Strichartz (Constr. Approx. 9 (1993) 327).

  12. INTERACTION OF GENERAL PLANE P WAVE AND CYLINDRICAL INCLUSION PARTIALLY DEBONDED FROM ITS VISCOELASTIC MATRIX

    Institute of Scientific and Technical Information of China (English)

    魏培君; 章梓茂; 汪越胜

    2002-01-01

    The interaction of a general plane P wave and an elastic cylindrical inclusion of infinite length partially debonded from its surrounding viscoelastic matrix of infinite extension is investigated. The debonded region is modeled as an arc-shaped interface crack between inclusion and matrix with non-contacting faces. With wave functions expansion and singular integral equation technique, the interaction problem is reduced to a set of simultaneous singular integral equations of crack dislocation density function. By analysis of the fundamental solution of the singular integral equation, it is found that dynamic stress field at the crack tip is oscillatory singular,which is related to the frequency of incident wave. The singular integral equations are solved numerically, and the crack open displacement and dynamic stress intensity factor are evaluated for various incident angles and frequencies.

  13. Hierarchical Shrinkage Priors and Model Fitting for High-dimensional Generalized Linear Models

    Science.gov (United States)

    Yi, Nengjun; Ma, Shuangge

    2013-01-01

    Genetic and other scientific studies routinely generate very many predictor variables, which can be naturally grouped, with predictors in the same groups being highly correlated. It is desirable to incorporate the hierarchical structure of the predictor variables into generalized linear models for simultaneous variable selection and coefficient estimation. We propose two prior distributions: hierarchical Cauchy and double-exponential distributions, on coefficients in generalized linear models. The hierarchical priors include both variable-specific and group-specific tuning parameters, thereby not only adopting different shrinkage for different coefficients and different groups but also providing a way to pool the information within groups. We fit generalized linear models with the proposed hierarchical priors by incorporating flexible expectation-maximization (EM) algorithms into the standard iteratively weighted least squares as implemented in the general statistical package R. The methods are illustrated with data from an experiment to identify genetic polymorphisms for survival of mice following infection with Listeria monocytogenes. The performance of the proposed procedures is further assessed via simulation studies. The methods are implemented in a freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/). PMID:23192052

  14. Estimate of influenza cases using generalized linear, additive and mixed models.

    Science.gov (United States)

    Oviedo, Manuel; Domínguez, Ángela; Pilar Muñoz, M

    2015-01-01

    We investigated the relationship between reported cases of influenza in Catalonia (Spain). Covariates analyzed were: population, age, data of report of influenza, and health region during 2010-2014 using data obtained from the SISAP program (Institut Catala de la Salut - Generalitat of Catalonia). Reported cases were related with the study of covariates using a descriptive analysis. Generalized Linear Models, Generalized Additive Models and Generalized Additive Mixed Models were used to estimate the evolution of the transmission of influenza. Additive models can estimate non-linear effects of the covariates by smooth functions; and mixed models can estimate data dependence and variability in factor variables using correlations structures and random effects, respectively. The incidence rate of influenza was calculated as the incidence per 100 000 people. The mean rate was 13.75 (range 0-27.5) in the winter months (December, January, February) and 3.38 (range 0-12.57) in the remaining months. Statistical analysis showed that Generalized Additive Mixed Models were better adapted to the temporal evolution of influenza (serial correlation 0.59) than classical linear models.

  15. A TRUST REGION ALGORITHM VIA BILEVEL LINEAR PROGRAMMING FOR SOLVING THE GENERAL MULTICOMMODITY MINIMAL COST FLOW PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    ZhuDetong

    2004-01-01

    This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems. Using the duality theory of the linear programming and convex theory, the generalized directional derivative of the general multicommodity minimal cost flow problems is derived. The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.

  16. Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schroedinger model

    Energy Technology Data Exchange (ETDEWEB)

    Kozlowski, K.K.

    2010-12-15

    Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)

  17. An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2013-01-01

    Full Text Available It is known that the steepest-descent method converges normally at the first few iterations, and then it slows down. We modify the original steplength and descent direction by an optimization argument with the new steplength as being a merit function to be maximized. An optimal iterative algorithm with m-vector descent direction in a Krylov subspace is constructed, of which the m optimal weighting parameters are solved in closed-form to accelerate the convergence speed in solving ill-posed linear problems. The optimally generalized steepest-descent algorithm (OGSDA is proven to be convergent with very fast convergence speed, accurate and robust against noisy disturbance, which is confirmed by numerical tests of some well-known ill-posed linear problems and linear inverse problems.

  18. General job stress: a unidimensional measure and its non-linear relations with outcome variables.

    Science.gov (United States)

    Yankelevich, Maya; Broadfoot, Alison; Gillespie, Jennifer Z; Gillespie, Michael A; Guidroz, Ashley

    2012-04-01

    This article aims to examine the non-linear relations between a general measure of job stress [Stress in General (SIG)] and two outcome variables: intentions to quit and job satisfaction. In so doing, we also re-examine the factor structure of the SIG and determine that, as a two-factor scale, it obscures non-linear relations with outcomes. Thus, in this research, we not only test for non-linear relations between stress and outcome variables but also present an updated version of the SIG scale. Using two distinct samples of working adults (sample 1, N = 589; sample 2, N = 4322), results indicate that a more parsimonious eight-item SIG has better model-data fit than the 15-item two-factor SIG and that the eight-item SIG has non-linear relations with job satisfaction and intentions to quit. Specifically, the revised SIG has an inverted curvilinear J-shaped relation with job satisfaction such that job satisfaction drops precipitously after a certain level of stress; the SIG has a J-shaped curvilinear relation with intentions to quit such that turnover intentions increase exponentially after a certain level of stress.

  19. Semiparametric Analysis of Heterogeneous Data Using Varying-Scale Generalized Linear Models.

    Science.gov (United States)

    Xie, Minge; Simpson, Douglas G; Carroll, Raymond J

    2008-01-01

    This article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically, and develops efficient semiparametric inferences for the parametric components of the models. Such models provide a means to adapt for heterogeneity in the data due to varying exposures, varying levels of aggregation, and so on. The class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases. We present an algorithm to estimate the scale function nonparametrically, and obtain asymptotic distribution theory for regression parameter estimates. In particular, we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound. We also describe bootstrap-based goodness-of-scale test. We illustrate the methodology with simulations, published data, and data from collaborative research on ultrasound safety.

  20. The generalized transmission matrix for electron-wave-optics through biased heterostructures: Quantum device applications

    Science.gov (United States)

    Kan'an, A. M.; Puri, A.

    1994-01-01

    The transmission matrix approach is generalized to calculate the transmission probability of obliquely incident electrons through arbitrary shape potential profiles. Transmission probability is obtained as a function of the electron energy, the angle of incidence, and the applied voltage across the structure. Applications to electron waveguide and quantum resonant tunneling are outlined. Numerical results are presented for angle dependent resonant tunneling through biased multibarrier GaAs-AlxGa1-xAs heterostructures. As a consequence, various novel quantum devices, i.e., high speed switch, tunable electron wave filter, and electron wave beam splitter are proposed.

  1. A review of linear response theory for general differentiable dynamical systems

    Science.gov (United States)

    Ruelle, David

    2009-04-01

    The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium steady states (NESS) and study how these vary under perturbations of the dynamics. Remarkably, it turns out that for uniformly hyperbolic dynamical systems (those satisfying the 'chaotic hypothesis'), the linear response away from equilibrium is very similar to the linear response close to equilibrium: the Kramers-Kronig dispersion relations hold, and the fluctuation-dispersion theorem survives in a modified form (which takes into account the oscillations around the 'attractor' corresponding to the NESS). If the chaotic hypothesis does not hold, two new phenomena may arise. The first is a violation of linear response in the sense that the NESS does not depend differentiably on parameters (but this nondifferentiability may be hard to see experimentally). The second phenomenon is a violation of the dispersion relations: the susceptibility has singularities in the upper half complex plane. These 'acausal' singularities are actually due to 'energy nonconservation': for a small periodic perturbation of the system, the amplitude of the linear response is arbitrarily large. This means that the NESS of the dynamical system under study is not 'inert' but can give energy to the outside world. An 'active' NESS of this sort is very different from an equilibrium state, and it would be interesting to see what happens for active states to the Gallavotti-Cohen fluctuation theorem.

  2. Convergence analysis for general linear methods applied to stiff delay differential equations

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    For Runge-Kutta methods applied to stiff delay differential equations (DDEs), the concept of D-convergence was proposed, which is an extension to that of B-convergence in ordinary differential equations (ODEs). In this paper, D-convergence of general linear methods is discussed and the previous related results are improved. Some order results to determine D-convergence of the methods are obtained.

  3. Bayesian prediction of spatial count data using generalized linear mixed models

    DEFF Research Database (Denmark)

    Christensen, Ole Fredslund; Waagepetersen, Rasmus Plenge

    2002-01-01

    Spatial weed count data are modeled and predicted using a generalized linear mixed model combined with a Bayesian approach and Markov chain Monte Carlo. Informative priors for a data set with sparse sampling are elicited using a previously collected data set with extensive sampling. Furthermore, we...... demonstrate that so-called Langevin-Hastings updates are useful for efficient simulation of the posterior distributions, and we discuss computational issues concerning prediction....

  4. Damping of a system of linear oscillators using the generalized dry friction

    OpenAIRE

    Ovseevich, Alexander; Fedorov, Aleksey

    2015-01-01

    The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with discontinuous right-hand side. A uniqueness and continuity theorem is proved for the phase flow of this system. Thus, the control in the form of generalized dry friction defines the motion of the system of oscillators uniquely.

  5. Representations of general linear groups and categorical actions of Kac-Moody algebras

    OpenAIRE

    Losev, Ivan

    2012-01-01

    This is an expanded version of the lectures given by the author on the 3rd school "Lie algebras, algebraic groups and invariant theory" in Togliatti, Russia. In these notes we explain the concept of a categorical Kac-Moody action by studying an example of the category of rational representations of a general linear group in positive characteristic. We also deal with some more advanced topics: a categorical action on the polynomial representations and crystals of categorical actions.

  6. An Entropy-Based Approach to Path Analysis of Structural Generalized Linear Models: A Basic Idea

    Directory of Open Access Journals (Sweden)

    Nobuoki Eshima

    2015-07-01

    Full Text Available A path analysis method for causal systems based on generalized linear models is proposed by using entropy. A practical example is introduced, and a brief explanation of the entropy coefficient of determination is given. Direct and indirect effects of explanatory variables are discussed as log odds ratios, i.e., relative information, and a method for summarizing the effects is proposed. The example dataset is re-analyzed by using the method.

  7. An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation

    Directory of Open Access Journals (Sweden)

    Maobo Zheng

    2014-01-01

    Full Text Available An average linear finite difference scheme for the numerical solution of the initial-boundary value problem of Generalized Rosenau-KdV equation is proposed. The existence, uniqueness, and conservation for energy of the difference solution are proved by the discrete energy norm method. It is shown that the finite difference scheme is 2nd-order convergent and unconditionally stable. Numerical experiments verify that the theoretical results are right and the numerical method is efficient and reliable.

  8. Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blondel's technique. We give a complete answer to the open problem proposed by Patel et al., which automatically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature.

  9. The Time Evolution of the Surface Segregation of Hyperbranched Molecules from a Linear Matrix

    Science.gov (United States)

    Swader, Onome; Dadmun, Mark; Hutchings, Lian; Thompson, Richard

    2010-03-01

    Modification of a surface by the selective surface segregation of an additive in a mixture is a process with many commercial applications including biocompatibility, wettability, and anti-fouling in coatings. In a blend of branched and linear polymers, there exists an entropic driving force for the selective surface segregation of the branched polymer. Unfortunately, a systematic study of the impact of the branched copolymer structure on the dynamics and thermodynamics of this surface segregation is not currently available. Neutron reflectivity experiments that seek to fill this void have been completed and will be discussed. High molecular weight poly(styrene) (PS) hyperbranched molecules, hypermacs (HM) and dendrimacs (DM), with 10 % HM or DM and 90 % deuterated PS are the model systems studied. Reflectivity profiles for all blends were obtained as a function of annealing time from 30 minutes up to 48 hours.

  10. Second degree generalized Jacobi iteration method for solving system of linear equations

    Directory of Open Access Journals (Sweden)

    Tesfaye Kebede Enyew

    2016-05-01

    Full Text Available In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1}=b_{1}[D_{m}^{-1}(L_{m}+U_{m}x^{(n}+k_{1m}]-a_{1}x^{(n-1}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ in comparison with FDJ, FDGJ, SDJ.

  11. LINEAR LAYER AND GENERALIZED REGRESSION COMPUTATIONAL INTELLIGENCE MODELS FOR PREDICTING SHELF LIFE OF PROCESSED CHEESE

    Directory of Open Access Journals (Sweden)

    S. Goyal

    2012-03-01

    Full Text Available This paper highlights the significance of computational intelligence models for predicting shelf life of processed cheese stored at 7-8 g.C. Linear Layer and Generalized Regression models were developed with input parameters: Soluble nitrogen, pH, Standard plate count, Yeast & mould count, Spores, and sensory score as output parameter. Mean Square Error, Root Mean Square Error, Coefficient of Determination and Nash - Sutcliffo Coefficient were used in order to compare the prediction ability of the models. The study revealed that Generalized Regression computational intelligence models are quite effective in predicting the shelf life of processed cheese stored at 7-8 g.C.

