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Sample records for optimal preconditioned eigenvalue

  1. Preconditioned iterations to calculate extreme eigenvalues

    Brand, C.W.; Petrova, S. [Institut fuer Angewandte Mathematik, Leoben (Austria)

    1994-12-31

    Common iterative algorithms to calculate a few extreme eigenvalues of a large, sparse matrix are Lanczos methods or power iterations. They converge at a rate proportional to the separation of the extreme eigenvalues from the rest of the spectrum. Appropriate preconditioning improves the separation of the eigenvalues. Davidson`s method and its generalizations exploit this fact. The authors examine a preconditioned iteration that resembles a truncated version of Davidson`s method with a different preconditioning strategy.

  2. Preconditioned Krylov subspace methods for eigenvalue problems

    Wu, Kesheng; Saad, Y.; Stathopoulos, A. [Univ. of Minnesota, Minneapolis, MN (United States)

    1996-12-31

    Lanczos algorithm is a commonly used method for finding a few extreme eigenvalues of symmetric matrices. It is effective if the wanted eigenvalues have large relative separations. If separations are small, several alternatives are often used, including the shift-invert Lanczos method, the preconditioned Lanczos method, and Davidson method. The shift-invert Lanczos method requires direct factorization of the matrix, which is often impractical if the matrix is large. In these cases preconditioned schemes are preferred. Many applications require solution of hundreds or thousands of eigenvalues of large sparse matrices, which pose serious challenges for both iterative eigenvalue solver and preconditioner. In this paper we will explore several preconditioned eigenvalue solvers and identify the ones suited for finding large number of eigenvalues. Methods discussed in this paper make up the core of a preconditioned eigenvalue toolkit under construction.

  3. A subspace preconditioning algorithm for eigenvector/eigenvalue computation

    Bramble, J.H.; Knyazev, A.V.; Pasciak, J.E.

    1996-12-31

    We consider the problem of computing a modest number of the smallest eigenvalues along with orthogonal bases for the corresponding eigen-spaces of a symmetric positive definite matrix. In our applications, the dimension of a matrix is large and the cost of its inverting is prohibitive. In this paper, we shall develop an effective parallelizable technique for computing these eigenvalues and eigenvectors utilizing subspace iteration and preconditioning. Estimates will be provided which show that the preconditioned method converges linearly and uniformly in the matrix dimension when used with a uniform preconditioner under the assumption that the approximating subspace is close enough to the span of desired eigenvectors.

  4. An Optimal Lower Eigenvalue System

    Yingfan Liu

    2011-01-01

    Full Text Available An optimal lower eigenvalue system is studied, and main theorems including a series of necessary and suffcient conditions concerning existence and a Lipschitz continuity result concerning stability are obtained. As applications, solvability results to some von-Neumann-type input-output inequalities, growth, and optimal growth factors, as well as Leontief-type balanced and optimal balanced growth paths, are also gotten.

  5. Perturbation of eigenvalues of preconditioned Navier-Stokes operators

    Elman, H.C. [Univ. of Maryland, College Park, MD (United States)

    1996-12-31

    We study the sensitivity of algebraic eigenvalue problems associated with matrices arising from linearization and discretization of the steady-state Navier-Stokes equations. In particular, for several choices of preconditioners applied to the system of discrete equations, we derive upper bounds on perturbations of eigenvalues as functions of the viscosity and discretization mesh size. The bounds suggest that the sensitivity of the eigenvalues is at worst linear in the inverse of the viscosity and quadratic in the inverse of the mesh size, and that scaling can be used to decrease the sensitivity in some cases. Experimental results supplement these results and confirm the relatively mild dependence on viscosity. They also indicate a dependence on the mesh size of magnitude smaller than the analysis suggests.

  6. Frequency response as a surrogate eigenvalue problem in topology optimization

    Andreassen, Erik; Ferrari, Federico; Sigmund, Ole

    2018-01-01

    This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...

  7. Maximal imaginery eigenvalues in optimal systems

    David Di Ruscio

    1991-07-01

    Full Text Available In this note we present equations that uniquely determine the maximum possible imaginary value of the closed loop eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen, provided a real symmetric solution of the algebraic Riccati equation exists. In addition, the corresponding state weight matrix and the solution to the algebraic Riccati equation are derived for a class of linear systems. A fundamental lemma for the existence of a real symmetric solution to the algebraic Riccati equation is derived for this class of linear systems.

  8. A parallel additive Schwarz preconditioned Jacobi-Davidson algorithm for polynomial eigenvalue problems in quantum dot simulation

    Hwang, F-N; Wei, Z-H; Huang, T-M; Wang Weichung

    2010-01-01

    We develop a parallel Jacobi-Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi-Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc's efficient and various parallel operations, linear solvers, preconditioning schemes, and easy usages. The parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by Schroedinger's equations. We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi-Davidson algorithm, very efficiently in parallel. Besides, the overall performance is quite satisfactory. We have observed near perfect superlinear speedup by using up to 320 processors. The parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 Intel 3.0 GHz processors.

  9. Maximization of eigenvalues using topology optimization

    Pedersen, Niels Leergaard

    2000-01-01

    to localized modes in low density areas. The topology optimization problem is formulated using the SIMP method. Special attention is paid to a numerical method for removing localized eigenmodes in low density areas. The method is applied to numerical examples of maximizing the first eigenfrequency, One example...

  10. On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

    Pestana, Jennifer

    2014-01-01

    Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related. © 2014 Society for Industrial and Applied Mathematics.

  11. New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems

    Al-Bayati, A.; Al-Asadi, N.

    1997-01-01

    This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab

  12. Constraint interface preconditioning for topology optimization problems

    Kočvara, Michal; Loghin, D.; Turner, J.

    2016-01-01

    Roč. 38, č. 1 (2016), A128-A145 ISSN 1064-8275 R&D Projects: GA AV ČR IAA100750802 Grant - others:European Commission - EC(XE) 313781 Institutional support: RVO:67985556 Keywords : topology optimization * domain decomposition * Newton-Krylov Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/kocvara-0460325.pdf

  13. Aerodynamic shape optimization using preconditioned conjugate gradient methods

    Burgreen, Greg W.; Baysal, Oktay

    1993-01-01

    In an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures, a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure. It is demonstrated that preconditioned conjugate gradient-like methodologies dramatically decrease the computational efforts required for such procedures. The design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric (NACA-012) airfoil in inviscid transonic flow and at zero degree angle-of-attack. The complete surface shape is represented using a Bezier-Bernstein polynomial. The present optimization method then automatically obtains supercritical airfoil shapes over a variety of freestream Mach numbers. Furthermore, the best optimization strategy examined resulted in a factor of 8 decrease in computational time as well as a factor of 4 decrease in memory over the most efficient strategies in current use.

  14. Preconditioning of matrices partitioned in 2 x 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM

    Axelsson, Owe; Blaheta, Radim

    2010-01-01

    Roč. 17, č. 5 (2010), s. 787-810 ISSN 1070-5325 R&D Projects: GA ČR GA105/09/1830 Institutional research plan: CEZ:AV0Z30860518 Keywords : iterative solution methods * saddle point problems * preconditioning block matrices * domain decomposition * heterogeneous problems * regularization Subject RIV: JC - Computer Hardware ; Software Impact factor: 1.163, year: 2010 http://onlinelibrary.wiley.com/doi/10.1002/nla.v17:5/issuetoc

  15. Some remarks on the optimization of eigenvalue problems involving the p-Laplacian

    Wacław Pielichowski

    2008-01-01

    Full Text Available Given a bounded domain \\(\\Omega \\subset \\mathbb{R}^n\\, numbers \\(p \\gt 1\\, \\(\\alpha \\geq 0\\ and \\(A \\in [0,|\\Omega |]\\, consider the optimization problem: find a subset \\(D \\subset \\Omega \\, of measure \\(A\\, for which the first eigenvalue of the operator \\(u\\mapsto -\\text{div} (|\

  16. A multilevel, level-set method for optimizing eigenvalues in shape design problems

    Haber, E.

    2004-01-01

    In this paper, we consider optimal design problems that involve shape optimization. The goal is to determine the shape of a certain structure such that it is either as rigid or as soft as possible. To achieve this goal we combine two new ideas for an efficient solution of the problem. First, we replace the eigenvalue problem with an approximation by using inverse iteration. Second, we use a level set method but rather than propagating the front we use constrained optimization methods combined with multilevel continuation techniques. Combining these two ideas we obtain a robust and rapid method for the solution of the optimal design problem

  17. A Preconditioning Technique for First-Order Primal-Dual Splitting Method in Convex Optimization

    Meng Wen

    2017-01-01

    Full Text Available We introduce a preconditioning technique for the first-order primal-dual splitting method. The primal-dual splitting method offers a very general framework for solving a large class of optimization problems arising in image processing. The key idea of the preconditioning technique is that the constant iterative parameters are updated self-adaptively in the iteration process. We also give a simple and easy way to choose the diagonal preconditioners while the convergence of the iterative algorithm is maintained. The efficiency of the proposed method is demonstrated on an image denoising problem. Numerical results show that the preconditioned iterative algorithm performs better than the original one.

  18. A Schur Method for Designing LQ-optimal Systems with Prescribed Eigenvalues

    David Di Ruscio

    1990-01-01

    Full Text Available In this paper a new algorithm for solving the LQ-optimal pole placement problem is presented. The method studied is a variant of the classical eigenvector approach and instead uses a set of Schur vectors, thereby gaining substantial numerical advantages. An important task in this method is the LQ-optimal pole placement problem for a second order (sub system. The paper presents a detailed analytical solution to this problem. This part is not only important for solving the general n-dimensional problem but also provides an understanding of the behaviour of an optimal system: The paper shows that in some cases it is an infinite number; in others a finite number, and in still others, non state weighting matrices Q that give the system a set of prescribed eigenvalues. Equations are presented that uniquely determine these state weight matrices as a function of the new prescribed eigcnvalues. From this result we have been able to derive the maximum possible imaginary part of the eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen.

  19. Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

    Axelsson, Owe; Farouq, S.; Neytcheva, M.

    2017-01-01

    Roč. 74, č. 1 (2017), s. 19-37 ISSN 1017-1398 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution method s * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

  20. Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems

    Axelsson, Owe; Farouq, S.; Neytcheva, M.

    2017-01-01

    Roč. 74, č. 1 (2017), s. 19-37 ISSN 1017-1398 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods * preconditioning Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.241, year: 2016 https://link.springer.com/article/10.1007%2Fs11075-016-0136-5

  1. Highly indefinite multigrid for eigenvalue problems

    Borges, L.; Oliveira, S.

    1996-12-31

    Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.

  2. Response to Comment on Preconditioning of matrices partitioned in 2 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM

    Axelsson, Owe; Blaheta, Radim

    2013-01-01

    Roč. 20, č. 3 (2013), s. 536-539 ISSN 1070-5325 Institutional support: RVO:68145535 Keywords : saddle point matrices * inverses * preconditioning Subject RIV: BA - General Mathematics Impact factor: 1.424, year: 2013 http://onlinelibrary.wiley.com/doi/10.1002/nla.816/pdf

  3. Preconditioning for partial differential equation constrained optimization with control constraints

    Stoll, Martin; Wathen, Andy

    2011-01-01

    Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

  4. Preconditioning for partial differential equation constrained optimization with control constraints

    Stoll, Martin

    2011-10-18

    Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

  5. Transmission eigenvalues

    Cakoni, Fioralba; Haddar, Houssem

    2013-10-01

    In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission

  6. Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm.

    Vogel, Curtis R; Yang, Qiang

    2006-08-21

    We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.

  7. Eigenvalue-eigenvector decomposition (EED) analysis of dissimilarity and covariance matrix obtained from total synchronous fluorescence spectral (TSFS) data sets of herbal preparations: Optimizing the classification approach

    Tarai, Madhumita; Kumar, Keshav; Divya, O.; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar

    2017-09-01

    The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix.

  8. Eigenvalue-eigenvector decomposition (EED) analysis of dissimilarity and covariance matrix obtained from total synchronous fluorescence spectral (TSFS) data sets of herbal preparations: Optimizing the classification approach.

    Tarai, Madhumita; Kumar, Keshav; Divya, O; Bairi, Partha; Mishra, Kishor Kumar; Mishra, Ashok Kumar

    2017-09-05

    The present work compares the dissimilarity and covariance based unsupervised chemometric classification approaches by taking the total synchronous fluorescence spectroscopy data sets acquired for the cumin and non-cumin based herbal preparations. The conventional decomposition method involves eigenvalue-eigenvector analysis of the covariance of the data set and finds the factors that can explain the overall major sources of variation present in the data set. The conventional approach does this irrespective of the fact that the samples belong to intrinsically different groups and hence leads to poor class separation. The present work shows that classification of such samples can be optimized by performing the eigenvalue-eigenvector decomposition on the pair-wise dissimilarity matrix. Copyright © 2017 Elsevier B.V. All rights reserved.

  9. A fast, preconditioned conjugate gradient Toeplitz solver

    Pan, Victor; Schrieber, Robert

    1989-01-01

    A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

  10. Modern algorithms for large sparse eigenvalue problems

    Meyer, A.

    1987-01-01

    The volume is written for mathematicians interested in (numerical) linear algebra and in the solution of large sparse eigenvalue problems, as well as for specialists in engineering, who use the considered algorithms in the investigation of eigenoscillations of structures, in reactor physics, etc. Some variants of the algorithms based on the idea of a gradient-type direction of movement are presented and their convergence properties are discussed. From this, a general strategy for the direct use of preconditionings for the eigenvalue problem is derived. In this new approach the necessity of the solution of large linear systems is entirely avoided. Hence, these methods represent a new alternative to some other modern eigenvalue algorithms, as they show a slightly slower convergence on the one hand but essentially lower numerical and data processing problems on the other hand. A brief description and comparison of some well-known methods (i.e. simultaneous iteration, Lanczos algorithm) completes this volume. (author)

  11. Formation of the Optimal Investment Portfolio as a Precondition for the Bank’s Financial Security

    Anna Shapovalova

    2015-01-01

    Full Text Available This article analyses the definition of the bank’s financial security and investment activities. It describes a few types of models of bank’s risks management and the method CAPM, which is chosen for use. In support for the chosen CAPM method, we included the mathematical model that allows elaborating an optimal investment portfolio. The model stands at the basis of this method and a case study of one of Ukrainian banks.

  12. Formation of the Optimal Investment Portfolio as a Precondition for the Bank’s Financial Security

    Anna Shapovalova

    2016-01-01

    Full Text Available This article analyses the definition of the bank’s financial security and investment activities. It describes a few types of models of bank’s risks management and the method CAPM, which is chosen for use. In support for the chosen CAPM method, we included the mathematical model that allows elaborating an optimal investment portfolio. The model stands at the basis of this method and a case study of one of Ukrainian banks.

  13. Kronecker Products on Preconditioning

    Gao, Longfei

    2013-08-01

    Numerical techniques for linear systems arising from discretization of partial differential equations are nowadays essential for understanding the physical world. Among these techniques, iterative methods and the accompanying preconditioning techniques have become increasingly popular due to their great potential on large scale computation. In this work, we present preconditioning techniques for linear systems built with tensor product basis functions. Efficient algorithms are designed for various problems by exploiting the Kronecker product structure in the matrices, inherited from tensor product basis functions. Specifically, we design preconditioners for mass matrices to remove the complexity from the basis functions used in isogeometric analysis, obtaining numerical performance independent of mesh size, polynomial order and continuity order; we also present a compound iteration preconditioner for stiffness matrices in two dimensions, obtaining fast convergence speed; lastly, for the Helmholtz problem, we present a strategy to `hide\\' its indefiniteness from Krylov subspace methods by eliminating the part of initial error that corresponds to those negative generalized eigenvalues. For all three cases, the Kronecker product structure in the matrices is exploited to achieve high computational efficiency.

  14. Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

    Vecharynski, Eugene [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Brabec, Jiri [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Shao, Meiyue [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Govind, Niranjan [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab.; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division

    2017-12-01

    We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.

  15. Investigation, development and application of optimal output feedback theory. Vol. 4: Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics

    Halyo, Nesim

    1987-01-01

    Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.

  16. Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

    Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

    2018-01-01

    An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

  17. Covariance expressions for eigenvalue and eigenvector problems

    Liounis, Andrew J.

    There are a number of important scientific and engineering problems whose solutions take the form of an eigenvalue--eigenvector problem. Some notable examples include solutions to linear systems of ordinary differential equations, controllability of linear systems, finite element analysis, chemical kinetics, fitting ellipses to noisy data, and optimal estimation of attitude from unit vectors. In many of these problems, having knowledge of the eigenvalue and eigenvector Jacobians is either necessary or is nearly as important as having the solution itself. For instance, Jacobians are necessary to find the uncertainty in a computed eigenvalue or eigenvector estimate. This uncertainty, which is usually represented as a covariance matrix, has been well studied for problems similar to the eigenvalue and eigenvector problem, such as singular value decomposition. There has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue-eigenvector problem. In this thesis we develop two general expressions for the Jacobians of eigenvalues and eigenvectors with respect to the elements of their parent matrix. The expressions developed make use of only the parent matrix and the eigenvalue and eigenvector pair under consideration. In addition, they are applicable to any general matrix (including complex valued matrices, eigenvalues, and eigenvectors) as long as the eigenvalues are simple. Alongside this, we develop expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue-eigenvector problem given the uncertainty of the terms of the matrix. The Jacobian expressions developed are numerically validated with forward finite, differencing and the covariance expressions are validated using Monte Carlo analysis. Finally, the results from this work are used to determine covariance expressions for a variety of estimation problem examples and are also applied to the design of a dynamical system.

  18. Colpitts, Eigenvalues and Chaos

    Lindberg, Erik

    1997-01-01

    It is possible to obtain insight in the chaotic nature of a nonlinear oscillator by means of a study of the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator. The movements of the eigenvalues as functions of time are found. The instantaneous power in t...

  19. Natural Preconditioning and Iterative Methods for Saddle Point Systems

    Pestana, Jennifer

    2015-01-01

    © 2015 Society for Industrial and Applied Mathematics. The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness - in terms of rapidity of convergence - is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.

  20. The BR eigenvalue algorithm

    Geist, G.A. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.; Howell, G.W. [Florida Inst. of Tech., Melbourne, FL (United States). Dept. of Applied Mathematics; Watkins, D.S. [Washington State Univ., Pullman, WA (United States). Dept. of Pure and Applied Mathematics

    1997-11-01

    The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrowband, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30--60 in computing time and a factor of over 100 in matrix storage space.

  1. The Schrodinger Eigenvalue March

    Tannous, C.; Langlois, J.

    2011-01-01

    A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…

  2. On Selberg's small eigenvalue conjecture and residual eigenvalues

    Risager, Morten S.

    2011-01-01

    We show that Selberg’s eigenvalue conjecture concerning small eigenvalues of the automorphic Laplacian for congruence groups is equivalent to a conjecture about the non-existence of residual eigenvalues for a perturbed system. We prove this using a combination of methods from asymptotic perturbat...

  3. Eigenvalues and expansion of bipartite graphs

    Høholdt, Tom; Janwa, Heeralal

    2012-01-01

    We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes that are optimal with respect to the bouns. We prove that BIBD-graphs are characterized by ...

  4. Oscillators and Eigenvalues

    Lindberg, Erik

    1997-01-01

    In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....

  5. Body measurements and the variability of sitting postures at preschool age as preconditions for an optimal adjustment of chairs and tables.

    Voigt, Andrea; Greil, Holle

    2009-03-01

    Preschool age is a biological stage of intensive longitudinal growth with high plasticity of the growing body and of body postures. It is the period where children learn to persist in a sitting posture for a longer time and to use furniture like chairs or other body supporting systems. The growing body shows a special sensitivity for the manifestation of inappropriate postures. In this study the development of body measurements and sitting behaviour of preschool age children is investigated as a precondition for an optimal adjustment of seats and desks to the growing body. Accordingly to the instructions of Knussmann (1988) and Jiirgens (1988) 6 body measurements were taken from 122 German children aged 3 to 7 years from Potsdam, Province Brandenburg. Additionally, every child was videotaped for 10 minutes while crayoning in a sitting position of its own choice using a chair and a desk. To analyse the tapes, the software Noldus Observer was used and examined, picture by picture, to define the different types of sitting postures as well as the duration of persistence in a posture and the number of changes of postures. The used chairs and desks were also measured. Furthermore, the data of the furniture guideline DIN ISO 5970 (DIN, 1981), which regulates the dimensions of furniture for sitting in educational institutions, were compared with the results of the body measurements and with the dimensions of the furniture used by the children.

  6. Fourier analysis of finite element preconditioned collocation schemes

    Deville, Michel O.; Mund, Ernest H.

    1990-01-01

    The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

  7. Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems - Poisson and convection-diffusion control

    Axelsson, Owe; Farouq, S.; Neytcheva, M.

    2016-01-01

    Roč. 73, č. 3 (2016), s. 631-633 ISSN 1017-1398 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : PDE-constrained optimization problems * finite elements * iterative solution methods Subject RIV: BA - General Mathematics Impact factor: 1.241, year: 2016 http://link.springer.com/article/10.1007%2Fs11075-016-0111-1

  8. Sturm--Liouville eigenvalue problem

    Bailey, P.B.

    1977-01-01

    The viewpoint is taken that Sturn--Liouville problem is specified and the problem of computing one or more of the eigenvalues and possibly the corresponding eigenfunctions is presented for solution. The procedure follows the construction of a computer code, although such a code is not constructed, intended to solve Sturn--Liouville eigenvalue problems whether singular or nonsingular

  9. A Bootstrap Approach to Eigenvalue Correction

    Hendrikse, A.J.; Spreeuwers, Lieuwe Jan; Veldhuis, Raymond N.J.

    2009-01-01

    Eigenvalue analysis is an important aspect in many data modeling methods. Unfortunately, the eigenvalues of the sample covariance matrix (sample eigenvalues) are biased estimates of the eigenvalues of the covariance matrix of the data generating process (population eigenvalues). We present a new

  10. Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

    Wu, Sheng-Jhih; Chu, Moody T.

    2017-08-01

    An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

  11. Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

    Wu, Sheng-Jhih; Chu, Moody T

    2017-01-01

    An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing–Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations. (paper)

  12. A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

    Vecharynski, Eugene; Yang, Chao; Pask, John E.

    2015-01-01

    We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer

  13. Tensor eigenvalues and their applications

    Qi, Liqun; Chen, Yannan

    2018-01-01

    This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

  14. Kronecker Products on Preconditioning

    Gao, Longfei

    2013-01-01

    techniques have become increasingly popular due to their great potential on large scale computation. In this work, we present preconditioning techniques for linear systems built with tensor product basis functions. Efficient algorithms are designed

  15. Parallel Symmetric Eigenvalue Problem Solvers

    2015-05-01

    Research” and the use of copyright material. Approved by Major Professor(s): Approved by: Head of the Departmental Graduate Program Date Alicia Marie... matrix . . . . . . . . . . . . . . . . . 106 8.15 Sparsity patterns for the Nastran benchmark of order 1.5 million . . . . 108 8.16 Sparsity patterns...magnitude eigenvalues of a given matrix pencil (A,B) along with their associated eigenvectors. Computing the smallest eigenvalues is more difficult

  16. On the use of rigid body modes in the deflated preconditioned conjugate gradient method

    Jönsthövel, T.B.; Van Gijzen, M.B.; Vuik, C.; Scarpas, A.

    2011-01-01

    Large discontinuities in material properties, such as encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the Preconditioned

  17. Implementation of a direct procedure for critical point computations using preconditioned iterative solvers

    Kouhia, R.; Tůma, Miroslav; Mäkinen, J.; Fedoroff, A.; Marjamäki, H.

    108-109, October (2012), s. 110-117 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GAP108/11/0853 Institutional research plan: CEZ:AV0Z10300504 Keywords : non-linear eigenvalue problem * equilibrium equations * critical points * preconditioned iterations Subject RIV: BA - General Mathematics Impact factor: 1.509, year: 2012

  18. Minimal residual method stronger than polynomial preconditioning

    Faber, V.; Joubert, W.; Knill, E. [Los Alamos National Lab., NM (United States)] [and others

    1994-12-31

    Two popular methods for solving symmetric and nonsymmetric systems of equations are the minimal residual method, implemented by algorithms such as GMRES, and polynomial preconditioning methods. In this study results are given on the convergence rates of these methods for various classes of matrices. It is shown that for some matrices, such as normal matrices, the convergence rates for GMRES and for the optimal polynomial preconditioning are the same, and for other matrices such as the upper triangular Toeplitz matrices, it is at least assured that if one method converges then the other must converge. On the other hand, it is shown that matrices exist for which restarted GMRES always converges but any polynomial preconditioning of corresponding degree makes no progress toward the solution for some initial error. The implications of these results for these and other iterative methods are discussed.

  19. Perturbation Theory of Embedded Eigenvalues

    Engelmann, Matthias

    project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...

  20. Eigenvalue treatment of cosmological models

    Novello, M.; Soares, D.

    1976-08-01

    From the decomposition of Weyl tensor into its electric and magnetic parts, it is formulated the eigenvalue problem for cosmological models, and is used quasi-maxwellian form of Einstein's equation to propagate it along a time-like congruence. Three related theorems are presented

  1. Generalized eigenvalue based spectrum sensing

    Shakir, Muhammad

    2012-01-01

    Spectrum sensing is one of the fundamental components in cognitive radio networks. In this chapter, a generalized spectrum sensing framework which is referred to as Generalized Mean Detector (GMD) has been introduced. In this context, we generalize the detectors based on the eigenvalues of the received signal covariance matrix and transform the eigenvalue based spectrum sensing detectors namely: (i) the Eigenvalue Ratio Detector (ERD) and two newly proposed detectors which are referred to as (ii) the GEometric Mean Detector (GEMD) and (iii) the ARithmetic Mean Detector (ARMD) into an unified framework of generalize spectrum sensing. The foundation of the proposed framework is based on the calculation of exact analytical moments of the random variables of the decision threshold of the respective detectors. The decision threshold has been calculated in a closed form which is based on the approximation of Cumulative Distribution Functions (CDFs) of the respective test statistics. In this context, we exchange the analytical moments of the two random variables of the respective test statistics with the moments of the Gaussian (or Gamma) distribution function. The performance of the eigenvalue based detectors is compared with the several traditional detectors including the energy detector (ED) to validate the importance of the eigenvalue based detectors and the performance of the GEMD and the ARMD particularly in realistic wireless cognitive radio network. Analytical and simulation results show that the newly proposed detectors yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, the presented results based on proposed approximation approaches are in perfect agreement with the empirical results. © 2012 Springer Science+Business Media Dordrecht.

  2. The multigrid preconditioned conjugate gradient method

    Tatebe, Osamu

    1993-01-01

    A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.

  3. Eigenvalue pinching on spinc manifolds

    Roos, Saskia

    2017-02-01

    We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.

  4. The nonconforming virtual element method for eigenvalue problems

    Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications

    2018-02-05

    We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L2-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

  5. Incomplete block factorization preconditioning for indefinite elliptic problems

    Guo, Chun-Hua [Univ. of Calgary, Alberta (Canada)

    1996-12-31

    The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.

  6. Scientific computing vol II - eigenvalues and optimization

    Trangenstein, John A

    2017-01-01

    This is the second of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses more advanced topics than volume one, and is largely not a prerequisite for volume three. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 49 examples, 110 exercises, 66 algorithms, 24 interactive JavaScript programs, 77 references to software programs and 1 case study. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduate...

  7. Eigenvalue distributions of Wilson loops

    Lohmayer, Robert

    2010-01-01

    In the first part of this thesis, we focus on the distribution of the eigenvalues of the unitary Wilson loop matrix in the two-dimensional case at arbitrary finite N. To characterize the distribution of the eigenvalues, we introduce three density functions (the ''symmetric'', the ''antisymmetric'', and the ''true'' eigenvalue density) which differ at finite N but possess the same infinite-N limit, exhibiting the Durhuus-Olesen phase transition. Using expansions of determinants and inverse determinants in characters of totally symmetric or totally antisymmetric representations of SU(N), the densities at finite N can be expressed in terms of simple sums involving only dimensions and quadratic Casimir invariants of certain irreducible representations of SU(N), allowing for a numerical computation of the densities at arbitrary N to any desired accuracy. We find that the true eigenvalue density, adding N oscillations to the monotonic symmetric density, is in some sense intermediate between the symmetric and the antisymmetric density, which in turn is given by a sum of N delta peaks located at the zeros of the average of the characteristic polynomial. Furthermore, we show that the dependence on N can be made explicit by deriving integral representations for the resolvents associated to the three eigenvalue densities. Using saddle-point approximations, we confirm that all three densities reduce to the Durhuus-Olesen result in the infinite-N limit. In the second part, we study an exponential form of the multiplicative random complex matrix model introduced by Gudowska-Nowak et al. Varying a parameter which can be identified with the area of the Wilson loop in the unitary case, the region of non-vanishing eigenvalue density of the N-dimensional complex product matrix undergoes a topological change at a transition point in the infinite-N limit. We study the transition by a detailed analysis of the average of the modulus square of the characteristic polynomial. Furthermore

  8. Eigenvalue distributions of Wilson loops

    Lohmayer, Robert

    2010-07-01

    In the first part of this thesis, we focus on the distribution of the eigenvalues of the unitary Wilson loop matrix in the two-dimensional case at arbitrary finite N. To characterize the distribution of the eigenvalues, we introduce three density functions (the ''symmetric'', the ''antisymmetric'', and the ''true'' eigenvalue density) which differ at finite N but possess the same infinite-N limit, exhibiting the Durhuus-Olesen phase transition. Using expansions of determinants and inverse determinants in characters of totally symmetric or totally antisymmetric representations of SU(N), the densities at finite N can be expressed in terms of simple sums involving only dimensions and quadratic Casimir invariants of certain irreducible representations of SU(N), allowing for a numerical computation of the densities at arbitrary N to any desired accuracy. We find that the true eigenvalue density, adding N oscillations to the monotonic symmetric density, is in some sense intermediate between the symmetric and the antisymmetric density, which in turn is given by a sum of N delta peaks located at the zeros of the average of the characteristic polynomial. Furthermore, we show that the dependence on N can be made explicit by deriving integral representations for the resolvents associated to the three eigenvalue densities. Using saddle-point approximations, we confirm that all three densities reduce to the Durhuus-Olesen result in the infinite-N limit. In the second part, we study an exponential form of the multiplicative random complex matrix model introduced by Gudowska-Nowak et al. Varying a parameter which can be identified with the area of the Wilson loop in the unitary case, the region of non-vanishing eigenvalue density of the N-dimensional complex product matrix undergoes a topological change at a transition point in the infinite-N limit. We study the transition by a detailed analysis of the average of the

  9. Singular perturbation of simple eigenvalues

    Greenlee, W.M.

    1976-01-01

    Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem

  10. Interior transmission eigenvalues of a rectangle

    Sleeman, B D; Stocks, D C

    2016-01-01

    The problem of scattering of acoustic waves by an inhomogeneous medium is intimately connected with so called inside–outside duality, in which the interior transmission eigenvalue problem plays a fundamental role. Here a study of the interior transmission eigenvalues for rectangular domains of constant refractive index is made. By making a nonstandard use of the classical separation of variables technique both real and complex eigenvalues are determined. (paper)

  11. 40 CFR 80.52 - Vehicle preconditioning.

    2010-07-01

    ... 40 Protection of Environment 16 2010-07-01 2010-07-01 false Vehicle preconditioning. 80.52 Section...) REGULATION OF FUELS AND FUEL ADDITIVES Reformulated Gasoline § 80.52 Vehicle preconditioning. (a) Initial vehicle preconditioning and preconditioning between tests with different fuels shall be performed in...

  12. Overlapping domain decomposition preconditioners for the generalized Davidson method for the eigenvalue problem

    Stathopoulos, A.; Fischer, C.F. [Vanderbilt Univ., Nashville, TN (United States); Saad, Y.

    1994-12-31

    The solution of the large, sparse, symmetric eigenvalue problem, Ax = {lambda}x, is central to many scientific applications. Among many iterative methods that attempt to solve this problem, the Lanczos and the Generalized Davidson (GD) are the most widely used methods. The Lanczos method builds an orthogonal basis for the Krylov subspace, from which the required eigenvectors are approximated through a Rayleigh-Ritz procedure. Each Lanczos iteration is economical to compute but the number of iterations may grow significantly for difficult problems. The GD method can be considered a preconditioned version of Lanczos. In each step the Rayleigh-Ritz procedure is solved and explicit orthogonalization of the preconditioned residual ((M {minus} {lambda}I){sup {minus}1}(A {minus} {lambda}I)x) is performed. Therefore, the GD method attempts to improve convergence and robustness at the expense of a more complicated step.