  12. Scheme for purifying a general mixed entangled state and its linear optical implementation

    Institute of Scientific and Technical Information of China (English)

    董冬; 张延磊; 邹长铃; 邹旭波; 郭光灿

    2015-01-01

    We propose a scheme for purification of a general mixed entangled state. In this scheme, we start from a large number of general mixed entangled states and end up, after local operation and classical communication, with a smaller number of Bell diagonal states with higher entanglement. In particular, the scheme can purify one maximally entangled state from two entangled pairs prepared in a class of mixed entangled state. Furthermore we propose a linear optical implementation of the present scheme with polarization beam splitters and photon detectors.

  13. Interactions in Generalized Linear Models: Theoretical Issues and an Application to Personal Vote-Earning Attributes

    Directory of Open Access Journals (Sweden)

    Tsung-han Tsai

    2013-05-01

    Full Text Available There is some confusion in political science, and the social sciences in general, about the meaning and interpretation of interaction effects in models with non-interval, non-normal outcome variables. Often these terms are casually thrown into a model specification without observing that their presence fundamentally changes the interpretation of the resulting coefficients. This article explains the conditional nature of reported coefficients in models with interactions, defining the necessarily different interpretation required by generalized linear models. Methodological issues are illustrated with an application to voter information structured by electoral systems and resulting legislative behavior and democratic representation in comparative politics.

  14. Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials

    Science.gov (United States)

    Borzov, V. V.; Damaskinsky, E. V.

    2017-02-01

    We consider the families of polynomials P = { P n ( x)} n=0 ∞ and Q = { Q n ( x)} n=0 ∞ orthogonal on the real line with respect to the respective probability measures μ and ν. We assume that { Q n ( x)} n=0 ∞ and { P n ( x)} n=0 ∞ are connected by linear relations. In the case k = 2, we describe all pairs (P,Q) for which the algebras A P and A Q of generalized oscillators generated by { Qn(x)} n=0 ∞ and { Pn(x)} n=0 ∞ coincide. We construct generalized oscillators corresponding to pairs (P,Q) for arbitrary k ≥ 1.

  15. 一类广义的Fibonacci矩阵与Riordan矩阵%A Class of the Generalized Fibonacci Matrix and Riordan Matrix

    Institute of Scientific and Technical Information of China (English)

    鱼璐; 王辉

    2013-01-01

    给出一类广义Fibonacci矩阵形式,构造出一个Riordan阵,得到此类广义Fibonacci矩阵分解;并利用三对角行列式的理论和Riordan矩阵理论,证明了一些有关Fibonacci数的恒等式.%A generalized Fibonacci matrix form is given. The factorization of the generalized Fibonacci matrix is derived by constructing a Riordan array. However, by using the triangular determinants theory and the Riordan method, some identities involving Fibonacci numbers are proved.

  16. 矩阵二阶线性系统的观测器设计:一种参数化方法%Observer design for matrix second-order linear systems:a parametric approach

    Institute of Scientific and Technical Information of China (English)

    武云丽; 段广仁

    2004-01-01

    The issue of designing a type of generalized Luenberger observers for matrix secondorder linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.

  17. Iterative solution of general sparse linear systems on clusters of workstations

    Energy Technology Data Exchange (ETDEWEB)

    Lo, Gen-Ching; Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)

    1996-12-31

    Solving sparse irregularly structured linear systems on parallel platforms poses several challenges. First, sparsity makes it difficult to exploit data locality, whether in a distributed or shared memory environment. A second, perhaps more serious challenge, is to find efficient ways to precondition the system. Preconditioning techniques which have a large degree of parallelism, such as multicolor SSOR, often have a slower rate of convergence than their sequential counterparts. Finally, a number of other computational kernels such as inner products could ruin any gains gained from parallel speed-ups, and this is especially true on workstation clusters where start-up times may be high. In this paper we discuss these issues and report on our experience with PSPARSLIB, an on-going project for building a library of parallel iterative sparse matrix solvers.

  18. Convergence estimates for iterative methods via the Kriess Matrix Theorem on a general complex domain

    Energy Technology Data Exchange (ETDEWEB)

    Toh, K.C.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

    1994-12-31

    What properties of a nonsymmetric matrix A determine the convergence rate of iterations such as GMRES, QMR, and Arnoldi? If A is far from normal, should one replace the usual Ritz values {r_arrow} eigenvalues notion of convergence of Arnoldi by alternative notions such as Arnoldi lemniscates {r_arrow} pseudospectra? Since Krylov subspace iterations can be interpreted as minimization processes involving polynomials of matrices, the answers to questions such as these depend upon mathematical problems of the following kind. Given a polynomial p(z), how can one bound the norm of p(A) in terms of (1) the size of p(z) on various sets in the complex plane, and (2) the locations of the spectrum and pseudospectra of A? This talk reports some progress towards solving these problems. In particular, the authors present theorems that generalize the Kreiss matrix theorem from the unit disk (for the monomial A{sup n}) to a class of general complex domains (for polynomials p(A)).

  19. Linear and non-linear heart rate metrics for the assessment of anaesthetists' workload during general anaesthesia.

    Science.gov (United States)

    Martin, J; Schneider, F; Kowalewskij, A; Jordan, D; Hapfelmeier, A; Kochs, E F; Wagner, K J; Schulz, C M

    2016-12-01

    Excessive workload may impact the anaesthetists' ability to adequately process information during clinical practice in the operation room and may result in inaccurate situational awareness and performance. This exploratory study investigated heart rate (HR), linear and non-linear heart rate variability (HRV) metrics and subjective ratings scales for the assessment of workload associated with the anaesthesia stages induction, maintenance and emergence. HR and HRV metrics were calculated based on five min segments from each of the three anaesthesia stages. The area under the receiver operating characteristics curve (AUC) of the investigated metrics was calculated to assess their ability to discriminate between the stages of anaesthesia. Additionally, a multiparametric approach based on logistic regression models was performed to further evaluate whether linear or non-linear heart rate metrics are suitable for the assessment of workload. Mean HR and several linear and non-linear HRV metrics including subjective workload ratings differed significantly between stages of anaesthesia. Permutation Entropy (PeEn, AUC=0.828) and mean HR (AUC=0.826) discriminated best between the anaesthesia stages induction and maintenance. In the multiparametric approach using logistic regression models, the model based on non-linear heart rate metrics provided a higher AUC compared with the models based on linear metrics. In this exploratory study based on short ECG segment analysis, PeEn and HR seem to be promising to separate workload levels between different stages of anaesthesia. The multiparametric analysis of the regression models favours non-linear heart rate metrics over linear metrics. © The Author 2016. Published by Oxford University Press on behalf of the British Journal of Anaesthesia. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

  20. Robust thyristor-controlled series capacitor controller design based on linear matrix inequality for a multi-machine power system

    Energy Technology Data Exchange (ETDEWEB)

    Ishimaru, Masachika; Yokoyama, Ryuichi [Tokyo Metropolitan Univ., Hachioji, Tokyo (Japan); Shirai, Goro [Hosei Univ., Koganei, Tokyo (Japan); Niimura, Takahide [British Columbia Univ., Vancouver, BC (Canada)

    2002-10-01

    Power system stabilizing control has an important role in maintaining synchronism in power systems during major disturbances resulting from sudden changes of load and configuration. The thyristor- controlled series capacitor (TCSC) is one of the representative devices in flexible AC transmission systems. In this paper, robust TCSC controllers are applied to suppress disturbances in realistic power systems. H{sub {infinity}} control is adopted as the methodology of the robust controller design along with a linear matrix inequality (LMI), which solves the Lyapunov inequality without the weighting coefficients used in other control theories. In the proposed design, load changes are treated as a system uncertainty in the LMI approach. The proposed LMI -based approach is shown to be effective in the design of TCSC controllers to enhance robustness and response by simulations on a test system. (Author)

  1. Linear and nonlinear intraband optical properties of ZnO quantum dots embedded in SiO2 matrix

    Directory of Open Access Journals (Sweden)

    Deepti Maikhuri

    2012-03-01

    Full Text Available In this work we investigate some optical properties of semiconductor ZnO spherical quantum dot embedded in an amorphous SiO2 dielectric matrix. Using the framework of effective mass approximation, we have studied intraband S-P, and P-D transitions in a singly charged spherical ZnO quantum dot. The optical properties are investigated in terms of the linear and nonlinear photoabsorption coefficient, the change in refractive index, and the third order nonlinear susceptibility and oscillator strengths. Using the parabolic confinement potential of electron in the dot these parameters are studied with the variation of the dot size, and the energy and intensity of incident radiation. The photoionization cross sections are also obtained for the different dot radii from the initial ground state of the dot. It is found that dot size, confinement potential, and incident radiation intensity affects intraband optical properties of the dot significantly.

  2. Computation of Raman Spectra from Density Matrix Linear Response Theory in Extended Lagrangian Born-Oppenheimer Molecular Dynamics

    Science.gov (United States)

    Niklasson, Anders; Coe, Joshua; Cawkwell, Marc

    2011-06-01

    Linear response calculations based on density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] have been developed within a self-consistent tight-binding method for extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett., 100, 123004 (2008)]. Besides the nuclear coordinates, extended auxiliary electronic degrees of freedom are added to the regular Born-Oppenheimer Lagrangian, both for the electronic ground state and response densities. This formalism enables highly efficient, on-the-fly, analytic computations of the polarizability autocorrelation functions and the Raman spectra during energy conserving Born-Oppenheimer molecular dynamics trajectories. We will illustrate these capabilities via time-resolved Raman spectra computed during explicit, reactive molecular dynamics simulations of the shock compression of methane, benzene, tert-butylacetylene. Comparisons will be made with experimental results where possible.

  3. Generalized Distributed Network Coding Based on Nonbinary Linear Block Codes for Multi-User Cooperative Communications

    CERN Document Server

    Rebelatto, João Luiz; Li, Yonghui; Vucetic, Branka

    2010-01-01

    In this work, we propose and analyze a generalized construction of distributed network codes for a network consisting of M users sending different information to a common base station through independent block fading channels. The aim is to increase the diversity order of the system without reducing its code rate. The proposed scheme, called generalized dynamic network codes (GDNC), is a generalization of the dynamic network codes (DNC) recently proposed by Xiao and Skoglung. The design of the network codes that maximizes the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. The proposed scheme offers a much better tradeoff between rate and diversity order. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results.

  4. Bayesian Variable Selection and Computation for Generalized Linear Models with Conjugate Priors.

    Science.gov (United States)

    Chen, Ming-Hui; Huang, Lan; Ibrahim, Joseph G; Kim, Sungduk

    2008-07-01

    In this paper, we consider theoretical and computational connections between six popular methods for variable subset selection in generalized linear models (GLM's). Under the conjugate priors developed by Chen and Ibrahim (2003) for the generalized linear model, we obtain closed form analytic relationships between the Bayes factor (posterior model probability), the Conditional Predictive Ordinate (CPO), the L measure, the Deviance Information Criterion (DIC), the Aikiake Information Criterion (AIC), and the Bayesian Information Criterion (BIC) in the case of the linear model. Moreover, we examine computational relationships in the model space for these Bayesian methods for an arbitrary GLM under conjugate priors as well as examine the performance of the conjugate priors of Chen and Ibrahim (2003) in Bayesian variable selection. Specifically, we show that once Markov chain Monte Carlo (MCMC) samples are obtained from the full model, the four Bayesian criteria can be simultaneously computed for all possible subset models in the model space. We illustrate our new methodology with a simulation study and a real dataset.

  5. Normality of raw data in general linear models: The most widespread myth in statistics

    Science.gov (United States)

    Kery, Marc; Hatfield, Jeff S.

    2003-01-01

    In years of statistical consulting for ecologists and wildlife biologists, by far the most common misconception we have come across has been the one about normality in general linear models. These comprise a very large part of the statistical models used in ecology and include t tests, simple and multiple linear regression, polynomial regression, and analysis of variance (ANOVA) and covariance (ANCOVA). There is a widely held belief that the normality assumption pertains to the raw data rather than to the model residuals. We suspect that this error may also occur in countless published studies, whenever the normality assumption is tested prior to analysis. This may lead to the use of nonparametric alternatives (if there are any), when parametric tests would indeed be appropriate, or to use of transformations of raw data, which may introduce hidden assumptions such as multiplicative effects on the natural scale in the case of log-transformed data. Our aim here is to dispel this myth. We very briefly describe relevant theory for two cases of general linear models to show that the residuals need to be normally distributed if tests requiring normality are to be used, such as t and F tests. We then give two examples demonstrating that the distribution of the response variable may be nonnormal, and yet the residuals are well behaved. We do not go into the issue of how to test normality; instead we display the distributions of response variables and residuals graphically.