  13. Solving Eigenvalue response matrix equations with Jacobian-Free Newton-Krylov methods

    Roberts, Jeremy A.; Forget, Benoit

    2011-01-01

    The response matrix method for reactor eigenvalue problems is motivated as a technique for solving coarse mesh transport equations, and the classical approach of power iteration (PI) for solution is described. The method is then reformulated as a nonlinear system of equations, and the associated Jacobian is derived. A Jacobian-Free Newton-Krylov (JFNK) method is employed to solve the system, using an approximate Jacobian coupled with incomplete factorization as a preconditioner. The unpreconditioned JFNK slightly outperforms PI, and preconditioned JFNK outperforms both PI and Steffensen-accelerated PI significantly. (author)

  14. High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

    Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

    2017-08-21

    In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

  15. Eigenvalue Decomposition-Based Modified Newton Algorithm

    Wen-jun Wang

    2013-01-01

    Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.

  16. Computation of standard deviations in eigenvalue calculations

    Gelbard, E.M.; Prael, R.

    1990-01-01

    In Brissenden and Garlick (1985), the authors propose a modified Monte Carlo method for eigenvalue calculations, designed to decrease particle transport biases in the flux and eigenvalue estimates, and in corresponding estimates of standard deviations. Apparently a very similar method has been used by Soviet Monte Carlo specialists. The proposed method is based on the generation of ''superhistories'', chains of histories run in sequence without intervening renormalization of the fission source. This method appears to have some disadvantages, discussed elsewhere. Earlier numerical experiments suggest that biases in fluxes and eigenvalues are negligibly small, even for very small numbers of histories per generation. Now more recent experiments, run on the CRAY-XMP, tend to confirm these earlier conclusions. The new experiments, discussed in this paper, involve the solution of one-group 1D diffusion theory eigenvalue problems, in difference form, via Monte Carlo. Experiments covered a range of dominance ratios from ∼0.75 to ∼0.985. In all cases flux and eigenvalue biases were substantially smaller than one standard deviation. The conclusion that, in practice, the eigenvalue bias is negligible has strong theoretical support. (author)

  17. Use of a preconditioned Bi-conjugate gradient method for hybrid plasma stability analysis

    Mikic, Z.; Morse, E.C.

    1985-01-01

    The numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled, 2-dimensional, elliptic partial differential equations for the field quantities at every timestep. When the equations are spatially finite-differenced and written in matrix form, the resulting matrix is large, sparse, complex, non-Hermitian, and indefinite. The use of the preconditioned bi-conjugate gradient method for solving these equations is discussed. The effect of block-diagonal preconditioning and incomplete block-LU preconditionig on the convergence of the method is investigated. For typical matrices arising in our studies, the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning. We show that the preconditioned bi-conjugate gradient method coverages more rapidly than the conjugate gradient method applied to the normal equations, and that it is an effective iterative method for the class of non-Hermitian, indefinite problems of interest

  18. Sorting waves and associated eigenvalues

    Carbonari, Costanza; Colombini, Marco; Solari, Luca

    2017-04-01

    The presence of mixed sediment always characterizes gravel bed rivers. Sorting processes take place during bed load transport of heterogeneous sediment mixtures. The two main elements necessary to the occurrence of sorting are the heterogeneous character of sediments and the presence of an active sediment transport. When these two key ingredients are simultaneously present, the segregation of bed material is consistently detected both in the field [7] and in laboratory [3] observations. In heterogeneous sediment transport, bed altimetric variations and sorting always coexist and both mechanisms are independently capable of driving the formation of morphological patterns. Indeed, consistent patterns of longitudinal and transverse sorting are identified almost ubiquitously. In some cases, such as bar formation [2] and channel bends [5], sorting acts as a stabilizing effect and therefore the dominant mechanism driving pattern formation is associated with bed altimetric variations. In other cases, such as longitudinal streaks, sorting enhances system instability and can therefore be considered the prevailing mechanism. Bedload sheets, first observed by Khunle and Southard [1], represent another classic example of a morphological pattern essentially triggered by sorting, as theoretical [4] and experimental [3] results suggested. These sorting waves cause strong spatial and temporal fluctuations of bedload transport rate typical observed in gravel bed rivers. The problem of bed load transport of a sediment mixture is formulated in the framework of a 1D linear stability analysis. The base state consists of a uniform flow in an infinitely wide channel with active bed load transport. The behaviour of the eigenvalues associated with fluid motion, bed evolution and sorting processes in the space of the significant flow and sediment parameters is analysed. A comparison is attempted with the results of the theoretical analysis of Seminara Colombini and Parker [4] and Stecca

  19. Orderings for conjugate gradient preconditionings

    Ortega, James M.

    1991-01-01

    The effect of orderings on the rate of convergence of the conjugate gradient method with SSOR or incomplete Cholesky preconditioning is examined. Some results also are presented that help to explain why red/black ordering gives an inferior rate of convergence.

  20. Macro-elementwise preconditioning methods

    Axelsson, Owe

    2012-01-01

    Roč. 82, č. 10 (2012), s. 1952-1963 ISSN 0378-4754 Institutional research plan: CEZ:AV0Z30860518 Keywords : heterogeniety * elementwise preconditioning * block matrix partitioning * macro-elements Subject RIV: BA - General Mathematics Impact factor: 0.836, year: 2012 http://www.sciencedirect.com/science/journal/03784754

  1. Modified Bateman solution for identical eigenvalues

    Dreher, Raymond

    2013-01-01

    Highlights: ► Solving indeterminacies due to identical eigenvalues in Bateman’s solution. ► Exact analytical solution of Bateman’s equations for identical eigenvalues. ► Algorithm calculating higher order derivatives appearing in this solution. ► Alternative evaluation of the derivatives through the Taylor polynomial. ► Implementation of an example program demonstrating the developed solution. - Abstract: In this paper we develop a general solution to the Bateman equations taking into account the special case of identical eigenvalues. A characteristic of this new solution is the presence of higher order derivatives. It is shown that the derivatives can be obtained analytically and also computed in an efficient manner

  2. The eigenvalue problem in phase space.

    Cohen, Leon

    2018-06-30

    We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  3. An additive subspace preconditioning method for the iterative solution of some problems with extreme contrasts in coefficients

    Axelsson, Owe

    2014-01-01

    Roč. 22, č. 4 (2014), s. 289-310 ISSN 1570-2820 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : preconditioning * additive subspace * small eigenvalues Subject RIV: BA - General Mathematics Impact factor: 2.310, year: 2014 http://www.degruyter.com/view/j/jnma.2014.22.issue-4/jnma-2014-0013/jnma-2014-0013. xml

  4. Collaborative spectrum sensing based on the ratio between largest eigenvalue and Geometric mean of eigenvalues

    Shakir, Muhammad

    2011-12-01

    In this paper, we introduce a new detector referred to as Geometric mean detector (GEMD) which is based on the ratio of the largest eigenvalue to the Geometric mean of the eigenvalues for collaborative spectrum sensing. The decision threshold has been derived by employing Gaussian approximation approach. In this approach, the two random variables, i.e. The largest eigenvalue and the Geometric mean of the eigenvalues are considered as independent Gaussian random variables such that their cumulative distribution functions (CDFs) are approximated by a univariate Gaussian distribution function for any number of cooperating secondary users and received samples. The approximation approach is based on the calculation of exact analytical moments of the largest eigenvalue and the Geometric mean of the eigenvalues of the received covariance matrix. The decision threshold has been calculated by exploiting the CDF of the ratio of two Gaussian distributed random variables. In this context, we exchange the analytical moments of the two random variables with the moments of the Gaussian distribution function. The performance of the detector is compared with the performance of the energy detector and eigenvalue ratio detector. Analytical and simulation results show that our newly proposed detector yields considerable performance advantage in realistic spectrum sensing scenarios. Moreover, our results based on proposed approximation approach are in perfect agreement with the empirical results. © 2011 IEEE.

  5. Eigenvalue ratio detection based on exact moments of smallest and largest eigenvalues

    Shakir, Muhammad; Tang, Wuchen; Rao, Anlei; Imran, Muhammad Ali; Alouini, Mohamed-Slim

    2011-01-01

    Detection based on eigenvalues of received signal covariance matrix is currently one of the most effective solution for spectrum sensing problem in cognitive radios. However, the results of these schemes always depend on asymptotic assumptions since the close-formed expression of exact eigenvalues ratio distribution is exceptionally complex to compute in practice. In this paper, non-asymptotic spectrum sensing approach to approximate the extreme eigenvalues is introduced. In this context, the Gaussian approximation approach based on exact analytical moments of extreme eigenvalues is presented. In this approach, the extreme eigenvalues are considered as dependent Gaussian random variables such that the joint probability density function (PDF) is approximated by bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. In this context, the definition of Copula is cited to analyze the extent of the dependency between the extreme eigenvalues. Later, the decision threshold based on the ratio of dependent Gaussian extreme eigenvalues is derived. The performance analysis of our newly proposed approach is compared with the already published asymptotic Tracy-Widom approximation approach. © 2011 ICST.

  6. The eigenvalue problem for a singular quasilinear elliptic equation

    Benjin Xuan

    2004-02-01

    Full Text Available We show that many results about the eigenvalues and eigenfunctions of a quasilinear elliptic equation in the non-singular case can be extended to the singular case. Among these results, we have the first eigenvalue is associated to a $C^{1,alpha}(Omega$ eigenfunction which is positive and unique (up to a multiplicative constant, that is, the first eigenvalue is simple. Moreover the first eigenvalue is isolated and is the unique positive eigenvalue associated to a non-negative eigenfunction. We also prove some variational properties of the second eigenvalue.

  7. Eigenvalue study of a chaotic resonator

    Banova, Todorka [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany); Technische Universitaet Darmstadt, Graduate School of Computational Engineering, Dolivostrasse 15, D-64293 Darmstadt (Germany); Ackermann, Wolfgang; Weiland, Thomas [Technische Universitaet Darmstadt, Institut fuer Theorie Elektromagnetischer Felder (TEMF), Schlossgartenstrasse 8, D-64289 Darmstadt (Germany)

    2013-07-01

    The field of quantum chaos comprises the study of the manifestations of classical chaos in the properties of the corresponding quantum systems. Within this work, we compute the eigenfrequencies that are needed for the level spacing analysis of a microwave resonator with chaotic characteristics. The major challenges posed by our work are: first, the ability of the approaches to tackle the large scale eigenvalue problem and second, the capability to extract many, i.e. order of thousands, eigenfrequencies for the considered cavity. The first proposed approach for an accurate eigenfrequency extraction takes into consideration the evaluated electric field computations in time domain of a superconducting cavity and by means of signal-processing techniques extracts the eigenfrequencies. The second approach is based on the finite element method with curvilinear elements, which transforms the continuous eigenvalue problem to a discrete generalized eigenvalue problem. Afterwards, the Lanczos algorithm is used for the solution of the generalized eigenvalue problem. In the poster, a summary of the applied algorithms, as well as, critical implementation details together with the simulation results are provided.

  8. Analysis of eigenvalue correction applied to biometrics

    Hendrikse, A.J.; Veldhuis, Raymond N.J.; Spreeuwers, Lieuwe Jan; Bazen, A.M.

    Eigenvalue estimation plays an important role in biometrics. However, if the number of samples is limited, estimates are significantly biased. In this article we analyse the influence of this bias on the error rates of PCA/LDA based verification systems, using both synthetic data with realistic

  9. A note on quasilinear elliptic eigenvalue problems

    Gianni Arioli

    1999-11-01

    Full Text Available We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

  10. Eigenvalues of the -Laplacian and disconjugacy criteria

    Pinasco Juan P

    2006-01-01

    Full Text Available We derive oscillation and nonoscillation criteria for the one-dimensional -Laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willett, and the proof is based on a Picone-type identity.

  11. A new localization set for generalized eigenvalues

    Jing Gao

    2017-05-01

    Full Text Available Abstract A new localization set for generalized eigenvalues is obtained. It is shown that the new set is tighter than that in (Numer. Linear Algebra Appl. 16:883-898, 2009. Numerical examples are given to verify the corresponding results.

  12. A robust multilevel simultaneous eigenvalue solver

    Costiner, Sorin; Taasan, Shlomo

    1993-01-01

    Multilevel (ML) algorithms for eigenvalue problems are often faced with several types of difficulties such as: the mixing of approximated eigenvectors by the solution process, the approximation of incomplete clusters of eigenvectors, the poor representation of solution on coarse levels, and the existence of close or equal eigenvalues. Algorithms that do not treat appropriately these difficulties usually fail, or their performance degrades when facing them. These issues motivated the development of a robust adaptive ML algorithm which treats these difficulties, for the calculation of a few eigenvectors and their corresponding eigenvalues. The main techniques used in the new algorithm include: the adaptive completion and separation of the relevant clusters on different levels, the simultaneous treatment of solutions within each cluster, and the robustness tests which monitor the algorithm's efficiency and convergence. The eigenvectors' separation efficiency is based on a new ML projection technique generalizing the Rayleigh Ritz projection, combined with a technique, the backrotations. These separation techniques, when combined with an FMG formulation, in many cases lead to algorithms of O(qN) complexity, for q eigenvectors of size N on the finest level. Previously developed ML algorithms are less focused on the mentioned difficulties. Moreover, algorithms which employ fine level separation techniques are of O(q(sub 2)N) complexity and usually do not overcome all these difficulties. Computational examples are presented where Schrodinger type eigenvalue problems in 2-D and 3-D, having equal and closely clustered eigenvalues, are solved with the efficiency of the Poisson multigrid solver. A second order approximation is obtained in O(qN) work, where the total computational work is equivalent to only a few fine level relaxations per eigenvector.

  13. Inversion for Eigenvalues and Modes Using Sierra-SD and ROL.

    Walsh, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Aquino, Wilkins [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ridzal, Denis [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Kouri, Drew Philip [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-12-01

    In this report we formulate eigenvalue-based methods for model calibration using a PDE-constrained optimization framework. We derive the abstract optimization operators from first principles and implement these methods using Sierra-SD and the Rapid Optimization Library (ROL). To demon- strate this approach, we use experimental measurements and an inverse solution to compute the joint and elastic foam properties of a low-fidelity unit (LFU) model.

  14. Generalization of Samuelson's inequality and location of eigenvalues

    We prove a generalization of Samuelson's inequality for higher order central moments. Bounds for the eigenvalues are obtained when a given complex × matrix has real eigenvalues. Likewise, we discuss bounds for the roots of polynomial equations.

  15. Management of Preconditioned Calves and Impacts of Preconditioning.

    Hilton, W Mark

    2015-07-01

    When studying the practice of preconditioning (PC) calves, many factors need to be examined to determine if cow-calf producers should make this investment. Factors such as average daily gain, feed efficiency, available labor, length of the PC period, genetics, and marketing options must be analyzed. The health sales price advantage is an additional benefit in producing and selling PC calves but not the sole determinant of PC's financially feasibility. Studies show that a substantial advantage of PC is the selling of additional pounds at a cost of gain well below the marginal return of producing those additional pounds. Copyright © 2015 Elsevier Inc. All rights reserved.

  16. Eigenstructure of of singular systems. Perturbation analysis of simple eigenvalues

    García Planas, María Isabel; Tarragona Romero, Sonia

    2014-01-01

    The problem to study small perturbations of simple eigenvalues with a change of parameters is of general interest in applied mathematics. After to introduce a systematic way to know if an eigenvalue of a singular system is simple or not, the aim of this work is to study the behavior of a simple eigenvalue of singular linear system family

  17. Computing the eigenvalues and eigenvectors of a fuzzy matrix

    A. Kumar

    2012-08-01

    Full Text Available Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully fuzzy linear system $widetilde{A}widetilde{X}= widetilde{lambda} widetilde{X}.$

  18. Monotonicity of energy eigenvalues for Coulomb systems

    Englisch, R.

    1983-01-01

    Generalising results by earlier workers for a large class of Hamiltonians (among others, Hamiltonians of Coulomb systems) which can be written in the form H(α) = H 0 + αH' the present works shows that their eigenvalues decrease with increasing α. This result is applied to Coulomb systems in which the distances between the infinitely heavy particles are varying and also is used to obtain a completion and simplification of proof for the stability of the biexciton. (author)

  19. Lagrangian Differentiation, Integration and Eigenvalues Problems

    Durand, L.

    1983-01-01

    Calogero recently proposed a new and very powerful method for the solution of Sturm-Liouville eigenvalue problems based on Lagrangian differentiation. In this paper, some results of a numerical investigation of Calogero's method for physical interesting problems are presented. It is then shown that one can 'invert' his differentiation technique to obtain a flexible, factorially convergent Lagrangian integration scheme which should be useful in a variety of problems, e.g. solution of integral equations

  20. Eigenvalue translation method for mode calculations

    Gerck, E.; Cruz, C.H.B.

    1978-11-01

    A new method is described for the first few modes calculations in a interferometer that has several advantages over the ALLMAT subroutine, the Prony Method and the Fox and Li Method. In the illustrative results shown for the same cases it can be seen that the eigenvalue translation method is typically 100 fold times faster than the usual Fox and Li Method and 10 times faster than ALLMAT [pt

  1. New approach to calculate bound state eigenvalues

    Gerck, E.; Gallas, J.A.C.

    1983-01-01

    A method of solving the radial Schrodinger equation for bound states is discussed. The method is based on a new piecewise representation of the second derivative operator on a set of functions that obey the boundary conditions. This representation is trivially diagonalised and leads to closed form expressions of the type E sub(n)=E(ab+b+c/n+...) for the eigenvalues. Examples are given for the power-law and logarithmic potentials. (Author) [pt

  2. Recurrence quantity analysis based on matrix eigenvalues

    Yang, Pengbo; Shang, Pengjian

    2018-06-01

    Recurrence plots is a powerful tool for visualization and analysis of dynamical systems. Recurrence quantification analysis (RQA), based on point density and diagonal and vertical line structures in the recurrence plots, is considered to be alternative measures to quantify the complexity of dynamical systems. In this paper, we present a new measure based on recurrence matrix to quantify the dynamical properties of a given system. Matrix eigenvalues can reflect the basic characteristics of the complex systems, so we show the properties of the system by exploring the eigenvalues of the recurrence matrix. Considering that Shannon entropy has been defined as a complexity measure, we propose the definition of entropy of matrix eigenvalues (EOME) as a new RQA measure. We confirm that EOME can be used as a metric to quantify the behavior changes of the system. As a given dynamical system changes from a non-chaotic to a chaotic regime, the EOME will increase as well. The bigger EOME values imply higher complexity and lower predictability. We also study the effect of some factors on EOME,including data length, recurrence threshold, the embedding dimension, and additional noise. Finally, we demonstrate an application in physiology. The advantage of this measure lies in a high sensitivity and simple computation.

  3. Generalized Eigenvalues for pairs on heritian matrices

    Rublein, George

    1988-01-01

    A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.

  4. Isoflurane preconditions myocardium against infarction via release of free radicals

    Müllenheim, Jost; Ebel, Dirk; Frässdorf, Jan; Preckel, Benedikt; Thämer, Volker; Schlack, Wolfgang

    2002-01-01

    BACKGROUND: Isoflurane exerts cardioprotective effects that mimic the ischemic preconditioning phenomenon. Generation of free radicals is implicated in ischemic preconditioning. The authors investigated whether isoflurane-induced preconditioning may involve release of free radicals. METHODS:

  5. Ischemic preconditioning protects against ischemic brain injury

    Xiao-meng Ma

    2016-01-01

    Full Text Available In this study, we hypothesized that an increase in integrin αv ß 3 and its co-activator vascular endothelial growth factor play important neuroprotective roles in ischemic injury. We performed ischemic preconditioning with bilateral common carotid artery occlusion for 5 minutes in C57BL/6J mice. This was followed by ischemic injury with bilateral common carotid artery occlusion for 30 minutes. The time interval between ischemic preconditioning and lethal ischemia was 48 hours. Histopathological analysis showed that ischemic preconditioning substantially diminished damage to neurons in the hippocampus 7 days after ischemia. Evans Blue dye assay showed that ischemic preconditioning reduced damage to the blood-brain barrier 24 hours after ischemia. This demonstrates the neuroprotective effect of ischemic preconditioning. Western blot assay revealed a significant reduction in protein levels of integrin αv ß 3, vascular endothelial growth factor and its receptor in mice given ischemic preconditioning compared with mice not given ischemic preconditioning 24 hours after ischemia. These findings suggest that the neuroprotective effect of ischemic preconditioning is associated with lower integrin αv ß 3 and vascular endothelial growth factor levels in the brain following ischemia.

  6. Random matrices, Frobenius eigenvalues, and monodromy

    Katz, Nicholas M

    1998-01-01

    The main topic of this book is the deep relation between the spacings between zeros of zeta and L-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and L-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinit

  7. On the Shape Sensitivity of the First Dirichlet Eigenvalue for Two-Phase Problems

    Dambrine, M.; Kateb, D.

    2011-01-01

    We consider a two-phase problem in thermal conductivity: inclusions filled with a material of conductivity σ 1 are layered in a body of conductivity σ 2 . We address the shape sensitivity of the first eigenvalue associated with Dirichlet boundary conditions when both the boundaries of the inclusions and the body can be modified. We prove a differentiability result and provide the expressions of the first and second order derivatives. We apply the results to the optimal design of an insulated body. We prove the stability of the optimal design thanks to a second order analysis. We also continue the study of an extremal eigenvalue problem for a two-phase conductor in a ball initiated by Conca et al. (Appl. Math. Optim. 60(2):173-184, 2009) and pursued in Conca et al. (CANUM 2008, ESAIM Proc., vol. 27, pp. 311-321, EDP Sci., Les Ulis, 2009).

  8. INDEFINITE COPOSITIVE MATRICES WITH EXACTLY ONE POSITIVE EIGENVALUE OR EXACTLY ONE NEGATIVE EIGENVALUE

    Jargalsaikhan, Bolor

    Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out

  9. On a quadratic inverse eigenvalue problem

    Cai, Yunfeng; Xu, Shufang

    2009-01-01

    This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

  10. Block-triangular preconditioners for PDE-constrained optimization

    Rees, Tyrone; Stoll, Martin

    2010-01-01

    In this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.

  11. Block-triangular preconditioners for PDE-constrained optimization

    Rees, Tyrone

    2010-11-26

    In this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.

  12. MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems

    Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.

    1986-01-01

    1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real

  13. On the distribution of eigenvalues of certain matrix ensembles

    Bogomolny, E.; Bohigas, O.; Pato, M.P.

    1995-01-01

    Invariant random matrix ensembles with weak confinement potentials of the eigenvalues, corresponding to indeterminate moment problems, are investigated. These ensembles are characterized by the fact that the mean density of eigenvalues tends to a continuous function with increasing matrix dimension contrary to the usual cases where it grows indefinitely. It is demonstrated that the standard asymptotic formulae are not applicable in these cases and that the asymptotic distribution of eigenvalues can deviate from the classical ones. (author)

  14. Application of collocation meshless method to eigenvalue problem

    Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

    2012-01-01

    The numerical method for solving the nonlinear eigenvalue problem has been developed by using the collocation Element-Free Galerkin Method (EFGM) and its performance has been numerically investigated. The results of computations show that the approximate solution of the nonlinear eigenvalue problem can be obtained stably by using the developed method. Therefore, it can be concluded that the developed method is useful for solving the nonlinear eigenvalue problem. (author)

  15. Asymptotic Distribution of Eigenvalues of Weakly Dilute Wishart Matrices

    Khorunzhy, A. [Institute for Low Temperature Physics (Ukraine)], E-mail: khorunjy@ilt.kharkov.ua; Rodgers, G. J. [Brunel University, Uxbridge, Department of Mathematics and Statistics (United Kingdom)], E-mail: g.j.rodgers@brunel.ac.uk

    2000-03-15

    We study the eigenvalue distribution of large random matrices that are randomly diluted. We consider two random matrix ensembles that in the pure (nondilute) case have a limiting eigenvalue distribution with a singular component at the origin. These include the Wishart random matrix ensemble and Gaussian random matrices with correlated entries. Our results show that the singularity in the eigenvalue distribution is rather unstable under dilution and that even weak dilution destroys it.

  16. Critical eigenvalue in LMFBRs: a physics assessment

    McKnight, R.D.; Collins, P.J.; Olsen, D.N.

    1984-01-01

    This paper summarizes recent work to put the analysis of past critical eigenvalue measurements from the US critical experiments program on a consistent basis. The integral data base includes 53 configurations built in 11 ZPPR assemblies which simulate mixed oxide LMFBRs. Both conventional and heterogeneous designs representing 350, 700, and 900 MWe sizes and with and without simulated control rods and/or control rod positions have been studied. The review of the integral data base includes quantitative assessment of experimental uncertainties in the measured excess reactivity. Analyses have been done with design level and higher-order methods using ENDF/B-IV data. Comparisons of these analyses with the experiments are used to generate recommended bias factors for criticality predictions. Recommended methods for analysis of LMFBR fast critical assemblies and LMFBR design calculations are presented. Unresolved issues and areas which require additional experimental or analytical study are identified

  17. Uncertainty Estimates in Cold Critical Eigenvalue Predictions

    Karve, Atul A.; Moore, Brian R.; Mills, Vernon W.; Marrotte, Gary N.

    2005-01-01

    A recent cycle of a General Electric boiling water reactor performed two beginning-of-cycle local cold criticals. The eigenvalues estimated by the core simulator were 0.99826 and 1.00610. The large spread in them (= 0.00784) is a source of concern, and it is studied here. An analysis process is developed using statistical techniques, where first a transfer function relating the core observable Y (eigenvalue) to various factors (X's) is established. Engineering judgment is used to recognize the best candidates for X's. They are identified as power-weighted assembly k ∞ 's of selected assemblies around the withdrawn rods. These are a small subset of many X's that could potentially influence Y. However, the intention here is not to do a comprehensive study by accounting for all the X's. Rather, the scope is to demonstrate that the process developed is reasonable and to show its applicability to performing detailed studies. Variability in X's is obtained by perturbing nodal k ∞ 's since they directly influence the buckling term in the quasi-two-group diffusion equation model of the core simulator. Any perturbations introduced in them are bounded by standard well-established uncertainties. The resulting perturbations in the X's may not necessarily be directly correlated to physical attributes, but they encompass numerous biases and uncertainties credited to input and modeling uncertainties. The 'vital few' from the 'unimportant many' X's are determined, and then they are subgrouped according to assembly type, location, exposure, and control rod insertion. The goal is to study how the subgroups influence Y in order to have a better understanding of the variability observed in it

  18. Advanced quadrature sets and acceleration and preconditioning techniques for the discrete ordinates method in parallel computing environments

    Longoni, Gianluca

    decomposition strategies. The accuracy and performance of PENSSn has been tested for both criticality eigenvalue and fixed source problems. PENSSn has been coupled as a preconditioner and accelerator for the S N method using the PENTRAN code. This work has culminated in the development of the Flux Acceleration Simplified Transport (FAST(c)) preconditioning algorithm, which constitutes a completely automated system for preconditioning radiation transport calculations in parallel computing environments.

  19. Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

    Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

    2012-01-01

    We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. (paper)

  20. Eigenvalues of the volume operator in loop quantum gravity

    Meissner, Krzysztof A

    2006-01-01

    We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins, which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity

  1. Deflation of Eigenvalues for GMRES in Lattice QCD

    Morgan, Ronald B.; Wilcox, Walter

    2002-01-01

    Versions of GMRES with deflation of eigenvalues are applied to lattice QCD problems. Approximate eigenvectors corresponding to the smallest eigenvalues are generated at the same time that linear equations are solved. The eigenvectors improve convergence for the linear equations, and they help solve other right-hand sides

  2. Energy eigenvalues of helium-like atoms in dense plasmas

    Hashino, Tasuke; Nakazaki, Shinobu; Kato, Takako; Kashiwabara, Hiromichi.

    1987-04-01

    Calculations based on a variational method with wave functions including the correlation of electrons are carried out to obtain energy eigenvalues of Schroedinger's equation for helium-like atoms embedded in dense plasmas, taking the Debye-Hueckel approximation. Energy eigenvalues for the 1 1 S, 2 1 S, and 2 3 S states are obtained as a function of Debye screening length. (author)

  3. A numerical method to compute interior transmission eigenvalues

    Kleefeld, Andreas

    2013-01-01

    In this paper the numerical calculation of eigenvalues of the interior transmission problem arising in acoustic scattering for constant contrast in three dimensions is considered. From the computational point of view existing methods are very expensive, and are only able to show the existence of such transmission eigenvalues. Furthermore, they have trouble finding them if two or more eigenvalues are situated closely together. We present a new method based on complex-valued contour integrals and the boundary integral equation method which is able to calculate highly accurate transmission eigenvalues. So far, this is the first paper providing such accurate values for various surfaces different from a sphere in three dimensions. Additionally, the computational cost is even lower than those of existing methods. Furthermore, the algorithm is capable of finding complex-valued eigenvalues for which no numerical results have been reported yet. Until now, the proof of existence of such eigenvalues is still open. Finally, highly accurate eigenvalues of the interior Dirichlet problem are provided and might serve as test cases to check newly derived Faber–Krahn type inequalities for larger transmission eigenvalues that are not yet available. (paper)

  4. Estimates for lower order eigenvalues of a clamped plate problem

    Cheng, Qing-Ming; Huang, Guangyue; Wei, Guoxin

    2009-01-01

    For a bounded domain $\\Omega$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.

  5. Jacobi-Davidson methods for generalized MHD-eigenvalue problems

    J.G.L. Booten; D.R. Fokkema; G.L.G. Sleijpen; H.A. van der Vorst (Henk)

    1995-01-01

    textabstractA Jacobi-Davidson algorithm for computing selected eigenvalues and associated eigenvectors of the generalized eigenvalue problem $Ax = lambda Bx$ is presented. In this paper the emphasis is put on the case where one of the matrices, say the B-matrix, is Hermitian positive definite. The

  6. A method for the solution of the RPA eigenvalue

    Hoffman, M.J.H.; De Kock, P.R.

    1986-01-01

    The RPA eigenvalue problem requires the diagonalization of a 2nx2n matrix. In practical calculations, n (the number of particle-hole basis states) can be a few hundred and the diagonalization of such a large non-symmetric matrix may take quite a long time. In this report we firstly discuss sufficient conditions for real and non-zero RPA eigenvalues. The presence of zero or imaginary eigenvalues is related to the relative importance of the groundstate correlations to the total interaction energy. We then rewrite the RPA eigenvalue problem for the cases where these conditions are fulfilled in a form which only requires the diagonalization of two symmetric nxn matrices. The extend to which this method can be applied when zero eigenvalues occur, is also discussed

  7. Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

    Desmal, Abdulla; Bagci, Hakan

    2014-01-01

    Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

  8. Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

    Desmal, Abdulla

    2014-05-04

    Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

  9. Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

    Desmal, Abdulla

    2014-01-06

    Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

  10. Ischemic Preconditioning of One Forearm Enhances Static and Dynamic Apnea

    Kjeld, Thomas; Rasmussen, Mads Reinholdt; Jattu, Timo

    2014-01-01

    INTRODUCTION: Ischemic preconditioning enhances ergometer cycling and swimming performance. We evaluated whether ischemic preconditioning of one forearm (four times for 5 min) also affects static breath hold and underwater swimming, whereas the effect of similar preconditioning on ergometer rowing...... preconditioning reduced the forearm oxygen saturation from 65% ± 7% to 19% ± 7% (mean ± SD; P right thigh.......05). CONCLUSIONS: We conclude that while the effect of ischemic preconditioning (of one forearm) on ergometer rowing was minimal, probably because of reduced muscle oxygenation during the warm-up, ischemic preconditioning does enhance both static and dynamic apnea, supporting that muscle ischemia is an important...

  11. The eigenvalues of the SN transport matrix

    Ourique, L.E.; Vilhena, M.T. de

    2005-01-01

    In a recent paper, we analyze the dependence of the eigenvalues of the S N matrix transport, associated with the system of linear differential equations that corresponds to the S N approximations of the transport equation [1]. By considering a control parameter, we have shown that there exist some bifurcation points. This means that the solutions of S N approximations change from oscillatory to non-oscillatory behavior, a different approach of the study by [2]. Nowadays, the one-dimensional transport equation and related problems have been a source of new techniques for solving particular cases as well the development of analytical methods that search aspects of existence and uniqueness of the solutions [3], [4]. In this work, we generalize the results shown in [1], searching for a model of the distribution of the bifurcation points of the S N matrix transport, studying the one-dimensional case in a slab, with anisotropic differential cross section of order 3. The result indicates that the bifurcation points obey a certain rule of distribution. Beside that, the condition number of the matrix transport increases too much in the neighborhood of these points, as we have seen in [1]. (author)

  12. A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

    Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas

    2015-12-01

    Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.

  13. Eigenvalues of the simplified ideal MHD ballooning equation

    Paris, R.B.; Auby, N.; Dagazian, R.Y.

    1986-01-01

    The investigation of the spectrum of the simplified differential equation describing the variation of the amplitude of the ideal MHD ballooning instability along magnetic field lines constitutes a multiparameter Schroedinger eigenvalue problem. An exact eigenvalue relation for the discrete part of the spectrum is obtained in terms of the oblate spheroidal functions. The dependence of the eigenvalues lambda on the two free parameters γ 2 and μ 2 of the equation is discussed, together with certain analytical approximations in the limits of small and large γ 2 . A brief review of the principal properties of the spheroidal functions is given in an appendix

  14. Solving complex band structure problems with the FEAST eigenvalue algorithm

    Laux, S. E.

    2012-08-01

    With straightforward extension, the FEAST eigenvalue algorithm [Polizzi, Phys. Rev. B 79, 115112 (2009)] is capable of solving the generalized eigenvalue problems representing traveling-wave problems—as exemplified by the complex band-structure problem—even though the matrices involved are complex, non-Hermitian, and singular, and hence outside the originally stated range of applicability of the algorithm. The obtained eigenvalues/eigenvectors, however, contain spurious solutions which must be detected and removed. The efficiency and parallel structure of the original algorithm are unaltered. The complex band structures of Si layers of varying thicknesses and InAs nanowires of varying radii are computed as test problems.

  15. Use of the preconditioned conjugate gradient algorithm as a generic solver for mixed-model equations in animal breeding applications.

    Tsuruta, S; Misztal, I; Strandén, I

    2001-05-01

    Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is

  16. Xenon preconditioning: molecular mechanisms and biological effects

    Liu Wenwu

    2013-01-01

    Full Text Available Abstract Xenon is one of noble gases and has been recognized as an anesthetic for more than 50 years. Xenon possesses many of the characteristics of an ideal anesthetic, but it is not widely applied in clinical practice mainly because of its high cost. In recent years, numerous studies have demonstrated that xenon as an anesthetic can exert neuroprotective and cardioprotective effects in different models. Moreover, xenon has been applied in the preconditioning, and the neuroprotective and cardioprotective effects of xenon preconditioning have been investigated in a lot of studies in which some mechanisms related to these protections are proposed. In this review, we summarized these mechanisms and the biological effects of xenon preconditioning.

  17. Projection preconditioning for Lanczos-type methods

    Bielawski, S.S.; Mulyarchik, S.G.; Popov, A.V. [Belarusian State Univ., Minsk (Belarus)

    1996-12-31

    We show how auxiliary subspaces and related projectors may be used for preconditioning nonsymmetric system of linear equations. It is shown that preconditioned in such a way (or projected) system is better conditioned than original system (at least if the coefficient matrix of the system to be solved is symmetrizable). Two approaches for solving projected system are outlined. The first one implies straightforward computation of the projected matrix and consequent using some direct or iterative method. The second approach is the projection preconditioning of conjugate gradient-type solver. The latter approach is developed here in context with biconjugate gradient iteration and some related Lanczos-type algorithms. Some possible particular choices of auxiliary subspaces are discussed. It is shown that one of them is equivalent to using colorings. Some results of numerical experiments are reported.

  18. On the decision threshold of eigenvalue ratio detector based on moments of joint and marginal distributions of extreme eigenvalues

    Shakir, Muhammad Zeeshan

    2013-03-01

    Eigenvalue Ratio (ER) detector based on the two extreme eigenvalues of the received signal covariance matrix is currently one of the most effective solution for spectrum sensing. However, the analytical results of such scheme often depend on asymptotic assumptions since the distribution of the ratio of two extreme eigenvalues is exceptionally complex to compute. In this paper, a non-asymptotic spectrum sensing approach for ER detector is introduced to approximate the marginal and joint distributions of the two extreme eigenvalues. The two extreme eigenvalues are considered as dependent Gaussian random variables such that their joint probability density function (PDF) is approximated by a bivariate Gaussian distribution function for any number of cooperating secondary users and received samples. The PDF approximation approach is based on the moment matching method where we calculate the exact analytical moments of joint and marginal distributions of the two extreme eigenvalues. The decision threshold is calculated by exploiting the statistical mean and the variance of each of the two extreme eigenvalues and the correlation coefficient between them. The performance analysis of our newly proposed approximation approach is compared with the already published asymptotic Tracy-Widom approximation approach. It has been shown that our results are in perfect agreement with the simulation results for any number of secondary users and received samples. © 2002-2012 IEEE.

  19. Extreme eigenvalues of sample covariance and correlation matrices

    Heiny, Johannes

    This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance...... matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the sample size n. We generalize the growth rates of p existing in the literature. Assuming a regular variation condition with tail index ... eigenvalues are essentially determined by the extreme order statistics from an array of iid random variables. The asymptotic behavior of the extreme eigenvalues is then derived routinely from classical extreme value theory. The resulting approximations are strikingly simple considering the high dimension...

  20. Complex eigenvalue analysis of railway wheel/rail squeal

    DR OKE

    Squeal noise from wheel/rail and brake disc/pad frictional contact is typical in railways. ... squeal noise by multibody simulation of a rail car running on rigid rails. ... system, traditional complex eigenvalue analysis by finite element was used.

  1. Inequalities among eigenvalues of Sturm–Liouville problems

    Kong Q

    1999-01-01

    Full Text Available There are well-known inequalities among the eigenvalues of Sturm–Liouville problems with periodic, semi-periodic, Dirichlet and Neumann boundary conditions. In this paper, for an arbitrary coupled self-adjoint boundary condition, we identify two separated boundary conditions corresponding to the Dirichlet and Neumann conditions in the classical case, and establish analogous inequalities. It is also well-known that the lowest periodic eigenvalue is simple; here we prove a similar result for the general case. Moreover, we show that the algebraic and geometric multiplicities of the eigenvalues of self-adjoint regular Sturm–Liouville problems with coupled boundary conditions are the same. An important step in our approach is to obtain a representation of the fundamental solutions for sufficiently negative values of the spectral parameter. Our approach yields the existence and boundedness from below of the eigenvalues of arbitrary self-adjoint regular Sturm–Liouville problems without using operator theory.

  2. An eigenvalue localization set for tensors and its applications

    Jianxing Zhao

    2017-03-01

    Full Text Available Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al. (Linear Algebra Appl. 481:36-53, 2015 and Huang et al. (J. Inequal. Appl. 2016:254, 2016. As an application of this set, new bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al., the advantage of our results is that, without considering the selection of nonempty proper subsets S of N = { 1 , 2 , … , n } $N=\\{1,2,\\ldots,n\\}$ , we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of M $\\mathcal{M}$ -tensors. Finally, numerical examples are given to verify the theoretical results.

  3. An eigenvalue localization set for tensors and its applications.

    Zhao, Jianxing; Sang, Caili

    2017-01-01

    A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al . (Linear Algebra Appl. 481:36-53, 2015) and Huang et al . (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al ., the advantage of our results is that, without considering the selection of nonempty proper subsets S of [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.

  4. Fourier convergence analysis applied to neutron diffusion Eigenvalue problem

    Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

    2004-01-01

    Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Though the methods can be applied to Eigenvalue problems too, all the Fourier convergence analyses have been performed only for fixed source problems and a Fourier convergence analysis for Eigenvalue problem has never been reported. Lee et al proposed new 2-D/1-D coupling methods and they showed that the new ones are unconditionally stable while one of the two existing ones is unstable at a small mesh size and that the new ones are better than the existing ones in terms of the convergence rate. In this paper the convergence of method A in reference 4 for the diffusion Eigenvalue problem was analyzed by the Fourier analysis. The Fourier convergence analysis presented in this paper is the first one applied to a neutronics eigenvalue problem to the best of our knowledge

  5. Eigenvalues of Words in Two Positive Definite Letters

    Hillar, Christopher J; Johnson, Charles R

    2005-01-01

    The question of whether all words in two real positive definite letters have only positive eigenvalues is addressed and settled (negatively). This question was raised some time ago in connection with a long-standing problem in theoretical physics. A large class of words that do guarantee positive eigenvalues is identified, and considerable evidence is given for the conjecture that no other words do. In the process, a fundamental question about solvability of symmetric word equations is encoun...

  6. Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

    Sjoestrand, N.G.

    1981-01-01

    Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

  7. Bound-state Dirac eigenvalues for scalar potentials

    Ram, B.; Arafah, M.

    1981-01-01

    The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)

  8. An adjoint-based scheme for eigenvalue error improvement

    Merton, S.R.; Smedley-Stevenson, R.P.; Pain, C.C.; El-Sheikh, A.H.; Buchan, A.G.

    2011-01-01

    A scheme for improving the accuracy and reducing the error in eigenvalue calculations is presented. Using a rst order Taylor series expansion of both the eigenvalue solution and the residual of the governing equation, an approximation to the error in the eigenvalue is derived. This is done using a convolution of the equation residual and adjoint solution, which is calculated in-line with the primal solution. A defect correction on the solution is then performed in which the approximation to the error is used to apply a correction to the eigenvalue. The method is shown to dramatically improve convergence of the eigenvalue. The equation for the eigenvalue is shown to simplify when certain normalizations are applied to the eigenvector. Two such normalizations are considered; the rst of these is a fission-source type of normalisation and the second is an eigenvector normalisation. Results are demonstrated on a number of demanding elliptic problems using continuous Galerkin weighted nite elements. Moreover, the correction scheme may also be applied to hyperbolic problems and arbitrary discretization. This is not limited to spatial corrections and may be used throughout the phase space of the discrete equation. The applied correction not only improves fidelity of the calculation, it allows assessment of the reliability of numerical schemes to be made and could be used to guide mesh adaption algorithms or to automate mesh generation schemes. (author)

  9. Preconditioning mesenchymal stem cells with the mood stabilizers lithium and valproic acid enhances therapeutic efficacy in a mouse model of Huntington's disease.

    Linares, Gabriel R; Chiu, Chi-Tso; Scheuing, Lisa; Leng, Yan; Liao, Hsiao-Mei; Maric, Dragan; Chuang, De-Maw

    2016-07-01

    Huntington's disease (HD) is a fatal neurodegenerative disorder caused by CAG repeat expansions in the huntingtin gene. Although, stem cell-based therapy has emerged as a potential treatment for neurodegenerative diseases, limitations remain, including optimizing delivery to the brain and donor cell loss after transplantation. One strategy to boost cell survival and efficacy is to precondition cells before transplantation. Because the neuroprotective actions of the mood stabilizers lithium and valproic acid (VPA) induce multiple pro-survival signaling pathways, we hypothesized that preconditioning bone marrow-derived mesenchymal stem cells (MSCs) with lithium and VPA prior to intranasal delivery to the brain would enhance their therapeutic efficacy, and thereby facilitate functional recovery in N171-82Q HD transgenic mice. MSCs were treated in the presence or absence of combined lithium and VPA, and were then delivered by brain-targeted single intranasal administration to eight-week old HD mice. Histological analysis confirmed the presence of MSCs in the brain. Open-field test revealed that ambulatory distance and mean velocity were significantly improved in HD mice that received preconditioned MSCs, compared to HD vehicle-control and HD mice transplanted with non-preconditioned MSCs. Greater benefits on motor function were observed in HD mice given preconditioned MSCs, while HD mice treated with non-preconditioned MSCs showed no functional benefits. Moreover, preconditioned MSCs reduced striatal neuronal loss and huntingtin aggregates in HD mice. Gene expression profiling of preconditioned MSCs revealed a robust increase in expression of genes involved in trophic effects, antioxidant, anti-apoptosis, cytokine/chemokine receptor, migration, mitochondrial energy metabolism, and stress response signaling pathways. Consistent with this finding, preconditioned MSCs demonstrated increased survival after transplantation into the brain compared to non-preconditioned cells

  10. Preconditioning the modified conjugate gradient method ...

    In this paper, the convergence analysis of the conventional conjugate Gradient method was reviewed. And the convergence analysis of the modified conjugate Gradient method was analysed with our extension on preconditioning the algorithm. Convergence of the algorithm is a function of the condition number of M-1A.

  11. Equivalent operator preconditioning for elliptic problems

    Axelsson, Owe; Karátson, J.

    2009-01-01

    Roč. 50, č. 3 (2009), s. 297-380 ISSN 1017-1398 Institutional research plan: CEZ:AV0Z30860518 Keywords : Elliptic problem * Conjugate gradient method * preconditioning * equivalent operators * compact operators Subject RIV: BA - General Mathematics Impact factor: 0.716, year: 2009 http://en.scientificcommons.org/42514649

  12. Preconditioning of iterative methods - theory and applications

    Axelsson, Owe; Blaheta, Radim; Neytcheva, M.; Pultarová, I.

    2015-01-01

    Roč. 22, č. 6 (2015), s. 901-902 ISSN 1070-5325 Institutional support: RVO:68145535 Keywords : preconditioning * iterative methods * applications Subject RIV: BA - General Mathematics Impact factor: 1.431, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/nla.2016/epdf

  13. The structure of the polynomials in preconditioned BiCG algorithms and the switching direction of preconditioned systems

    Itoh, Shoji; Sugihara, Masaaki

    2016-01-01

    We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithms. We show that the direction of a preconditioned system is switched by construction and by the settings of the initial shadow residual vector. We analyze and compare the polynomial structures of four preconditioned BiCG algorithms.

  14. Moving force identification based on modified preconditioned conjugate gradient method

    Chen, Zhen; Chan, Tommy H. T.; Nguyen, Andy

    2018-06-01

    This paper develops a modified preconditioned conjugate gradient (M-PCG) method for moving force identification (MFI) by improving the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods with a modified Gram-Schmidt algorithm. The method aims to obtain more accurate and more efficient identification results from the responses of bridge deck caused by vehicles passing by, which are known to be sensitive to ill-posed problems that exist in the inverse problem. A simply supported beam model with biaxial time-varying forces is used to generate numerical simulations with various analysis scenarios to assess the effectiveness of the method. Evaluation results show that regularization matrix L and number of iterations j are very important influence factors to identification accuracy and noise immunity of M-PCG. Compared with the conventional counterpart SVD embedded in the time domain method (TDM) and the standard form of CG, the M-PCG with proper regularization matrix has many advantages such as better adaptability and more robust to ill-posed problems. More importantly, it is shown that the average optimal numbers of iterations of M-PCG can be reduced by more than 70% compared with PCG and this apparently makes M-PCG a preferred choice for field MFI applications.

  15. Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices

    Kabashima, Yoshiyuki; Takahashi, Hisanao; Watanabe, Osamu

    2010-01-01

    A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity fields that are handled in cavity analysis. We show that the first eigenvalue is determined in such a way that the distribution of the cavity fields has a finite value for the second order moment with respect to the cavity fields of the first order coefficient. The validity and utility of the developed methodology are examined by applying it to two analytically solvable and one simple but non-trivial examples in conjunction with numerical justification.

  16. EISPACK, Subroutines for Eigenvalues, Eigenvectors, Matrix Operations

    Garbow, Burton S.; Cline, A.K.; Meyering, J.

    1993-01-01

    1 - Description of problem or function: EISPACK3 is a collection of 75 FORTRAN subroutines, both single- and double-precision, that compute the eigenvalues and eigenvectors of nine classes of matrices. The package can determine the Eigen-system of complex general, complex Hermitian, real general, real symmetric, real symmetric band, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices. In addition, there are two routines which use the singular value decomposition to solve certain least squares problem. The individual subroutines are - Identification/Description: BAKVEC: Back transform vectors of matrix formed by FIGI; BALANC: Balance a real general matrix; BALBAK: Back transform vectors of matrix formed by BALANC; BANDR: Reduce sym. band matrix to sym. tridiag. matrix; BANDV: Find some vectors of sym. band matrix; BISECT: Find some values of sym. tridiag. matrix; BQR: Find some values of sym. band matrix; CBABK2: Back transform vectors of matrix formed by CBAL; CBAL: Balance a complex general matrix; CDIV: Perform division of two complex quantities; CG: Driver subroutine for a complex general matrix; CH: Driver subroutine for a complex Hermitian matrix; CINVIT: Find some vectors of complex Hess. matrix; COMBAK: Back transform vectors of matrix formed by COMHES; COMHES: Reduce complex matrix to complex Hess. (elementary); COMLR: Find all values of complex Hess. matrix (LR); COMLR2: Find all values/vectors of cmplx Hess. matrix (LR); CCMQR: Find all values of complex Hessenberg matrix (QR); COMQR2: Find all values/vectors of cmplx Hess. matrix (QR); CORTB: Back transform vectors of matrix formed by CORTH; CORTH: Reduce complex matrix to complex Hess. (unitary); CSROOT: Find square root of complex quantity; ELMBAK: Back transform vectors of matrix formed by ELMHES; ELMHES: Reduce real matrix to real Hess. (elementary); ELTRAN: Accumulate transformations from ELMHES (for HQR2); EPSLON: Estimate unit roundoff

  17. Cessna Citation X Business Aircraft Eigenvalue Stability – Part2: Flight Envelope Analysis

    Yamina BOUGHARI

    2017-12-01

    Full Text Available Civil aircraft flight control clearance is a time consuming, thus an expensive process in the aerospace industry. This process has to be investigated and proved to be safe for thousands of combinations in terms of speeds, altitudes, gross weights, Xcg / weight configurations and angles of attack. Even in this case, a worst-case condition that could lead to a critical situation might be missed. To address this problem, models that are able to describe an aircraft’s dynamics by taking into account all uncertainties over a region within a flight envelope have been developed using Linear Fractional Representation. In order to investigate the Cessna Citation X aircraft Eigenvalue Stability envelope, the Linear Fractional Representation models are implemented using the speeds and the altitudes as varying parameters. In this paper Part 2, the aircraft longitudinal eigenvalue stability is analyzed in a continuous range of flight envelope with varying parameter of True airspeed and altitude, instead of a single point, like classical methods. This is known as the aeroelastic stability envelope, required for civil aircraft certification as given by the Circular Advisory “Aeroelastic Stability Substantiation of Transport Category Airplanes AC No: 25.629-18”. In this new methodology the analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms by using the linear matrix inequalities to evaluate the eigenvalue stability, which is reduced to search for the negative eigenvalues in a region of flight envelope. It can also be used to study the stability of a system during an arbitrary motion from one point to another in the flight envelope. A whole aircraft analysis results’ for its entire envelope are presented in the form of graphs, thus offering good readability, and making them easily exploitable.

  18. Solving the generalized symmetric eigenvalue problem using tile algorithms on multicore architectures

    Ltaief, Hatem

    2012-01-01

    This paper proposes an efficient implementation of the generalized symmetric eigenvalue problem on multicore architecture. Based on a four-stage approach and tile algorithms, the original problem is first transformed into a standard symmetric eigenvalue problem by computing the Cholesky factorization of the right hand side symmetric definite positive matrix (first stage), and applying the inverse of the freshly computed triangular Cholesky factors to the original dense symmetric matrix of the problem (second stage). Calculating the eigenpairs of the resulting problem is then equivalent to the eigenpairs of the original problem. The computation proceeds by reducing the updated dense symmetric matrix to symmetric band form (third stage). The band structure is further reduced by applying a bulge chasing procedure, which annihilates the extra off-diagonal entries using orthogonal transformations (fourth stage). More details on the third and fourth stage can be found in Haidar et al. [Accepted at SC\\'11, November 2011]. The eigenvalues are then calculated from the tridiagonal form using the standard LAPACK QR algorithm (i.e., DTSEQR routine), while the complex and challenging eigenvector computations will be addressed in a companion paper. The tasks from the various stages can concurrently run in an out-of-order fashion. The data dependencies are cautiously tracked by the dynamic runtime system environment QUARK, which ensures the dependencies are not violated for numerical correctness purposes. The obtained tile four-stage generalized symmetric eigenvalue solver significantly outperforms the state-of-the-art numerical libraries (up to 21-fold speed up against multithreaded LAPACK with optimized multithreaded MKL BLAS and up to 4-fold speed up against the corresponding routine from the commercial numerical software Intel MKL) on four sockets twelve cores AMD system with a 24000×24000 matrix size. © 2012 The authors and IOS Press. All rights reserved.

  19. Hessian eigenvalue distribution in a random Gaussian landscape

    Yamada, Masaki; Vilenkin, Alexander

    2018-03-01

    The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of 1/ N expansion, where N is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.

  20. A Hybrid Parallel Preconditioning Algorithm For CFD

    Barth,Timothy J.; Tang, Wei-Pai; Kwak, Dochan (Technical Monitor)

    1995-01-01

    A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

  1. Preconditions for Citizen Journalism: A Sociological Assessment

    Hayley Watson

    2011-01-01

    The rise of the citizen journalist and increased attention to this phenomenon requires a sociological assessment that seeks to develop an understanding of how citizen journalism has emerged in contemporary society. This article makes a distinction between two different subcategories of citizen journalism, that is independent and dependent citizen journalism. The purpose of this article is to present four preconditions for citizen journalism to emerge in contemporary society: advanced technolo...

  2. Error Estimation in Preconditioned Conjugate Gradients

    Strakoš, Zdeněk; Tichý, Petr

    2005-01-01

    Roč. 45, - (2005), s. 789-817 ISSN 0006-3835 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB1030306 Institutional research plan: CEZ:AV0Z10300504 Keywords : preconditioned conjugate gradient method * error bounds * stopping criteria * evaluation of convergence * numerical stability * finite precision arithmetic * rounding errors Subject RIV: BA - General Mathematics Impact factor: 0.509, year: 2005

  3. M-step preconditioned conjugate gradient methods

    Adams, L.

    1983-01-01

    Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

  4. Solving the RPA eigenvalue equation in real-space

    Muta, A; Hashimoto, Y; Yabana, K

    2002-01-01

    We present a computational method to solve the RPA eigenvalue equation employing a uniform grid representation in three-dimensional Cartesian coordinates. The conjugate gradient method is used for this purpose as an interactive method for a generalized eigenvalue problem. No construction of unoccupied orbitals is required in the procedure. We expect this method to be useful for systems lacking spatial symmetry to calculate accurate eigenvalues and transition matrix elements of a few low-lying excitations. Some applications are presented to demonstrate the feasibility of the method, considering the simplified mean-field model as an example of a nuclear physics system and the electronic excitations in molecules with time-dependent density functional theory as an example of an electronic system. (author)

  5. Efficient methods for time-absorption (α) eigenvalue calculations

    Hill, T.R.

    1983-01-01

    The time-absorption eigenvalue (α) calculation is one of the options found in most discrete-ordinates transport codes. Several methods have been developed at Los Alamos to improve the efficiency of this calculation. Two procedures, based on coarse-mesh rebalance, to accelerate the α eigenvalue search are derived. A hybrid scheme to automatically choose the more-effective rebalance method is described. The α rebalance scheme permits some simple modifications to the iteration strategy that eliminates many unnecessary calculations required in the standard search procedure. For several fast supercritical test problems, these methods resulted in convergence with one-fifth the number of iterations required for the conventional eigenvalue search procedure

  6. Evaluation of Eigenvalue Routines for Large Scale Applications

    V.A. Tischler

    1994-01-01

    Full Text Available The NASA structural analysis (NASTRAN∗ program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this article is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the block Lanczos aLgorithm. This eigenvalue routine is now availabLe in several mathematics libraries as well as in severaL commerciaL versions of NASTRAN. In addition, the eRA Y library maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The block Lanczos algorithm was found to be extremely efficient, particularly for very large problems.

  7. Bounds and estimates for the linearly perturbed eigenvalue problem

    Raddatz, W.D.

    1983-01-01

    This thesis considers the problem of bounding and estimating the discrete portion of the spectrum of a linearly perturbed self-adjoint operator, M(x). It is supposed that one knows an incomplete set of data consisting in the first few coefficients of the Taylor series expansions of one or more of the eigenvalues of M(x) about x = 0. The foundations of the variational study of eigen-values are first presented. These are then used to construct the best possible upper bounds and estimates using various sets of given information. Lower bounds are obtained by estimating the error in the upper bounds. The extension of these bounds and estimates to the eigenvalues of the doubly-perturbed operator M(x,y) is discussed. The results presented have numerous practical application in the physical sciences, including problems in atomic physics and the theory of vibrations of acoustical and mechanical systems

  8. An algebraic substructuring using multiple shifts for eigenvalue computations

    Ko, Jin Hwan; Jung, Sung Nam; Byun, Do Young; Bai, Zhaojun

    2008-01-01

    Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large-sized problems, but originally it was designed to calculate only the smallest eigenvalues. Recently, an updated version of AS has been introduced to calculate the interior eigenvalues over a specified range by using a shift concept that is referred to as the shifted AS. In this work, we propose a combined method of both AS and the shifted AS by using multiple shifts for solving a considerable number of eigensolutions in a large-sized problem, which is an emerging computational issue of noise or vibration analysis in vehicle design. In addition, we investigated the accuracy of the shifted AS by presenting an error criterion. The proposed method has been applied to the FE model of an automobile body. The combined method yielded a higher efficiency without loss of accuracy in comparison to the original AS

  9. Eigenvalues of PT-symmetric oscillators with polynomial potentials

    Shin, Kwang C

    2005-01-01

    We study the eigenvalue problem -u''(z) - [(iz) m + P m-1 (iz)]u(z) λu(z) with the boundary condition that u(z) decays to zero as z tends to infinity along the rays arg z = -π/2 ± 2π/(m+2) in the complex plane, where P m-1 (z) = a 1 z m-1 + a 2 z m-2 + . . . + a m-1 z is a polynomial and integers m ≥ 3. We provide an asymptotic expansion of the eigenvalues λ n as n → +∞, and prove that for each real polynomial P m-1 , the eigenvalues are all real and positive, with only finitely many exceptions

  10. Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

    Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

    2017-11-01

    Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

  11. Radiographers' preconditions for evidence-based radiography

    Ahonen, Sanna-Mari; Liikanen, Eeva

    2010-01-01

    Evidence-based practice (EBP) is essential in today's health care, but its establishment requires several preconditions from individuals and organizations (e.g. knowledge, understanding, attitudes, abilities, self-confidence, support, and resources). Previous studies suggest that radiographers do generate and use evidence in their work, but evidence-based radiography (EBR) is not yet used routinely as established practice, especially in terms of research utilization. This paper aims to describe radiographers' preconditions for EBR, and their participation in research activities. Main focus is on research utilization. Using an electronic questionnaire developed for this study, a survey was conducted: data collected from Finnish radiographers and radiotherapists (N = 438) were analysed both statistically and qualitatively. The final response rate was 39%. The results suggest radiographers' preconditions for EBR to consist of knowledge of research, significance of research activities, research-orientated way of working, and support. In addition, adequate resourcing is essential. Reading scientific journals, participation in research activities, a higher degree of education, and senior post seem to be significant promoters of EBR and research utilization. The results support the notion that EBR, and especially research utilization, are not yet well-established in Finland, and radiographers' viewpoints concerning the role and significance of research evidence and research activities still seem to vary.

  12. Joint density of eigenvalues in spiked multivariate models.

    Dharmawansa, Prathapasinghe; Johnstone, Iain M

    2014-01-01

    The classical methods of multivariate analysis are based on the eigenvalues of one or two sample covariance matrices. In many applications of these methods, for example to high dimensional data, it is natural to consider alternative hypotheses which are a low rank departure from the null hypothesis. For rank one alternatives, this note provides a representation for the joint eigenvalue density in terms of a single contour integral. This will be of use for deriving approximate distributions for likelihood ratios and 'linear' statistics used in testing.

  13. Recent developments in semiclassical mechanics: eigenvalues and reaction rate constants

    Miller, W.H.

    1976-04-01

    A semiclassical treatment of eigenvalues for a multidimensional non-separable potential function and of the rate constant for a chemical reaction with an activation barrier is presented. Both phenomena are seen to be described by essentially the same semiclassical formalism, which is based on a construction of the total Hamiltonian in terms of the complete set of ''good'' action variables (or adiabatic invariants) associated with the minimum in the potential energy surface for the eigenvalue case, or the saddle point in the potential energy surface for the case of chemical reaction

  14. A teaching proposal for the study of Eigenvectors and Eigenvalues

    María José Beltrán Meneu

    2017-03-01

    Full Text Available In this work, we present a teaching proposal which emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. These concepts are introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was motivated after observing students’ difficulties when treating eigenvectors and eigenvalues from a geometric point of view. It was designed following a particular sequence of activities with the schema: exploration, introduction of concepts, structuring of knowledge and application, and considering the three worlds of mathematical thinking provided by Tall: embodied, symbolic and formal.

  15. Eigenvalues of the Transferences of Gaussian Optical Systems

    W.F. Harris

    2005-12-01

    Full Text Available The  problem  of  how  to  define  an  average eye leads to the question of what eigenvalues are  possible  for  ray  transferences.  This  paper examines the set of possible eigenvalues in the simplest possible case, that of optical systems consisting  of  elements  that  are  stigmatic  and centred on a common axis.

  16. Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

    Kaporin, I. E.

    2012-02-01

    In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

  17. Energy eigenvalues and squeezing properties of general systems of coupled quantum anharmonic oscillators

    Chung, N. N.; Chew, L. Y.

    2007-01-01

    We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems

  18. Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications

    Axelsson, Owe

    2017-01-01

    Roč. 62, č. 6 (2017), s. 537-559 ISSN 0862-7940. [SNA´17 - Seminar on numerical analysis. Ostrava, 30.01.2017-03.02.2017] Institutional support: RVO:68145535 Keywords : preconditioning * Schur complement * transformation * optimal control * implicit time integration Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.618, year: 2016 http://articles.math.cas.cz/10.21136/AM.2017.0222-17/?type=F

  19. Fundaments of transport equation splitting and the eigenvalue problem

    Stancic, V.

    2000-01-01

    In order to remove some singularities concerning the boundary conditions of one dimensional transport equation, a split form of transport equation describing the forward i.e. μ≥0, and a backward μ<0 directed neutrons is being proposed here. The eigenvalue problem has also been considered here (author)

  20. Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition

    Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)

    2014-12-15

    In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.

  1. A Universal Quantum Circuit Scheme For Finding Complex Eigenvalues

    Daskin, Anmer; Grama, Ananth; Kais, Sabre

    2013-01-01

    We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of resonance states for quantum systems.

  2. Eigenvalue estimates for submanifolds with bounded f-mean curvature

    GUANGYUE HUANG

    1College of Mathematics and Information Science, Henan Normal University,. Xinxiang 453007 ... submanifolds in a hyperbolic space with the norm of their mean curvature vector bounded above by a constant. ..... [2] Batista M, Cavalcante M P and Pyo J, Some isoperimetric inequalities and eigenvalue estimates in ...

  3. Hardy inequality, compact embeddings and properties of certain eigenvalue problems

    Drábek, P.; Kufner, Alois

    2017-01-01

    Roč. 49, č. 1 (2017), s. 5-17 ISSN 0049-4704 Institutional support: RVO:67985840 Keywords : BD-property * compact embeddings * degenerate and singular eigenvalue problem Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics https://www.openstarts.units.it/handle/10077/16201

  4. Escape rate from strange sets as an eigenvalue

    Tel, T.

    1986-06-01

    A new method is applied for calculating the escape rate from chaotic repellers or semi-attractors, based on the eigenvalue problem of the master equation of discrete dynamical systems. The corresponding eigenfunction is found to be smooth along unstable directions and to be, in general, a fractal measure. Examples of one and two dimensional maps are investigated. (author)

  5. First-order optical systems with unimodular eigenvalues

    Bastiaans, M.J.; Alieva, T.

    2006-01-01

    It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only unimodular eigenvalues, is similar to a separable fractional Fourier transformer in the sense that the ray transformation matrices of the unimodular system and the

  6. Eigenvalue estimates of positive integral operators with analytic ...

    Eigenvalue estimates of positive integral operators. 337 will be used to denote, respectively, the complex line integral of f along γ and the integral of f with respect to arc-length measure. In the first case we assume γ has an orientation. The notation Lp(γ ) will denote the Lp space of normalized arc length measure on γ with.

  7. New algorithms for the symmetric tridiagonal eigenvalue computation

    Pan, V. [City Univ. of New York, Bronx, NY (United States)]|[International Computer Sciences Institute, Berkeley, CA (United States)

    1994-12-31

    The author presents new algorithms that accelerate the bisection method for the symmetric eigenvalue problem. The algorithms rely on some new techniques, which include acceleration of Newton`s iteration and can also be further applied to acceleration of some other iterative processes, in particular, of iterative algorithms for approximating polynomial zeros.

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

    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.

  9. Ischemic preconditioning protects against gap junctional uncoupling in cardiac myofibroblasts.

    Sundset, Rune; Cooper, Marie; Mikalsen, Svein-Ole; Ytrehus, Kirsti

    2004-01-01

    Ischemic preconditioning increases the heart's tolerance to a subsequent longer ischemic period. The purpose of this study was to investigate the role of gap junction communication in simulated preconditioning in cultured neonatal rat cardiac myofibroblasts. Gap junctional intercellular communication was assessed by Lucifer yellow dye transfer. Preconditioning preserved intercellular coupling after prolonged ischemia. An initial reduction in coupling in response to the preconditioning stimulus was also observed. This may protect neighboring cells from damaging substances produced during subsequent regional ischemia in vivo, and may preserve gap junctional communication required for enhanced functional recovery during subsequent reperfusion.