  6. The potential in general linear electrodynamics. Causal structure, propagators and quantization

    Energy Technology Data Exchange (ETDEWEB)

    Siemssen, Daniel [Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw (Poland); Pfeifer, Christian [Institute for Theoretical Physics, Leibniz Universitaet Hannover (Germany); Center of Applied Space Technology and Microgravity (ZARM), Universitaet Bremen (Germany)

    2016-07-01

    From an axiomatic point of view, the fundamental input for a theory of electrodynamics are Maxwell's equations dF=0 (or F=dA) and dH=J, and a constitutive law H=F, which relates the field strength 2-form F and the excitation 2-form H. In this talk we consider general linear electrodynamics, the theory of electrodynamics defined by a linear constitutive law. The best known application of this theory is the effective description of electrodynamics inside (linear) media (e.g. birefringence). We analyze the classical theory of the electromagnetic potential A before we use methods familiar from mathematical quantum field theory in curved spacetimes to quantize it. Our analysis of the classical theory contains the derivation of retarded and advanced propagators, the analysis of the causal structure on the basis of the constitutive law (instead of a metric) and a discussion of the classical phase space. This classical analysis sets the stage for the construction of the quantum field algebra and quantum states, including a (generalized) microlocal spectrum condition.

  7. A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

    CERN Document Server

    Lagos, Macarena; Ferreira, Pedro G; Noller, Johannes

    2016-01-01

    We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (\\`a la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic act...

  8. Generalized linear sampling method for elastic-wave sensing of heterogeneous fractures

    CERN Document Server

    Pourahmadian, Fatemeh; Haddar, Houssem

    2016-01-01

    A theoretical foundation is developed for active seismic reconstruction of fractures endowed with spatially-varying interfacial condition (e.g.~partially-closed fractures, hydraulic fractures). The proposed indicator functional carries a superior localization property with no significant sensitivity to the fracture's contact condition, measurement errors, and illumination frequency. This is accomplished through the paradigm of the $F_\\sharp$-factorization technique and the recently developed Generalized Linear Sampling Method (GLSM) applied to elastodynamics. The direct scattering problem is formulated in the frequency domain where the fracture surface is illuminated by a set of incident plane waves, while monitoring the induced scattered field in the form of (elastic) far-field patterns. The analysis of the well-posedness of the forward problem leads to an admissibility condition on the fracture's (linearized) contact parameters. This in turn contributes toward establishing the applicability of the $F_\\sharp...

  9. Model Checking for a General Linear Model with Nonignorable Missing Covariates

    Institute of Scientific and Technical Information of China (English)

    Zhi-hua SUN; Wai-Cheung IP; Heung WONG

    2012-01-01

    In this paper,we investigate the model checking problem for a general linear model with nonignorable missing covariates.We show that,without any parametric model assumption for the response probability,the least squares method yields consistent estimators for the linear model even if only the complete data are applied.This makes it feasible to propose two testing procedures for the corresponding model checking problem:a score type lack-of-fit test and a test based on the empirical process.The asymptotic properties of the test statistics are investigated.Both tests are shown to have asymptotic power 1 for local alternatives converging to the null at the rate n-(r),0 ≤ (r) < 1/2.Simulation results show that both tests perform satisfactorily.

  10. General Formulations of Finite-field Method Classified by Symmetry for Molecular Linear and Nonlinear Polarizabilities

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients mi, aij, bijk and gijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.

  11. Non-cooperative stochastic differential game theory of generalized Markov jump linear systems

    CERN Document Server

    Zhang, Cheng-ke; Zhou, Hai-ying; Bin, Ning

    2017-01-01

    This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the...

  12. AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

    Science.gov (United States)

    Lefkoff, L.J.; Gorelick, S.M.

    1987-01-01

    A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

  13. Assessing correlation of clustered mixed outcomes from a multivariate generalized linear mixed model.

    Science.gov (United States)

    Chen, Hsiang-Chun; Wehrly, Thomas E

    2015-02-20

    The classic concordance correlation coefficient measures the agreement between two variables. In recent studies, concordance correlation coefficients have been generalized to deal with responses from a distribution from the exponential family using the univariate generalized linear mixed model. Multivariate data arise when responses on the same unit are measured repeatedly by several methods. The relationship among these responses is often of interest. In clustered mixed data, the correlation could be present between repeated measurements either within the same observer or between different methods on the same subjects. Indices for measuring such association are needed. This study proposes a series of indices, namely, intra-correlation, inter-correlation, and total correlation coefficients to measure the correlation under various circumstances in a multivariate generalized linear model, especially for joint modeling of clustered count and continuous outcomes. The proposed indices are natural extensions of the concordance correlation coefficient. We demonstrate the methodology with simulation studies. A case example of osteoarthritis study is provided to illustrate the use of these proposed indices. Copyright © 2014 John Wiley & Sons, Ltd.

  14. Galaxy Bias and non-Linear Structure Formation in General Relativity

    CERN Document Server

    Baldauf, Tobias; Senatore, Leonardo; Zaldarriaga, Matias

    2011-01-01

    Length scales probed by large scale structure surveys are becoming closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest distances. It is therefore important to include General Relativistic effects. Here we provide a General Relativistic generalization of the bias, valid both for Gaussian and non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every collapsing region, it is therefore possible to find a reference frame that is valid for all times and where the space time is almost flat: the Fermi frame. Here the Newtonian approximation is applicable and the equations of motion are the ones of the N-body codes. The effects of long-wavelength modes are encoded in the mapping from the cosmological frame to the local frame. For the linear bias, the effect of the long-wave...

  15. A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

    Institute of Scientific and Technical Information of China (English)

    锁要红; 黄虎

    2004-01-01

    Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green's second identity. This theory can be reduced to a number of the most typical mild-slope equations currently in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.

  16. Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

    Institute of Scientific and Technical Information of China (English)

    YUE Li; CHEN Xiru

    2004-01-01

    Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions,it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.

  17. ASYMPTOTIC NORMALITY OF MAXIMUM QUASI-LIKELIHOOD ESTIMATORS IN GENERALIZED LINEAR MODELS WITH FIXED DESIGN

    Institute of Scientific and Technical Information of China (English)

    Qibing GAO; Yaohua WU; Chunhua ZHU; Zhanfeng WANG

    2008-01-01

    In generalized linear models with fixed design, under the assumption ~ →∞ and otherregularity conditions, the asymptotic normality of maximum quasi-likelihood estimator (β)n, which is the root of the quasi-likelihood equation with natural link function ∑n/i=1Xi(yi-μ(X1/iβ))=0, is obtained,where λ/-n denotes the minimum eigenvalue of ∑n/i=1XiX/1/i, Xi are bounded p x q regressors, and yi are q × 1 responses.

  18. An Investigation on the Parabolic Subgroups of the General Linear Groups by Using GAP

    Institute of Scientific and Technical Information of China (English)

    SaadABedaiwi; LIShang-zhi

    2004-01-01

    A typical example for the algebraic groups is the general linear groups G=GL(n,F), we have studied the structure of such groups and paid special attention to its important substructures, namely the Parabolic subgroups. For a given G we computed all the Parabolic subgroups and determined their number, depending on the fact that any finite group has a composition series and the composition factors of a composition series are simple groups which are completely classified, we report here some investigations on the computed Parabolic subgroups. This has been done with the utility of GAP.

  19. Set Matrix Theory as a Physically Motivated Generalization of Zermelo-Fraenkel Set Theory

    CERN Document Server

    Cabbolet, Marcoen J T F

    2012-01-01

    Recently, the Elementary Process Theory (EPT) has been developed as a set of fundamental principles that might underlie a gravitational repulsion of matter and antimatter. This paper presents set matrix theory (SMT) as the foundation of the mathematical-logical framework in which the EPT has been formalized: Zermelo-Fraenkel set theory (ZF), namely, cannot be used as such. SMT is a generalization of ZF: whereas ZF uses only sets as primitive objects, in the framework of SMT finite matrices with set-valued entries are objects sui generis, with a 1\\times1 set matrix [x] being identical to the set x. It is proved that every set that can be constructed in ZF can also be constructed in SMT: as a mathematical foundation, SMT is thus not weaker than ZF. In addition, it is shown that SMT is more suitable han ZF for the intended application to physics. The conclusion is that SMT, contrary to ZF, is acceptable as the mathematical-logical foundation of the framework for physics that is determined by the EPT.

  20. Complex CKM matrix, spontaneous CP violation and generalized $\\mu$-$\\tau$ symmetry

    CERN Document Server

    Joshipura, Anjan S

    2007-01-01

    The multi-Higgs models having spontaneous CP violation (SPCV) and natural flavor conservation (NFC) lead to a real CKM matrix $V$ contradicting current evidence in favour of a complex $V$. This contradiction can be removed by using a generalized $\\mu$-$\\tau$ (called 23) symmetry in place of the discrete symmetry conventionally used to obtain NFC. If 23 symmetry is exact then the Higgs induced flavour changing neutral currents (FCNC) vanish as in case of NFC. 23 breaking introduces SPCV, a phase in $V$ and suppressed FCNC among quarks. The FCNC couplings $F_{ij}^{d,u}$ between $i$ and $j$ generations show a hierarchy $|F_{12}^{d,u}|<|F_{13}^{d,u}|<|F_{23}^{d,u}|$ with the result that the FCNC can have observable consequences in $B$ mixing without conflicting with the $K^0-\\bar{K}^0$ mixing. Detailed fits to the quark masses and the CKM matrix are used to obtain the (complex) couplings $F_{ij}^d$ and $F_{ij}^u$. Combined constraints from flavour and CP violations in the $K,B_d,B_s,D$ mesons are analyzed w...

  1. Three-frame generalized phase-shifting interferometry by a Euclidean matrix norm algorithm

    Science.gov (United States)

    Xu, Yuanyuan; Wang, Yawei; Ji, Ying; Han, Hao; Jin, Weifeng

    2016-09-01

    Generalized phase-shifting interferometry (GPSI) is one of the most effective techniques in imaging of a phase object, in which phase retrieval is an essential and important procedure. In this paper, a simple and rapid algorithm for retrieval of the unknown phase shifts in three-frame GPSI is proposed. Using this algorithm, the value of phase shift can be calculated by a determinate formula consisting of three different Euclidean matrix norms of the intensity difference between two phase shifted interferograms, and then the phase can be retrieved easily. The algorithm has the advantages of freeing from the background elimination and less computation, since it only needs three phase-shifted interferograms without no extra measurements, the iterative procedure or the integral transformation. The reliability and accuracy of this algorithm were demonstrated by simulation and experimental results.

  2. Wigner Quantization of Hamiltonians Describing Harmonic Oscillators Coupled by a General Interaction Matrix

    Directory of Open Access Journals (Sweden)

    Gilles Regniers

    2009-11-01

    Full Text Available In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n and osp(1|2n. We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case.

  3. Testing a generalized cooling procedure in the complex Langevin simulation of chiral Random Matrix Theory

    CERN Document Server

    Nagata, Keitaro; Shimasaki, Shinji

    2015-01-01

    The complex Langevin method has been attracting much attention as a solution to the sign problem since the method was shown to work in finite density QCD in the deconfined phase by using the so-called gauge cooling procedure. Whether it works also in the confined phase with light quarks is still an open question, though. In order to shed light on this question, we apply the method to the chiral Random Matrix Theory, which describes the epsilon regime of finite density QCD. Earlier works reported that a naive implementation of the method fails to reproduce the known exact results and that the problem can be solved by choosing a suitable coordinate. In this work we stick to the naive implementation, and show that a generalized gauge cooling procedure can be used to avoid the problem.

  4. Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems

    CERN Document Server

    Caballero, B; Cuevas, J C

    2012-01-01

    We present here a generalization of the scattering-matrix approach for the description of the propagation of electromagnetic waves in nanostructured magneto-optical systems. Our formalism allows us to describe all the key magneto-optical effects in any configuration in periodically patterned multilayer structures. The method can also be applied to describe periodic multilayer systems comprising materials with any type of optical anisotropy. We illustrate the method with the analysis of a recent experiment in which the transverse magneto-optical Kerr effect was measured in a Fe film with a periodic array of subwavelength circular holes. We show, in agreement with the experiments, that the excitation of surface plasmon polaritons in this system leads to a resonant enhancement of the transverse magneto-optical Kerr effect.

  5. Vector generalized linear and additive models with an implementation in R

    CERN Document Server

    Yee, Thomas W

    2015-01-01

    This book presents a statistical framework that expands generalized linear models (GLMs) for regression modelling. The framework shared in this book allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. This is possible through the approximately half-a-dozen major classes of statistical models included in the book and the software infrastructure component, which makes the models easily operable.    The book’s methodology and accompanying software (the extensive VGAM R package) are directed at these limitations, and this is the first time the methodology and software are covered comprehensively in one volume. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. The demands of practical data analysis, however, require a flexibility that GLMs do not have. Data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. This book ...

  6. Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in d dimensions

    CERN Document Server

    d'Eon, Eugene

    2013-01-01

    We derive new diffusion solutions to the monoenergetic generalized linear Boltzmann transport equation (GLBE) for the stationary collision density and scalar flux about an isotropic point source in an infinite $d$-dimensional absorbing medium with isotropic scattering. We consider both classical transport theory with exponentially-distributed free paths in arbitrary dimensions as well as a number of non-classical transport theories (non-exponential random flights) that describe a broader class of transport processes within partially-correlated random media. New rigorous asymptotic diffusion approximations are derived where possible. We also generalize Grosjean's moment-preserving approach of separating the first (or uncollided) distribution from the collided portion and approximating only the latter using diffusion. We find that for any spatial dimension and for many free-path distributions Grosjean's approach produces compact, analytic approximations that are, overall, more accurate for high absorption and f...