  10. Solving eigenvalue response matrix equations with nonlinear techniques

    Roberts, Jeremy A.; Forget, Benoit

    2014-01-01

    Highlights: • High performance solvers were applied within ERMM for the first time. • Accelerated fixed-point methods were developed that reduce computational times by 2–3. • A nonlinear, Newton-based ERMM led to similar improvement and more robustness. • A 3-D, SN-based ERMM shows how ERMM can apply fine-mesh methods to full-core analysis. - Abstract: This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness

  11. Tranexamic Acid Does Not Influence Cardioprotection by Ischemic Preconditioning and Remote Ischemic Preconditioning

    van Caster, Patrick; Eiling, Sandra; Boekholt, Yvonne; Behmenburg, Friederike; Dorsch, Marianne; Heinen, André; Hollmann, Markus W.; Huhn, Ragnar

    2018-01-01

    Prior studies have suggested that the antifibrinolytic drug aprotinin increases the infarct size after ischemia and reperfusion (I/R) and attenuates the effect of ischemic preconditioning (IPC). Aprotinin was replaced by tranexamic acid (TXA) in clinical practice. Here, we investigated whether TXA

  12. Parallel preconditioning techniques for sparse CG solvers

    Basermann, A.; Reichel, B.; Schelthoff, C. [Central Institute for Applied Mathematics, Juelich (Germany)

    1996-12-31

    Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial differential equations. The large size and the condition of many technical or physical applications in this area result in the need for efficient parallelization and preconditioning techniques of the CG method. In particular for very ill-conditioned matrices, sophisticated preconditioner are necessary to obtain both acceptable convergence and accuracy of CG. Here, we investigate variants of polynomial and incomplete Cholesky preconditioners that markedly reduce the iterations of the simply diagonally scaled CG and are shown to be well suited for massively parallel machines.

  13. Preconditioning, postconditioning and their application to clinical cardiology.

    Kloner, Robert A; Rezkalla, Shereif H

    2006-05-01

    Ischemic preconditioning is a well-established phenomenon first described in experimental preparations in which brief episodes of ischemia/reperfusion applied prior to a longer coronary artery occlusion reduce myocardial infarct size. There are ample correlates of ischemic preconditioning in the clinical realm. Preconditioning mimetic agents that stimulate the biochemical pathways of ischemic preconditioning and protect the heart without inducing ischemia have been examined in numerous experimental studies. However, despite the effectiveness of ischemic preconditioning and preconditioning mimetics for protecting ischemic myocardium, there are no preconditioning-based therapies that are routinely used in clinical medicine at the current time. Part of the problem is the need to administer therapy prior to the known ischemic event. Other issues are that percutaneous coronary intervention technology has advanced so far (with the development of stents and drug-eluting stents) that ischemic preconditioning or preconditioning mimetics have not been needed in most interventional cases. Recent clinical trials such as AMISTAD I and II (Acute Myocardial Infarction STudy of ADenosine) suggest that some preconditioning mimetics may reduce myocardial infarct size when given along with reperfusion or, as in the IONA trial, have benefit on clinical events when administered chronically in patients with known coronary artery disease. It is possible that some of the benefit described for adenosine in the AMISTAD 1 and 2 trials represents a manifestation of the recently described postconditioning phenomenon. It is probable that postconditioning--in which reperfusion is interrupted with brief coronary occlusions and reperfusion sequences--is more likely than preconditioning to be feasible as a clinical application to patients undergoing percutaneous coronary intervention for acute myocardial infarction.

  14. Effect of Different Preconditioning Regimens on the Expression Profile of Murine Adipose-Derived Stromal/Stem Cells

    Patrick C. Baer

    2018-06-01

    Full Text Available Stem cell-based therapies require cells with a maximum regenerative capacity in order to support regeneration after tissue injury and organ failure. Optimization of this regenerative potential of mesenchymal stromal/stem cells (MSC or their conditioned medium by in vitro preconditioning regimens are considered to be a promising strategy to improve the release of regenerative factors. In the present study, MSC were isolated from inguinal adipose tissue (mASC from C57BL/6 mice, cultured, and characterized. Then, mASC were either preconditioned by incubation in a hypoxic environment (0.5% O2, or in normoxia in the presence of murine epidermal growth factor (EGF or tumor necrosis factor α (TNFα for 48 h. Protein expression was measured by a commercially available array. Selected factors were verified by PCR analysis. The expression of 83 out of 308 proteins (26.9% assayed was found to be increased after preconditioning with TNFα, whereas the expression of 61 (19.8% and 70 (22.7% proteins was increased after incubation with EGF or in hypoxia, respectively. Furthermore, we showed the proliferation-promoting effects of the preconditioned culture supernatants on injured epithelial cells in vitro. Our findings indicate that each preconditioning regimen tested induced an individual expression profile with a wide variety of factors, including several growth factors and cytokines, and therefore may enhance the regenerative potential of mASC for cell-based therapies.

  15. An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions

    Wei Wang

    2014-01-01

    Full Text Available We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.

  16. On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue

    Asadzadeh, M.; Thevenot, L.

    2010-01-01

    The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (D G) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ??in R3 with a polygonal convex cross-section ? The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.

  17. Field-Split Preconditioned Inexact Newton Algorithms

    Liu, Lulu

    2015-06-02

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

  18. Field-Split Preconditioned Inexact Newton Algorithms

    Liu, Lulu; Keyes, David E.

    2015-01-01

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.

  19. Limb remote-preconditioning protects against focal ischemia in rats and contradicts the dogma of therapeutic time windows for preconditioning

    Ren, Chuancheng; Gao, Xuwen; Steinberg, Gary K.; Zhao, Heng

    2009-01-01

    Remote ischemic preconditioning is an emerging concept for stroke treatment, but its protection against focal stroke has not been established. We tested whether remote preconditioning, performed in the ipsilateral hind limb, protects against focal stroke and explored its protective parameters. Stroke was generated by a permanent occlusion of the left distal middle cerebral artery (MCA) combined with a 30 minute occlusion of the bilateral common carotid arteries (CCA) in male rats. Limb preconditioning was generated by 5 or 15 minute occlusion followed with the same period of reperfusion of the left hind femoral artery, and repeated for 2 or 3 cycles. Infarct was measured 2 days later. The results showed that rapid preconditioning with 3 cycles of 15 minutes performed immediately before stroke reduced infarct size from 47.7±7.6% of control ischemia to 9.8±8.6%; at 2 cycles of 15 minutes, infarct was reduced to 24.7±7.3%; at 2 cycles of 5 minutes, infarct was not reduced. Delayed preconditioning with 3 cycles of 15 minutes conducted 2 days before stroke also reduced infarct to 23.0 ±10.9%, but with 2 cycles of 15 minutes it offered no protection. The protective effects at these two therapeutic time windows of remote preconditioning are consistent with those of conventional preconditioning, in which the preconditioning ischemia is induced in the brain itself. Unexpectedly, intermediate preconditioning with 3 cycles of 15 minutes performed 12 hours before stroke also reduced infarct to 24.7±4.7%, which contradicts the current dogma for therapeutic time windows for the conventional preconditioning that has no protection at this time point. In conclusion, remote preconditioning performed in one limb protected against ischemic damage after focal cerebral ischemia. PMID:18201834

  20. 40 CFR 86.532-78 - Vehicle preconditioning.

    2010-07-01

    ... 40 Protection of Environment 18 2010-07-01 2010-07-01 false Vehicle preconditioning. 86.532-78... (CONTINUED) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES Emission Regulations for 1978 and Later New Motorcycles; Test Procedures § 86.532-78 Vehicle preconditioning. (a) The vehicle...

  1. Helium induces preconditioning in human endothelium in vivo

    Smit, Kirsten F.; Oei, Gezina T. M. L.; Brevoord, Daniel; Stroes, Erik S.; Nieuwland, Rienk; Schlack, Wolfgang S.; Hollmann, Markus W.; Weber, Nina C.; Preckel, Benedikt

    2013-01-01

    Helium protects myocardium by inducing preconditioning in animals. We investigated whether human endothelium is preconditioned by helium inhalation in vivo. Forearm ischemia-reperfusion (I/R) in healthy volunteers (each group n = 10) was performed by inflating a blood pressure cuff for 20 min.

  2. The universal eigenvalue bounds of Payne–Pólya–Weinberger, Hile ...

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    following universal inequalities for the λi's in the case when n = 2: λk+1 − λk ≤. 2 .... with V ≥ 0 on and eigenvalue problems with a weight (e.g., the fixed ...... [29] Protter M H, Universal inequalities for eigenvalues, Maximum Principles and Eigenvalue. Problems in ... minimal submanifolds, Ann. Scuola Norm. Sup. Pisa Cl.

  3. Parallelization of the preconditioned IDR solver for modern multicore computer systems

    Bessonov, O. A.; Fedoseyev, A. I.

    2012-10-01

    This paper present the analysis, parallelization and optimization approach for the large sparse matrix solver CNSPACK for modern multicore microprocessors. CNSPACK is an advanced solver successfully used for coupled solution of stiff problems arising in multiphysics applications such as CFD, semiconductor transport, kinetic and quantum problems. It employs iterative IDR algorithm with ILU preconditioning (user chosen ILU preconditioning order). CNSPACK has been successfully used during last decade for solving problems in several application areas, including fluid dynamics and semiconductor device simulation. However, there was a dramatic change in processor architectures and computer system organization in recent years. Due to this, performance criteria and methods have been revisited, together with involving the parallelization of the solver and preconditioner using Open MP environment. Results of the successful implementation for efficient parallelization are presented for the most advances computer system (Intel Core i7-9xx or two-processor Xeon 55xx/56xx).

  4. Asymptotics of the Eigenvalues of a Self-Adjoint Fourth Order Boundary Value Problem with Four Eigenvalue Parameter Dependent Boundary Conditions

    Manfred Möller

    2013-01-01

    Full Text Available Considered is a regular fourth order ordinary differential equation which depends quadratically on the eigenvalue parameter λ and which has separable boundary conditions depending linearly on λ. It is shown that the eigenvalues lie in the closed upper half plane or on the imaginary axis and are symmetric with respect to the imaginary axis. The first four terms in the asymptotic expansion of the eigenvalues are provided.

  5. Two new eigenvalue localization sets for tensors and theirs applications

    Zhao Jianxing

    2017-10-01

    Full Text Available A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324 and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50. As an application, a weaker checkable sufficient condition for the positive (semi-definiteness of an even-order real symmetric tensor is obtained. Meanwhile, an S-type E-eigenvalue localization set for tensors is given and proved to be tighter than that presented by Wang et al. (Discrete Cont. Dyn.-B, 2017, 22(1, 187-198. As an application, an S-type upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained. Finally, numerical examples are given to verify the theoretical results.

  6. EISPACK-J: subprogram package for solving eigenvalue problems

    Fujimura, Toichiro; Tsutsui, Tsuneo

    1979-05-01

    EISPACK-J, a subprogram package for solving eigenvalue problems, has been developed and subprograms with a variety of functions have been prepared. These subprograms can solve standard problems of complex matrices, general problems of real matrices and special problems in which only the required eigenvalues and eigenvectors are calculated. They are compared to existing subprograms, showing their features through benchmark tests. Many test problems, including realistic scale problems, are provided for the benchmark tests. Discussions are made on computer core storage and computing time required for each subprogram, and accuracy of the solution. The results show that the subprograms of EISPACK-J, based on Householder, QR and inverse iteration methods, are the best in computing time and accuracy. (author)

  7. Weighted SGD for ℓp Regression with Randomized Preconditioning*

    Yang, Jiyan; Chow, Yin-Lam; Ré, Christopher; Mahoney, Michael W.

    2018-01-01

    In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. SGD methods are easy to implement and applicable to a wide range of convex optimization problems. In contrast, RLA algorithms provide much stronger performance guarantees but are applicable to a narrower class of problems. We aim to bridge the gap between these two methods in solving constrained overdetermined linear regression problems—e.g., ℓ2 and ℓ1 regression problems. We propose a hybrid algorithm named pwSGD that uses RLA techniques for preconditioning and constructing an importance sampling distribution, and then performs an SGD-like iterative process with weighted sampling on the preconditioned system.By rewriting a deterministic ℓp regression problem as a stochastic optimization problem, we connect pwSGD to several existing ℓp solvers including RLA methods with algorithmic leveraging (RLA for short).We prove that pwSGD inherits faster convergence rates that only depend on the lower dimension of the linear system, while maintaining low computation complexity. Such SGD convergence rates are superior to other related SGD algorithm such as the weighted randomized Kaczmarz algorithm.Particularly, when solving ℓ1 regression with size n by d, pwSGD returns an approximate solution with ε relative error in the objective value in 𝒪(log n·nnz(A)+poly(d)/ε2) time. This complexity is uniformly better than that of RLA methods in terms of both ε and d when the problem is unconstrained. In the presence of constraints, pwSGD only has to solve a sequence of much simpler and smaller optimization problem over the same constraints. In general this is more efficient than solving the constrained subproblem required in RLA.For ℓ2 regression, pwSGD returns an approximate solution with ε relative error in the objective value and the solution vector measured in

  8. Gravitational lensing by eigenvalue distributions of random matrix models

    Martínez Alonso, Luis; Medina, Elena

    2018-05-01

    We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.

  9. On Polya's inequality for torsional rigidity and first Dirichlet eigenvalue

    Berg, M. van den; Ferone, V.; Nitsch, C.; Trombetti, C.

    2016-01-01

    Let $\\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\\Omega|$. We obtain some properties of the set function $F:\\Omega\\mapsto \\R^+$ defined by $$ F(\\Omega)=\\frac{T(\\Omega)\\lambda_1(\\Omega)}{|\\Omega|} ,$$ where $T(\\Omega)$ and $\\lambda_1(\\Omega)$ are the torsional rigidity and the first eigenvalue of the Dirichlet Laplacian respectively. We improve the classical P\\'olya bound $F(\\Omega)\\le 1,$ and show that $$F(\\Omega)\\le 1- \

  10. A method for eigenvalues of sparse lambda-matrices

    Yang, W.H.

    1982-01-01

    The matrix N(lambda) whose elements are functions of a parameter lambda is called the lambda-matrix. Those values of lambda that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a lambda-matrix is presented. A simple explicit convergence criterion is given as well as the algorithm and two numerical examples

  11. Eigenvalue inequalities for the Laplacian with mixed boundary conditions

    Lotoreichik, Vladimir; Rohleder, J.

    2017-01-01

    Roč. 263, č. 1 (2017), s. 491-508 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplace operator * mixed boundary conditions * eigenvalue inequality * polyhedral domain * Lipschitz domain Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016

  12. Fourth-order Perturbed Eigenvalue Equation for Stepwise Damage Detection of Aeroplane Wing

    Wong Chun Nam

    2016-01-01

    Full Text Available Perturbed eigenvalue equations up to fourth-order are established to detect structural damage in aeroplane wing. Complete set of perturbation terms including orthogonal and non-orthogonal coefficients are computed using perturbed eigenvalue and orthonormal equations. Then the perturbed eigenparameters are optimized using BFGS approach. Finite element model with small to large stepwise damage is used to represent actual aeroplane wing. In small damaged level, termination number is the same for both approaches, while rms errors and termination d-norms are very close. For medium damaged level, termination number is larger for third-order perturbation with lower d-norm and smaller rms error. In large damaged level, termination number is much larger for third-order perturbation with same d-norm and larger rms error. These trends are more significant as the damaged level increases. As the stepwise damage effect increases with damage level, the increase in stepwise effect leads to the increase in model order. Hence, fourth-order perturbation is more accurate to estimate the model solution.

  13. Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code

    Gill, D. F.; Nease, B. R.; Griesheimer, D. P.

    2013-01-01

    A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)

  14. Movable geometry and eigenvalue search capability in the MC21 Monte Carlo code

    Gill, D. F.; Nease, B. R.; Griesheimer, D. P. [Bettis Atomic Power Laboratory, PO Box 79, West Mifflin, PA 15122 (United States)

    2013-07-01

    A description of a robust and flexible movable geometry implementation in the Monte Carlo code MC21 is described along with a search algorithm that can be used in conjunction with the movable geometry capability to perform eigenvalue searches based on the position of some geometric component. The natural use of the combined movement and search capability is searching to critical through variation of control rod (or control drum) position. The movable geometry discussion provides the mathematical framework for moving surfaces in the MC21 combinatorial solid geometry description. A discussion of the interface between the movable geometry system and the user is also described, particularly the ability to create a hierarchy of movable groups. Combined with the hierarchical geometry description in MC21 the movable group framework provides a very powerful system for inline geometry modification. The eigenvalue search algorithm implemented in MC21 is also described. The foundations of this algorithm are a regula falsi search though several considerations are made in an effort to increase the efficiency of the algorithm for use with Monte Carlo. Specifically, criteria are developed to determine after each batch whether the Monte Carlo calculation should be continued, the search iteration can be rejected, or the search iteration has converged. These criteria seek to minimize the amount of time spent per iteration. Results for the regula falsi method are shown, illustrating that the method as implemented is indeed convergent and that the optimizations made ultimately reduce the total computational expense. (authors)

  15. Eigenvalue solutions in finite element thermal transient problems

    Stoker, J.R.

    1975-01-01

    The eigenvalue economiser concept can be useful in solving large finite element transient heat flow problems in which the boundary heat transfer coefficients are constant. The usual economiser theory is equivalent to applying a unit thermal 'force' to each of a small sub-set of nodes on the finite element mesh, and then calculating sets of resulting steady state temperatures. Subsequently it is assumed that the required transient temperature distributions can be approximated by a linear combination of this comparatively small set of master temperatures. The accuracy of a reduced eigenvalue calculation depends upon a good choice of master nodes, which presupposes at least a little knowledge about what sort of shape is expected in the unknown temperature distributions. There are some instances, however, where a reasonably good idea exists of the required shapes, permitting a modification to the economiser process which leads to greater economy in the number of master temperatures. The suggested new approach is to use manually prescribed temperature distributions as the master distributions, rather than using temperatures resulting from unit thermal forces. Thus, with a little pre-knowledge one may write down a set of master distributions which, as a linear combination, can represent the required solution over the range of interest to a reasonable engineering accuracy, and using the minimum number of variables. The proposed modified eigenvalue economiser technique then uses the master distributions in an automatic way to arrive at the required solution. The technique is illustrated by some simple finite element examples

  16. New exact approaches to the nuclear eigenvalue problem

    Andreozzi, F.; Lo Iudice, N.; Porrino, A.; Knapp, F.; Kvasil, J.

    2005-01-01

    In a recent past some of us have developed a new algorithm for diagonalizing the shell model Hamiltonian which consists of an iterative sequence of diagonalization of sub-matrices of small dimensions. The method, apart from being easy to implement, is robust, yielding always stable numerical solutions, and free of ghost eigenvalues. Subsequently, we have endowed the algorithm with an importance sampling, which leads to a drastic truncation of the shell model space, while keeping the accuracy of the solutions under control. Applications to typical nuclei show that the sampling yields also an extrapolation law to the exact eigenvalues. Complementary to the shell model algorithm is a method we are developing for studying collective and non collective excitations. To this purpose we solve the nuclear eigenvalue problem in a space which is the direct sum of Tamm-Dancoff n-phonon subspaces (n=0,1, ...N). The multiphonon basis is constructed by an iterative equation of motion method, which generates an over complete set of n-phonon states from the (n-1)-phonon basis. The redundancy is removed completely and exactly by a method based on the Choleski decomposition. The full Hamiltonian matrix comes out to have a simple structure and, therefore, can be drastically truncated before diagonalization by the mentioned importance sampling method. The phonon composition of the basis states allows removing naturally and maximally the spurious admixtures induced by the centre of mass motion. An application of the method to 16 O will be given for illustrative purposes. (authors)

  17. Ab initio nuclear structure - the large sparse matrix eigenvalue problem

    Vary, James P; Maris, Pieter [Department of Physics, Iowa State University, Ames, IA, 50011 (United States); Ng, Esmond; Yang, Chao [Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sosonkina, Masha, E-mail: jvary@iastate.ed [Scalable Computing Laboratory, Ames Laboratory, Iowa State University, Ames, IA, 50011 (United States)

    2009-07-01

    The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10{sup 10} and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

  18. Ab initio nuclear structure - the large sparse matrix eigenvalue problem

    Vary, James P; Maris, Pieter; Ng, Esmond; Yang, Chao; Sosonkina, Masha

    2009-01-01

    The structure and reactions of light nuclei represent fundamental and formidable challenges for microscopic theory based on realistic strong interaction potentials. Several ab initio methods have now emerged that provide nearly exact solutions for some nuclear properties. The ab initio no core shell model (NCSM) and the no core full configuration (NCFC) method, frame this quantum many-particle problem as a large sparse matrix eigenvalue problem where one evaluates the Hamiltonian matrix in a basis space consisting of many-fermion Slater determinants and then solves for a set of the lowest eigenvalues and their associated eigenvectors. The resulting eigenvectors are employed to evaluate a set of experimental quantities to test the underlying potential. For fundamental problems of interest, the matrix dimension often exceeds 10 10 and the number of nonzero matrix elements may saturate available storage on present-day leadership class facilities. We survey recent results and advances in solving this large sparse matrix eigenvalue problem. We also outline the challenges that lie ahead for achieving further breakthroughs in fundamental nuclear theory using these ab initio approaches.

  19. Stratified source-sampling techniques for Monte Carlo eigenvalue analysis

    Mohamed, A.

    1998-01-01

    In 1995, at a conference on criticality safety, a special session was devoted to the Monte Carlo ''Eigenvalue of the World'' problem. Argonne presented a paper, at that session, in which the anomalies originally observed in that problem were reproduced in a much simplified model-problem configuration, and removed by a version of stratified source-sampling. In this paper, stratified source-sampling techniques are generalized and applied to three different Eigenvalue of the World configurations which take into account real-world statistical noise sources not included in the model problem, but which differ in the amount of neutronic coupling among the constituents of each configuration. It is concluded that, in Monte Carlo eigenvalue analysis of loosely-coupled arrays, the use of stratified source-sampling reduces the probability of encountering an anomalous result over that if conventional source-sampling methods are used. However, this gain in reliability is substantially less than that observed in the model-problem results

  20. AMDLIBF, IBM 360 Subroutine Library, Eigenvalues, Eigenvectors, Matrix Inversion

    Wang, Jesse Y.

    1980-01-01

    Description of problem or function: AMDLIBF is a subset of the IBM 360 Subroutine Library at the Applied Mathematics Division at Argonne. This subset includes library category F: Identification/Description: F152S F SYMINV: Invert sym. matrices, solve lin. systems; F154S A DOTP: Double plus precision accum. inner prod.; F156S F RAYCOR: Rayleigh corrections for eigenvalues; F161S F XTRADP: A fast extended precision inner product; F162S A XTRADP: Inner product of two DP real vectors; F202S F1 EIGEN: Eigen-system for real symmetric matrix; F203S F: Driver for F202S; F248S F RITZIT: Largest eigenvalue and vec. real sym. matrix; F261S F EIGINV: Inverse eigenvalue problem; F313S F CQZHES: Reduce cmplx matrices to upper Hess and tri; F314S F CQZVAL: Reduce complex matrix to upper Hess. form; F315S F CQZVEC: Eigenvectors of cmplx upper triang. syst.; F316S F CGG: Driver for complex general Eigen-problem; F402S F MATINV: Matrix inversion and sol. of linear eqns.; F403S F: Driver for F402S; F452S F CHOLLU,CHOLEQ: Sym. decomp. of pos. def. band matrices; F453S F MATINC: Inversion of complex matrices; F454S F CROUT: Solution of simultaneous linear equations; F455S F CROUTC: Sol. of simultaneous complex linear eqns.; F456S F1 DIAG: Integer preserving Gaussian elimination

  1. Large deviations of the maximum eigenvalue in Wishart random matrices

    Vivo, Pierpaolo; Majumdar, Satya N; Bohigas, Oriol

    2007-01-01

    We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X T X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value (λ) = N/c decreases for large N as ∼exp[-β/2 N 2 Φ - (2√c + 1: c)], where β = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M ≤ 1 and Φ - (x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions

  2. Large deviations of the maximum eigenvalue in Wishart random matrices

    Vivo, Pierpaolo [School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge, Middlesex, UB8 3PH (United Kingdom) ; Majumdar, Satya N [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France); Bohigas, Oriol [Laboratoire de Physique Theorique et Modeles Statistiques (UMR 8626 du CNRS), Universite Paris-Sud, Batiment 100, 91405 Orsay Cedex (France)

    2007-04-20

    We analytically compute the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues of a (N x N) Wishart matrix W = X{sup T}X (where X is a rectangular M x N matrix with independent Gaussian entries) are smaller than the mean value ({lambda}) = N/c decreases for large N as {approx}exp[-{beta}/2 N{sup 2}{phi}{sub -} (2{radical}c + 1: c)], where {beta} = 1, 2 corresponds respectively to real and complex Wishart matrices, c = N/M {<=} 1 and {phi}{sub -}(x; c) is a rate (sometimes also called large deviation) function that we compute explicitly. The result for the anti-Wishart case (M < N) simply follows by exchanging M and N. We also analytically determine the average spectral density of an ensemble of Wishart matrices whose eigenvalues are constrained to be smaller than a fixed barrier. Numerical simulations are in excellent agreement with the analytical predictions.

  3. Photonic band structure calculations using nonlinear eigenvalue techniques

    Spence, Alastair; Poulton, Chris

    2005-01-01

    This paper considers the numerical computation of the photonic band structure of periodic materials such as photonic crystals. This calculation involves the solution of a Hermitian nonlinear eigenvalue problem. Numerical methods for nonlinear eigenvalue problems are usually based on Newton's method or are extensions of techniques for the standard eigenvalue problem. We present a new variation on existing methods which has its derivation in methods for bifurcation problems, where bordered matrices are used to compute critical points in singular systems. This new approach has several advantages over the current methods. First, in our numerical calculations the new variation is more robust than existing techniques, having a larger domain of convergence. Second, the linear systems remain Hermitian and are nonsingular as the method converges. Third, the approach provides an elegant and efficient way of both thinking about the problem and organising the computer solution so that only one linear system needs to be factorised at each stage in the solution process. Finally, first- and higher-order derivatives are calculated as a natural extension of the basic method, and this has advantages in the electromagnetic problem discussed here, where the band structure is plotted as a set of paths in the (ω,k) plane

  4. Optimal algebraic multilevel preconditioning for local refinement along a line

    Margenov, S.D.; Maubach, J.M.L.

    1995-01-01

    The application of some recently proposed algebraic multilevel methods for the solution of two-dimensional finite element problems on nonuniform meshes is studied. The locally refined meshes are created by the newest vertex mesh refinement method. After the introduction of this refinement technique

  5. Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

    Costiner, Sorin; Taasan, Shlomo

    1994-01-01

    This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

  6. Accounting for Sampling Error in Genetic Eigenvalues Using Random Matrix Theory.

    Sztepanacz, Jacqueline L; Blows, Mark W

    2017-07-01

    The distribution of genetic variance in multivariate phenotypes is characterized by the empirical spectral distribution of the eigenvalues of the genetic covariance matrix. Empirical estimates of genetic eigenvalues from random effects linear models are known to be overdispersed by sampling error, where large eigenvalues are biased upward, and small eigenvalues are biased downward. The overdispersion of the leading eigenvalues of sample covariance matrices have been demonstrated to conform to the Tracy-Widom (TW) distribution. Here we show that genetic eigenvalues estimated using restricted maximum likelihood (REML) in a multivariate random effects model with an unconstrained genetic covariance structure will also conform to the TW distribution after empirical scaling and centering. However, where estimation procedures using either REML or MCMC impose boundary constraints, the resulting genetic eigenvalues tend not be TW distributed. We show how using confidence intervals from sampling distributions of genetic eigenvalues without reference to the TW distribution is insufficient protection against mistaking sampling error as genetic variance, particularly when eigenvalues are small. By scaling such sampling distributions to the appropriate TW distribution, the critical value of the TW statistic can be used to determine if the magnitude of a genetic eigenvalue exceeds the sampling error for each eigenvalue in the spectral distribution of a given genetic covariance matrix. Copyright © 2017 by the Genetics Society of America.

  7. Cluster structure in the correlation coefficient matrix can be characterized by abnormal eigenvalues

    Nie, Chun-Xiao

    2018-02-01

    In a large number of previous studies, the researchers found that some of the eigenvalues of the financial correlation matrix were greater than the predicted values of the random matrix theory (RMT). Here, we call these eigenvalues as abnormal eigenvalues. In order to reveal the hidden meaning of these abnormal eigenvalues, we study the toy model with cluster structure and find that these eigenvalues are related to the cluster structure of the correlation coefficient matrix. In this paper, model-based experiments show that in most cases, the number of abnormal eigenvalues of the correlation matrix is equal to the number of clusters. In addition, empirical studies show that the sum of the abnormal eigenvalues is related to the clarity of the cluster structure and is negatively correlated with the correlation dimension.

  8. Anesthetic Preconditioning as Endogenous Neuroprotection in Glaucoma

    Tsung-Han Chou

    2018-01-01

    Full Text Available Blindness in glaucoma is the result of death of Retinal Ganglion Cells (RGCs and their axons. RGC death is generally preceded by a stage of reversible dysfunction and structural remodeling. Current treatments aimed at reducing intraocular pressure (IOP are ineffective or incompletely effective in management of the disease. IOP-independent neuroprotection or neuroprotection as adjuvant to IOP lowering in glaucoma remains a challenge as effective agents without side effects have not been identified yet. We show in DBA/2J mice with spontaneous IOP elevation and glaucoma that the lifespan of functional RGCs can be extended by preconditioning RGCs with retrobulbar lidocaine in one eye at four months of age that temporary blocks RGC axonal transport. The contralateral, PBS-injected eye served as control. Lidocaine-induced impairment of axonal transport to superior colliculi was assessed by intravitreal injection of cholera toxin B. Long-term (nine months effect of lidocaine were assessed on RGC electrical responsiveness (PERG, IOP, expression of relevant protein (BDNF, TrkB, PSD95, GFAP, Synaptophysin, and GAPDH and RGC density. While lidocaine treatment did not alter the age-related increase of IOP, TrkB expression was elevated, GFAP expression was decreased, RGC survival was improved by 35%, and PERG function was preserved. Results suggest that the lifespan of functional RGCs in mouse glaucoma can be extended by preconditioning RGCs in early stages of the disease using a minimally invasive treatment with retrobulbar lidocaine, a common ophthalmologic procedure. Lidocaine is inexpensive, safe and is approved by Food and Drug Administration (FDA to be administered intravenously.

  9. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.

    2014-01-01

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology

  10. On a Volume Constrained for the First Eigenvalue of the P-Laplacian Operator

    Ly, Idrissa

    2009-10-01

    In this paper, we are interested in a shape optimization problem which consists in minimizing the functional that associates to an open set the first eigenvalue for p-Laplacian operator with homogeneous boundary condition. The minimum is taken among all open subsets with prescribed measure of a given bounded domain. We study an existence result for the associate variational problem. Our technique consists in enlarging the class of admissible functions to the whole space W 0 1,p (D), penalizing those functions whose level sets have a measure which is less than those required. In fact, we study the minimizers of a family of penalized functionals J λ , λ > 0 showing they are Hoelder continuous. And we prove that such functions minimize the initial problem provided the penalization parameter λ is large enough. (author)

  11. Quadratic partial eigenvalue assignment in large-scale stochastic dynamic systems for resilient and economic design

    Das, Sonjoy; Goswami, Kundan [University at Buffalo, NY (United States); Datta, Biswa N. [Northern Illinois University, IL (United States)

    2014-12-10

    Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.

  12. Imaginary eigenvalue solution in RPA and phase transition

    Yao Yujie; Jing Xiaogong; Zhao Guoquan; Wu Shishu

    1993-01-01

    The phase transition (PT) of a many-particle system with a close-shell configuration, the stability of the Hartree-Fock (HF) solution and the random phase approximation (RPA) are studied by means of a generalized three-level solvable model. The question whether the occurrence of an imaginary eigenvalue solution in RPA (OISA) may be considered as a signature of PT is explored in some detail. It is found that there is no close relation between OISA and PT. Generally, OISA shows that RPA becomes poor

  13. Perturbative stability of the approximate Killing field eigenvalue problem

    Beetle, Christopher; Wilder, Shawn

    2014-01-01

    An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity. (paper)

  14. Wielandt acceleration for MCNP5 Monte Carlo eigenvalue calculations

    Brown, F.

    2007-01-01

    Monte Carlo criticality calculations use the power iteration method to determine the eigenvalue (k eff ) and eigenfunction (fission source distribution) of the fundamental mode. A recently proposed method for accelerating convergence of the Monte Carlo power iteration using Wielandt's method has been implemented in a test version of MCNP5. The method is shown to provide dramatic improvements in convergence rates and to greatly reduce the possibility of false convergence assessment. The method is effective and efficient, improving the Monte Carlo figure-of-merit for many problems. In addition, the method should eliminate most of the underprediction bias in confidence intervals for Monte Carlo criticality calculations. (authors)

  15. Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study

    Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.

    1985-01-01

    The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures

  16. A parallel algorithm for the non-symmetric eigenvalue problem

    Sidani, M.M.

    1991-01-01

    An algorithm is presented for the solution of the non-symmetric eigenvalue problem. The algorithm is based on a divide-and-conquer procedure that provides initial approximations to the eigenpairs, which are then refined using Newton iterations. Since the smaller subproblems can be solved independently, and since Newton iterations with different initial guesses can be started simultaneously, the algorithm - unlike the standard QR method - is ideal for parallel computers. The author also reports on his investigation of deflation methods designed to obtain further eigenpairs if needed. Numerical results from implementations on a host of parallel machines (distributed and shared-memory) are presented

  17. p-Norm SDD tensors and eigenvalue localization

    Qilong Liu

    2016-07-01

    Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.

  18. Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media

    Vicenţiu RăDulescu

    2005-06-01

    Full Text Available We study nonlinear eigenvalue problems of the type −div(a(x∇u=g(λ,x,u in ℝN, where a(x is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.

  19. A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

    Fatemeh Mohammad

    2014-05-01

    Full Text Available In this paper‎, ‎we represent an inexact inverse‎ ‎subspace iteration method for computing a few eigenpairs of the‎ ‎generalized eigenvalue problem $Ax = \\lambda Bx$[Q.~Ye and P.~Zhang‎, ‎Inexact inverse subspace iteration for generalized eigenvalue‎ ‎problems‎, ‎Linear Algebra and its Application‎, ‎434 (2011 1697-1715‎‎]‎. ‎In particular‎, ‎the linear convergence property of the inverse‎ ‎subspace iteration is preserved‎.

  20. Eigenvalues calculation algorithms for {lambda}-modes determination. Parallelization approach

    Vidal, V. [Universidad Politecnica de Valencia (Spain). Departamento de Sistemas Informaticos y Computacion; Verdu, G.; Munoz-Cobo, J.L. [Universidad Politecnica de Valencia (Spain). Departamento de Ingenieria Quimica y Nuclear; Ginestart, D. [Universidad Politecnica de Valencia (Spain). Departamento de Matematica Aplicada

    1997-03-01

    In this paper, we review two methods to obtain the {lambda}-modes of a nuclear reactor, Subspace Iteration method and Arnoldi`s method, which are popular methods to solve the partial eigenvalue problem for a given matrix. In the developed application for the neutron diffusion equation we include improved acceleration techniques for both methods. Also, we propose two parallelization approaches for these methods, a coarse grain parallelization and a fine grain one. We have tested the developed algorithms with two realistic problems, focusing on the efficiency of the methods according to the CPU times. (author).

  1. Dimensionality of social networks using motifs and eigenvalues.

    Anthony Bonato

    Full Text Available We consider the dimensionality of social networks, and develop experiments aimed at predicting that dimension. We find that a social network model with nodes and links sampled from an m-dimensional metric space with power-law distributed influence regions best fits samples from real-world networks when m scales logarithmically with the number of nodes of the network. This supports a logarithmic dimension hypothesis, and we provide evidence with two different social networks, Facebook and LinkedIn. Further, we employ two different methods for confirming the hypothesis: the first uses the distribution of motif counts, and the second exploits the eigenvalue distribution.

  2. Dynamic Eigenvalue Problem of Concrete Slab Road Surface

    Pawlak, Urszula; Szczecina, Michał

    2017-10-01

    The paper presents an analysis of the dynamic eigenvalue problem of concrete slab road surface. A sample concrete slab was modelled using Autodesk Robot Structural Analysis software and calculated with Finite Element Method. The slab was set on a one-parameter elastic subsoil, for which the modulus of elasticity was separately calculated. The eigen frequencies and eigenvectors (as maximal vertical nodal displacements) were presented. On the basis of the results of calculations, some basic recommendations for designers of concrete road surfaces were offered.

  3. Psychological preconditions of game activity development in the early childhood

    Valeriya Spitsyna; Ekaterina Saraykina

    2013-01-01

    The article is devoted for detection the psychological preconditions of game activity development at early age and interrelation of game formation with the development of subject actions, informative activity and procedural game.

  4. Association of Exercise Preconditioning With Immediate Cardioprotection: A Review.

    Thijssen, D.H.J.; Redington, A.; George, K.P.; Hopman, M.T.E.; Jones, H.

    2018-01-01

    Importance: Exercise reduces the risk of cardiovascular events, including through an underrecognized, clinically useful form of acute cardioprotection accessible after a single episode of exercise, which is called cardiovascular preconditioning. Observations: Preclinical evidence shows that 1 to 3

  5. On the solution of two-point linear differential eigenvalue problems. [numerical technique with application to Orr-Sommerfeld equation

    Antar, B. N.

    1976-01-01

    A numerical technique is presented for locating the eigenvalues of two point linear differential eigenvalue problems. The technique is designed to search for complex eigenvalues belonging to complex operators. With this method, any domain of the complex eigenvalue plane could be scanned and the eigenvalues within it, if any, located. For an application of the method, the eigenvalues of the Orr-Sommerfeld equation of the plane Poiseuille flow are determined within a specified portion of the c-plane. The eigenvalues for alpha = 1 and R = 10,000 are tabulated and compared for accuracy with existing solutions.

  6. Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

    Liu, Lulu; Zhang, Wei; Keyes, David E.

    2017-01-01

    A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

  7. Decentralisation in developing countries: preconditions for successful implementation

    Yasin Olum

    2014-07-01

    Full Text Available Decentralisation has been implemented and is being implemented in many developing countries without much success. Although several unique factors inhibit the implementation of decentralisation in individual countries, the paper argues that there are six pre-conditions that these countries should fulfill before decentralisation can be successfully implemented. These preconditions are: institutional mechanisms; creation of spaces for participation; political will and civil will; capacity development at the local level; careful implementation; and democratic governance.

  8. Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow

    Liu, Lulu

    2017-03-17

    A natural convection cavity flow problem is solved using nonlinear multiplicative Schwarz preconditioners, as a Gauss-Seidel-like variant of additive Schwarz preconditioned inexact Newton (ASPIN). The nonlinear preconditioning extends the domain of convergence of Newton’s method to high Rayleigh numbers. Convergence performance varies widely with respect to different groupings of the fields of this multicomponent problem, and with respect to different orderings of the groupings.

  9. A simple method to optimize HMC performance

    Bussone, Andrea; Drach, Vincent; Hansen, Martin; Hietanen, Ari; Rantaharju, Jarno; Pica, Claudio

    2016-01-01

    We present a practical strategy to optimize a set of Hybrid Monte Carlo parameters in simulations of QCD and QCD-like theories. We specialize to the case of mass-preconditioning, with multiple time-step Omelyan integrators. Starting from properties of the shadow Hamiltonian we show how the optimal setup for the integrator can be chosen once the forces and their variances are measured, assuming that those only depend on the mass-preconditioning parameter.

  10. Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.

    Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene

    2016-03-01

    Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.

  11. Intergenerational Correlation in Monte Carlo k-Eigenvalue Calculation

    Ueki, Taro

    2002-01-01

    This paper investigates intergenerational correlation in the Monte Carlo k-eigenvalue calculation of a neutron effective multiplicative factor. To this end, the exponential transform for path stretching has been applied to large fissionable media with localized highly multiplying regions because in such media an exponentially decaying shape is a rough representation of the importance of source particles. The numerical results show that the difference between real and apparent variances virtually vanishes for an appropriate value of the exponential transform parameter. This indicates that the intergenerational correlation of k-eigenvalue samples could be eliminated by the adjoint biasing of particle transport. The relation between the biasing of particle transport and the intergenerational correlation is therefore investigated in the framework of collision estimators, and the following conclusion has been obtained: Within the leading order approximation with respect to the number of histories per generation, the intergenerational correlation vanishes when immediate importance is constant, and the immediate importance under simulation can be made constant by the biasing of particle transport with a function adjoint to the source neutron's distribution, i.e., the importance over all future generations

  12. Reflectance variability of surface coatings reveals characteristic eigenvalue spectra

    Medina, José M.; Díaz, José A.; Barros, Rui

    2012-10-01

    We have examined the trial-to-trial variability of the reflectance spectra of surface coatings containing effect pigments. Principal component analysis of reflectances was done at each detection angle separately. A method for classification of principal components is applied based on the eigenvalue spectra. It was found that the eigenvalue spectra follow characteristic power laws and depend on the detection angle. Three different subsets of principal components were examined to separate the relevant spectral features related to the pigments from other noise sources. Reconstruction of the reflectance spectra by taking only the first subset indicated that reflectance variability was higher at near-specular reflection, suggesting a correlation with the trial-to-trial deposition of effect pigments. Reconstruction by using the second subset indicates that variability was higher at short wavelengths. Finally, reconstruction by using only the third subset indicates that reflectance variability was not totally random as a function of the wavelength. The methods employed can be useful in the evaluation of color variability in industrial paint application processes.

  13. Eigenvalue-dependent neutron energy spectra: Definitions, analyses, and applications

    Cacuci, D.G.; Ronen, Y.; Shayer, Z.; Wagschal, J.J.; Yeivin, Y.

    1982-01-01

    A general qualitative analysis of spectral effects that arise from solving the kappa-, α-, γ-, and sigma-eigenvalue formulations of the neutron transport equation for nuclear systems that deviate (to first order) from criticality is presented. Hierarchies of neutron spectra softness are established and expressed concisely in terms of the newly introduced spatialdependent local spectral indices for the core and for the reflector. It is shown that each hierarchy is preserved, regardless of the nature of the specific physical mechanism that cause the system to deviate from criticality. Qualitative conclusions regarding the general behavior of the spectrum-dependent integral spectral indices and ICRs corresponding to the kappa-, α-, γ-, and sigma-eigenvalue formalisms are also presented. By defining spectral indices separately for the core and for the reflector, it is possible to account for the characteristics of neutron spectra in both the core and the reflector. The distinctions between the spectra in the core and in the reflector could not have been accounted for by using a single type of spectral index (e.g., a spectral index for the entire system or a spectral index solely for the core)

  14. Ukraine Agricultural Land Market Formation Preconditions

    Evgen Dankevych

    2017-01-01

    Full Text Available The theoretical land relations reforming principles were reviewed.Land relations in agriculture transformation process was studied. The land use features were detected and agricultural land use efficiency analysis was conducted.Ukraine land market formation research problems results have been shown. It was established that private land ownership institution ambiguous attitude, rent relations deformation, lack of the property rights ensure mechanism inhibit the land market development. Sociological research of Ukrainian Polesie region to determine the prerequisites for agricultural land marketformation preconditions has been conducted. 787 respondents from Zhytomyr, Rivne and Volyn regions were interviewed. Land shares owners age structure, their distribution by education level, their employment, land shares owners and agricultural enterprises executives to the agricultural land sale moratorium cancellation attitudes, land purchase financial resources, directions of Ukrainian Polissya region land shares use, shares owners land issues level of awareness have been determined during the research. Was substantiated that agricultural land market turnover includes not only land sale moratorium cancellation but also the adoption of the legislative framework and the appropriate infrastructure development, one of the key elements of which is land relations regulation specialized state agency – State Land Bank.

  15. A scheme for the evaluation of dominant time-eigenvalues of a nuclear reactor

    Modak, R.S.; Gupta, Anurag

    2007-01-01

    This paper presents a scheme to obtain the fundamental and few dominant solutions of the prompt time eigenvalue problem (referred to as α-eigenvalue problem) for a nuclear reactor using multi-group neutron diffusion theory. The scheme is based on the use of an algorithm called Orthomin(1). This algorithm was originally proposed by Suetomi and Sekimoto [Suetomi, E., Sekimoto, H., 1991. Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations. Ann. Nucl. Energy 18 (4), 205-227] to obtain the fundamental K-eigenvalue (K-effective) of nuclear reactors. Recently, it has been shown that the algorithm can be used to obtain the further dominant K-modes also. Since α-eigenvalue problem is usually more difficult to solve than the K-eigenvalue problem, an attempt has been made here to use Orthomin(1) for its solution. Numerical results are given for realistic 3-D test case

  16. The protective effect of ischemic preconditioning on rat testis

    Ciralik Harun

    2007-12-01

    Full Text Available Abstract Background It has been demonstrated that brief episodes of sublethal ischemia-reperfusion, so-called ischemic preconditioning, provide powerful tissue protection in different tissues such as heart, brain, skeletal muscle, lung, liver, intestine, kidney, retina, and endothelial cells. Although a recent study has claimed that there are no protective effects of ischemic preconditioning in rat testis, the protective effects of ischemic preconditioning on testicular tissue have not been investigated adequately. The present study was thus planned to investigate whether ischemic preconditioning has a protective effect on testicular tissue. Methods Rats were divided into seven groups that each contained seven rats. In group 1 (control group, only unilateral testicular ischemia was performed by creating a testicular torsion by a 720 degree clockwise rotation for 180 min. In group 2, group 3, group 4, group 5, group 6, and group 7, unilateral testicular ischemia was performed for 180 min following different periods of ischemic preconditioning. The ischemic preconditioning periods were as follows: 10 minutes of ischemia with 10 minutes of reperfusion in group 2; 20 minutes of ischemia with 10 minutes of reperfusion in group 3; 30 minutes of ischemia with 10 minutes of reperfusion in group 4; multiple preconditioning periods were used (3 × 10 min early phase transient ischemia with 10 min reperfusion in all episodes in group 5; multiple preconditioning periods were used (5, 10, and 15 min early phase transient ischemia with 10 min reperfusion in all episodes in group 6; and, multiple preconditioning periods were used (10, 20, and 30 min early phase transient ischemia with 10 min reperfusion in all episodes in group 7. After the ischemic protocols were carried out, animals were sacrificed by cervical dislocation and testicular tissue samples were taken for biochemical measurements (protein, malondialdehyde, nitric oxide and histological examination

  17. Existence of solutions for a fourth order eigenvalue problem ] {Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions

    Khalil Ben Haddouch

    2016-04-01

    Full Text Available In this work we will study the eigenvalues for a fourth order elliptic equation with $p(x$-growth conditions $\\Delta^2_{p(x} u=\\lambda |u|^{p(x-2} u$, under Neumann boundary conditions, where $p(x$ is a continuous function defined on the bounded domain with $p(x>1$. Through the Ljusternik-Schnireleman theory on $C^1$-manifold, we prove the existence of infinitely many eigenvalue sequences and $\\sup \\Lambda =+\\infty$, where $\\Lambda$ is the set of all eigenvalues.

  18. A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices

    Wang Xiaoxiao

    2018-04-01

    Full Text Available A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic matrix is obtained. Lastly, we fix n parameters in [0, 1] to give a new set including all eigenvalues different from 1, which is tighter than those provided by Shen et al. (Linear Algebra Appl. 447 (2014 74-87 and Li et al. (Linear and Multilinear Algebra 63(11 (2015 2159-2170 for estimating the moduli of subdominant eigenvalues.

  19. Periodic Solutions, Eigenvalue Curves, and Degeneracy of the Fractional Mathieu Equation

    Parra-Hinojosa, A; Gutiérrez-Vega, J C

    2016-01-01

    We investigate the eigenvalue curves, the behavior of the periodic solutions, and the orthogonality properties of the Mathieu equation with an additional fractional derivative term using the method of harmonic balance. The addition of the fractional derivative term breaks the hermiticity of the equation in such a way that its eigenvalues need not be real nor its eigenfunctions orthogonal. We show that for a certain choice of parameters the eigenvalue curves reveal the appearance of degenerate eigenvalues. We offer a detailed discussion of the matrix representation of the differential operator corresponding to the fractional Mathieu equation, as well as some numerical examples of its periodic solutions. (paper)

  20. An algorithm of α-and γ-mode eigenvalue calculations by Monte Carlo method

    Yamamoto, Toshihiro; Miyoshi, Yoshinori

    2003-01-01

    A new algorithm for Monte Carlo calculation was developed to obtain α- and γ-mode eigenvalues. The α is a prompt neutron time decay constant measured in subcritical experiments, and the γ is a spatial decay constant measured in an exponential method for determining the subcriticality. This algorithm can be implemented into existing Monte Carlo eigenvalue calculation codes with minimum modifications. The algorithm was implemented into MCNP code and the performance of calculating the both mode eigenvalues were verified through comparison of the calculated eigenvalues with the ones obtained by fixed source calculations. (author)

  1. Super-quantum curves from super-eigenvalue models

    Ciosmak, Paweł [Faculty of Mathematics, Informatics and Mechanics, University of Warsaw,ul. Banacha 2, 02-097 Warsaw (Poland); Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagiellonian University,ul. Łojasiewicza 11, 30-348 Kraków (Poland); Manabe, Masahide [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Sułkowski, Piotr [Faculty of Physics, University of Warsaw,ul. Pasteura 5, 02-093 Warsaw (Poland); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E. California Blvd, Pasadena, CA 91125 (United States)

    2016-10-10

    In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

  2. Instability of the cored barotropic disc: the linear eigenvalue formulation

    Polyachenko, E. V.

    2018-05-01

    Gaseous rotating razor-thin discs are a testing ground for theories of spiral structure that try to explain appearance and diversity of disc galaxy patterns. These patterns are believed to arise spontaneously under the action of gravitational instability, but calculations of its characteristics in the gas are mostly obscured. The paper suggests a new method for finding the spiral patterns based on an expansion of small amplitude perturbations over Lagrange polynomials in small radial elements. The final matrix equation is extracted from the original hydrodynamical equations without the use of an approximate theory and has a form of the linear algebraic eigenvalue problem. The method is applied to a galactic model with the cored exponential density profile.

  3. Super-quantum curves from super-eigenvalue models

    Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

    2016-01-01

    In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

  4. Super-quantum curves from super-eigenvalue models

    Ciosmak, Paweł; Hadasz, Leszek; Manabe, Masahide; Sułkowski, Piotr

    2016-10-01

    In modern mathematical and theoretical physics various generalizations, in particular supersymmetric or quantum, of Riemann surfaces and complex algebraic curves play a prominent role. We show that such supersymmetric and quantum generalizations can be combined together, and construct supersymmetric quantum curves, or super-quantum curves for short. Our analysis is conducted in the formalism of super-eigenvalue models: we introduce β-deformed version of those models, and derive differential equations for associated α/ β-deformed super-matrix integrals. We show that for a given model there exists an infinite number of such differential equations, which we identify as super-quantum curves, and which are in one-to-one correspondence with, and have the structure of, super-Virasoro singular vectors. We discuss potential applications of super-quantum curves and prospects of other generalizations.

  5. Convergence diagnostics for Eigenvalue problems with linear regression model

    Shi, Bo; Petrovic, Bojan

    2011-01-01

    Although the Monte Carlo method has been extensively used for criticality/Eigenvalue problems, a reliable, robust, and efficient convergence diagnostics method is still desired. Most methods are based on integral parameters (multiplication factor, entropy) and either condense the local distribution information into a single value (e.g., entropy) or even disregard it. We propose to employ the detailed cycle-by-cycle local flux evolution obtained by using mesh tally mechanism to assess the source and flux convergence. By applying a linear regression model to each individual mesh in a mesh tally for convergence diagnostics, a global convergence criterion can be obtained. We exemplify this method on two problems and obtain promising diagnostics results. (author)

  6. Multivariate analysis of eigenvalues and eigenvectors in tensor based morphometry

    Rajagopalan, Vidya; Schwartzman, Armin; Hua, Xue; Leow, Alex; Thompson, Paul; Lepore, Natasha

    2015-01-01

    We develop a new algorithm to compute voxel-wise shape differences in tensor-based morphometry (TBM). As in standard TBM, we non-linearly register brain T1-weighed MRI data from a patient and control group to a template, and compute the Jacobian of the deformation fields. In standard TBM, the determinants of the Jacobian matrix at each voxel are statistically compared between the two groups. More recently, a multivariate extension of the statistical analysis involving the deformation tensors derived from the Jacobian matrices has been shown to improve statistical detection power.7 However, multivariate methods comprising large numbers of variables are computationally intensive and may be subject to noise. In addition, the anatomical interpretation of results is sometimes difficult. Here instead, we analyze the eigenvalues and the eigenvectors of the Jacobian matrices. Our method is validated on brain MRI data from Alzheimer's patients and healthy elderly controls from the Alzheimer's Disease Neuro Imaging Database.

  7. Coarse-mesh rebalancing acceleration for eigenvalue problems

    Asaoka, T.; Nakahara, Y.; Miyasaka, S.

    1974-01-01

    The coarse-mesh rebalance method is adopted for Monte Carlo schemes for aiming at accelerating the convergence of a source iteration process. At every completion of the Monte Carlo game for one batch of neutron histories, the scaling factor for the neutron flux is calculated to achieve the neutron balance in each coarse-mesh zone into which the total system is divided. This rebalance factor is multiplied to the weight of each fission source neutron in the coarse-mesh zone for playing the next Monte Carlo game. The numerical examples have shown that the coarse-mesh rebalance Monte Carlo calculation gives a good estimate of the eigenvalue already after several batches with a negligible extra computer time compared to the standard Monte Carlo. 5 references. (U.S.)

  8. Perturbation of embedded eigenvalue by a near-lying resonance

    Belyaev, V B; Motovilov, A K

    1997-12-31

    The case of quantum-mechanical system (including electronic molecules) is considered where Hamiltonian allows a separation, in particular by the Faddeev method, of a weakly coupled channel. Width (i.e. the imaginary part) of the resonance generated by a discrete spectrum eigenvalue of the separated channel is studied in the case where main part of the Hamiltonian gives itself another resonance. It is shown that if real parts of these resonances coincide and, at the same time, a coupling between the separated and main channels is sufficiently small then the width of the resonance generated by the separated (molecular) channel is inversely proportional to the width of the main (nuclear) channel resonance. This phenomenon being a kind of universal law, may play an important role increasing the `cold fusion` probability in electronic molecules whose nuclear constituents have narrow pre-threshold resonances. 21 refs.

  9. A numerical method for eigenvalue problems in modeling liquid crystals

    Baglama, J.; Farrell, P.A.; Reichel, L.; Ruttan, A. [Kent State Univ., OH (United States); Calvetti, D. [Stevens Inst. of Technology, Hoboken, NJ (United States)

    1996-12-31

    Equilibrium configurations of liquid crystals in finite containments are minimizers of the thermodynamic free energy of the system. It is important to be able to track the equilibrium configurations as the temperature of the liquid crystals decreases. The path of the minimal energy configuration at bifurcation points can be computed from the null space of a large sparse symmetric matrix. We describe a new variant of the implicitly restarted Lanczos method that is well suited for the computation of extreme eigenvalues of a large sparse symmetric matrix, and we use this method to determine the desired null space. Our implicitly restarted Lanczos method determines adoptively a polynomial filter by using Leja shifts, and does not require factorization of the matrix. The storage requirement of the method is small, and this makes it attractive to use for the present application.

  10. ADI as a preconditioning for solving the convection-diffusion equation

    Chin, R.C.Y.; Manteuffel, T.A.; De Pillis, J.

    1984-01-01

    The authors examine a splitting of the operator obtained from a steady convection-diffusion equation with variable coefficients in which the convection term dominates. The operator is split into a dominant and subdominant parts consistent with the inherent directional property of the partial differential equation. The equations involving the dominant parts should be easily solved. The authors accelerate the convergence of this splitting or the outer iteration by a Chebyshev semi-iterative method. When the dominant part has constant coefficients, it can be easily solved using alternating direction implicit (ADI) methods. This is called the inner iteration. The optimal parameters for a stationary two-parameter ADI method are obtained when the eigenvalues become complex. This corresponds to either the horizontal or the vertical half-grid Reynolds number larger than unity. The Chebyshev semi-iterative method is used to accelerate the convergence of the inner ADI iteration. A two-fold increase in speed is obtained when the ADI iteration matrix has real eigenvalues, and the increase is less significant when the eigenvalues are complex. If either the horizontal or the vertical half-grid Reynolds number is equal to one, the spectral radius of the optimal ADI iterative matrix is zero. However, a high degree of nilpotency impairs rapid convergence. This problem is removed by introducing a more implicit iterative method called ADI/Gauss-Seidel (ADI/GS). ADI/GS resolves the nilpotency and, thus, converges more rapidly for half-grid Reynolds number near 1. Finally, these methods are compared with several well-known schemes on test problems. 23 references, 5 figures

  11. [Anaesthetic-induced myocardial preconditioning: fundamental basis and clinical implications].

    Chiari, P; Bouvet, F; Piriou, V

    2005-04-01

    Volatile halogenated anaesthetics offer a myocardial protection when they are administrated before a myocardial ischaemia. Cellular mechanisms involved in anaesthetic preconditioning are now better understood. The objectives of this review are to understand the anaesthetic-induced preconditioning underlying mechanisms and to know the clinical implications. References were obtained from PubMed data bank (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi) using the following keywords: volatile anaesthetic, isoflurane, halothane, sevoflurane, desflurane, preconditioning, protection, myocardium. Ischaemic preconditioning (PC) is a myocardial endogenous protection against ischaemia. It has been described as one or several short ischaemia before a sustained ischemia. These short ischaemia trigger a protective signal against this longer ischaemia. An ischemic organ is able to precondition a remote organ. It is possible to replace the short ischaemia by a preadministration of halogenated volatile anaesthetic with the same protective effect, this is called anaesthetic PC (APC). APC and ischaemic PC share similar underlying biochemical mechanisms including protein kinase C, tyrosine kinase activation and mitochondrial and sarcolemnal K(ATP) channels opening. All halogenated anaesthetics can produce an anaesthetic PC effect. Myocardial protection during reperfusion, after the long ischaemia, has been shown by successive short ischaemia or volatile anaesthetic administration, this is called postconditioning. Ischaemic PC has been described in humans in 1993. Clinical studies in human cardiac surgery have shown the possibility of anaesthetic PC with volatile anaesthetics. These studies have shown a decrease of postoperative troponin in patient receiving halogenated anaesthetics.

  12. Absence of positive eigenvalues for hard-core N-body systems

    Ito, K.; Skibsted, Erik

    We show absence of positive eigenvalues for generalized 2-body hard-core Schrödinger operators under the condition of bounded strictly convex obstacles. A scheme for showing absence of positive eigenvalues for generalized N-body hard-core Schrödinger operators, N≥ 2, is presented. This scheme inv...

  13. Estimates of the first Dirichlet eigenvalue from exit time moment spectra

    Hurtado, Ana; Markvorsen, Steen; Palmer, Vicente

    2013-01-01

    We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball...

  14. Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

    Tang Wen-Lin; Tian Gui-Hua

    2011-01-01

    Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.

  15. Accurate high-lying eigenvalues of Schroedinger and Sturm-Liouville problems

    Vanden Berghe, G.; Van Daele, M.; De Meyer, H.

    1994-01-01

    A modified difference and a Numerov-like scheme have been introduced in a shooting algorithm for the determination of the (higher-lying) eigenvalues of Schroedinger equations and Sturm-Liouville problems. Some numerical experiments are introduced. Time measurements have been performed. The proposed algorithms are compared with other previously introduced shooting schemes. The structure of the eigenvalue error is discussed. ((orig.))

  16. Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

    Sloss, J. M.; Kranzler, S. K.

    1972-01-01

    The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

  17. An asymptotic expression for the eigenvalues of the normalization kernel of the resonating group method

    Lomnitz-Adler, J.; Brink, D.M.

    1976-01-01

    A generating function for the eigenvalues of the RGM Normalization Kernel is expressed in terms of the diagonal matrix elements of thw GCM Overlap Kernel. An asymptotic expression for the eigenvalues is obtained by using the Method of Steepest Descent. (Auth.)

  18. An Extremal Eigenvalue Problem for a Two-Phase Conductor in a Ball

    Conca, Carlos; Mahadevan, Rajesh; Sanz, Leon

    2009-01-01

    The pioneering works of Murat and Tartar (Topics in the mathematical modeling of composite materials. PNLDE 31. Birkhaeuser, Basel, 1997) go a long way in showing, in general, that problems of optimal design may not admit solutions if microstructural designs are excluded from consideration. Therefore, assuming, tactilely, that the problem of minimizing the first eigenvalue of a two-phase conducting material with the conducting phases to be distributed in a fixed proportion in a given domain has no true solution in general domains, Cox and Lipton only study conditions for an optimal microstructural design (Cox and Lipton in Arch. Ration. Mech. Anal. 136:101-117, 1996). Although, the problem in one dimension has a solution (cf. Krein in AMS Transl. Ser. 2(1):163-187, 1955) and, in higher dimensions, the problem set in a ball can be deduced to have a radially symmetric solution (cf. Alvino et al. in Nonlinear Anal. TMA 13(2):185-220, 1989), these existence results have been regarded so far as being exceptional owing to complete symmetry. It is still not clear why the same problem in domains with partial symmetry should fail to have a solution which does not develop microstructure and respecting the symmetry of the domain. We hope to revive interest in this question by giving a new proof of the result in a ball using a simpler symmetrization result from Alvino and Trombetti (J. Math. Anal. Appl. 94:328-337, 1983)

  19. Operator-Based Preconditioning of Stiff Hyperbolic Systems

    Reynolds, Daniel R.; Samtaney, Ravi; Woodward, Carol S.

    2009-01-01

    We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of partial differential equations posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for solution to any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydro- dynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study

  20. Efficient solutions to the NDA-NCA low-order eigenvalue problem

    Willert, J. A.; Kelley, C. T.

    2013-01-01

    Recent algorithmic advances combine moment-based acceleration and Jacobian-Free Newton-Krylov (JFNK) methods to accelerate the computation of the dominant eigenvalue in a k-eigenvalue calculation. In particular, NDA-NCA [1], builds a sequence of low-order (LO) diffusion-based eigenvalue problems in which the solution converges to the true eigenvalue solution. Within NDA-NCA, the solution to the LO k-eigenvalue problem is computed by solving a system of nonlinear equation using some variant of Newton's method. We show that we can speed up the solution to the LO problem dramatically by abandoning the JFNK method and exploiting the structure of the Jacobian matrix. (authors)

  1. 2nd International Workshop on Eigenvalue Problems : Algorithms, Software and Applications in Petascale Computing

    Zhang, Shao-Liang; Imamura, Toshiyuki; Yamamoto, Yusaku; Kuramashi, Yoshinobu; Hoshi, Takeo

    2017-01-01

    This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.

  2. The Role of Ionospheric Outflow Preconditioning in Determining Storm Geoeffectiveness

    Welling, D. T.; Liemohn, M. W.; Ridley, A. J.

    2012-12-01

    It is now well accepted that ionospheric outflow plays an important role in the development of the plasma sheet and ring current during geomagnetic storms. Furthermore, even during quiet times, ionospheric plasma populates the magnetospheric lobes, producing a reservoir of hydrogen and oxygen ions. When the Interplanetary Magnetic Field (IMF) turns southward, this reservoir is connected to the plasma sheet and ring current through magnetospheric convection. Hence, the conditions of the ionosphere and magnetospheric lobes leading up to magnetospheric storm onset have important implications for storm development. Despite this, there has been little research on this preconditioning; most global simulations begin just before storm onset, neglecting preconditioning altogether. This work explores the role of preconditioning in determining the geoeffectiveness of storms using a coupled global model system. A model of ionospheric outflow (the Polar Wind Outflow Model, PWOM) is two-way coupled to a global magnetohydrodynamic model (the Block-Adaptive Tree Solar wind Roe-type Upwind Scheme, BATS-R-US), which in turn drives a ring current model (the Ring current Atmosphere interactions Model, RAM). This unique setup is used to simulate an idealized storm. The model is started at many different times, from 1 hour before storm onset to 12 hours before. The effects of storm preconditioning are examined by investigating the total ionospheric plasma content in the lobes just before onset, the total ionospheric contribution in the ring current just after onset, and the effects on Dst, magnetic elevation angle at geosynchronous, and total ring current energy density. This experiment is repeated for different solar activity levels as set by F10.7 flux. Finally, a synthetic double-dip storm is constructed to see how two closely spaced storms affect each other by changing the preconditioning environment. It is found that preconditioning of the magnetospheric lobes via ionospheric

  3. Evaluation of a new preconditioning algorithm based on the 3-D even-parity simplified SN equations for discrete ordinates in parallel environments

    Longoni, G.; Haghighat, A.; Sjoden, G.

    2005-01-01

    This paper discusses a new preconditioned Sn algorithm referred to as FAST (Flux Acceleration Sn Transport). This algorithm uses the PENSSn code as the pre-conditioner, and the PENTRANSSn code system as the transport solver. PENSSn is developed based on the even-parity simplified Sn formulation in a parallel environment, and PENTRAN-SSn is a version of PENTRAN that uses PENSSn as the pre-conditioner with the FAST system. The paper briefly discusses the EP-SSn formulation and important numerical features of PENSSn. The FAST algorithm is discussed and tested for the C5G7 MOX eigenvalue benchmark problem. It is demonstrated that FAST leads to significant speedups (∼7) over the standard PENTRAN code. Moreover, FAST shows closer agreement with a reference Monte Carlo simulation. (authors)

  4. Effects of ketamine and its isomers on ischemic preconditioning in the isolated rat heart

    Molojavyi, A.; Preckel, B.; Comfère, T.; Müllenheim, J.; Thämer, V.; Schlack, W.