  7. A general derivation of the subharmonic threshold for non-linear bubble oscillations.

    Science.gov (United States)

    Prosperetti, Andrea

    2013-06-01

    The paper describes an approximate but rather general derivation of the acoustic threshold for a subharmonic component to be possible in the sound scattered by an insonified gas bubble. The general result is illustrated with several specific models for the mechanical behavior of the surface coating of bubbles used as acoustic contrast agents. The approximate results are found to be in satisfactory agreement with fully non-linear numerical results in the literature. The amplitude of the first harmonic is also found by the same method. A fundamental feature identified by the analysis is that the subharmonic threshold can be considerably lowered with respect to that of an uncoated free bubble if the mechanical response of the coating varies rapidly in the neighborhood of certain specific values of the bubble radius, e.g., because of buckling.

  8. Wave packet dynamics in one-dimensional linear and nonlinear generalized Fibonacci lattices.

    Science.gov (United States)

    Zhang, Zhenjun; Tong, Peiqing; Gong, Jiangbin; Li, Baowen

    2011-05-01

    The spreading of an initially localized wave packet in one-dimensional linear and nonlinear generalized Fibonacci (GF) lattices is studied numerically. The GF lattices can be classified into two classes depending on whether or not the lattice possesses the Pisot-Vijayaraghavan property. For linear GF lattices of the first class, both the second moment and the participation number grow with time. For linear GF lattices of the second class, in the regime of a weak on-site potential, wave packet spreading is close to ballistic diffusion, whereas in the regime of a strong on-site potential, it displays stairlike growth in both the second moment and the participation number. Nonlinear GF lattices are then investigated in parallel. For the first class of nonlinear GF lattices, the second moment of the wave packet still grows with time, but the corresponding participation number does not grow simultaneously. For the second class of nonlinear GF lattices, an analogous phenomenon is observed for the weak on-site potential only. For a strong on-site potential that leads to an enhanced nonlinear self-trapping effect, neither the second moment nor the participation number grows with time. The results can be useful in guiding experiments on the expansion of noninteracting or interacting cold atoms in quasiperiodic optical lattices.

  9. A New Method for Computing the Generalized Inverses of a Matrix and Its Application to the Lyapunov Matrix Equation.

    Science.gov (United States)

    1985-12-01

    given early during this treatment to motivate and assist the understand- ing of the theorems presented. Chapter III applies the theorems developed in...Ellis Horowitz. Fundamentals QL Computer * Algrithms. Rockville,Maryland: Computer Science Press, 1984. ., 26. Strang, Gilbert. Linear Algbra And its

  10. Spatial variability in floodplain sedimentation: the use of generalized linear mixed-effects models

    Directory of Open Access Journals (Sweden)

    A. Cabezas

    2010-02-01

    Full Text Available Sediment, Total Organic Carbon (TOC and total nitrogen (TN accumulation during one overbank flood (1.15 y were examined at one reach of the Middle Ebro River (NE Spain for elucidating spatial patterns. To achieve this goal, four areas with different geomorphological features and located within the study reach were examined by using artificial grass mats. Within each area, 1 m2 study plots consisting on three pseudo-replicates were placed in a semi-regular grid oriented perpendicular to the main channel. TOC, TN and Particle-Size composition of deposited sediments were examined and accumulation rates estimated. Generalized linear mixed-effects models were used to analyze sedimentation patterns in order to handle clustered sampling units, specific-site effects and spatial self-correlation between observations. Our results confirm the importance of channel-floodplain morphology and site micro-topography in explaining sediment, TOC and TN deposition patterns, although the importance of another factors as vegetation morphology should be included in further studies to explain small scale variability. Generalized linear mixed-effect models provide a good framework to deal with the high spatial heterogeneity of this phenomenon at different spatial scales, and should be further investigated in order to explore its validity when examining the importance of factors such as flood magnitude or suspended sediment solid concentration.

  11. Spatial variability in floodplain sedimentation: the use of generalized linear mixed-effects models

    Science.gov (United States)

    Cabezas, A.; Angulo-Martínez, M.; Gonzalez-Sanchís, M.; Jimenez, J. J.; Comín, F. A.

    2010-08-01

    Sediment, Total Organic Carbon (TOC) and total nitrogen (TN) accumulation during one overbank flood (1.15 y return interval) were examined at one reach of the Middle Ebro River (NE Spain) for elucidating spatial patterns. To achieve this goal, four areas with different geomorphological features and located within the study reach were examined by using artificial grass mats. Within each area, 1 m2 study plots consisting of three pseudo-replicates were placed in a semi-regular grid oriented perpendicular to the main channel. TOC, TN and Particle-Size composition of deposited sediments were examined and accumulation rates estimated. Generalized linear mixed-effects models were used to analyze sedimentation patterns in order to handle clustered sampling units, specific-site effects and spatial self-correlation between observations. Our results confirm the importance of channel-floodplain morphology and site micro-topography in explaining sediment, TOC and TN deposition patterns, although the importance of other factors as vegetation pattern should be included in further studies to explain small-scale variability. Generalized linear mixed-effect models provide a good framework to deal with the high spatial heterogeneity of this phenomenon at different spatial scales, and should be further investigated in order to explore its validity when examining the importance of factors such as flood magnitude or suspended sediment concentration.

  12. Blended General Linear Methods based on Boundary Value Methods in the GBDF family

    CERN Document Server

    Brugnano, Luigi

    2010-01-01

    Among the methods for solving ODE-IVPs, the class of General Linear Methods (GLMs) is able to encompass most of them, ranging from Linear Multistep Formulae (LMF) to RK formulae. Moreover, it is possible to obtain methods able to overcome typical drawbacks of the previous classes of methods. For example, order barriers for stable LMF and the problem of order reduction for RK methods. Nevertheless, these goals are usually achieved at the price of a higher computational cost. Consequently, many efforts have been made in order to derive GLMs with particular features, to be exploited for their efficient implementation. In recent years, the derivation of GLMs from particular Boundary Value Methods (BVMs), namely the family of Generalized BDF (GBDF), has been proposed for the numerical solution of stiff ODE-IVPs. In particular, this approach has been recently developed, resulting in a new family of L-stable GLMs of arbitrarily high order, whose theory is here completed and fully worked-out. Moreover, for each one o...

  13. Generalized linear mixed models for multi-reader multi-case studies of diagnostic tests.

    Science.gov (United States)

    Liu, Wei; Pantoja-Galicia, Norberto; Zhang, Bo; Kotz, Richard M; Pennello, Gene; Zhang, Hui; Jacob, Jessie; Zhang, Zhiwei

    2017-06-01

    Diagnostic tests are often compared in multi-reader multi-case (MRMC) studies in which a number of cases (subjects with or without the disease in question) are examined by several readers using all tests to be compared. One of the commonly used methods for analyzing MRMC data is the Obuchowski-Rockette (OR) method, which assumes that the true area under the receiver operating characteristic curve (AUC) for each combination of reader and test follows a linear mixed model with fixed effects for test and random effects for reader and the reader-test interaction. This article proposes generalized linear mixed models which generalize the OR model by incorporating a range-appropriate link function that constrains the true AUCs to the unit interval. The proposed models can be estimated by maximizing a pseudo-likelihood based on the approximate normality of AUC estimates. A Monte Carlo expectation-maximization algorithm can be used to maximize the pseudo-likelihood, and a non-parametric bootstrap procedure can be used for inference. The proposed method is evaluated in a simulation study and applied to an MRMC study of breast cancer detection.

  14. On the Generalization of the Timoshenko Beam Model Based on the Micropolar Linear Theory: Static Case

    Directory of Open Access Journals (Sweden)

    Andrea Nobili

    2015-01-01

    Full Text Available Three generalizations of the Timoshenko beam model according to the linear theory of micropolar elasticity or its special cases, that is, the couple stress theory or the modified couple stress theory, recently developed in the literature, are investigated and compared. The analysis is carried out in a variational setting, making use of Hamilton’s principle. It is shown that both the Timoshenko and the (possibly modified couple stress models are based on a microstructural kinematics which is governed by kinosthenic (ignorable terms in the Lagrangian. Despite their difference, all models bring in a beam-plane theory only one microstructural material parameter. Besides, the micropolar model formally reduces to the couple stress model upon introducing the proper constraint on the microstructure kinematics, although the material parameter is generally different. Line loading on the microstructure results in a nonconservative force potential. Finally, the Hamiltonian form of the micropolar beam model is derived and the canonical equations are presented along with their general solution. The latter exhibits a general oscillatory pattern for the microstructure rotation and stress, whose behavior matches the numerical findings.

  15. Misconceptions in the use of the General Linear Model applied to functional MRI: a tutorial for junior neuro-imagers

    Directory of Open Access Journals (Sweden)

    Cyril R Pernet

    2014-01-01

    Full Text Available This tutorial presents several misconceptions related to the use the General Linear Model (GLM in functional Magnetic Resonance Imaging (fMRI. The goal is not to present mathematical proofs but to educate using examples and computer code (in Matlab. In particular, I address issues related to (i model parameterization (modelling baseline or null events and scaling of the design matrix; (ii hemodynamic modelling using basis functions, and (iii computing percentage signal change. Using a simple controlled block design and an alternating block design, I first show why 'baseline' should not be modelled (model over-parameterization, and how this affects effect sizes. I also show that, depending on what is tested; over-parameterization does not necessarily impact upon statistical results. Next, using a simple periodic vs. random event related design, I show how the haemodynamic model (haemodynamic function only or using derivatives can affects parameter estimates, as well as detail the role of orthogonalization. I then relate the above results to the computation of percentage signal change. Finally, I discuss how these issues affect group analysis and give some recommendations.

  16. Sampled-data Consensus of Multi-agent Systems with General Linear Dynamics Based on a Continuous-time Mo del

    Institute of Scientific and Technical Information of China (English)

    ZHANG Xie-Yan; ZHANG Jing

    2014-01-01

    This paper discusses the sampled-data consensus problem of multi-agent systems with general linear dynamics and time-varying sampling intervals. To investigate the allowable upper bound of sampling intervals, we employ the property of discretization of sampled-data to identify the upper bound on the variable sampling intervals via a continuous-time model. Without considering the states in the sampling intervals, the decrease of Lyapunov function is guaranteed only at each sampling time. Consequently, it results in a more robust sampling interval which is obtained by verifying the feasibility of LMIs. Subsequently, provided a limited matrix variable, the control gain matrix K is solved by the LMI approach. Numerical simulations are provided to demonstrate the effectiveness of theoretical results.

  17. The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann--Hilbert problems

    CERN Document Server

    Alvarez-Fernandez, Carlos; Manas, Manuel

    2009-01-01

    We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal polynomials are studied. In particular for these polynomials we consider the recursion relations, and for rank one weights its relation with multiple orthogonal polynomials of mixed type with a type II normalization and the corresponding link with a Riemann--Hilbert problem.

  18. Complex CKM matrix, spontaneous CP violation and generalized {mu}-{tau} symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Joshipura, Anjan S. [Physical Research Laboratory, Navarangpura, Ahmedabad 380 009 (India)], E-mail: anjan@prl.res.in; Kodrani, Bhavik P. [Physical Research Laboratory, Navarangpura, Ahmedabad 380 009 (India)

    2009-01-05

    The multi-Higgs models having spontaneous CP violation (SPCPV) and natural flavor conservation (NFC) lead to a real CKM matrix V contradicting current evidence in favour of a complex V. This contradiction can be removed by using a generalized {mu}-{tau} (called 23) symmetry in place of the discrete symmetry conventionally used to obtain NFC. If the 23 symmetry is exact then the Higgs induced flavour changing neutral currents (FCNC) vanish as in the case of NFC. 23 breaking introduces SPCPV, a phase in V and suppressed FCNC among quarks. The FCNC couplings F{sub ij}{sup d,u} between i and j generations show a hierarchy |F{sub 12}{sup d,u}|<|F{sub 13}{sup d,u}|<|F{sub 23}{sup d,u}| with the result that the FCNC can have observable consequences in B mixing without conflicting with the K{sup 0}-K-bar{sup 0} mixing. Detailed fits to the quark masses and the CKM matrix are used to obtain the (complex) couplings F{sub ij}{sup d} and F{sub ij}{sup u}. Combined constraints from flavour and CP violations in the K, B{sub d}, B{sub s}, D mesons are analyzed within the model. They allow (i) relatively light Higgs, 100-150 GeV (ii) measurable extra contributions to the magnitudes and phases of the B{sub d,s}{sup 0}-B-bar{sub d,s}{sup 0} mixing amplitudes and (iii) the D{sup 0}-D-bar{sup 0} mixing at the current sensitivity level.

  19. Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm.

    Science.gov (United States)

    Nakatani, Naoki; Chan, Garnet Kin-Lic

    2013-04-07

    We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.