    2001-01-01

    BACKGROUND: Ischemic preconditioning protects the heart against subsequent ischemia. Opening of the adenosine triphosphate-sensitive potassium (KATP) channel is a key mechanism of preconditioning. Ketamine blocks KATP channels of isolated cardiomyocytes. The authors investigated the effects of

  5. Time-domain full waveform inversion using the gradient preconditioning based on transmitted waves energy

    Zhang, Xiao-bo; Tan, Jun; Song, Peng; Li, Jin-shan; Xia, Dong-ming; Liu, Zhao-lun

    2017-01-01

    The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge storage consumption in the gradient preconditioning algorithms based on Hessian matrices in time-domain full waveform inversion (FWI), but the accuracy

  6. Eigenvalue sensitivity of sampled time systems operating in closed loop

    Bernal, Dionisio

    2018-05-01

    The use of feedback to create closed-loop eigenstructures with high sensitivity has received some attention in the Structural Health Monitoring field. Although practical implementation is necessarily digital, and thus in sampled time, work thus far has center on the continuous time framework, both in design and in checking performance. It is shown in this paper that the performance in discrete time, at typical sampling rates, can differ notably from that anticipated in the continuous time formulation and that discrepancies can be particularly large on the real part of the eigenvalue sensitivities; a consequence being important error on the (linear estimate) of the level of damage at which closed-loop stability is lost. As one anticipates, explicit consideration of the sampling rate poses no special difficulties in the closed-loop eigenstructure design and the relevant expressions are developed in the paper, including a formula for the efficient evaluation of the derivative of the matrix exponential based on the theory of complex perturbations. The paper presents an easily reproduced numerical example showing the level of error that can result when the discrete time implementation of the controller is not considered.

  7. Depletion GPT-free sensitivity analysis for reactor eigenvalue problems

    Kennedy, C.; Abdel-Khalik, H.

    2013-01-01

    This manuscript introduces a novel approach to solving depletion perturbation theory problems without the need to set up or solve the generalized perturbation theory (GPT) equations. The approach, hereinafter denoted generalized perturbation theory free (GPT-Free), constructs a reduced order model (ROM) using methods based in perturbation theory and computes response sensitivity profiles in a manner that is independent of the number or type of responses, allowing for an efficient computation of sensitivities when many responses are required. Moreover, the reduction error from using the ROM is quantified in the GPT-Free approach by means of a Wilks' order statistics error metric denoted the K-metric. Traditional GPT has been recognized as the most computationally efficient approach for performing sensitivity analyses of models with many input parameters, e.g. when forward sensitivity analyses are computationally intractable. However, most neutronics codes that can solve the fundamental (homogenous) adjoint eigenvalue problem do not have GPT capabilities unless envisioned during code development. The GPT-Free approach addresses this limitation by requiring only the ability to compute the fundamental adjoint. This manuscript demonstrates the GPT-Free approach for depletion reactor calculations performed in SCALE6 using the 7x7 UAM assembly model. A ROM is developed for the assembly over a time horizon of 990 days. The approach both calculates the reduction error over the lifetime of the simulation using the K-metric and benchmarks the obtained sensitivities using sample calculations. (authors)

  8. Overview of the ArbiTER edge plasma eigenvalue code

    Baver, Derek; Myra, James; Umansky, Maxim

    2011-10-01

    The Arbitrary Topology Equation Reader, or ArbiTER, is a flexible eigenvalue solver that is currently under development for plasma physics applications. The ArbiTER code builds on the equation parser framework of the existing 2DX code, extending it to include a topology parser. This will give the code the capability to model problems with complicated geometries (such as multiple X-points and scrape-off layers) or model equations with arbitrary numbers of dimensions (e.g. for kinetic analysis). In the equation parser framework, model equations are not included in the program's source code. Instead, an input file contains instructions for building a matrix from profile functions and elementary differential operators. The program then executes these instructions in a sequential manner. These instructions may also be translated into analytic form, thus giving the code transparency as well as flexibility. We will present an overview of how the ArbiTER code is to work, as well as preliminary results from early versions of this code. Work supported by the U.S. DOE.

  9. Effective Perron-Frobenius eigenvalue for a correlated random map

    Pool, Roman R.; Cáceres, Manuel O.

    2010-09-01

    We investigate the evolution of random positive linear maps with various type of disorder by analytic perturbation and direct simulation. Our theoretical result indicates that the statistics of a random linear map can be successfully described for long time by the mean-value vector state. The growth rate can be characterized by an effective Perron-Frobenius eigenvalue that strongly depends on the type of correlation between the elements of the projection matrix. We apply this approach to an age-structured population dynamics model. We show that the asymptotic mean-value vector state characterizes the population growth rate when the age-structured model has random vital parameters. In this case our approach reveals the nontrivial dependence of the effective growth rate with cross correlations. The problem was reduced to the calculation of the smallest positive root of a secular polynomial, which can be obtained by perturbations in terms of Green’s function diagrammatic technique built with noncommutative cumulants for arbitrary n -point correlations.

  10. EvArnoldi: A New Algorithm for Large-Scale Eigenvalue Problems.

    Tal-Ezer, Hillel

    2016-05-19

    Eigenvalues and eigenvectors are an essential theme in numerical linear algebra. Their study is mainly motivated by their high importance in a wide range of applications. Knowledge of eigenvalues is essential in quantum molecular science. Solutions of the Schrödinger equation for the electrons composing the molecule are the basis of electronic structure theory. Electronic eigenvalues compose the potential energy surfaces for nuclear motion. The eigenvectors allow calculation of diople transition matrix elements, the core of spectroscopy. The vibrational dynamics molecule also requires knowledge of the eigenvalues of the vibrational Hamiltonian. Typically in these problems, the dimension of Hilbert space is huge. Practically, only a small subset of eigenvalues is required. In this paper, we present a highly efficient algorithm, named EvArnoldi, for solving the large-scale eigenvalues problem. The algorithm, in its basic formulation, is mathematically equivalent to ARPACK ( Sorensen , D. C. Implicitly Restarted Arnoldi/Lanczos Methods for Large Scale Eigenvalue Calculations ; Springer , 1997 ; Lehoucq , R. B. ; Sorensen , D. C. SIAM Journal on Matrix Analysis and Applications 1996 , 17 , 789 ; Calvetti , D. ; Reichel , L. ; Sorensen , D. C. Electronic Transactions on Numerical Analysis 1994 , 2 , 21 ) (or Eigs of Matlab) but significantly simpler.

  11. 40 CFR 86.132-00 - Vehicle preconditioning.

    2010-07-01

    ... 40 Protection of Environment 18 2010-07-01 2010-07-01 false Vehicle preconditioning. 86.132-00... (CONTINUED) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES Emission Regulations for 1977 and Later Model Year New Light-Duty Vehicles and New Light-Duty Trucks and New Otto-Cycle Complete...

  12. 40 CFR 86.232-94 - Vehicle preconditioning.

    2010-07-01

    ... 40 Protection of Environment 18 2010-07-01 2010-07-01 false Vehicle preconditioning. 86.232-94... (CONTINUED) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES Emission Regulations for 1994 and Later Model Year Gasoline-Fueled New Light-Duty Vehicles, New Light-Duty Trucks and New Medium...

  13. Preconditioned stochastic gradient descent optimisation for monomodal image registration

    Klein, S.; Staring, M.; Andersson, J.P.; Pluim, J.P.W.; Fichtinger, G.; Martel, A.; Peters, T.

    2011-01-01

    We present a stochastic optimisation method for intensity-based monomodal image registration. The method is based on a Robbins-Monro stochastic gradient descent method with adaptive step size estimation, and adds a preconditioning matrix. The derivation of the pre-conditioner is based on the

  14. Manipulation in political stock markets: Preconditions and evidence

    Hansen, Jan; Schmidt, Carsten; Strobel, Martin

    2001-01-01

    Political stock markets (PSM) are sometimes seen as substitutes for opinion polls. On the bases of a behavioral model, specific preconditions were drawn out under which manipulation in PSM can weaken this argument. Evidence for manipulation is reported from the data of two separate PSM during the Berlin 99 state elections.

  15. Preconditioned Iterative Methods for Solving Weighted Linear Least Squares Problems

    Bru, R.; Marín, J.; Mas, J.; Tůma, Miroslav

    2014-01-01

    Roč. 36, č. 4 (2014), A2002-A2022 ISSN 1064-8275 Institutional support: RVO:67985807 Keywords : preconditioned iterative methods * incomplete decompositions * approximate inverses * linear least squares Subject RIV: BA - General Mathematics Impact factor: 1.854, year: 2014

  16. Preconditions of origin, essence and assignment of strategic managerial accounting

    Boiko, I.

    2010-01-01

    The article is devoted to the research of preconditions and necessity of creation strategic managerial accounting in the accounting system of enterprise. There are investigated economic essence and assignment of strategic managerial accounting and substantiated its importance for making strategic decisions on an enterprise.

  17. Deflation in preconditioned conjugate gradient methods for Finite Element Problems

    Vermolen, F.J.; Vuik, C.; Segal, A.

    2002-01-01

    We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous

  18. Accurate reanalysis of structures by a preconditioned conjugate gradient method

    Kirsch, U.; Kočvara, Michal; Zowe, J.

    2002-01-01

    Roč. 55, č. 2 (2002), s. 233-251 ISSN 0029-5981 R&D Projects: GA AV ČR IAA1075005 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : preconditioned conjugate gradient s * structural reanalysis Subject RIV: BA - General Mathematics Impact factor: 1.468, year: 2002

  19. The Deflated Preconditioned Conjugate Gradient Method Applied to Composite Materials

    Jönsthövel, T.B.

    2012-01-01

    Simulations with composite materials often involve large jumps in the coefficients of the underlying stiffness matrix. These jumps can introduce unfavorable eigenvalues in the spectrum of the stiffness matrix. We show that the rigid body modes; the translations and rotations, of the disjunct rigid

  20. Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

    Anistratov, Dmitriy Y.

    2011-01-01

    The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

  1. On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

    Heinrich Voss

    2016-06-01

    Full Text Available Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi–Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example.

  2. Complex energy eigenvalues of a linear potential with a parabolical barrier

    Malherbe, J.B.

    1978-01-01

    The physical meaning and restrictions of complex energy eigenvalues are briefly discussed. It is indicated that a quasi-stationary phase describes an idealised disintegration system. Approximate resonance-eigenvalues of the one dimensional Schrodinger equation with a linear potential and parabolic barrier are calculated by means of Connor's semiclassical method. This method is based on the generalized WKB-method of Miller and Good. The results obtained confirm the correctness of a model representation which explains the unusual distribution of eigenvalues by certain other linear potentials in a complex energy level [af

  3. Pharmacological preconditioning with GYKI 52466: a prophylactic approach to neuroprotection

    Chelsea S Goulton

    2010-08-01

    Full Text Available Some toxins and drugs can trigger lasting neuroprotective mechanisms that enable neurons to resist a subsequent severe insult. This ‘pharmacological preconditioning’ has far-reaching implications for conditions in which blood flow to the brain is interrupted. We have previously shown that in vitro preconditioning with the AMPA receptor antagonist GYKI 52466 induces tolerance to kainic acid (KA toxicity in hippocampus. This effect persists well after washout of the drug and may be mediated via inverse agonism of G protein linked receptors. Given the amplifying nature of metabotropic modulation, we hypothesised that GYKI 52466 may be effective in reducing seizure severity at doses well below those normally associated with adverse side effects. Here we report that pharmacological preconditioning with low-dose GYKI imparts a significant protection against KA-induced seizures in vivo. GYKI (3 mg/kg, s.c., 90 to 180 min. prior to high-dose KA, markedly reduced seizure scores, virtually abolished all level 3 and level 4 seizures, and completely suppressed KA-induced hippocampal cFOS expression. In addition, preconditioned animals exhibited significant reductions in high frequency/high amplitude spiking and ECoG power in the delta, theta, alpha and beta bands during KA. Adverse behaviours often associated with higher doses of GYKI were not evident during preconditioning. The fact that GYKI is effective at doses well-below, and at pre-administration intervals well-beyond previous studies, suggests that a classical blockade of ionotropic AMPA receptors does not underlie anticonvulsant effects. Low-dose GYKI preconditioning may represent a novel, prophylactic strategy for neuroprotection in a field almost completely devoid of effective pharmaceuticals.

  4. Priming of the Cells: Hypoxic Preconditioning for Stem Cell Therapy.

    Wei, Zheng Z; Zhu, Yan-Bing; Zhang, James Y; McCrary, Myles R; Wang, Song; Zhang, Yong-Bo; Yu, Shan-Ping; Wei, Ling

    2017-10-05

    Stem cell-based therapies are promising in regenerative medicine for protecting and repairing damaged brain tissues after injury or in the context of chronic diseases. Hypoxia can induce physiological and pathological responses. A hypoxic insult might act as a double-edged sword, it induces cell death and brain damage, but on the other hand, sublethal hypoxia can trigger an adaptation response called hypoxic preconditioning or hypoxic tolerance that is of immense importance for the survival of cells and tissues. This review was based on articles published in PubMed databases up to August 16, 2017, with the following keywords: "stem cells," "hypoxic preconditioning," "ischemic preconditioning," and "cell transplantation." Original articles and critical reviews on the topics were selected. Hypoxic preconditioning has been investigated as a primary endogenous protective mechanism and possible treatment against ischemic injuries. Many cellular and molecular mechanisms underlying the protective effects of hypoxic preconditioning have been identified. In cell transplantation therapy, hypoxic pretreatment of stem cells and neural progenitors markedly increases the survival and regenerative capabilities of these cells in the host environment, leading to enhanced therapeutic effects in various disease models. Regenerative treatments can mobilize endogenous stem cells for neurogenesis and angiogenesis in the adult brain. Furthermore, transplantation of stem cells/neural progenitors achieves therapeutic benefits via cell replacement and/or increased trophic support. Combinatorial approaches of cell-based therapy with additional strategies such as neuroprotective protocols, anti-inflammatory treatment, and rehabilitation therapy can significantly improve therapeutic benefits. In this review, we will discuss the recent progress regarding cell types and applications in regenerative medicine as well as future applications.

  5. Classical scattering theory of waves from the view point of an eigenvalue problem and application to target identification

    Bottcher, C.; Strayer, M.R.; Werby, M.F.

    1993-01-01

    The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWE's. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can by obtained in matrix form be expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways to long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology will be explained in detail and examples will be presented

  6. [The relationship between ischemic preconditioning-induced infarction size limitation and duration of test myocardial ischemia].

    Blokhin, I O; Galagudza, M M; Vlasov, T D; Nifontov, E M; Petrishchev, N N

    2008-07-01

    Traditionally infarction size reduction by ischemic preconditioning is estimated in duration of test ischemia. This approach limits the understanding of real antiischemic efficacy of ischemic preconditioning. Present study was performed in the in vivo rat model of regional myocardial ischemia-reperfusion and showed that protective effect afforded by ischemic preconditioning progressively decreased with prolongation of test ischemia. There were no statistically significant differences in infarction size between control and preconditioned animals when the duration of test ischemia was increased up to 1 hour. Preconditioning ensured maximal infarction-limiting effect in duration of test ischemia varying from 20 to 40 minutes.

  7. Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

    Garmon, Savannah; Ordonez, Gonzalo

    2017-06-01

    It has been reported in the literature that the survival probability P(t) near an exceptional point where two eigenstates coalesce should generally exhibit an evolution P (t ) ˜t2e-Γ t, in which Γ is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz et al., Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify that the survival probability exhibits the previously reported modified exponential decay on intermediate time scales, but this is replaced with an inverse power law on very long time scales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all time scales and the heuristic approach fails completely. When the EP2A appears very near the threshold, we obtain the novel evolution P (t ) ˜1 -C1√{t } on intermediate time scales, while further away the parabolic decay (Zeno dynamics) on short time scales is enhanced.

  8. Solving the generalized symmetric eigenvalue problem using tile algorithms on multicore architectures

    Ltaief, Hatem; Luszczek, Piotr R.; Haidar, Azzam; Dongarra, Jack

    2012-01-01

    This paper proposes an efficient implementation of the generalized symmetric eigenvalue problem on multicore architecture. Based on a four-stage approach and tile algorithms, the original problem is first transformed into a standard symmetric

  9. On the numerical solution of coupled eigenvalue differential equations arising in molecular spectroscopy

    Friedman, R.S.; Jamieson, M.J.; Preston, S.C.

    1990-01-01

    A method for solving coupled eigenvalue differential equations is given and its relation to an existing technique is shown. Use of the Gram-Schmidt process to overcome the severe instabilities arising in molecular problems is described in detail. (orig.)

  10. Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type

    Serguei I. Iakovlev

    2013-01-01

    Full Text Available It is shown that any \\(\\mu \\in \\mathbb{C}\\ is an infinite multiplicity eigenvalue of the Steklov smoothing operator \\(S_h\\ acting on the space \\(L^1_{loc}(\\mathbb{R}\\. For \\(\\mu \

  11. Absolute Monotonicity of Functions Related To Estimates of First Eigenvalue of Laplace Operator on Riemannian Manifolds

    Feng Qi

    2014-10-01

    Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.

  12. TWO-DIMENSIONAL APPROXIMATION OF EIGENVALUE PROBLEMS IN SHELL THEORY: FLEXURAL SHELLS

    2000-01-01

    The eigenvalue problem for a thin linearly elastic shell, of thickness 2e, clamped along its lateral surface is considered. Under the geometric assumption on the middle surface of the shell that the space of inextensional displacements is non-trivial, the authors obtain, as ε→0,the eigenvalue problem for the two-dimensional"flexural shell"model if the dimension of the space is infinite. If the space is finite dimensional, the limits of the eigenvalues could belong to the spectra of both flexural and membrane shells. The method consists of rescaling the variables and studying the problem over a fixed domain. The principal difficulty lies in obtaining suitable a priori estimates for the scaled eigenvalues.

  13. Schiffer's Conjecture, Interior Transmission Eigenvalues and Invisibility Cloaking: Singular Problem vs. Nonsingular Problem

    Liu, Hongyu

    2012-01-01

    In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.

  14. A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential

    Craig Haile

    2000-01-01

    Full Text Available We study the time-independent Schrodinger equation with radially symmetric potential $k|x|^alpha$, $k ge 0$, $k in mathbb{R}, alpha ge 2$ on a bounded domain $Omega$ in $mathbb{R}^n$, $(n ge 2$ with Dirichlet boundary conditions. In particular, we compare the eigenvalue $lambda_2(Omega$ of the operator $-Delta + k |x|^alpha $ on $Omega$ with the eigenvalue $lambda_2(S_1$ of the same operator $-Delta +kr^alpha$ on a ball $S_1$, where $S_1$ has radius such that the first eigenvalues are the same ($lambda_1(Omega = lambda_1(S_1$. The main result is to show $lambda_2(Omega le lambda_2(S_1$. We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain $Omega$ with Dirichlet boundary conditions.

  15. Analytic approximation to the largest eigenvalue distribution of a white Wishart matrix

    Vlok, JD

    2012-08-14

    Full Text Available offers largely simplified computation and provides statistics such as the mean value and region of support of the largest eigenvalue distribution. Numeric results from the literature are compared with the approximation and Monte Carlo simulation results...

  16. Parallelization of mathematical library for generalized eigenvalue problem for real band matrices

    Tanaka, Yasuhisa.

    1997-05-01

    This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)

  17. On a minimization of the eigenvalues of Schroedinger operator relatively domains

    Gasymov, Yu.S.; Niftiev, A.A.

    2001-01-01

    Minimization of the eigenvalues plays an important role in the operators spectral theory. The problem on the minimization of the eigenvalues of the Schroedinger operator by areas is considered in this work. The algorithm, analogous to the conditional gradient method, is proposed for the numerical solution of this problem in the common case. The result is generalized for the case of the positively determined completely continuous operator [ru

  18. Numerical Investigations on Several Stabilized Finite Element Methods for the Stokes Eigenvalue Problem

    Pengzhan Huang

    2011-01-01

    Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.

  19. Local fisheries management at the Swedish coast: biological and social preconditions.

    Bruckmeier, Karl; Neuman, Erik

    2005-03-01

    Most of the Swedish coastal fisheries are not sustainable from either a social, economic or ecological point of view. We propose the introduction of local fisheries management (LFM) as a tool for restructuring the present large-scale management system in order to achieve sustainability. To implement LFM two questions need to be answered: How to distribute the resource fish among different resource user groups? How to restructure present fisheries management to meet the criteria of sustainability? Starting from these questions we describe possible forms of LFM for Swedish coastal fishery supported by recent research. The biological and social preconditions for restructuring fisheries management are derived from an analysis of the ecological and managerial situation in Swedish fishery. Three types of LFM--owner based, user based, and community based management--are analyzed with regard to the tasks to be carried outin LFM, the roles of management groups, and the definition and optimal size of management areas.

  20. HMC algorithm with multiple time scale integration and mass preconditioning

    Urbach, C.; Jansen, K.; Shindler, A.; Wenger, U.

    2006-01-01

    We present a variant of the HMC algorithm with mass preconditioning (Hasenbusch acceleration) and multiple time scale integration. We have tested this variant for standard Wilson fermions at β=5.6 and at pion masses ranging from 380 to 680 MeV. We show that in this situation its performance is comparable to the recently proposed HMC variant with domain decomposition as preconditioner. We give an update of the "Berlin Wall" figure, comparing the performance of our variant of the HMC algorithm to other published performance data. Advantages of the HMC algorithm with mass preconditioning and multiple time scale integration are that it is straightforward to implement and can be used in combination with a wide variety of lattice Dirac operators.

  1. Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.

    Yang, Qiang; Vogel, Curtis R; Ellerbroek, Brent L

    2006-07-20

    By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.

  2. PRECONDITIONS AND DETERMINING CAUSES OF THE SHADOW ECONOMY IN UKRAINE

    Z. Varnalii

    2014-03-01

    Full Text Available The article analyzes the main processes that led to the high level of the economy shadowing. The historical aspects of the formation of the shadow economy in Ukraine are highlighted. The socio-economic aspects of the shadow economy of Ukraine causality are discussed. The theoretical contribution of foreign and domestic researchers on the preconditions of formation of the shadow economy in transition economies is studied. Theoretical perspective on the factors of the shadowing processes in the economy of Ukraine from the standpoint of modern scientific researches is analyzed. The paper also provides scientific vectors for further development of researches aimed at studying the causes and preconditions of the shadow economy.

  3. Combined incomplete LU and strongly implicit procedure preconditioning

    Meese, E.A. [Univ. of Trondheim (Norway)

    1996-12-31

    For the solution of large sparse linear systems of equations, the Krylov-subspace methods have gained great merit. Their efficiency are, however, largely dependent upon preconditioning of the equation-system. A family of matrix factorisations often used for preconditioning, is obtained from a truncated Gaussian elimination, ILU(p). Less common, supposedly due to it`s restriction to certain sparsity patterns, is factorisations generated by the strongly implicit procedure (SIP). The ideas from ILU(p) and SIP are used in this paper to construct a generalized strongly implicit procedure, applicable to matrices with any sparsity pattern. The new algorithm has been run on some test equations, and efficiency improvements over ILU(p) was found.

  4. Remote Ischemic Preconditioning and Outcomes of Cardiac Surgery.

    Hausenloy, DJ; Candilio, L; Evans, R; Ariti, C; Jenkins, DP; Kolvekar, S; Knight, R; Kunst, G; Laing, C; Nicholas, J; Pepper, J; Robertson, S; Xenou, M; Clayton, T; Yellon, DM

    2015-01-01

    : Whether remote ischemic preconditioning (transient ischemia and reperfusion of the arm) can improve clinical outcomes in patients undergoing coronary-artery bypass graft (CABG) surgery is not known. We investigated this question in a randomized trial. : We conducted a multicenter, sham-controlled trial involving adults at increased surgical risk who were undergoing on-pump CABG (with or without valve surgery) with blood cardioplegia. After anesthesia induction and before surgical incision, ...

  5. Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

    Liu, Lulu

    2016-10-26

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

  6. Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

    Liu, Lulu; Keyes, David E.

    2016-01-01

    The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm, based on decomposition by field type rather than by subdomain, was recently introduced to improve the convergence of systems with unbalanced nonlinearities. This paper provides a convergence analysis of the MSPIN algorithm. Under reasonable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be obtained when the forcing terms are picked suitably.

  7. Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning

    Rozložník, Miroslav; Simoncini, V.

    2002-01-01

    Roč. 24, č. 2 (2002), s. 368-391 ISSN 0895-4798 R&D Projects: GA ČR GA101/00/1035; GA ČR GA201/00/0080 Institutional research plan: AV0Z1030915 Keywords : saddle point problems * preconditioning * indefinite linear systems * finite precision arithmetic * conjugate gradients Subject RIV: BA - General Mathematics Impact factor: 0.753, year: 2002

  8. Ischemic preconditioning enhances integrity of coronary endothelial tight junctions

    Li, Zhao; Jin, Zhu-Qiu

    2012-01-01

    Highlights: ► Cardiac tight junctions are present between coronary endothelial cells. ► Ischemic preconditioning preserves the structural and functional integrity of tight junctions. ► Myocardial edema is prevented in hearts subjected to ischemic preconditioning. ► Ischemic preconditioning enhances translocation of ZO-2 from cytosol to cytoskeleton. -- Abstract: Ischemic preconditioning (IPC) is one of the most effective procedures known to protect hearts against ischemia/reperfusion (IR) injury. Tight junction (TJ) barriers occur between coronary endothelial cells. TJs provide barrier function to maintain the homeostasis of the inner environment of tissues. However, the effect of IPC on the structure and function of cardiac TJs remains unknown. We tested the hypothesis that myocardial IR injury ruptures the structure of TJs and impairs endothelial permeability whereas IPC preserves the structural and functional integrity of TJs in the blood–heart barrier. Langendorff hearts from C57BL/6J mice were prepared and perfused with Krebs–Henseleit buffer. Cardiac function, creatine kinase release, and myocardial edema were measured. Cardiac TJ function was evaluated by measuring Evans blue-conjugated albumin (EBA) content in the extravascular compartment of hearts. Expression and translocation of zonula occludens (ZO)-2 in IR and IPC hearts were detected with Western blot. A subset of hearts was processed for the observation of ultra-structure of cardiac TJs with transmission electron microscopy. There were clear TJs between coronary endothelial cells of mouse hearts. IR caused the collapse of TJs whereas IPC sustained the structure of TJs. IR increased extravascular EBA content in the heart and myocardial edema but decreased the expression of ZO-2 in the cytoskeleton. IPC maintained the structure of TJs. Cardiac EBA content and edema were reduced in IPC hearts. IPC enhanced the translocation of ZO-2 from cytosol to cytoskeleton. In conclusion, TJs occur in

  9. An Adaptive Multilevel Factorized Sparse Approximate Inverse Preconditioning

    Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav

    2017-01-01

    Roč. 113, November (2017), s. 19-24 ISSN 0965-9978 R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : approximate inverse * Gram–Schmidt orthogonalization * incomplete factorization * multilevel methods * preconditioned conjugate gradient method Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.000, year: 2016

  10. Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems

    Duintjer Tebbens, Jurjen; Tůma, Miroslav

    2007-01-01

    Roč. 29, č. 5 (2007), s. 1918-1941 ISSN 1064-8275 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : preconditioned iterative methods * sparse matrices * sequences of linear algebraic systems * incomplete factorizations * factorization updates * Gauss–Jordan transformations * minimum spanning tree Subject RIV: BA - General Mathematics Impact factor: 1.784, year: 2007

  11. Unified analysis of preconditioning methods for saddle point matrices

    Axelsson, Owe

    2015-01-01

    Roč. 22, č. 2 (2015), s. 233-253 ISSN 1070-5325 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : saddle point problems * preconditioning * spectral properties Subject RIV: BA - General Mathematics Impact factor: 1.431, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/nla.1947/pdf

  12. Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

    Costiner, Sorin; Ta'asan, Shlomo

    1995-07-01

    Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

  13. Remote ischaemic preconditioning and prevention of cerebral injury.

    Rehni, Ashish K; Shri, Richa; Singh, Manjeet

    2007-03-01

    Bilateral carotid artery occlusion of 10 min followed by reperfusion for 24 hr was employed in present study to produce ischaemia and reperfusion induced cerebral injury in mice. Cerebral infarct size was measured using triphenyltetrazolium chloride staining. Short-term memory was evaluated using elevated plus maze. Inclined beam walking test was employed to assess motor incoordination. Bilateral carotid artery occlusion followed by reperfusion produced cerebral infarction and impaired short-term memory, motor co-ordination and lateral push response. A preceding episode of mesenteric artery occlusion for 15 min and reperfusion of 15 min (remote mesenteric ischaemic preconditioning) prevented markedly ischaemia-reperfusion-induced cerebral injury measured in terms of infarct size, loss of short-term memory, motor coordination and lateral push response. Glibenclamide (5 mg/kg, iv) a KATP channel blocker and caffeine (7 mg/kg, iv) an adenosine receptor blocker attenuated the neuroprotective effect of remote mesenteric ischaemic preconditioning. It may be concluded that neuroprotective effect of remote mesenteric ischaemic preconditioning may be due to activation of adenosine receptors and consequent activation of KATP channels in mice.

  14. Preconditioned conjugate gradient methods for the Navier-Stokes equations

    Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

    1994-01-01

    A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

  15. Accurate Valence Ionization Energies from Kohn-Sham Eigenvalues with the Help of Potential Adjustors.

    Thierbach, Adrian; Neiss, Christian; Gallandi, Lukas; Marom, Noa; Körzdörfer, Thomas; Görling, Andreas

    2017-10-10

    An accurate yet computationally very efficient and formally well justified approach to calculate molecular ionization potentials is presented and tested. The first as well as higher ionization potentials are obtained as the negatives of the Kohn-Sham eigenvalues of the neutral molecule after adjusting the eigenvalues by a recently [ Görling Phys. Rev. B 2015 , 91 , 245120 ] introduced potential adjustor for exchange-correlation potentials. Technically the method is very simple. Besides a Kohn-Sham calculation of the neutral molecule, only a second Kohn-Sham calculation of the cation is required. The eigenvalue spectrum of the neutral molecule is shifted such that the negative of the eigenvalue of the highest occupied molecular orbital equals the energy difference of the total electronic energies of the cation minus the neutral molecule. For the first ionization potential this simply amounts to a ΔSCF calculation. Then, the higher ionization potentials are obtained as the negatives of the correspondingly shifted Kohn-Sham eigenvalues. Importantly, this shift of the Kohn-Sham eigenvalue spectrum is not just ad hoc. In fact, it is formally necessary for the physically correct energetic adjustment of the eigenvalue spectrum as it results from ensemble density-functional theory. An analogous approach for electron affinities is equally well obtained and justified. To illustrate the practical benefits of the approach, we calculate the valence ionization energies of test sets of small- and medium-sized molecules and photoelectron spectra of medium-sized electron acceptor molecules using a typical semilocal (PBE) and two typical global hybrid functionals (B3LYP and PBE0). The potential adjusted B3LYP and PBE0 eigenvalues yield valence ionization potentials that are in very good agreement with experimental values, reaching an accuracy that is as good as the best G 0 W 0 methods, however, at much lower computational costs. The potential adjusted PBE eigenvalues result in

  16. Smallest eigenvalue distribution of the fixed-trace Laguerre beta-ensemble

    Chen Yang; Liu Dangzheng; Zhou Dasheng

    2010-01-01

    In this paper we study the entanglement of the reduced density matrix of a bipartite quantum system in a random pure state. It transpires that this involves the computation of the smallest eigenvalue distribution of the fixed-trace Laguerre ensemble of N x N random matrices. We showed that for finite N the smallest eigenvalue distribution may be expressed in terms of Jack polynomials. Furthermore, based on the exact results, we found a limiting distribution when the smallest eigenvalue is suitably scaled with N followed by a large N limit. Our results turn out to be the same as the smallest eigenvalue distribution of the classical Laguerre ensembles without the fixed-trace constraint. This suggests in a broad sense, the global constraint does not influence local correlations, at least, in the large N limit. Consequently, we have solved an open problem: the determination of the smallest eigenvalue distribution of the reduced density matrix-obtained by tracing out the environmental degrees of freedom-for a bipartite quantum system of unequal dimensions.

  17. On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

    Hulko, Artem

    2018-03-01

    In this paper we define a one-dimensional discrete Dirac operator on Z . We study the eigenvalues of the Dirac operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity. We also estimate the number of eigenvalues for the discrete Schrödinger operator with complex potential on Z . That is we extend the result obtained by Hulko (Bull Math Sci, to appear) to the whole Z.

  18. Nuclear medicine methods in the field of studying the mechanisms of delayed phase of myocardial preconditioning

    Wang Shuxia

    2001-01-01

    Ischemic preconditioning is the intrinsic and most potently myocardial protection. Its mechanism is the foundation of rational therapeutic application. Nowadays there are some theories about delayed phase of preconditioning such as nitric oxide hypothesis, free radical mechanisms, protective protein synthesis and opening of ATP-sensitive potassium channels. By incorporation 3 H-leucine, using liquid scintillation counter, the authors know there was protective protein synthesis during preconditioning. SPECT could study the characteristics of preconditioned myocardium in vivo, and PET might further show the metabolism, energy consumption and its relationship to myocardium dysfunction

  19. Preconditioned iterative methods for space-time fractional advection-diffusion equations

    Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.

    2016-08-01

    In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.