  20. The heritability of general cognitive ability increases linearly from childhood to young adulthood.

    Science.gov (United States)

    Haworth, C M A; Wright, M J; Luciano, M; Martin, N G; de Geus, E J C; van Beijsterveldt, C E M; Bartels, M; Posthuma, D; Boomsma, D I; Davis, O S P; Kovas, Y; Corley, R P; Defries, J C; Hewitt, J K; Olson, R K; Rhea, S-A; Wadsworth, S J; Iacono, W G; McGue, M; Thompson, L A; Hart, S A; Petrill, S A; Lubinski, D; Plomin, R

    2010-11-01

    Although common sense suggests that environmental influences increasingly account for individual differences in behavior as experiences accumulate during the course of life, this hypothesis has not previously been tested, in part because of the large sample sizes needed for an adequately powered analysis. Here we show for general cognitive ability that, to the contrary, genetic influence increases with age. The heritability of general cognitive ability increases significantly and linearly from 41% in childhood (9 years) to 55% in adolescence (12 years) and to 66% in young adulthood (17 years) in a sample of 11 000 pairs of twins from four countries, a larger sample than all previous studies combined. In addition to its far-reaching implications for neuroscience and molecular genetics, this finding suggests new ways of thinking about the interface between nature and nurture during the school years. Why, despite life's 'slings and arrows of outrageous fortune', do genetically driven differences increasingly account for differences in general cognitive ability? We suggest that the answer lies with genotype-environment correlation: as children grow up, they increasingly select, modify and even create their own experiences in part based on their genetic propensities.

  1. Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data

    KAUST Repository

    Cheng, Guang

    2014-02-01

    We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based on a spline approximation of the nonparametric part of the model and the generalized estimating equations (GEE). Although the model in consideration is natural and useful in many practical applications, the literature on this model is very limited because of challenges in dealing with dependent data for nonparametric additive models. We show that the proposed estimators are consistent and asymptotically normal even if the covariance structure is misspecified. An explicit consistent estimate of the asymptotic variance is also provided. Moreover, we derive the semiparametric efficiency score and information bound under general moment conditions. By showing that our estimators achieve the semiparametric information bound, we effectively establish their efficiency in a stronger sense than what is typically considered for GEE. The derivation of our asymptotic results relies heavily on the empirical processes tools that we develop for the longitudinal/clustered data. Numerical results are used to illustrate the finite sample performance of the proposed estimators. © 2014 ISI/BS.

  2. Neutrino mixing matrix and masses from a generalized Friedberg-Lee model

    Science.gov (United States)

    Razzaghi, N.; Gousheh, S. S.

    2014-02-01

    The overall characteristics of the solar and atmospheric neutrino oscillation are approximately consistent with a tribimaximal form of the mixing matrix U of the lepton sector. Exact tribimaximal mixing leads to θ13=0. However, recent results from the Daya Bay and RENO experiments have established a nonzero value for θ13. Keeping the leading behavior of U as tribimaximal, we use a generalized Friedberg-Lee neutrino mass model along with a complementary ansatz to incorporate a nonzero θ13 along with CP violation. We generalize this model in two stages: In the first stage, we assume μ -τ symmetry and add imaginary components which leads to nonzero phases. In the second stage, we add a perturbation with real components which breaks the μ-τ symmetry, and this leads to a nonzero value for θ13. The combination of these two generalizations leads to CP violation. Using only two sets of the experimental data, we can fix all of the parameters of our model and predict not only values for the other experimental data, which agree well with the available data, but also the masses of neutrinos and the CP-violating phases and parameters. These predictions include the following: ⟨mνe⟩≈(0.033-0.037) eV, ⟨mνμ⟩≈(0.043-0.048) eV, ⟨mντ⟩≈(0.046-0.051) eV, and 59.21°≲δ ≲59.34°.

  3. Geometric and growth rate tests of General Relativity with recovered linear cosmological perturbations

    CERN Document Server

    Wilson, Michael J

    2016-01-01

    I investigate the consistency of the VIMOS Public Extragalactic Redshift Survey v7 galaxy sample with the expansion history and linear growth rate predicted by General Relativity (GR) and a Planck (2015) cosmology. To do so, I measure the redshift-space power spectrum, which is anisotropic due to both redshift-space distortions (RSD) and the Alcock-Paczynski (AP) effect. In Chapter 6, I place constraints of $f \\sigma_8(0.76) = 0.44 \\pm 0.04$ and $f \\sigma_8(1.05) = 0.28 \\pm 0.08$, which remain consistent with GR at 95% confidence. Marginalising over the anisotropic AP effect degrades the constraints by a factor of three but allows $F_{AP} \\equiv (1+z) D_A H/c$ to be simultaneously constrained. The VIPERS v7 joint-posterior on $(f \\sigma_8, F_{AP})$ shows no compelling deviation from GR. Chapter 7 investigates the inclusion of a simple density transform: `clipping' prior to the RSD analysis. This tackles the root-cause of non-linearity and may extend the validity of perturbation theory. Moreover, this marked s...

  4. Developing minds of tomorrow: exploring students' strategies involved in the generalization of linear patterns

    Directory of Open Access Journals (Sweden)

    Areej IsamBarham

    2011-11-01

    Full Text Available The study investigates students' strategies involved in the generalization of "linear patterns". The study followed thequalitative research approach by conducting task-based interviews with twenty-nine primary second grade students fromdifferent high, intermediate and low ability levels. Results of the study presented several strategies involved in thegeneralization of the patterns including visual, auditory, mental, finger counting, verbal counting, and traditional (paper andpencil strategies. The findings revealed that the type of the assigned pattern (simple or complex and the type of the structureof the pattern itself (increasing or decreasing play a big role for students' strategies involved to either discover the rule of thepattern or to extend it. However, students in early ages could master several skills and choose appropriate procedures to dealwith patterns, which indicate that they could develop their algebraic thinking from early stages. Findings of the study alsorevealed that using different senses, using the idea of coins, using the numbers line, recognizing musical sounds, using concretematerials like fingers, applying different visual and mental strategies, and even applying traditional calculations could helpstudents to work with “linear patterns". It is recommended that teachers introduce different strategies and procedures inteaching patterns to meet the needs of students as different learners, give them the opportunities to develop their thinkingstrategies and explore their thoughts. More research is recommended to explore students' strategies involved in thegeneralization of different kinds of patters at different stages.

  5. MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package

    Directory of Open Access Journals (Sweden)

    Jarrod Had

    2010-02-01

    Full Text Available Generalized linear mixed models provide a flexible framework for modeling a range of data, although with non-Gaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distributions that can be evaluated. The R package MCMCglmm implements such an algorithm for a range of model fitting problems. More than one response variable can be analyzed simultaneously, and these variables are allowed to follow Gaussian, Poisson, multi(binominal, exponential, zero-inflated and censored distributions. A range of variance structures are permitted for the random effects, including interactions with categorical or continuous variables (i.e., random regression, and more complicated variance structures that arise through shared ancestry, either through a pedigree or through a phylogeny. Missing values are permitted in the response variable(s and data can be known up to some level of measurement error as in meta-analysis. All simu- lation is done in C/ C++ using the CSparse library for sparse linear systems.

  6. The Potential in General Linear Electrodynamics: Causal Structure, Propagators and Quantization

    CERN Document Server

    Pfeifer, Christian

    2016-01-01

    An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics is just one instance of a variety of theories for which the name electrodynamics is justified. They all have in common that their fundamental input are Maxwell's equations $\\textrm{d} F = 0$ (or $F = \\textrm{d} A$) and $\\textrm{d} H = J$ and a constitutive law $H = \\# F$ which relates the field strength two-form $F$ and the excitation two-form $H$. A local and linear constitutive law defines what is called general linear electrodynamics whose best known application are the effective description of electrodynamics inside media including, e.g., birefringence. We will analyze the classical theory of the electromagnetic potential $A$ before we use methods familiar from mathematical quantum field theory in curved spacetimes to quantize it in a locally covariant way. Our analysis of the classical theory contains the derivation of retarded and advanced propagators, the analysis of the causal structure on the basis of the constitutive law (...

  7. General Explicit Solution of Planar Weakly Delayed Linear Discrete Systems and Pasting Its Solutions

    Directory of Open Access Journals (Sweden)

    Josef Diblík

    2014-01-01

    Full Text Available Planar linear discrete systems with constant coefficients and delays x(k+1=Ax(k+∑l=1n‍Blxl(k-ml are considered where k∈ℤ0∞:={0,1,…,∞}, m1,m2,…,mn are constant integer delays, 0linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained.

  8. Tuning, Diagnostics & Data Preparation for Generalized Linear Models Supervised Algorithm in Data Mining Technologies

    Directory of Open Access Journals (Sweden)

    Sachin Bhaskar

    2015-07-01

    Full Text Available Data mining techniques are the result of a long process of research and product development. Large amount of data are searched by the practice of Data Mining to find out the trends and patterns that go beyond simple analysis. For segmentation of data and also to evaluate the possibility of future events, complex mathematical algorithms are used here. Specific algorithm produces each Data Mining model. More than one algorithms are used to solve in best way by some Data Mining problems. Data Mining technologies can be used through Oracle. Generalized Linear Models (GLM Algorithm is used in Regression and Classification Oracle Data Mining functions. For linear modelling, GLM is one the popular statistical techniques. For regression and binary classification, GLM is implemented by Oracle Data Mining. Row diagnostics as well as model statistics and extensive co-efficient statistics are provided by GLM. It also supports confidence bounds.. This paper outlines and produces analysis of GLM algorithm, which will guide to understand the tuning, diagnostics & data preparation process and the importance of Regression & Classification supervised Oracle Data Mining functions and it is utilized in marketing, time series prediction, financial forecasting, overall business planning, trend analysis, environmental modelling, biomedical and drug response modelling, etc.

  9. A generalized fuzzy linear programming approach for environmental management problem under uncertainty.

    Science.gov (United States)

    Fan, Yurui; Huang, Guohe; Veawab, Amornvadee

    2012-01-01

    In this study, a generalized fuzzy linear programming (GFLP) method was developed to deal with uncertainties expressed as fuzzy sets that exist in the constraints and objective function. A stepwise interactive algorithm (SIA) was advanced to solve GFLP model and generate solutions expressed as fuzzy sets. To demonstrate its application, the developed GFLP method was applied to a regional sulfur dioxide (SO2) control planning model to identify effective SO2 mitigation polices with a minimized system performance cost under uncertainty. The results were obtained to represent the amount of SO2 allocated to different control measures from different sources. Compared with the conventional interval-parameter linear programming (ILP) approach, the solutions obtained through GFLP were expressed as fuzzy sets, which can provide intervals for the decision variables and objective function, as well as related possibilities. Therefore, the decision makers can make a tradeoff between model stability and the plausibility based on solutions obtained through GFLP and then identify desired policies for SO2-emission control under uncertainty.

  10. Towards downscaling precipitation for Senegal - An approach based on generalized linear models and weather types

    Science.gov (United States)

    Rust, H. W.; Vrac, M.; Lengaigne, M.; Sultan, B.

    2012-04-01

    Changes in precipitation patterns with potentially less precipitation and an increasing risk for droughts pose a threat to water resources and agricultural yields in Senegal. Precipitation in this region is dominated by the West-African Monsoon being active from May to October, a seasonal pattern with inter-annual to decadal variability in the 20th century which is likely to be affected by climate change. We built a generalized linear model for a full spatial description of rainfall in Senegal. The model uses season, location, and a discrete set of weather types as predictors and yields a spatially continuous description of precipitation occurrences and intensities. Weather types have been defined on NCEP/NCAR reanalysis using zonal and meridional winds, as well as relative humidity. This model is suitable for downscaling precipitation, particularly precipitation occurrences relevant for drough risk mapping.

  11. Quasi-Maximum Likelihood Estimators in Generalized Linear Models with Autoregressive Processes

    Institute of Scientific and Technical Information of China (English)

    Hong Chang HU; Lei SONG

    2014-01-01

    The paper studies a generalized linear model (GLM) yt=h(xTtβ)+εt, t=1, 2, . . . , n, whereε1=η1,εt=ρεt-1+ηt, t=2,3,...,n, h is a continuous diff erentiable function,ηt’s are independent and identically distributed random errors with zero mean and finite varianceσ 2. Firstly, the quasi-maximum likelihood (QML) estimators ofβ,ρandσ 2 are given. Secondly, under mild conditions, the asymptotic properties (including the existence, weak consistency and asymptotic distribution) of the QML estimators are investigated. Lastly, the validity of method is illuminated by a simulation example.

  12. A Fuzzy Approach Using Generalized Dinkelbach’s Algorithm for Multiobjective Linear Fractional Transportation Problem

    Directory of Open Access Journals (Sweden)

    Nurdan Cetin

    2014-01-01

    Full Text Available We consider a multiobjective linear fractional transportation problem (MLFTP with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach.

  13. Dimension Reduction and Alleviation of Confounding for Spatial Generalized Linear Mixed Models

    CERN Document Server

    Hughes, John

    2010-01-01

    Non-gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model (SGLMM) offers a very popular and flexible approach to modeling such data, but the SGLMM suffers from three major shortcomings: (1) uninterpretability of parameters due to spatial confounding, (2) variance inflation due to spatial confounding, and (3) high-dimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. We propose a new parameterization of the SGLMM that alleviates spatial confounding and speeds computation by greatly reducing the dimension of the spatial random effects. We illustrate the application of our approach to simulated binary, count, and Gaussian spatial datasets, and to a large infant mortali...

  14. Bayesian model choice and information criteria in sparse generalized linear models

    CERN Document Server

    Foygel, Rina

    2011-01-01

    We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to p. Treating the covariates as random and adopting an asymptotic scenario in which p increases with n, we show that Bayesian model selection using certain priors on the set of models is asymptotically equivalent to selecting a model using an extended Bayesian information criterion. Moreover, we prove that the smallest true model is selected by either of these methods with probability tending to one. Having addressed random covariates, we are also able to give a consistency result for pseudo-likelihood approaches to high-dimensional sparse graphical modeling. Experiments on real data demonstrate good performance of the extended Bayesian information criterion for regression and for graphical models.

  15. Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

    Science.gov (United States)

    Delorme, Rolland; Tabiai, Ilyass; Laberge Lebel, Louis; Lévesque, Martin

    2017-02-01

    This paper presents a generalization of the original ordinary state-based peridynamic model for isotropic linear viscoelasticity. The viscoelastic material response is represented using the thermodynamically acceptable Prony series approach. It can feature as many Prony terms as required and accounts for viscoelastic spherical and deviatoric components. The model was derived from an equivalence between peridynamic viscoelastic parameters and those appearing in classical continuum mechanics, by equating the free energy densities expressed in both frameworks. The model was simplified to a uni-dimensional expression and implemented to simulate a creep-recovery test. This implementation was finally validated by comparing peridynamic predictions to those predicted from classical continuum mechanics. An exact correspondence between peridynamics and the classical continuum approach was shown when the peridynamic horizon becomes small, meaning peridynamics tends toward classical continuum mechanics. This work provides a clear and direct means to researchers dealing with viscoelastic phenomena to tackle their problem within the peridynamic framework.

  16. Master equation solutions in the linear regime of characteristic formulation of general relativity

    CERN Document Server

    M., C E Cedeño

    2015-01-01

    From the field equations in the linear regime of the characteristic formulation of general relativity, Bishop, for a Schwarzschild's background, and M\\"adler, for a Minkowski's background, were able to show that it is possible to derive a fourth order ordinary differential equation, called master equation, for the $J$ metric variable of the Bondi-Sachs metric. Once $\\beta$, another Bondi-Sachs potential, is obtained from the field equations, and $J$ is obtained from the master equation, the other metric variables are solved integrating directly the rest of the field equations. In the past, the master equation was solved for the first multipolar terms, for both the Minkowski's and Schwarzschild's backgrounds. Also, M\\"adler recently reported a generalisation of the exact solutions to the linearised field equations when a Minkowski's background is considered, expressing the master equation family of solutions for the vacuum in terms of Bessel's functions of the first and the second kind. Here, we report new sol...

  17. Balancing Chemical Reactions With Matrix Methods and Computer Assistance. Applications of Linear Algebra to Chemistry. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 339.

    Science.gov (United States)

    Grimaldi, Ralph P.

    This material was developed to provide an application of matrix mathematics in chemistry, and to show the concepts of linear independence and dependence in vector spaces of dimensions greater than three in a concrete setting. The techniques presented are not intended to be considered as replacements for such chemical methods as oxidation-reduction…

  18. Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

    Institute of Scientific and Technical Information of China (English)

    刘占芳; 颜世军; 符志

    2013-01-01

    The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine-matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre-ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion-deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and

  19. Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model.

    Science.gov (United States)

    Bazzoli, Caroline; Retout, Sylvie; Mentré, France

    2009-06-30

    We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic-pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation-maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first-order linearization estimation methods implemented in the NONMEM software (first-order (FO), first-order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.

  20. Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble

    CERN Document Server

    Mandal, Gautam

    2013-01-01

    Quantum quench dynamics is considered in a one dimensional unitary matrix model with a single trace potential. This model is integrable and has been studied in the context of non-critical string theory. We find dynamical phase transitions, and study the role of the quantum critical point. In course of the time evolutions, we find evidence of selective equilibration for a certain class of observables. The equilibrium is governed by the Generalized Gibbs Ensemble (GGE) and differs from the standard Gibbs ensemble. We compute the production of entropy which is O(N) for large N matrices. An important feature of the equilibration is the appearance of an energy cascade, reminiscent of the Richardson cascade in turbulence, where we find flow of energy from initial long wavelength modes to progressively shorter wavelength excitations. We discuss possible implication of the equilibration and of GGE in string theories and higher spin theories. In another related study, we compute time evolutions in a double trace unita...

  1. The Overlooked Potential of Generalized Linear Models in Astronomy-II: Gamma regression and photometric redshifts

    CERN Document Server

    Elliott, J; Krone-Martins, A; Cameron, E; Ishida, E E O; Hilbe, J

    2014-01-01

    Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the underlying physical processes of the data. In this article, and the companion papers of this series, we present the set of Generalized Linear Models (GLMs) as a fast alternative method for tackling general astronomical problems, including the ones related to the machine learning paradigm. To demonstrate the applicability of GLMs to inherently positive and continuous physical observables, we explore their use in estimating the photometric redshifts of galaxies from their multi-wavelength photometry. Using the gamma family with a log link function we predict redshifts from the photo-z Accuracy Testing simulated catalogue and a subset of the Sloan Digital Sky Survey from Data Release 10. We obtain fits that result in catastrophic outlier rates as low as ~1% for simulated and ~2% for...

  2. Generalized linear model for mapping discrete trait loci implemented with LASSO algorithm.

    Directory of Open Access Journals (Sweden)

    Jun Xing

    Full Text Available Generalized estimating equation (GEE algorithm under a heterogeneous residual variance model is an extension of the iteratively reweighted least squares (IRLS method for continuous traits to discrete traits. In contrast to mixture model-based expectation-maximization (EM algorithm, the GEE algorithm can well detect quantitative trait locus (QTL, especially large effect QTLs located in large marker intervals in the manner of high computing speed. Based on a single QTL model, however, the GEE algorithm has very limited statistical power to detect multiple QTLs because of ignoring other linked QTLs. In this study, the fast least absolute shrinkage and selection operator (LASSO is derived for generalized linear model (GLM with all possible link functions. Under a heterogeneous residual variance model, the LASSO for GLM is used to iteratively estimate the non-zero genetic effects of those loci over entire genome. The iteratively reweighted LASSO is therefore extended to mapping QTL for discrete traits, such as ordinal, binary, and Poisson traits. The simulated and real data analyses are conducted to demonstrate the efficiency of the proposed method to simultaneously identify multiple QTLs for binary and Poisson traits as examples.

  3. Criteria for the Single-Valued Metric Generalized Inverses of Multi-Valued Linear Operators in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Yu Wen WANG; Jian ZHANG; Yun An CUI

    2012-01-01

    Let X,Y be Banach spaces and M be a linear subspace in X × Y ={{x,y}|x ∈ X,y ∈ Y}.We may view M as a multi-valued linear operator from X to Y by taking M(x) ={y|{x,y} ∈ M}.In this paper,we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M.The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.

  4. Restoring the Duality between Principal Components of a Distance Matrix and Linear Combinations of Predictors, with Application to Studies of the Microbiome

    Science.gov (United States)

    Tyx, Robert E.; Rivera, Angel J.; Stanfill, Stephen

    2017-01-01

    Appreciation of the importance of the microbiome is increasing, as sequencing technology has made it possible to ascertain the microbial content of a variety of samples. Studies that sequence the 16S rRNA gene, ubiquitous in and nearly exclusive to bacteria, have proliferated in the medical literature. After sequences are binned into operational taxonomic units (OTUs) or species, data from these studies are summarized in a data matrix with the observed counts from each OTU for each sample. Analysis often reduces these data further to a matrix of pairwise distances or dissimilarities; plotting the first two or three principal components (PCs) of this distance matrix often reveals meaningful groupings in the data. However, once the distance matrix is calculated, it is no longer clear which OTUs or species are important to the observed clustering; further, the PCs are hard to interpret and cannot be calculated for subsequent observations. We show how to construct approximate decompositions of the data matrix that pair PCs with linear combinations of OTU or species frequencies, and show how these decompositions can be used to construct biplots, select important OTUs and partition the variability in the data matrix into contributions corresponding to PCs of an arbitrary distance or dissimilarity matrix. To illustrate our approach, we conduct an analysis of the bacteria found in 45 smokeless tobacco samples. PMID:28085878

  5. Restoring the Duality between Principal Components of a Distance Matrix and Linear Combinations of Predictors, with Application to Studies of the Microbiome.

    Science.gov (United States)

    Satten, Glen A; Tyx, Robert E; Rivera, Angel J; Stanfill, Stephen

    2017-01-01

    Appreciation of the importance of the microbiome is increasing, as sequencing technology has made it possible to ascertain the microbial content of a variety of samples. Studies that sequence the 16S rRNA gene, ubiquitous in and nearly exclusive to bacteria, have proliferated in the medical literature. After sequences are binned into operational taxonomic units (OTUs) or species, data from these studies are summarized in a data matrix with the observed counts from each OTU for each sample. Analysis often reduces these data further to a matrix of pairwise distances or dissimilarities; plotting the first two or three principal components (PCs) of this distance matrix often reveals meaningful groupings in the data. However, once the distance matrix is calculated, it is no longer clear which OTUs or species are important to the observed clustering; further, the PCs are hard to interpret and cannot be calculated for subsequent observations. We show how to construct approximate decompositions of the data matrix that pair PCs with linear combinations of OTU or species frequencies, and show how these decompositions can be used to construct biplots, select important OTUs and partition the variability in the data matrix into contributions corresponding to PCs of an arbitrary distance or dissimilarity matrix. To illustrate our approach, we conduct an analysis of the bacteria found in 45 smokeless tobacco samples.

  6. Summary goodness-of-fit statistics for binary generalized linear models with noncanonical link functions.

    Science.gov (United States)

    Canary, Jana D; Blizzard, Leigh; Barry, Ronald P; Hosmer, David W; Quinn, Stephen J

    2016-05-01

    Generalized linear models (GLM) with a canonical logit link function are the primary modeling technique used to relate a binary outcome to predictor variables. However, noncanonical links can offer more flexibility, producing convenient analytical quantities (e.g., probit GLMs in toxicology) and desired measures of effect (e.g., relative risk from log GLMs). Many summary goodness-of-fit (GOF) statistics exist for logistic GLM. Their properties make the development of GOF statistics relatively straightforward, but it can be more difficult under noncanonical links. Although GOF tests for logistic GLM with continuous covariates (GLMCC) have been applied to GLMCCs with log links, we know of no GOF tests in the literature specifically developed for GLMCCs that can be applied regardless of link function chosen. We generalize the Tsiatis GOF statistic originally developed for logistic GLMCCs, (TG), so that it can be applied under any link function. Further, we show that the algebraically related Hosmer-Lemeshow (HL) and Pigeon-Heyse (J(2) ) statistics can be applied directly. In a simulation study, TG, HL, and J(2) were used to evaluate the fit of probit, log-log, complementary log-log, and log models, all calculated with a common grouping method. The TG statistic consistently maintained Type I error rates, while those of HL and J(2) were often lower than expected if terms with little influence were included. Generally, the statistics had similar power to detect an incorrect model. An exception occurred when a log GLMCC was incorrectly fit to data generated from a logistic GLMCC. In this case, TG had more power than HL or J(2) .

  7. Documenting organisational development in general practice using a group-based assessment method: the Maturity Matrix.

    Science.gov (United States)

    Eriksson, Tina; Siersma, Volkert Dirk; Løgstrup, Louise; Buch, Martin Sandberg; Elwyn, Glyn; Edwards, Adrian

    2010-10-01

    The Maturity Matrix (MM) comprises a formative evaluation instrument for primary care practices to self-assess their degree of organisational development in a group setting, guided by an external facilitator. The practice teams discuss organisational development, score their own performance and set improvement goals for the following year. The objective of this project was to introduce a translated and culturally adapted version of the MM in Denmark, to test its feasibility, to promote and document organisational change in general practices and to analyse associations between the recorded change(s) and structural factors in practices and the factors associated with the MM process. MM was used by general practices in three counties in Denmark, in two assessment sessions 1 year apart. First rounds of MM visits were carried out in 2006-2007 in 60 practice teams (320 participants (163 GPs, 157 staff)) and the second round in 2007-2008. A total of 48 practice teams (228 participants (117 GPs; 111 staff) participated in both sessions. The MM sessions were the primary intervention. Moreover, in about half of the practices, the facilitator reminded practice teams of their goals by sending them the written report of the initial session and contacted the practices regularly by telephone reminding them of the goals they had set. Those practice teams had password-protected access to their own and benchmark data. Where the minimum possible is 0 and maximum possible is 8, the mean overall MM score increased from 4.4 to 5.3 (difference=0.9, 95%, CI 0.76 to 1.06) from first to second sessions, indicating that development had taken place as measured by this group-based self-evaluation method. There was some evidence that lower-scoring dimensions were prioritised and more limited evidence that the prioritisation and interventions between meetings were helpful to achieve changes. This study provides evidence that MM worked well in general practices in Denmark. Practice teams appeared

  8. Evolution equation of population genetics: relation to the density-matrix theory of quasiparticles with general dispersion laws.