  20. A Numerical method for solving a class of fractional Sturm-Liouville eigenvalue problems

    Muhammed I. Syam

    2017-11-01

    Full Text Available This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\\alpha $-order Sturm-Liouville problem where $\\frac{1}{2}< \\alpha \\leq 1$. In this paper, we implement the reproducing kernel method RKM to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy the boundary condition at $x=1$. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.

  1. Eigenvalue routines in NASTRAN: A comparison with the Block Lanczos method

    Tischler, V. A.; Venkayya, Vipperla B.

    1993-01-01

    The NASA STRuctural ANalysis (NASTRAN) program is one of the most extensively used engineering applications software in the world. It contains a wealth of matrix operations and numerical solution techniques, and they were used to construct efficient eigenvalue routines. The purpose of this paper is to examine the current eigenvalue routines in NASTRAN and to make efficiency comparisons with a more recent implementation of the Block Lanczos algorithm by Boeing Computer Services (BCS). This eigenvalue routine is now available in the BCS mathematics library as well as in several commercial versions of NASTRAN. In addition, CRAY maintains a modified version of this routine on their network. Several example problems, with a varying number of degrees of freedom, were selected primarily for efficiency bench-marking. Accuracy is not an issue, because they all gave comparable results. The Block Lanczos algorithm was found to be extremely efficient, in particular, for very large size problems.

  2. The method of fundamental solutions for computing acoustic interior transmission eigenvalues

    Kleefeld, Andreas; Pieronek, Lukas

    2018-03-01

    We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.

  3. A numerical study of the eigenvalues in the neutron diffusion theory

    Lima Bezerra, J. de.

    1982-12-01

    A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt

  4. Solving large-scale sparse eigenvalue problems and linear systems of equations for accelerator modeling

    Gene Golub; Kwok Ko

    2009-01-01

    The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.

  5. A comparison of maximum likelihood and other estimators of eigenvalues from several correlated Monte Carlo samples

    Beer, M.

    1980-01-01

    The maximum likelihood method for the multivariate normal distribution is applied to the case of several individual eigenvalues. Correlated Monte Carlo estimates of the eigenvalue are assumed to follow this prescription and aspects of the assumption are examined. Monte Carlo cell calculations using the SAM-CE and VIM codes for the TRX-1 and TRX-2 benchmark reactors, and SAM-CE full core results are analyzed with this method. Variance reductions of a few percent to a factor of 2 are obtained from maximum likelihood estimation as compared with the simple average and the minimum variance individual eigenvalue. The numerical results verify that the use of sample variances and correlation coefficients in place of the corresponding population statistics still leads to nearly minimum variance estimation for a sufficient number of histories and aggregates

  6. On the eigenvalues of S.Π for arbitrary spin in a constant magnetic field

    Jayaraman, J.; Oliveira, M.A.B. de.

    1985-01-01

    Utilizing the intimate connection of a charged particle in a nomogeneous magnetic field to that of a harmonic oscillator, it was established in a recent communication that the eigenvalue spectrum of the matrix operator S.Π for spin 1 is purely real for any intensity of the external magnetic field thereby removing a false impression to the contrary in the recent literature. Here these results are extended to arbitrary spin the reality of the eigenvalue spectrum. The case of spin 3/2 is discussed in some details and it is demonstrated that the complex eigenvalues implied the spectrum by a recent analysis of Weaver, for sufficiently intense magnetic field, when the particle number n assumes values 0 and 1 do not in fact appear at all. (Author) [pt

  7. A Decentralized Eigenvalue Computation Method for Spectrum Sensing Based on Average Consensus

    Mohammadi, Jafar; Limmer, Steffen; Stańczak, Sławomir

    2016-07-01

    This paper considers eigenvalue estimation for the decentralized inference problem for spectrum sensing. We propose a decentralized eigenvalue computation algorithm based on the power method, which is referred to as generalized power method GPM; it is capable of estimating the eigenvalues of a given covariance matrix under certain conditions. Furthermore, we have developed a decentralized implementation of GPM by splitting the iterative operations into local and global computation tasks. The global tasks require data exchange to be performed among the nodes. For this task, we apply an average consensus algorithm to efficiently perform the global computations. As a special case, we consider a structured graph that is a tree with clusters of nodes at its leaves. For an accelerated distributed implementation, we propose to use computation over multiple access channel (CoMAC) as a building block of the algorithm. Numerical simulations are provided to illustrate the performance of the two algorithms.

  8. Algorithm 589. SICEDR: a FORTRAN subroutine for improving the accuracy of computed matrix eigenvalues

    Dongarra, J.J.

    1982-01-01

    SICEDR is a FORTRAN subroutine for improving the accuracy of a computed real eigenvalue and improving or computing the associated eigenvector. It is first used to generate information during the determination of the eigenvalues by the Schur decomposition technique. In particular, the Schur decomposition technique results in an orthogonal matrix Q and an upper quasi-triangular matrix T, such that A = QTQ/sup T/. Matrices A, Q, and T and the approximate eigenvalue, say lambda, are then used in the improvement phase. SICEDR uses an iterative method similar to iterative improvement for linear systems to improve the accuracy of lambda and improve or compute the eigenvector x in O(n 2 ) work, where n is the order of the matrix A

  9. Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

    Yavuz, Musa

    1998-01-01

    We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods

  10. Methods for computing SN eigenvalues and eigenvectors of slab geometry transport problems

    Yavuz, M.

    1997-01-01

    We discuss computational methods for computing the eigenvalues and eigenvectors of single energy-group neutral particle transport (S N ) problems in homogeneous slab geometry, with an arbitrary scattering anisotropy of order L. These eigensolutions are important when exact (or very accurate) solutions are desired for coarse spatial cell problems demanding rapid execution times. Three methods, one of which is 'new', are presented for determining the eigenvalues and eigenvectors of such S N problems. In the first method, separation of variables is directly applied to the S N equations. In the second method, common characteristics of the S N and P N-1 equations are used. In the new method, the eigenvalues and eigenvectors can be computed provided that the cell-interface Green's functions (transmission and reflection factors) are known. Numerical results for S 4 test problems are given to compare the new method with the existing methods. (author)

  11. Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

    Codd, A. L.; Gross, L.

    2018-03-01

    We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

  12. Preconditioned Conjugate Gradient methods for low speed flow calculations

    Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

    1993-01-01

    An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

  13. Design Considerations for a Flexible Multigrid Preconditioning Library

    Jérémie Gaidamour

    2012-01-01

    Full Text Available MueLu is a library within the Trilinos software project [An overview of Trilinos, Technical Report SAND2003-2927, Sandia National Laboratories, 2003] and provides a framework for parallel multigrid preconditioning methods for large sparse linear systems. While providing efficient implementations of modern multigrid methods based on smoothed aggregation and energy minimization concepts, MueLu is designed to be customized and extended. This article gives an overview of design considerations for the MueLu package: user interfaces, internal design, data management, usage of modern software constructs, leveraging Trilinos capabilities, linear algebra operations and advanced application.

  14. Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

    Wildey, Tim; Xue, Guangri

    2013-01-01

    In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.

  15. Ischemic preconditioning enhances integrity of coronary endothelial tight junctions

    Li, Zhao [Department of Pharmaceutical Sciences, College of Pharmacy, South Dakota State University, Brookings, SD 57007 (United States); Jin, Zhu-Qiu, E-mail: zhu-qiu.jin@sdstate.edu [Department of Pharmaceutical Sciences, College of Pharmacy, South Dakota State University, Brookings, SD 57007 (United States)

    2012-08-31

    Highlights: Black-Right-Pointing-Pointer Cardiac tight junctions are present between coronary endothelial cells. Black-Right-Pointing-Pointer Ischemic preconditioning preserves the structural and functional integrity of tight junctions. Black-Right-Pointing-Pointer Myocardial edema is prevented in hearts subjected to ischemic preconditioning. Black-Right-Pointing-Pointer Ischemic preconditioning enhances translocation of ZO-2 from cytosol to cytoskeleton. -- Abstract: Ischemic preconditioning (IPC) is one of the most effective procedures known to protect hearts against ischemia/reperfusion (IR) injury. Tight junction (TJ) barriers occur between coronary endothelial cells. TJs provide barrier function to maintain the homeostasis of the inner environment of tissues. However, the effect of IPC on the structure and function of cardiac TJs remains unknown. We tested the hypothesis that myocardial IR injury ruptures the structure of TJs and impairs endothelial permeability whereas IPC preserves the structural and functional integrity of TJs in the blood-heart barrier. Langendorff hearts from C57BL/6J mice were prepared and perfused with Krebs-Henseleit buffer. Cardiac function, creatine kinase release, and myocardial edema were measured. Cardiac TJ function was evaluated by measuring Evans blue-conjugated albumin (EBA) content in the extravascular compartment of hearts. Expression and translocation of zonula occludens (ZO)-2 in IR and IPC hearts were detected with Western blot. A subset of hearts was processed for the observation of ultra-structure of cardiac TJs with transmission electron microscopy. There were clear TJs between coronary endothelial cells of mouse hearts. IR caused the collapse of TJs whereas IPC sustained the structure of TJs. IR increased extravascular EBA content in the heart and myocardial edema but decreased the expression of ZO-2 in the cytoskeleton. IPC maintained the structure of TJs. Cardiac EBA content and edema were reduced in IPC hearts. IPC

  16. Parallel preconditioned conjugate gradient algorithm applied to neutron diffusion problem

    Majumdar, A.; Martin, W.R.

    1992-01-01

    Numerical solution of the neutron diffusion problem requires solving a linear system of equations such as Ax = b, where A is an n x n symmetric positive definite (SPD) matrix; x and b are vectors with n components. The preconditioned conjugate gradient (PCG) algorithm is an efficient iterative method for solving such a linear system of equations. In this paper, the authors describe the implementation of a parallel PCG algorithm on a shared memory machine (BBN TC2000) and on a distributed workstation (IBM RS6000) environment created by the parallel virtual machine parallelization software

  17. Weighted graph based ordering techniques for preconditioned conjugate gradient methods

    Clift, Simon S.; Tang, Wei-Pai

    1994-01-01

    We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.

  18. The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

    Woznicki, Z.I.

    1994-01-01

    The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs

  19. Multi-level methods for solving multigroup transport eigenvalue problems in 1D slab geometry

    Anistratov, D. Y.; Gol'din, V. Y.

    2009-01-01

    A methodology for solving eigenvalue problems for the multigroup neutron transport equation in 1D slab geometry is presented. In this paper we formulate and compare different variants of nonlinear multi-level iteration methods. They are defined by means of multigroup and effective one-group low-order quasi diffusion (LOQD) equations. We analyze the effects of utilization of the effective one-group LOQD problem for estimating the eigenvalue. We present numerical results to demonstrate the performance of the iteration algorithms in different types of reactor-physics problems. (authors)

  20. Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations

    Winfried Auzinger

    2006-01-01

    Full Text Available We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.

  1. The total Hartree-Fock energy-eigenvalue sum relationship in atoms

    Sen, K.D.

    1979-01-01

    Using the well known relationships for the isoelectronic changes in the total Hartree-Fock energy, nucleus-electron attraction energy and electron-electron repulsion energy in atoms a simple polynomial expansion in Z is obtained for the sum of the eigenvalues which can be used to calculate the total Hartree-Fock energy. Numerical results are presented for 2-10 electron series to show that the present relationship is a better approximation than the other available energy-eigenvalue relationships. (author)

  2. Bonnesen-style inequality for the first eigenvalue on a complete surface of constant curvature

    Niufa Fang

    2017-08-01

    Full Text Available Abstract By Cheeger’s isoperimetric constants, some lower bounds and upper bounds of λ 1 $\\lambda_{1}$ , the first eigenvalue on a complete surface of constant curvature, are given. Some Bonnesen-style inequalities and reverse Bonnesen-style inequalities for the first eigenvalue are obtained. Those Bonnesen-style inequalities obtained are stronger than the well-known Osserman’s results and the upper bound is stronger than Osserman’s results (Osserman in Proceedings of the International Congress of Mathematicians, Helsinki, 1978.

  3. The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

    Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)

    1994-12-31

    The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.

  4. The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science.

    Marek, A; Blum, V; Johanni, R; Havu, V; Lang, B; Auckenthaler, T; Heinecke, A; Bungartz, H-J; Lederer, H

    2014-05-28

    Obtaining the eigenvalues and eigenvectors of large matrices is a key problem in electronic structure theory and many other areas of computational science. The computational effort formally scales as O(N(3)) with the size of the investigated problem, N (e.g. the electron count in electronic structure theory), and thus often defines the system size limit that practical calculations cannot overcome. In many cases, more than just a small fraction of the possible eigenvalue/eigenvector pairs is needed, so that iterative solution strategies that focus only on a few eigenvalues become ineffective. Likewise, it is not always desirable or practical to circumvent the eigenvalue solution entirely. We here review some current developments regarding dense eigenvalue solvers and then focus on the Eigenvalue soLvers for Petascale Applications (ELPA) library, which facilitates the efficient algebraic solution of symmetric and Hermitian eigenvalue problems for dense matrices that have real-valued and complex-valued matrix entries, respectively, on parallel computer platforms. ELPA addresses standard as well as generalized eigenvalue problems, relying on the well documented matrix layout of the Scalable Linear Algebra PACKage (ScaLAPACK) library but replacing all actual parallel solution steps with subroutines of its own. For these steps, ELPA significantly outperforms the corresponding ScaLAPACK routines and proprietary libraries that implement the ScaLAPACK interface (e.g. Intel's MKL). The most time-critical step is the reduction of the matrix to tridiagonal form and the corresponding backtransformation of the eigenvectors. ELPA offers both a one-step tridiagonalization (successive Householder transformations) and a two-step transformation that is more efficient especially towards larger matrices and larger numbers of CPU cores. ELPA is based on the MPI standard, with an early hybrid MPI-OpenMPI implementation available as well. Scalability beyond 10,000 CPU cores for problem

  5. Ordering non-bipartite unicyclic graphs with pendant vertices by the least Q-eigenvalue

    Shu-Guang Guo

    2016-05-01

    Full Text Available Abstract A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Fan et al. (Discrete Math. 313:903-909, 2013 and Liu et al. (Electron. J. Linear Algebra 26:333-344, 2013 determined, independently, the unique unicyclic graph whose least Q-eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with k pendant vertices. In this paper, we extend their results and determine the first three non-bipartite unicyclic graphs of order n with k pendant vertices ordering by least Q-eigenvalue.

  6. The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory

    Woznicki, Z.I.

    1995-01-01

    The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs

  7. Oscillatory Stability and Eigenvalue Sensitivity Analysis of A DFIG Wind Turbine System

    Yang, Lihui; Xu, Zhao; Østergaard, Jacob

    2011-01-01

    This paper focuses on modeling and oscillatory stability analysis of a wind turbine with doubly fed induction generator (DFIG). A detailed mathematical model of DFIG wind turbine with vector-control loops is developed, based on which the loci of the system Jacobian's eigenvalues have been analyzed......, showing that, without appropriate controller tuning a Hopf bifurcation can occur in such a system due to various factors, such as wind speed. Subsequently, eigenvalue sensitivity with respect to machine and control parameters is performed to assess their impacts on system stability. Moreover, the Hopf...

  8. On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems

    El-Sayed M. E. Mostafa

    2017-01-01

    Full Text Available The output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a logarithmic barrier method is proposed for finding the local solution. The conjugate gradient method is further extended to tackle the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. The performance of the methods is illustrated through various test examples.

  9. Roles of thioredoxin in nitric oxide-dependent preconditioning-induced tolerance against MPTP neurotoxin

    Chiueh, C.C.; Andoh, Tsugunobu; Chock, P. Boon

    2005-01-01

    Hormesis, a stress tolerance, can be induced by ischemic preconditioning stress. In addition to preconditioning, it may be induced by other means, such as gas anesthetics. Preconditioning mechanisms, which may be mediated by reprogramming survival genes and proteins, are obscure. A known neurotoxicant, 1-Methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP), causes less neurotoxicity in the mice that are preconditioned. Pharmacological evidences suggest that the signaling pathway of ·NO-cGMP-PKG (protein kinase G) may mediate preconditioning phenomenon. We developed a human SH-SY5Y cell model for investigating · NO-mediated signaling pathway, gene regulation, and protein expression following a sublethal preconditioning stress caused by a brief 2-h serum deprivation. Preconditioned human SH-SY5Y cells are more resistant against severe oxidative stress and apoptosis caused by lethal serum deprivation and 1-mehtyl-4-phenylpyridinium (MPP + ). Both sublethal and lethal oxidative stress caused by serum withdrawal increased neuronal nitric oxide synthase (nNOS/NOS1) expression and · NO levels to a similar extent. In addition to free radical scavengers, inhibition of nNOS, guanylyl cyclase, and PKG blocks hormesis induced by preconditioning. S-nitrosothiols and 6-Br-cGMP produce a cytoprotection mimicking the action of preconditioning tolerance. There are two distinct cGMP-mediated survival pathways: (i) the up-regulation of a redox protein thioredoxin (Trx) for elevating mitochondrial levels of antioxidant protein Mn superoxide dismutase (MnSOD) and antiapoptotic protein Bcl-2, and (ii) the activation of mitochondrial ATP-sensitive potassium channels [K(ATP)]. Preconditioning induction of Trx increased tolerance against MPP + , which was blocked by Trx mRNA antisense oligonucleotide and Trx reductase inhibitor. It is concluded that Trx plays a pivotal role in · NO-dependent preconditioning hormesis against MPTP/MPP +

  10. Preconditioning 2D Integer Data for Fast Convex Hull Computations.

    Cadenas, José Oswaldo; Megson, Graham M; Luengo Hendriks, Cris L

    2016-01-01

    In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

  11. Bilirubin nanoparticle preconditioning protects against hepatic ischemia-reperfusion injury.

    Kim, Jin Yong; Lee, Dong Yun; Kang, Sukmo; Miao, Wenjun; Kim, Hyungjun; Lee, Yonghyun; Jon, Sangyong

    2017-07-01

    Hepatic ischemia-reperfusion injury (IRI) remains a major concern in liver transplantation and resection, despite continuing efforts to prevent it. Accumulating evidence suggests that bilirubin possesses antioxidant, anti-inflammatory and anti-apoptotic properties. However, despite obvious potential health benefits of bilirubin, its clinical applications are limited by its poor solubility. We recently developed bilirubin nanoparticles (BRNPs) consisting of polyethylene glycol (PEG)-conjugated bilirubin. Here, we sought to investigate whether BRNPs protect against IRI in the liver by preventing oxidative stress. BRNPs exerted potent antioxidant and anti-apoptotic activity in primary hepatocytes exposed to hydrogen peroxide, a precursor of reactive oxygen species (ROS). In a model of hepatic IRI in mice, BRNP preconditioning exerted profound protective effects against hepatocellular injury by reducing oxidative stress, pro-inflammatory cytokine production, and recruitment of neutrophils. They also preferentially accumulated in IRI-induced inflammatory lesions. Collectively, our findings indicate that BRNP preconditioning provides a simple and safe approach that can be easily monitored in the blood like endogenous bilirubin, and could be a promising strategy to protect against IRI in a clinical setting. Copyright © 2017 Elsevier Ltd. All rights reserved.

  12. Stress preconditioning of spreading depression in the locust CNS.

    Corinne I Rodgers

    Full Text Available Cortical spreading depression (CSD is closely associated with important pathologies including stroke, seizures and migraine. The mechanisms underlying SD in its various forms are still incompletely understood. Here we describe SD-like events in an invertebrate model, the ventilatory central pattern generator (CPG of locusts. Using K(+ -sensitive microelectrodes, we measured extracellular K(+ concentration ([K(+](o in the metathoracic neuropile of the CPG while monitoring CPG output electromyographically from muscle 161 in the second abdominal segment to investigate the role K(+ in failure of neural circuit operation induced by various stressors. Failure of ventilation in response to different stressors (hyperthermia, anoxia, ATP depletion, Na(+/K(+ ATPase impairment, K(+ injection was associated with a disturbance of CNS ion homeostasis that shares the characteristics of CSD and SD-like events in vertebrates. Hyperthermic failure was preconditioned by prior heat shock (3 h, 45 degrees C and induced-thermotolerance was associated with an increase in the rate of clearance of extracellular K(+ that was not linked to changes in ATP levels or total Na(+/K(+ ATPase activity. Our findings suggest that SD-like events in locusts are adaptive to terminate neural network operation and conserve energy during stress and that they can be preconditioned by experience. We propose that they share mechanisms with CSD in mammals suggesting a common evolutionary origin.

  13. Parallelizable approximate solvers for recursions arising in preconditioning

    Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)

    1996-12-31

    For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.

  14. Ketamine, but not S(+)-ketamine, blocks ischemic preconditioning in rabbit hearts in vivo

    Müllenheim, J.; Frässdorf, J.; Preckel, B.; Thämer, V.; Schlack, W.

    2001-01-01

    BACKGROUND: Ketamine blocks KATP channels in isolated cells and abolishes the cardioprotective effect of ischemic preconditioning in vitro. The authors investigated the effects of ketamine and S(+)-ketamine on ischemic preconditioning in the rabbit heart in vivo. METHODS: In 46

  15. Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems

    Tang, J.M.

    2008-01-01

    The Preconditioned Conjugate Gradient (PCG) method is one of the most popular iterative methods for solving large linear systems with a symmetric and positive semi-definite coefficient matrix. However, if the preconditioned coefficient matrix is ill-conditioned, the convergence of the PCG method

  16. Sensory Preconditioning in Newborn Rabbits: From Common to Distinct Odor Memories

    Coureaud, Gerard; Tourat, Audrey; Ferreira, Guillaume

    2013-01-01

    This study evaluated whether olfactory preconditioning is functional in newborn rabbits and based on joined or independent memory of odorants. First, after exposure to odorants A+B, the conditioning of A led to high responsiveness to odorant B. Second, responsiveness to B persisted after amnesia of A. Third, preconditioning was also functional…

  17. Develop and implement preconditioning techniques to control face ejection rockbursts for safer mining in seismically hazardous areas

    Toper, AZ

    1998-01-01

    Full Text Available This research report discusses the development of preconditioning techniques to control face bursts, for safer mining in seismically hazardous areas. Preconditioning involves regularly setting off carefully tailored blasts in the fractured rock...

  18. Variational methods for eigenvalue problems an introduction to the weinstein method of intermediate problems

    Gould, S H

    1966-01-01

    The first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. This second edition presents new developments in the framework of the material contained in the first edition, which is retained in somewhat modified form.

  19. A multilevel in space and energy solver for multigroup diffusion eigenvalue problems

    Ben C. Yee

    2017-09-01

    Full Text Available In this paper, we present a new multilevel in space and energy diffusion (MSED method for solving multigroup diffusion eigenvalue problems. The MSED method can be described as a PI scheme with three additional features: (1 a grey (one-group diffusion equation used to efficiently converge the fission source and eigenvalue, (2 a space-dependent Wielandt shift technique used to reduce the number of PIs required, and (3 a multigrid-in-space linear solver for the linear solves required by each PI step. In MSED, the convergence of the solution of the multigroup diffusion eigenvalue problem is accelerated by performing work on lower-order equations with only one group and/or coarser spatial grids. Results from several Fourier analyses and a one-dimensional test code are provided to verify the efficiency of the MSED method and to justify the incorporation of the grey diffusion equation and the multigrid linear solver. These results highlight the potential efficiency of the MSED method as a solver for multidimensional multigroup diffusion eigenvalue problems, and they serve as a proof of principle for future work. Our ultimate goal is to implement the MSED method as an efficient solver for the two-dimensional/three-dimensional coarse mesh finite difference diffusion system in the Michigan parallel characteristics transport code. The work in this paper represents a necessary step towards that goal.

  20. A note on the gap between the first two eigenvalues for the Schroedinger operator

    Benguria, R.

    1986-01-01

    By means of a commutation formula, the author gives a simple proof of the upper bound of Wong et al on the gap between the first two eigenvalues in the Schrodinger operator. Unfortunately this proof does not seem to generalise into higher dimensions. (author)

  1. Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

    Raman, Aaswath; Fan, Shanhui

    2010-01-01

    We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.

  2. Parallel algorithms for 2-D cylindrical transport equations of Eigenvalue problem

    Wei, J.; Yang, S.

    2013-01-01

    In this paper, aimed at the neutron transport equations of eigenvalue problem under 2-D cylindrical geometry on unstructured grid, the discrete scheme of Sn discrete ordinate and discontinuous finite is built, and the parallel computation for the scheme is realized on MPI systems. Numerical experiments indicate that the designed parallel algorithm can reach perfect speedup, it has good practicality and scalability. (authors)

  3. Higher-order relationship between eigen-value separation and static flux tilts

    Beckner, W.D.

    1975-01-01

    Spatial kinetics phenomena in nuclear reactors, such as xenon-induced spatial flux oscillations, are currently being analyzed using the higher harmonic solutions to the static reactor balance equation. An important parameter in such an analysis is a global quantity called eigenvalue separation. It is desirable to be able to experimentally measure this parameter in power reactors in order to confirm design calculations. Since spatial distortions in the flux shape depend on the eigenvalue separation of the reactor, an attempt has been made previously to use this fact as a means of measuring the parameter. It was postulated that an induced flux distortion or ''static flux tilt'' could be measured and theoretically related to eigenvalue separation. Unfortunately, the behavior of experimental data did not exactly agree with theoretical predictions, and values of the parameter found using the original static flux tilt technique were consistently low. The theory has been re-evaluated here and the previously observed discrepancy eliminated. Techniques have been also developed to allow for more accurate interpretation of experimental data. In order to make the method applicable to real systems, the theory has been extended to two spatial dimensions; extension to three dimensions follows directly. Possible trouble areas have been investigated, and experimental procedures for use of the technique to measure the eigenvalue separation in power reactors are presented

  4. Correlation between eigenvalues and sorted diagonal matrix elements of a large dimensional matrix

    Arima, A.

    2008-01-01

    Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states. (author)

  5. Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem

    Raman, Aaswath

    2010-02-26

    We formulate the photonic band structure calculation of any lossless dispersive photonic crystal and optical metamaterial as a Hermitian eigenvalue problem. We further show that the eigenmodes of such lossless systems provide an orthonormal basis, which can be used to rigorously describe the behavior of lossy dispersive systems in general. © 2010 The American Physical Society.

  6. Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

    Bonito, Andrea; Guermond, Jean-Luc

    2011-01-01

    We propose and analyze an approximation technique for the Maxwell eigenvalue problem using H1-conforming finite elements. The key idea consists of considering a mixed method controlling the divergence of the electric field in a fractional Sobolev space H-α with α ∈ (1/2, 1). The method is shown to be convergent and spectrally correct. © 2011 American Mathematical Society.

  7. Eigenvalue for Densely Defined Perturbations of Multivalued Maximal Monotone Operators in Reflexive Banach Spaces

    Boubakari Ibrahimou

    2013-01-01

    maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.

  8. The discontinuous finite element method for solving Eigenvalue problems of transport equations

    Yang, Shulin; Wang, Ruihong

    2011-01-01

    In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)

  9. The Second Eigenvalue of the p-Laplacian as p Goes to 1

    Enea Parini

    2010-01-01

    Full Text Available The asymptotic behaviour of the second eigenvalue of the p-Laplacian operator as p goes to 1 is investigated. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if p is close enough to 1.

  10. Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras

    Scheunert, M.

    1982-10-01

    The generators of the algebras under consideration can be written in a canonical two-index form and hence the associated standard seuqence of Casimir elements can be constructed. Following the classical approach by Perelomov and Popov, we obtain the eigenvalues of these Casimir elements in an arbitrary highest weight module by calculating the corresponding generating functions. (orig.)

  11. Algorithm-Eigenvalue Estimation of Hyperspectral Wishart Covariance Matrices from a Limited Number of Samples

    2015-03-01

    biometrics for physiological characteristics, hyperspectral remote sensing for detecting signals buried in noise and clutter, and medical genetics for...s); %approximate bounds on the eigenvalues used in Eq. (8) that are derived %from the Marcenko- Pastur law k=p./n; %band

  12. MIMO Channel Model with Propagation Mechanism and the Properties of Correlation and Eigenvalue in Mobile Environments

    Yuuki Kanemiyo

    2012-01-01

    Full Text Available This paper described a spatial correlation and eigenvalue in a multiple-input multiple-output (MIMO channel. A MIMO channel model with a multipath propagation mechanism was proposed and showed the channel matrix. The spatial correlation coefficient formula −,′−′( between MIMO channel matrix elements was derived for the model and was expressed as a directive wave term added to the product of mobile site correlation −′( and base site correlation −′( without LOS path, which are calculated independently of each other. By using −,′−′(, it is possible to create the channel matrix element with a fixed correlation value estimated by −,′−′( for a given multipath condition and a given antenna configuration. Furthermore, the correlation and the channel matrix eigenvalue were simulated, and the simulated and theoretical correlation values agreed well. The simulated eigenvalue showed that the average of the first eigenvalue λ1 hardly depends on the correlation −,′−′(, but the others do depend on −,′−′( and approach 1 as −,′−′( decreases. Moreover, as the path moves into LOS, the 1 state with mobile movement becomes more stable than the 1 of NLOS path.

  13. A new formulation for the eigenvalue and the eigenfunction in the perturbation theory

    Korek, Mahmoud

    1999-01-01

    Full text.In infrared transitions, the problem of the ro vibrational eigenvalue and eigenfunction of a diatomic molecule is considered. It is shown that, for the transitions vJ↔v'J' the eigenvalues and the eigenfunctions of the two considered states can be expressed respectively in terms of one variable m (transition number), relating these two states, as E vm =Σ i=o e v (i) m i , Ψ vm =Σ i=0 φ v (i) m i and E v'm =Σ i=0 e v' (i) m i , Ψ v'm =Σ i=0 φ v' (i) m i , where m=[J'(J'+1)-J(J+1)]/2, and the coefficients e v (i) , φ v (i) , e v (i) , and φ v (i) , are given by analytical expressions. This m-representation of the eigenvalues and the eigenfunctions is more advantageous for the calculation of many factors in spectroscopy that are given in terms of m as the line intensities, the wave number of a transition, the Herman-Wallis coefficients,...etc. The numerical application to the ground state of the molecule CO shows that the present formulation provides a simple and accurate method for the calculation of the eigenvalues and the eigenfunctions for the two considered states

  14. Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel

    Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno

    2001-01-01

    The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...

  15. Eigenvalue condition for the Weinberg angle and possible new leptons and quarks

    Ma, E.

    1977-01-01

    In a given SU(2) x U(1) gauge model of the weak and electro-magnetic interactions, if one assumes that an eigenvalue condition exists for the mixing (Weinberg) angle, then its value can be computed in lower-order perturbation theory. This idea is illustrated with several examples, including two which are in agreement with all the present available data. (auth.)

  16. Asymptotic eigenvalue estimates for a Robin problem with a large parameter

    Exner, Pavel; Minakov, A.; Parnovski, L.

    2014-01-01

    Roč. 71, č. 2 (2014), s. 141-156 ISSN 0032-5155 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplacian * Robin problem * eigenvalue asymptotics Subject RIV: BE - Theoretical Physics Impact factor: 0.250, year: 2014

  17. On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries

    Dittrich, Jaroslav; Exner, Pavel; Kuhn, C.; Pankrashkin, K.

    2016-01-01

    Roč. 97, 1-2 (2016), s. 1-25 ISSN 0921-7134 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : singular Schrodinger operator * delta-interaction * strong coupling * eigenvalue Subject RIV: BE - Theoretical Physics Impact factor: 0.933, year: 2016

  18. Lq-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues

    Vladimir Kozlov

    2006-01-01

    Full Text Available We consider eigenvalues of elliptic boundary value problems, written in variational form, when the leading coefficients are perturbed by terms which are small in some integral sense. We obtain asymptotic formulae. The main specific of these formulae is that the leading term is different from that in the corresponding formulae when the perturbation is small in L∞-norm.

  19. Effect of continuous eigenvalue spectrum on plasma transport in toroidal systems

    Yamagishi, Tomejiro

    1993-03-01

    The effect of the continuous eigenvalue of the Vlasov equation on the cross field ion thermal flux is investigated. The continuum contribution due to the toroidal drift resonance is found to play an important role in ion transport particularly near the edge, which may apply to the interpretation of the sharp increase of ion heat conductivity near the periphery observed in large tokamaks. (author)

  20. Asymptotics of the Perron-Frobenius eigenvalue of nonnegative Hessenberg-Toeplitz matrices

    Janssen, A.J.E.M.

    1989-01-01

    Asymptotic results for the Perron-Frobenius eigenvalue of a nonnegative Hessenberg-Toeplitz matrix as the dimension of the matrix tends to 8 are given. The results are used and interpreted in terms of source entropies in the case where the Hessenberg-Toeplitz matrix arises as the transition matrix

  1. On the number of negative eigenvalues of the Laplacian on a metric graph

    Behrndt, Jussi; Luger, Annemarie

    2010-01-01

    The number of negative eigenvalues of self-adjoint Laplacians on metric graphs is calculated in terms of the boundary conditions and the underlying geometric structure. This extends and complements earlier results by Kostrykin and Schrader (2006 Contemp. Math. 415 201-25).