    Science.gov (United States)

    Bezák, V

    2003-02-01

    The Waxman-Peck theory of population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central objective is the calculation of the probability density with respect to p, Phi(p,t;p(0)), of the carriers living at time t>0, provided that initially at t(0)=0, all bacteria carried the phenotypic parameter p(0)=0. The theory involves two small parameters: the mutation probability mu and a parameter gamma involved in a function w(p) defining the fitness of the bacteria to survive the generation time tau and give birth to an offspring. The mutation from a state p to a state q is defined by a Gaussian with a dispersion sigma(2)(m). The author focuses our attention on a function phi(p,t) which determines uniquely the function Phi(p,t;p(0)) and satisfies a linear equation (Waxman's equation). The Green function of this equation is mathematically identical with the one-particle Bloch density matrix, where mu characterizes the order of magnitude of the potential energy. (In the x representation, the potential energy is proportional to the inverted Gaussian with the dispersion sigma(2)(m)). The author solves Waxman's equation in the standard style of a perturbation theory and discusses how the solution depends on the choice of the fitness function w(p). In a sense, the function c(p)=1-w(p)/w(0) is analogous to the dispersion function E(p) of fictitious quasiparticles. In contrast to Waxman's approximation, where c(p) was taken as a quadratic function, c(p) approximately gammap(2), the author exemplifies the problem with another function, c(p)=gamma[1-exp(-ap(2))], where gamma is small but a may be large. The author shows that the use of this function in the theory of the population genetics is the same as the use of a nonparabolic dispersion law E=E(p) in the density-matrix theory. With a general function c(p), the distribution function Phi(p,t;0) is composed of a delta-function component, N

  9. A generalized linear model for estimating spectrotemporal receptive fields from responses to natural sounds.

    Directory of Open Access Journals (Sweden)

    Ana Calabrese

    Full Text Available In the auditory system, the stimulus-response properties of single neurons are often described in terms of the spectrotemporal receptive field (STRF, a linear kernel relating the spectrogram of the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been used to estimate STRFs from responses to natural stimuli; these algorithms differ in their functional models, cost functions, and regularization methods. Here, we characterize the stimulus-response function of auditory neurons using a generalized linear model (GLM. In this model, each cell's input is described by: 1 a stimulus filter (STRF; and 2 a post-spike filter, which captures dependencies on the neuron's spiking history. The output of the model is given by a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs and modulation limited (ml noise. We compare this model to normalized reverse correlation (NRC, the traditional method for STRF estimation, in terms of predictive power and the basic tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs from the two models derived from the same responses can differ substantially and that GLM STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal tuning than does the NRC method when responses to complex sounds are studied in these neurons.

  10. Desphospho-uncarboxylated matrix Gla protein is associated with increased aortic stiffness in a general population.

    Science.gov (United States)

    Mayer, O; Seidlerová, J; Wohlfahrt, P; Filipovský, J; Vaněk, J; Cífková, R; Windrichová, J; Topolčan, O; Knapen, M H J; Drummen, N E A; Vermeer, C

    2016-07-01

    Matrix Gla protein (MGP), a natural inhibitor of calcification, strongly correlates with the extent of coronary calcification. Vitamin K is the essential cofactor for the activation of MGP. The nonphosphorylated-uncarboxylated isoform of MGP (dp-ucMGP) reflects the status of this vitamin. We investigated whether there is an association between dp-ucMGP and stiffness of elastic and muscular-type large arteries in a random sample from the general population. In a cross-sectional design, we analyzed 1087 subjects from the Czech post-MONICA study. Aortic and femoro-popliteal pulse wave velocities (PWVs) were measured using a Sphygmocor device. Dp-ucMGP concentrations were assessed in freshly frozen samples by enzyme-linked immunosorbent assay methods using the InaKtif MGP iSYS pre-commercial kit developed by IDS and VitaK. Aortic PWV significantly (P<0.0001) increased across the dp-ucMGP quartiles. After adjustment for all potential confounders, aortic PWV independently correlated with dp-ucMGP (with beta coefficient (s.d.) 11.61 (5.38) and P-value=0.031). In a categorized manner, subjects in the top quartile of dp-ucMGP (⩾ 671 pmol l(-1)) had a higher risk of elevated aortic PWV, with corresponding adjusted odds ratio (95% confidence interval) 1.73 (1.17-2.5). In contrast, no relation between dp-ucMGP and femoro-popliteal PWV was found. In conclusion, increased dp-ucMGP, which is a circulating biomarker of vitamin K status and vascular calcification, is independently associated with aortic stiffness, but not with stiffness of distal muscular-type arteries.

  11. c060: Extended Inference with Lasso and Elastic-Net Regularized Cox and Generalized Linear Models

    Directory of Open Access Journals (Sweden)

    Martin Sill

    2014-12-01

    Full Text Available We have developed the R package c060 with the aim of improving R software func- tionality for high-dimensional risk prediction modeling, e.g., for prognostic modeling of survival data using high-throughput genomic data. Penalized regression models provide a statistically appealing way of building risk prediction models from high-dimensional data. The popular CRAN package glmnet implements an efficient algorithm for fitting penalized Cox and generalized linear models. However, in practical applications the data analysis will typically not stop at the point where the model has been fitted. One is for example often interested in the stability of selected features and in assessing the prediction performance of a model and we provide functions to deal with both of these tasks. Our R functions are computationally efficient and offer the possibility of speeding up computing time through parallel computing. Another feature which can drastically reduce computing time is an efficient interval-search algorithm, which we have implemented for selecting the optimal parameter combination for elastic net penalties. These functions have been useful in our daily work at the Biostatistics department (C060 of the German Cancer Research Center where prognostic modeling of patient survival data is of particular interest. Although we focus on a survival data application of penalized Cox models in this article, the functions in our R package are in general applicable to all types of regression models implemented in the glmnet package, with the exception of prediction error curves, which are specific to time-to-event data.

  12. The overlooked potential of Generalized Linear Models in astronomy-II: Gamma regression and photometric redshifts

    Science.gov (United States)

    Elliott, J.; de Souza, R. S.; Krone-Martins, A.; Cameron, E.; Ishida, E. E. O.; Hilbe, J.

    2015-04-01

    Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the underlying physical processes of the data. In this article, and the companion papers of this series, we present the set of Generalized Linear Models (GLMs) as a fast alternative method for tackling general astronomical problems, including the ones related to the machine learning paradigm. To demonstrate the applicability of GLMs to inherently positive and continuous physical observables, we explore their use in estimating the photometric redshifts of galaxies from their multi-wavelength photometry. Using the gamma family with a log link function we predict redshifts from the PHoto-z Accuracy Testing simulated catalogue and a subset of the Sloan Digital Sky Survey from Data Release 10. We obtain fits that result in catastrophic outlier rates as low as ∼1% for simulated and ∼2% for real data. Moreover, we can easily obtain such levels of precision within a matter of seconds on a normal desktop computer and with training sets that contain merely thousands of galaxies. Our software is made publicly available as a user-friendly package developed in Python, R and via an interactive web application. This software allows users to apply a set of GLMs to their own photometric catalogues and generates publication quality plots with minimum effort. By facilitating their ease of use to the astronomical community, this paper series aims to make GLMs widely known and to encourage their implementation in future large-scale projects, such as the Large Synoptic Survey Telescope.

  13. Linear algebra

    CERN Document Server

    Shilov, Georgi E

    1977-01-01

    Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

  14. Fast inference in generalized linear models via expected log-likelihoods.

    Science.gov (United States)

    Ramirez, Alexandro D; Paninski, Liam

    2014-04-01

    Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a sum that appears in the exact log-likelihood by an expectation over the model covariates; the resulting "expected log-likelihood" can in many cases be computed significantly faster than the exact log-likelihood. In many neuroscience experiments the distribution over model covariates is controlled by the experimenter and the expected log-likelihood approximation becomes particularly useful; for example, estimators based on maximizing this expected log-likelihood (or a penalized version thereof) can often be obtained with orders of magnitude computational savings compared to the exact maximum likelihood estimators. A risk analysis establishes that these maximum EL estimators often come with little cost in accuracy (and in some cases even improved accuracy) compared to standard maximum likelihood estimates. Finally, we find that these methods can significantly decrease the computation time of marginal likelihood calculations for model selection and of Markov chain Monte Carlo methods for sampling from the posterior parameter distribution. We illustrate our results by applying these methods to a computationally-challenging dataset of neural spike trains obtained via large-scale multi-electrode recordings in the primate retina.

  15. Setting a generalized functional linear model (GFLM for the classification of different types of cancer

    Directory of Open Access Journals (Sweden)

    Miguel Flores

    2016-11-01

    Full Text Available This work aims to classify the DNA sequences of healthy and malignant cancer respectively. For this, supervised and unsupervised classification methods from a functional context are used; i.e. each strand of DNA is an observation. The observations are discretized, for that reason different ways to represent these observations with functions are evaluated. In addition, an exploratory study is done: estimating the mean and variance of each functional type of cancer. For the unsupervised classification method, hierarchical clustering with different measures of functional distance is used. On the other hand, for the supervised classification method, a functional generalized linear model is used. For this model the first and second derivatives are used which are included as discriminating variables. It has been verified that one of the advantages of working in the functional context is to obtain a model to correctly classify cancers by 100%. For the implementation of the methods it has been used the fda.usc R package that includes all the techniques of functional data analysis used in this work. In addition, some that have been developed in recent decades. For more details of these techniques can be consulted Ramsay, J. O. and Silverman (2005 and Ferraty et al. (2006.

  16. Developing a methodology to predict PM10 concentrations in urban areas using generalized linear models.

    Science.gov (United States)

    Garcia, J M; Teodoro, F; Cerdeira, R; Coelho, L M R; Kumar, Prashant; Carvalho, M G

    2016-09-01

    A methodology to predict PM10 concentrations in urban outdoor environments is developed based on the generalized linear models (GLMs). The methodology is based on the relationship developed between atmospheric concentrations of air pollutants (i.e. CO, NO2, NOx, VOCs, SO2) and meteorological variables (i.e. ambient temperature, relative humidity (RH) and wind speed) for a city (Barreiro) of Portugal. The model uses air pollution and meteorological data from the Portuguese monitoring air quality station networks. The developed GLM considers PM10 concentrations as a dependent variable, and both the gaseous pollutants and meteorological variables as explanatory independent variables. A logarithmic link function was considered with a Poisson probability distribution. Particular attention was given to cases with air temperatures both below and above 25°C. The best performance for modelled results against the measured data was achieved for the model with values of air temperature above 25°C compared with the model considering all ranges of air temperatures and with the model considering only temperature below 25°C. The model was also tested with similar data from another Portuguese city, Oporto, and results found to behave similarly. It is concluded that this model and the methodology could be adopted for other cities to predict PM10 concentrations when these data are not available by measurements from air quality monitoring stations or other acquisition means.

  17. Statistical Methods for Quality Control of Steel Coils Manufacturing Process using Generalized Linear Models

    Science.gov (United States)

    García-Díaz, J. Carlos

    2009-11-01

    Fault detection and diagnosis is an important problem in process engineering. Process equipments are subject to malfunctions during operation. Galvanized steel is a value added product, furnishing effective performance by combining the corrosion resistance of zinc with the strength and formability of steel. Fault detection and diagnosis is an important problem in continuous hot dip galvanizing and the increasingly stringent quality requirements in automotive industry has also demanded ongoing efforts in process control to make the process more robust. When faults occur, they change the relationship among these observed variables. This work compares different statistical regression models proposed in the literature for estimating the quality of galvanized steel coils on the basis of short time histories. Data for 26 batches were available. Five variables were selected for monitoring the process: the steel strip velocity, four bath temperatures and bath level. The entire data consisting of 48 galvanized steel coils was divided into sets. The first training data set was 25 conforming coils and the second data set was 23 nonconforming coils. Logistic regression is a modeling tool in which the dependent variable is categorical. In most applications, the dependent variable is binary. The results show that the logistic generalized linear models do provide good estimates of quality coils and can be useful for quality control in manufacturing process.

  18. Determination of a Differential Item Functioning Procedure Using the Hierarchical Generalized Linear Model

    Directory of Open Access Journals (Sweden)

    Tülin Acar

    2012-01-01

    Full Text Available The aim of this research is to compare the result of the differential item functioning (DIF determining with hierarchical generalized linear model (HGLM technique and the results of the DIF determining with logistic regression (LR and item response theory–likelihood ratio (IRT-LR techniques on the test items. For this reason, first in this research, it is determined whether the students encounter DIF with HGLM, LR, and IRT-LR techniques according to socioeconomic status (SES, in the Turkish, Social Sciences, and Science subtest items of the Secondary School Institutions Examination. When inspecting the correlations among the techniques in terms of determining the items having DIF, it was discovered that there was significant correlation between the results of IRT-LR and LR techniques in all subtests; merely in Science subtest, the results of the correlation between HGLM and IRT-LR techniques were found significant. DIF applications can be made on test items with other DIF analysis techniques that were not taken to the scope of this research. The analysis results, which were determined by using the DIF techniques in different sample sizes, can be compared.

  19. The mesoscopic conductance of disordered rings, its random matrix theory and the generalized variable range hopping picture

    Energy Technology Data Exchange (ETDEWEB)

    Stotland, Alexander; Peer, Tal; Cohen, Doron [Department of Physics, Ben-Gurion University, Beer-Sheva 84005 (Israel); Budoyo, Rangga; Kottos, Tsampikos [Department of Physics, Wesleyan University, Middletown, CT 06459 (United States)

    2008-07-11

    The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming 'mesoscopic' circumstances the analysis of the electro-driven transitions shows similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to capture the essential ingredients of the problem, and leads to a generalized variable range hopping picture. (fast track communication)

  20. Least Squares Tridiagonal Solutions of A Series of Linear Matrix Equations with the Least Norm%一类线性矩阵方程的三对角极小范数最小二乘解

    Institute of Scientific and Technical Information of China (English)

    顾友付; 曾晓辉

    2012-01-01

    根据三对角矩阵的几何特征,利用矩阵的Kronecker积和Moore—Penrose广义逆,给出一类线性矩阵方程的三对角极小范数最小二乘解的表达式.此外,还给出求解该问题的算法和算例.%According to the geometrical characteristics of the Tridiagonal matrix, we derive the expressions of the least squares tridiagonal solutions of a series of linear matrix equations with the least norm by using Moore- Penrose generalized inverse and the Kronecker product of matrices. In addition, a numerical example is used to show the feasibility of the numerical method.

  1. Assessing the tangent linear behaviour of common tracer transport schemes and their use in a linearised atmospheric general circulation model

    Directory of Open Access Journals (Sweden)

    Daniel Holdaway

    2015-09-01

    Full Text Available The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5. All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have non-linear behaviour. The piecewise parabolic method (PPM with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

  2. Continuous dependence of solutions of abstract generalized linear differential equations with potential converging uniformly with a weight

    OpenAIRE

    Monteiro, G.; Tvrdý, M. (Milan)

    2014-01-01

    In this paper we continue our research on continuous dependence on a parameter of solutions to generalized linear differential equations. These equations are described by linear integral equations containing the abstract Kurzweil-Stieltjes integral. In particular, we are interested in the situation when the kernels of these equations need not have uniformly bounded variations. Our main goal is the extension of our previous results to the nonhomogeneous case. Applications to second order syste...

  3. The Relationship between Two Kinds of Generalized Convex Set-Valued Maps in Real Ordered Linear Spaces

    Directory of Open Access Journals (Sweden)

    Zhi-Ang Zhou

    2013-01-01

    Full Text Available A new notion of the ic-cone convexlike set-valued map characterized by the algebraic interior and the vector closure is introduced in real ordered linear spaces. The relationship between the ic-cone convexlike set-valued map and the nearly cone subconvexlike set-valued map is established. The results in this paper generalize some known results in the literature from locally convex spaces to linear spaces.

  4. CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

    Science.gov (United States)

    Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

    1988-11-01

    Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

  5. A NEW ALGORITHM SOLVING THE LINEAR EQUATION SYSTEM WITH BLOCK CYCLE COEFFICIENT MATRIX%块循环矩阵方程组的新算法

    Institute of Scientific and Technical Information of China (English)

    张耀明

    2001-01-01

    A kind of new partitioning algorithm that solves the linear equation system with block cycle coefficient matrix is presented in this paper. The original problem is partitioned into a series of independent subproblems. Compared with the original problem, the dimension of all these subproblems are vary small.This point ensures that it have a better conditioning and give smaller round-off errors. More importantly, the technique leads to a higher efficiency of computation.

  6. Predicting stem borer density in maize using RapidEye data and generalized linear models

    Science.gov (United States)

    Abdel-Rahman, Elfatih M.; Landmann, Tobias; Kyalo, Richard; Ong'amo, George; Mwalusepo, Sizah; Sulieman, Saad; Ru, Bruno Le

    2017-05-01

    Average maize yield in eastern Africa is 2.03 t ha-1 as compared to global average of 6.06 t ha-1 due to biotic and abiotic constraints. Amongst the biotic production constraints in Africa, stem borers are the most injurious. In eastern Africa, maize yield losses due to stem borers are currently estimated between 12% and 21% of the total production. The objective of the present study was to explore the possibility of RapidEye spectral data to assess stem borer larva densities in maize fields in two study sites in Kenya. RapidEye images were acquired for the Bomet (western Kenya) test site on the 9th of December 2014 and on 27th of January 2015, and for Machakos (eastern Kenya) a RapidEye image was acquired on the 3rd of January 2015. Five RapidEye spectral bands as well as 30 spectral vegetation indices (SVIs) were utilized to predict per field maize stem borer larva densities using generalized linear models (GLMs), assuming Poisson ('Po') and negative binomial ('NB') distributions. Root mean square error (RMSE) and ratio prediction to deviation (RPD) statistics were used to assess the models performance using a leave-one-out cross-validation approach. The Zero-inflated NB ('ZINB') models outperformed the 'NB' models and stem borer larva densities could only be predicted during the mid growing season in December and early January in both study sites, respectively (RMSE = 0.69-1.06 and RPD = 8.25-19.57). Overall, all models performed similar when all the 30 SVIs (non-nested) and only the significant (nested) SVIs were used. The models developed could improve decision making regarding controlling maize stem borers within integrated pest management (IPM) interventions.

  7. Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models.

    Science.gov (United States)

    Fan, Ruzong; Wang, Yifan; Chiu, Chi-Yang; Chen, Wei; Ren, Haobo; Li, Yun; Boehnke, Michael; Amos, Christopher I; Moore, Jason H; Xiong, Momiao

    2016-02-01

    We developed generalized functional linear models (GFLMs) to perform a meta-analysis of multiple case-control studies to evaluate the relationship of genetic data to dichotomous traits adjusting for covariates. Unlike the previously developed meta-analysis for sequence kernel association tests (MetaSKATs), which are based on mixed-effect models to make the contributions of major gene loci random, GFLMs are fixed models; i.e., genetic effects of multiple genetic variants are fixed. Based on GFLMs, we developed chi-squared-distributed Rao's efficient score test and likelihood-ratio test (LRT) statistics to test for an association between a complex dichotomous trait and multiple genetic variants. We then performed extensive simulations to evaluate the empirical type I error rates and power performance of the proposed tests. The Rao's efficient score test statistics of GFLMs are very conservative and have higher power than MetaSKATs when some causal variants are rare and some are common. When the causal variants are all rare [i.e., minor allele frequencies (MAF) analysis of eight European studies and detected significant association for 18 genes (P < 3.10 × 10(-6)), tentative association for 2 genes (HHEX and HMGA2; P ≈ 10(-5)), and no association for 2 genes, while MetaSKATs detected none. In addition, the traditional additive-effect model detects association at gene HHEX. GFLMs and related tests can analyze rare or common variants or a combination of the two and can be useful in whole-genome and whole-exome association studies.

  8. Generalized functional linear models for gene-based case-control association studies.

    Science.gov (United States)

    Fan, Ruzong; Wang, Yifan; Mills, James L; Carter, Tonia C; Lobach, Iryna; Wilson, Alexander F; Bailey-Wilson, Joan E; Weeks, Daniel E; Xiong, Momiao

    2014-11-01

    By using functional data analysis techniques, we developed generalized functional linear models for testing association between a dichotomous trait and multiple genetic variants in a genetic region while adjusting for covariates. Both fixed and mixed effect models are developed and compared. Extensive simulations show that Rao's efficient score tests of the fixed effect models are very conservative since they generate lower type I errors than nominal levels, and global tests of the mixed effect models generate accurate type I errors. Furthermore, we found that the Rao's efficient score test statistics of the fixed effect models have higher power than the sequence kernel association test (SKAT) and its optimal unified version (SKAT-O) in most cases when the causal variants are both rare and common. When the causal variants are all rare (i.e., minor allele frequencies less than 0.03), the Rao's efficient score test statistics and the global tests have similar or slightly lower power than SKAT and SKAT-O. In practice, it is not known whether rare variants or common variants in a gene region are disease related. All we can assume is that a combination of rare and common variants influences disease susceptibility. Thus, the improved performance of our models when the causal variants are both rare and common shows that the proposed models can be very useful in dissecting complex traits. We compare the performance of our methods with SKAT and SKAT-O on real neural tube defects and Hirschsprung's disease datasets. The Rao's efficient score test statistics and the global tests are more sensitive than SKAT and SKAT-O in the real data analysis. Our methods can be used in either gene-disease genome-wide/exome-wide association studies or candidate gene analyses.

  9. Deriving robust and globalized robust solutions of uncertain linear programs having general convex uncertainty sets

    NARCIS (Netherlands)

    Gorissen, B.L.; Blanc, J.P.C.; den Hertog, D.; Ben-Tal, A.

    We propose a new way to derive tractable robust counterparts of a linear program based on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First we obtain a new convex reformulation of the dual problem of a robust linear program, and then show how to construct

  10. General Electric Company proposed demonstration Projects Matrix, commercial buildings, National Solar Demonstration Program

    Energy Technology Data Exchange (ETDEWEB)

    None

    1976-04-01

    The requirements for selecting commercial demonstrations are derived from the overall goal of the Federal program as stated in the ''National Program for Solar Heating and Cooling,'' ERDA 23-A, October 1975. This goal is to stimulate an industrial and commercial capability for producing and distributing solar heating and cooling (SHAC) systems. The development of the demonstration matrix consists of establishing selection criteria and developing a methodology for applying and evaluating these criteria. The output of this procedure results in a time phased matrix of location, SHAC systems, and building types which comprise the recommended National Solar Demonstration projects for commercial buildings. The Demonstration Matrix Definition is comprised of three principle elements: Demonstration identification; Specific Demonstration selection criteria; and Architect/Engineer (A/E) selection. (WDM)

  11. COVAR: Computer Program for Multifactor Relative Risks and Tests of Hypotheses Using a Variance-Covariance Matrix from Linear and Log-Linear Regression

    Directory of Open Access Journals (Sweden)

    Leif E. Peterson

    1997-11-01

    Full Text Available A computer program for multifactor relative risks, confidence limits, and tests of hypotheses using regression coefficients and a variance-covariance matrix obtained from a previous additive or multiplicative regression analysis is described in detail. Data used by the program can be stored and input from an external disk-file or entered via the keyboard. The output contains a list of the input data, point estimates of single or joint effects, confidence intervals and tests of hypotheses based on a minimum modified chi-square statistic. Availability of the program is also discussed.

  12. Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

    Science.gov (United States)

    Holdaway, Daniel; Kent, James

    2015-01-01

    The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

  13. Assessing the Tangent Linear Behaviour of Common Tracer Transport Schemes and Their Use in a Linearised Atmospheric General Circulation Model

    Science.gov (United States)

    Holdaway, Daniel; Kent, James

    2015-01-01

    The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.

  14. Generalization of the Mulliken-Hush treatment for the calculation of electron transfer matrix elements

    Science.gov (United States)

    Cave, Robert J.; Newton, Marshall D.

    1996-01-01

    A new method for the calculation of the electronic coupling matrix element for electron transfer processes is introduced and results for several systems are presented. The method can be applied to ground and excited state systems and can be used in cases where several states interact strongly. Within the set of states chosen it is a non-perturbative treatment, and can be implemented using quantities obtained solely in terms of the adiabatic states. Several applications based on quantum chemical calculations are briefly presented. Finally, since quantities for adiabatic states are the only input to the method, it can also be used with purely experimental data to estimate electron transfer matrix elements.

  15. Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

    Institute of Scientific and Technical Information of China (English)

    Dai Hao; Jia Li-Xin; Zhang Yan-Bin

    2012-01-01

    The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper.Based on Lyapunov stability theory and Barbalat's lemma,generalized matrix projective lag synchronization criteria are derived by using the adaptive control method.Furthermore,each network can be undirected or directed,connected or disconnected,and nodes in either network may have identical or different dynamics.The proposed strategy is applicable to almost all kinds of complex networks.In addition,numerical simulation results are presented to illustrate the effectiveness of this method,showing that the synchronization speed is sensitively influenced by the adaptive law strength,the network size,and the network topological structure.

  16. Documenting organisational development in general practice using a group-based assessment method: the Maturity Matrix.

    NARCIS (Netherlands)

    Eriksson, T.; Siersma, V.D.; Logstrup, L.; Buch, M.S.; Elwyn, G.; Edwards, A.

    2010-01-01

    OBJECTIVE: The Maturity Matrix (MM) comprises a formative evaluation instrument for primary care practices to self-assess their degree of organisational development in a group setting, guided by an external facilitator. The practice teams discuss organisational development, score their own performan

  17. Density Matrix and Squeezed Vacuum State for General Coupling Harmonic Oscillator

    Institute of Scientific and Technical Information of China (English)

    SONG Tong-Qiang

    2003-01-01

    By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordinate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.

  18. Direct formulation to Cholesky decomposition of a general nonsingular correlation matrix1

    Science.gov (United States)

    Madar, Vered

    2015-01-01

    We present two novel and explicit parametrizations of Cholesky factor of a nonsingular correlation matrix. One that uses semi-partial correlation coefficients, and a second that utilizes differences between the successive ratios of two determinants. To each, we offer a useful application. PMID:26052169

  19. GENERALIZED PRECONDITIONED HERMITIAN AND SKEW-HERMITIAN SPLITTING METHODS FOR NON-HERMITIAN POSITIVE-DEFINITE LINEAR SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    Junfeng Yin; Quanyu Dou

    2012-01-01

    In this paper,a generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) iteration method for a non-Hermitian positive-definite matrix is studied,which covers standard Hermitian and skew-Hermitian splitting (HSS) iteration and also many existing variants.Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix.From practical point of view,we have analyzed and implemented inexact generalized preconditioned Hermitian and skew-Hermitian splitting (IGPHSS) iteration,which employs Krylov subspace methods as its inner processes.Numerical experiments from three-dimensional convection-diffusion equation show that the GPHSS and IGPHSS iterations are efficient and competitive with standard HSS iteration and AHSS iteration.

  20. High Order A-stable Continuous General Linear Methods for Solution of Systems of Initial Value Problems in ODEs

    Directory of Open Access Journals (Sweden)

    Dauda GuliburYAKUBU

    2012-12-01

    Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.