  2. On the number of negative eigenvalues of the Laplacian on a metric graph

    Behrndt, Jussi [Institut fuer Mathematik, MA 6-4, Technische Universitaet Berlin, Strasse des 17. Juni 136, 10623 Berlin (Germany); Luger, Annemarie, E-mail: behrndt@math.tu-berlin.d, E-mail: luger@maths.lth.s [Center for Mathematical Sciences, Lund Institute of Technology/Lund University, Box 118, SE-221 00 Lund (Sweden)

    2010-11-26

    The number of negative eigenvalues of self-adjoint Laplacians on metric graphs is calculated in terms of the boundary conditions and the underlying geometric structure. This extends and complements earlier results by Kostrykin and Schrader (2006 Contemp. Math. 415 201-25).

  3. Distribution of the Largest Eigenvalues of the Levi-Smirnov Ensemble

    Wieczorek, W.

    2004-01-01

    We calculate the distribution of the k-th largest eigenvalue in the random matrix Levi - Smirnov Ensemble (LSE), using the spectral dualism between LSE and chiral Gaussian Unitary Ensemble (GUE). Then we reconstruct universal spectral oscillations and we investigate an asymptotic behavior of the spectral distribution. (author)

  4. Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

    Antunes, P. R. S.; Freitas, P.; Krejčiřík, David

    2017-01-01

    Roč. 10, č. 4 (2017), s. 357-379 ISSN 1864-8258 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Eigenvalue optimisation * Robin Laplacian * negative boundary parameter * Bareket's conjecture Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.182, year: 2016

  5. Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

    Guliyev, Namig J.

    2008-01-01

    International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

  6. A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues

    Schmidt, Tobias; Kümmel, Stephan; Kraisler, Eli; Makmal, Adi; Kronik, Leeor

    2014-01-01

    We present and test a new approximation for the exchange-correlation (xc) energy of Kohn-Sham density functional theory. It combines exact exchange with a compatible non-local correlation functional. The functional is by construction free of one-electron self-interaction, respects constraints derived from uniform coordinate scaling, and has the correct asymptotic behavior of the xc energy density. It contains one parameter that is not determined ab initio. We investigate whether it is possible to construct a functional that yields accurate binding energies and affords other advantages, specifically Kohn-Sham eigenvalues that reliably reflect ionization potentials. Tests for a set of atoms and small molecules show that within our local-hybrid form accurate binding energies can be achieved by proper optimization of the free parameter in our functional, along with an improvement in dissociation energy curves and in Kohn-Sham eigenvalues. However, the correspondence of the latter to experimental ionization potentials is not yet satisfactory, and if we choose to optimize their prediction, a rather different value of the functional's parameter is obtained. We put this finding in a larger context by discussing similar observations for other functionals and possible directions for further functional development that our findings suggest

  7. Eigenvalues of relaxed toroidal plasmas of arbitrary sharp edged cross sections. Vol. 2

    Khalil, Sh M [Plasma Physics and Nuclear Fusion Department, Nuclear Research Center, Atomic Energy Authority, Cairo, (Egypt)

    1996-03-01

    Relaxed (force-free) toroidal plasmas described by the equations cur 1 B={mu}B, and grad {mu}=O (B is the magnetic field) induces interest in nuclear fusion. Its solution is perceived to describe the gross of the reversed field pinch (RFP), spheromak configuration, current limitation in toroidal plasmas, and others. The parameter {mu} plays an important roll in relaxed states. It cannot exceed the smallest eigenvalue {mu} (min), and that for a toroidal discharge there is a maximum toroidal current which is connected to this value. The values of{mu} were calculated numerically, using the methods of collocation points, for toroids of arbitrary aspect ratio {alpha} ({alpha} = R/a, ratio of major/minor radii of tokamak) and arbitrary curved cross-sections (circle, ellipse, cassini, and D-shaped). The aim of present work is to prove the applicability of the numerical methods for calculating the eigenvalues for toroidal plasmas having sharp edged cross sections and arbitrary aspect ratio. The lowest eigenvalue {mu} (min), satisfy the boundary condition {beta} .n = O (or RB. = O) for which the toroidal flux are calculated. These are the zero field eigenvalues of the equation cur 1 b={mu}B. The poloidal magnetic field lines corresponding to different cross sections are shown by plotting the boundary condition B.n=O. The plots showed good fulfillment of the boundary condition along the whole boundaries of different cross sections. Dependence of eigenvalues {mu}a on aspect ratio {alpha} is also obtained. Several runs of the programme with various wave numbers K showed that {mu}a is very insensitive to the choice of K. 8 figs.

  8. Effects Of Ischemic Preconditioning On The Renal Ischemia- Reperfusion Injury

    Anyamanesh S

    2003-07-01

    Full Text Available  During kidney and other organ transplantation, the organ to be transplanted, must inevitably remain out of the body with little or no blood perfusion at all for a long period of time (ischemia. These events have been suggested to cause the formation of oxygen- derived free radicals (OFR. Reperfusion (reintroduction of blood flow will further exacerbate the initial damage caused by the ischemic insult and may result in the production of free radicals. The aim of this study was to investigate whether induction of brief periods of renal artery occlusion (ischemic pre¬conditioning, IPC can provide protection from the effects of a subsequent period of ischemia and reperfusion (IR in the rat kidney."nMaterials and Methods: In this regard, 28 white, male rats were randomly and equally divided into four groups: Control (sham- operated, IPC alone, IR alone (30 min ischemia followed by 10 min reperfusion, and IPC- IR. Preconditioning involved the sequential clamping of the right renal artery for 5 min and declamping for 5 min for a total of 3 cycles. To demonstrate the effectiveness of IPC regimen, vitamin E as an endogenous antioxidant and an index of lipid peroxidation was measured by HPLC after its extraction from right renal venous plasma and right renal tissue."nResults: Results of this study showed that the amount of vitamin E of renal tissue and venous plasma in the IR group had a significant decrease when compared to the control group (P< 0.0001. Whereas the amount of this vitamin in both renal tissue and venous plasma of the IPC- IR group was significantly higher than that in the IR group (P< 0.0001, but did not show any significant difference with the control group."nConclusion: In this study, preconditioning method prevented the reduction of the endogenous antioxidant (Vit. E in encountering the following sustained ischemic insult. Therefore, we suggest that ischemic preconditioning can be used to protect the Vit. E level of kidney from its

  9. Tackling bioactive glass excessive in vitro bioreactivity: Preconditioning approaches for cell culture tests.

    Ciraldo, Francesca E; Boccardi, Elena; Melli, Virginia; Westhauser, Fabian; Boccaccini, Aldo R

    2018-05-21

    Bioactive glasses (BGs) are being increasingly considered for biomedical applications in bone and soft tissue replacement approaches thanks to their ability to form strong bonding with tissues. However, due to their high reactivity once in contact with water-based solutions BGs rapidly exchange ions with the surrounding environment leading in most cases to an undesired increase of the pH under static in vitro conditions (due to alkaline ion "burst release"), making difficult or even impossible to perform cell culture studies. Several pre-conditioning treatments have been therefore proposed in laboratories worldwide to limit this problem. This paper presents an overview of the different strategies that have been put forward to pre-treat BG samples to tackle the pH raise issue in order to enable cell biology studies. The paper also discusses the relevant criteria that determine the selection of the optimal pre-treatment depending on the BG composition and morphology (e.g. particles, scaffolds). Bioactive glasses (BGs), since their discovery in 1971 by L.L Hench, have been widely used for bone replacement and repair, and, more recently, they are becoming highly attractive for bone and soft tissue engineering applications. BGs have in fact the ability to form a strong bond with both hard and soft tissues once in contact with biological fluid. The enhanced interaction of BGs with the biological environment is based on their significant surface bioreactivity. This surface effect of BGs is, on the other hand, problematic for cell biology studies by standard (static) cell culture methods: an excessive bioreactivity leads in most cases to a rapid and dramatic increase of the pH of the surrounding medium, which results in cell death and makes cell culture tests on BG samples impossible. The BG research community has been aware of this for many years and numerous pre-treatments have been proposed by different groups worldwide to limit this problem. For the first time, we have

  10. Institutionalized Ignorance as a Precondition for Rational Risk Expertise

    Merkelsen, Henrik

    2011-01-01

    the lowest organizational level, where concrete risks occur, to the highest organizational level, where the body of professional risk expertise is situated. The article emphasizes the role of knowledge, responsibility, loyalty, and trust as risk-attenuation factors and concludes by suggesting......The present case study seeks to explain the conditions for experts’ rational risk perception by analyzing the institutional contexts that constitute a field of food safety expertise in Denmark. The study highlights the role of risk reporting and how contextual factors affect risk reporting from...... that the preconditions for the expert's rationality may rather be a lack of risk-specific knowledge due to poor risk reporting than a superior level of risk knowledge....

  11. Explicit solution of Calderon preconditioned time domain integral equations

    Ulku, Huseyin Arda

    2013-07-01

    An explicit marching on-in-time (MOT) scheme for solving Calderon-preconditioned time domain integral equations is proposed. The scheme uses Rao-Wilton-Glisson and Buffa-Christiansen functions to discretize the domain and range of the integral operators and a PE(CE)m type linear multistep to march on in time. Unlike its implicit counterpart, the proposed explicit solver requires the solution of an MOT system with a Gram matrix that is sparse and well-conditioned independent of the time step size. Numerical results demonstrate that the explicit solver maintains its accuracy and stability even when the time step size is chosen as large as that typically used by an implicit solver. © 2013 IEEE.

  12. Least-squares reverse time migration with radon preconditioning

    Dutta, Gaurav

    2016-09-06

    We present a least-squares reverse time migration (LSRTM) method using Radon preconditioning to regularize noisy or severely undersampled data. A high resolution local radon transform is used as a change of basis for the reflectivity and sparseness constraints are applied to the inverted reflectivity in the transform domain. This reflects the prior that for each location of the subsurface the number of geological dips is limited. The forward and the adjoint mapping of the reflectivity to the local Radon domain and back are done through 3D Fourier-based discrete Radon transform operators. The sparseness is enforced by applying weights to the Radon domain components which either vary with the amplitudes of the local dips or are thresholded at given quantiles. Numerical tests on synthetic and field data validate the effectiveness of the proposed approach in producing images with improved SNR and reduced aliasing artifacts when compared with standard RTM or LSRTM.

  13. Can endurance exercise preconditioning prevention disuse muscle atrophy?

    Michael P Wiggs

    2015-03-01

    Full Text Available Emerging evidence suggests that exercise training can provide a level of protection against disuse muscle atrophy. Endurance exercise training imposes oxidative, metabolic, and heat stress on skeletal muscle which activates a variety of cellular signaling pathways that ultimately leads to the increased expression of proteins that have been demonstrated to protect muscle from inactivity –induced atrophy. This review will highlight the effect of exercise-induced oxidative stress on endogenous enzymatic antioxidant capacity (i.e., superoxide dismutase, glutathione peroxidase, and catalase, the role of oxidative and metabolic stress on PGC1-α, and finally highlight the effect heat stress and HSP70 induction. Finally, this review will discuss the supporting scientific evidence that these proteins can attenuate muscle atrophy through exercise preconditioning.

  14. Solving large mixed linear models using preconditioned conjugate gradient iteration.

    Strandén, I; Lidauer, M

    1999-12-01

    Continuous evaluation of dairy cattle with a random regression test-day model requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using iteration on data is presented. In the new computing technique, the calculations in multiplication of a vector by a matrix were recorded to three steps instead of the commonly used two steps. The three-step method was implemented in a general mixed linear model program that used preconditioned conjugate gradient iteration. Performance of this program in comparison to other general solving programs was assessed via estimation of breeding values using univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, at best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at least 20 and 435% more time to solve the univariate and multivariate animal models, respectively. Computations of the second best iteration on data took approximately three and five times longer for the animal and test-day models, respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large breeding value problems is supported by our findings.

  15. Effect of ozone oxidative preconditioning in preventing early radiation-induced lung injury in rats

    Bakkal, B.H. [Department of Radiation Oncology, School of Medicine, Bulent Ecevit University, Kozlu, Zonguldak (Turkey); Gultekin, F.A. [Department of General Surgery, School of Medicine, Bulent Ecevit University, Kozlu, Zonguldak (Turkey); Guven, B. [Department of Biochemistry, School of Medicine, Bulent Ecevit University, Kozlu, Zonguldak (Turkey); Turkcu, U.O. [Mugla School of Health Sciences, Mugla Sitki Kocman University, Mugla (Turkey); Bektas, S. [Department of Pathology, School of Medicine, Bulent Ecevit University, Kozlu, Zonguldak (Turkey); Can, M. [Department of Biochemistry, School of Medicine, Bulent Ecevit University, Kozlu, Zonguldak (Turkey)

    2013-09-27

    Ionizing radiation causes its biological effects mainly through oxidative damage induced by reactive oxygen species. Previous studies showed that ozone oxidative preconditioning attenuated pathophysiological events mediated by reactive oxygen species. As inhalation of ozone induces lung injury, the aim of this study was to examine whether ozone oxidative preconditioning potentiates or attenuates the effects of irradiation on the lung. Rats were subjected to total body irradiation, with or without treatment with ozone oxidative preconditioning (0.72 mg/kg). Serum proinflammatory cytokine levels, oxidative damage markers, and histopathological analysis were compared at 6 and 72 h after total body irradiation. Irradiation significantly increased lung malondialdehyde levels as an end-product of lipoperoxidation. Irradiation also significantly decreased lung superoxide dismutase activity, which is an indicator of the generation of oxidative stress and an early protective response to oxidative damage. Ozone oxidative preconditioning plus irradiation significantly decreased malondialdehyde levels and increased the activity of superoxide dismutase, which might indicate protection of the lung from radiation-induced lung injury. Serum tumor necrosis factor alpha and interleukin-1 beta levels, which increased significantly following total body irradiation, were decreased with ozone oxidative preconditioning. Moreover, ozone oxidative preconditioning was able to ameliorate radiation-induced lung injury assessed by histopathological evaluation. In conclusion, ozone oxidative preconditioning, repeated low-dose intraperitoneal administration of ozone, did not exacerbate radiation-induced lung injury, and, on the contrary, it provided protection against radiation-induced lung damage.

  16. Rural water-supply and sanitation planning: The use of socioeconomic preconditions in project identification

    Warner, Dennis B.

    1984-02-01

    Recognition of the socioeconomic preconditions for successful rural water-supply and sanitation projects in developing countries is the key to identifying a new project. Preconditions are the social, economic and technical characteristics defining the project environment. There are two basic types of preconditions: those existing at the time of the initial investigation and those induced by subsequent project activities. Successful project identification is dependent upon an accurate recognition of existing constraints and a carefully tailored package of complementary investments intended to overcome the constraints. This paper discusses the socioeconomic aspects of preconditions in the context of a five-step procedure for project identification. The procedure includes: (1) problem identification; (2) determination of socioeconomic status; (3) technology selection; (4) utilization of support conditions; and (5) benefit estimation. Although the establishment of specific preconditions should be based upon the types of projects likely to be implemented, the paper outlines a number of general relationships regarding favourable preconditions in water and sanitation planning. These relationships are used within the above five-step procedure to develop a set of general guidelines for the application of preconditions in the identification of rural water-supply and sanitation projects.

  17. Effect of ozone oxidative preconditioning in preventing early radiation-induced lung injury in rats

    Bakkal, B.H.; Gultekin, F.A.; Guven, B.; Turkcu, U.O.; Bektas, S.; Can, M.

    2013-01-01

    Ionizing radiation causes its biological effects mainly through oxidative damage induced by reactive oxygen species. Previous studies showed that ozone oxidative preconditioning attenuated pathophysiological events mediated by reactive oxygen species. As inhalation of ozone induces lung injury, the aim of this study was to examine whether ozone oxidative preconditioning potentiates or attenuates the effects of irradiation on the lung. Rats were subjected to total body irradiation, with or without treatment with ozone oxidative preconditioning (0.72 mg/kg). Serum proinflammatory cytokine levels, oxidative damage markers, and histopathological analysis were compared at 6 and 72 h after total body irradiation. Irradiation significantly increased lung malondialdehyde levels as an end-product of lipoperoxidation. Irradiation also significantly decreased lung superoxide dismutase activity, which is an indicator of the generation of oxidative stress and an early protective response to oxidative damage. Ozone oxidative preconditioning plus irradiation significantly decreased malondialdehyde levels and increased the activity of superoxide dismutase, which might indicate protection of the lung from radiation-induced lung injury. Serum tumor necrosis factor alpha and interleukin-1 beta levels, which increased significantly following total body irradiation, were decreased with ozone oxidative preconditioning. Moreover, ozone oxidative preconditioning was able to ameliorate radiation-induced lung injury assessed by histopathological evaluation. In conclusion, ozone oxidative preconditioning, repeated low-dose intraperitoneal administration of ozone, did not exacerbate radiation-induced lung injury, and, on the contrary, it provided protection against radiation-induced lung damage

  18. Applications of polynomial optimization in financial risk investment

    Zeng, Meilan; Fu, Hongwei

    2017-09-01

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

  19. A preconditioning nerve lesion inhibits mechanical pain hypersensitivity following subsequent neuropathic injury

    Wu Ann

    2011-01-01

    Full Text Available Abstract Background A preconditioning stimulus can trigger a neuroprotective phenotype in the nervous system - a preconditioning nerve lesion causes a significant increase in axonal regeneration, and cerebral preconditioning protects against subsequent ischemia. We hypothesized that a preconditioning nerve lesion induces gene/protein modifications, neuronal changes, and immune activation that may affect pain sensation following subsequent nerve injury. We examined whether a preconditioning lesion affects neuropathic pain and neuroinflammation after peripheral nerve injury. Results We found that a preconditioning crush injury to a terminal branch of the sciatic nerve seven days before partial ligation of the sciatic nerve (PSNL; a model of neuropathic pain induced a significant attenuation of pain hypersensitivity, particularly mechanical allodynia. A preconditioning lesion of the tibial nerve induced a long-term significant increase in paw-withdrawal threshold to mechanical stimuli and paw-withdrawal latency to thermal stimuli, after PSNL. A preconditioning lesion of the common peroneal induced a smaller but significant short-term increase in paw-withdrawal threshold to mechanical stimuli, after PSNL. There was no difference between preconditioned and unconditioned animals in neuronal damage and macrophage and T-cell infiltration into the dorsal root ganglia (DRGs or in astrocyte and microglia activation in the spinal dorsal and ventral horns. Conclusions These results suggest that prior exposure to a mild nerve lesion protects against adverse effects of subsequent neuropathic injury, and that this conditioning-induced inhibition of pain hypersensitivity is not dependent on neuroinflammation in DRGs and spinal cord. Identifying the underlying mechanisms may have important implications for the understanding of neuropathic pain due to nerve injury.

  20. A comparison of the eigenvalue equations in kappa, α, lambda and γ in reactor theory. Application to fast and thermal systems in unreflected and reflected configurations

    Velarde, G.; Ahnert, C.; Aragones, J.M.

    1977-01-01

    A comparative study of the eigenvalue transport in kappa, lambda, γ and α is made. The neutronic fluxes obtained by solving the transport equation in the four eigenvalue types are compared numerically for fast and thermal systems in unreflected and reflected configurations. Important conclusions will be obtained about the appropiate use of each eigenvalue depending on the calculation type to be performed. (author)

  1. LONG-TERM PRECONDITIONING OF PLANTLETS: A PRACTICAL METHOD FOR ENHANCING SURVIVAL OF PINEAPPLE (Ananas comosus Merr.) SHOOT TIPS CRYOPRESERVED USING VITRIFICATION.

    Hu, W H; Liu, S F; Liaw, S I

    2015-01-01

    The purpose of this study was to develop an efficient cryopreservation protocol for pineapple (Ananas comosus Merr.) shoot tips. The optimal state of pineapple plantlets was investigated by using sucrose preconditioning to enhance survival after cryostorage. To achieve a suitable state of plantlets before cryopreservation, 0.2 M to 0.4 M sucrose concentrations combined with short- (0-7 days), medium- (15-30 days), and long-term (75-150 days) preconditioning periods were compared. The highest survival (100 %) was achieved using the following procedure: intact plantlets underwent long-term preconditioning with 0.2 M sucrose for 135 days, dissected shoot tips were treated with a loading solution containing 2.0 M glycerol + 0.4 M sucrose for 60 min at 25 degree and the shoot tips were dehydrated in PVS2 for 2h at 0 degree C before being plunged in liquid nitrogen. Rewarming was conducted in a water-bath for 30 s at 40 degree C and PVS2 was replaced with a 1.2 M sucrose solution for 30 min at 25 degree C. The shoot tips were transferred on semisolid medium and left in the dark for 1 week, then in dim light for 3 weeks.

  2. The solution of a chiral random matrix model with complex eigenvalues

    Akemann, G

    2003-01-01

    We describe in detail the solution of the extension of the chiral Gaussian unitary ensemble (chGUE) into the complex plane. The correlation functions of the model are first calculated for a finite number of N complex eigenvalues, where we exploit the existence of orthogonal Laguerre polynomials in the complex plane. When taking the large-N limit we derive new correlation functions in the case of weak and strong non-Hermiticity, thus describing the transition from the chGUE to a generalized Ginibre ensemble. We briefly discuss applications to the Dirac operator eigenvalue spectrum in quantum chromodynamics with non-vanishing chemical potential. This is an extended version of hep-th/0204068

  3. Heuristic geometric ''eigenvalue universality'' in a one-dimensional neutron transport problem with anisotropic scattering

    Goncalves, G.A.; Vilhena, M.T. de; Bodmann, B.E.J.

    2010-01-01

    In the present work we propose a heuristic construction of a transport equation for neutrons with anisotropic scattering considering only the radial cylinder dimension. The eigenvalues of the solutions of the equation correspond to the positive values for the one dimensional case. The central idea of the procedure is the application of the S N method for the discretisation of the angular variable followed by the application of the zero order Hankel transformation. The basis the construction of the scattering terms in form of an integro-differential equation for stationary transport resides in the hypothesis that the eigenvalues that compose the elementary solutions are independent of geometry for a homogeneous medium. We compare the solutions for the cartesian one dimensional problem for an infinite cylinder with azimuthal symmetry and linear anisotropic scattering for two cases. (orig.)

  4. Topological derivatives of eigenvalues and neural networks in identification of imperfections

    Grzanek, M; Nowakowski, A; Sokolowski, J

    2008-01-01

    Numerical method for identification of imperfections is devised for elliptic spectral problems. The neural networks are employed for numerical solution. The topological derivatives of eigenvalues are used in the learning procedure of the neural networks. The topological derivatives of eigenvalues are determined by the methods of asymptotic analysis in singularly perturbed geometrical domains. The convergence of the numerical method in a probabilistic setting is analysed. The method is presented for the identification of small singular perturbations of the boundary of geometrical domain, however the framework is general and can be used for numerical solutions of inverse problems in the presence of small imperfections in the interior of the domain. Some numerical results are given for elliptic spectral problem in two spatial dimensions.

  5. Solving eigenvalue problems on curved surfaces using the Closest Point Method

    Macdonald, Colin B.

    2011-06-01

    Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace-Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach. © 2011 Elsevier Inc.

  6. Improved simple graphical solution for the eigenvalues of the finite square well potential

    Burge, E.J.

    1985-01-01

    The three principal graphical methods for obtaining the energy eigenvalues of the finite square well potential are presented. The forms of the wavefunctions within the well, and the corresponding linear probability densities, are derived directly from the method. A simple extension of the method allows the energy level spectrum to be obtained directly on a linear energy scale. The variations of the energy eigenvalues with well depth and width are separately and jointly displayed, and explicit corresponding functional relationships are derived. Two universal graphs are deduced which allow the rapid appreciation and calculation of the dependence of the energy levels on the depth and width of the well and on the mass of the particle. (author)

  7. Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem

    Lakshtanov, E.; Vainberg, B.

    2013-10-01

    The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).

  8. Generalization of the Fourier Convergence Analysis in the Neutron Diffusion Eigenvalue Problem

    Lee, Hyun Chul; Noh, Jae Man; Joo, Hyung Kook

    2005-01-01

    Fourier error analysis has been a standard technique for the stability and convergence analysis of linear and nonlinear iterative methods. Lee et al proposed new 2- D/1-D coupling methods and demonstrated several advantages of the new methods by performing a Fourier convergence analysis of the methods as well as two existing methods for a fixed source problem. We demonstrated the Fourier convergence analysis of one of the 2-D/1-D coupling methods applied to a neutron diffusion eigenvalue problem. However, the technique cannot be used directly to analyze the convergence of the other 2-D/1-D coupling methods since some algorithm-specific features were used in our previous study. In this paper we generalized the Fourier convergence analysis technique proposed and analyzed the convergence of the 2-D/1-D coupling methods applied to a neutron diffusion Eigenvalue problem using the generalized technique

  9. Toward a High Performance Tile Divide and Conquer Algorithm for the Dense Symmetric Eigenvalue Problem

    Haidar, Azzam

    2012-01-01

    Classical solvers for the dense symmetric eigenvalue problem suffer from the first step, which involves a reduction to tridiagonal form that is dominated by the cost of accessing memory during the panel factorization. The solution is to reduce the matrix to a banded form, which then requires the eigenvalues of the banded matrix to be computed. The standard divide and conquer algorithm can be modified for this purpose. The paper combines this insight with tile algorithms that can be scheduled via a dynamic runtime system to multicore architectures. A detailed analysis of performance and accuracy is included. Performance improvements of 14-fold and 4-fold speedups are reported relative to LAPACK and Intel\\'s Math Kernel Library.

  10. Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

    Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

    2006-09-28

    A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

  11. Inequalities among partial traces of hermitian operators and partial sums of their eigenvalues

    Daboul, J.

    1990-01-01

    Two different proofs of the following inequality are given: Tr sup(k)(H):= sup(k)Σ sub(i=1) h sub(i) :sup(k)Σ sub(i=1)(X sub(i), Hx sub(i))≥ sup(k)Σ sub(i=1)E sub(i), for k = 1,-,N, where H is a Hermitian matrix, the {X sub(i), i = 1,2-,k } are any k orthonormal vectors and the e sub(i) are the eigenvalues of H, ordered according to increasing values. This result is a generalization of the well-known fact, that ground state of a Hamiltonian is given by its lowest eigenvalue, E sub(i). It can also be regarded as a generalization, for Hermitian operators, of the invariance of the trace under unitary transformation. A few consequences of the above result are also derived. (author)

  12. A new S-type eigenvalue inclusion set for tensors and its applications.

    Huang, Zheng-Ge; Wang, Li-Gong; Xu, Zhong; Cui, Jing-Jing

    2016-01-01

    In this paper, a new S -type eigenvalue localization set for a tensor is derived by dividing [Formula: see text] into disjoint subsets S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, 2005), Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and Li et al. (Linear Algebra Appl. 481:36-53, 2015). As applications of the results, new bounds for the spectral radius of nonnegative tensors and the minimum H -eigenvalue of strong M -tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, 2014) and He and Huang (J. Inequal. Appl. 2014:114, 2014).

  13. Leak detection of complex pipelines based on the filter diagonalization method: robust technique for eigenvalue assessment

    Lay-Ekuakille, Aimé; Pariset, Carlo; Trotta, Amerigo

    2010-01-01

    The FDM (filter diagonalization method), an interesting technique used in nuclear magnetic resonance data processing for tackling FFT (fast Fourier transform) limitations, can be used by considering pipelines, especially complex configurations, as a vascular apparatus with arteries, veins, capillaries, etc. Thrombosis, which might occur in humans, can be considered as a leakage for the complex pipeline, the human vascular apparatus. The choice of eigenvalues in FDM or in spectra-based techniques is a key issue in recovering the solution of the main equation (for FDM) or frequency domain transformation (for FFT) in order to determine the accuracy in detecting leaks in pipelines. This paper deals with the possibility of improving the leak detection accuracy of the FDM technique thanks to a robust algorithm by assessing the problem of eigenvalues, making it less experimental and more analytical using Tikhonov-based regularization techniques. The paper starts from the results of previous experimental procedures carried out by the authors

  14. Some algorithms for the solution of the symmetric eigenvalue problem on a multiprocessor electronic computer

    Molchanov, I.N.; Khimich, A.N.

    1984-01-01

    This article shows how a reflection method can be used to find the eigenvalues of a matrix by transforming the matrix to tridiagonal form. The method of conjugate gradients is used to find the smallest eigenvalue and the corresponding eigenvector of symmetric positive-definite band matrices. Topics considered include the computational scheme of the reflection method, the organization of parallel calculations by the reflection method, the computational scheme of the conjugate gradient method, the organization of parallel calculations by the conjugate gradient method, and the effectiveness of parallel algorithms. It is concluded that it is possible to increase the overall effectiveness of the multiprocessor electronic computers by either letting the newly available processors of a new problem operate in the multiprocessor mode, or by improving the coefficient of uniform partition of the original information

  15. Elementary Baecklund transformations for a discrete Ablowitz-Ladik eigenvalue problem

    Rourke, David E

    2004-01-01

    Elementary Baecklund transformations (BTs) are described for a discretization of the Zakharov-Shabat eigenvalue problem (a special case of the Ablowitz-Ladik eigenvalue problem). Elementary BTs allow the process of adding bound states to a system (i.e., the add-one-soliton BT) to be 'factorized' to solving two simpler sub-problems. They are used to determine the effect on the scattering data when bound states are added. They are shown to provide a method of calculating discrete solitons-this is achieved by constructing a lattice of intermediate potentials, with the parameters used in the calculation of the lattice simply related to the soliton scattering data. When the potentials, S n , T n , in the system are related by S n = -T n , they enable simple derivations to be obtained of the add-one-soliton BT and the nonlinear superposition formula

  16. Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator

    Macfarlane, A J; Pfeiffer, Hendryk

    2003-01-01

    The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is now well known for powers up to four. The paper describes an extension of this uniformity for the totally antisymmetrized nth powers up to n = 9, identifying families of representations with integer eigenvalues 5, ..., 9 for the quadratic Casimir operator, in each case providing a formula for the dimensions of the representations in the family as a function of D = dim g. This generalizes previous results for powers j and Casimir eigenvalues j, j ≤ 4. Many intriguing, perhaps puzzling, features of the dimension formulae are discussed and the possibility that they may be valid for a wider class of not necessarily simple Lie algebras is considered

  17. Three-dimensional multiple reciprocity boundary element method for one-group neutron diffusion eigenvalue computations

    Itagaki, Masafumi; Sahashi, Naoki.

    1996-01-01

    The multiple reciprocity method (MRM) in conjunction with the boundary element method has been employed to solve one-group eigenvalue problems described by the three-dimensional (3-D) neutron diffusion equation. The domain integral related to the fission source is transformed into a series of boundary-only integrals, with the aid of the higher order fundamental solutions based on the spherical and the modified spherical Bessel functions. Since each degree of the higher order fundamental solutions in the 3-D cases has a singularity of order (1/r), the above series of boundary integrals requires additional terms which do not appear in the 2-D MRM formulation. The critical eigenvalue itself can be also described using only boundary integrals. Test calculations show that Wielandt's spectral shift technique guarantees rapid and stable convergence of 3-D MRM computations. (author)

  18. Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

    Pelinovsky, Dmitry E.; Sulem, Catherine

    A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

  19. On the calculation of the eigenvalues of the Faddeev equation kernel on the nonphysical sheet of energy

    Moeller, K.

    1978-01-01

    A system of three particles is considered which interacts by rank-1 separable potential. For the Faddeev equation kernel of this system a method is proposed for calculating the eigenvalues on the nonphysical sheet of the three-particle cms-energy. From the consideration of the analytical structure of the eigenvalues in the energy plane it follows that the analytical continuations of the eigenvalues from the physical to the nonphysical region are different above and below the three-particle threshold. In this paper the continuation below the threshold is discussed. (author)

  20. Experimental Validation of Model Updating and Damage Detection via Eigenvalue Sensitivity Methods with Artificial Boundary Conditions

    2017-09-01

    features can be evaluated such a welds and bolted connections. With these situations investigated, test articles with more complex geometry can be used...become more capable. Despite these advancements, the construction of physical prototypes remains an essential aspect of design and testing . FEM...prototype, there may be design deficiencies that cannot be identified until the prototype is tested . Using eigenvalue sensitivities, enhanced by

  1. Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

    Kramer, D.; Neugebauer, G.

    1981-01-01

    The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. Using the method of Wahlquist and Estabrook (J. Math Phys.; 16:1 (1975)) it is shown that the prolongation structure of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found. (author)

  2. Solution of the multigroup neutron diffusion Eigenvalue problem in slab geometry by modified power method

    Zanette, Rodrigo [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pós-Graduação em Matemática Aplicada; Petersen, Claudio Z.; Tavares, Matheus G., E-mail: rodrigozanette@hotmail.com, E-mail: claudiopetersen@yahoo.com.br, E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Programa de Pós-Graduação em Modelagem Matemática

    2017-07-01

    We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor (K{sub eff})) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the spatial variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes propose that it be reconstructed through an polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature. (author)

  3. Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

    Bäcker, A.

    Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

  4. Eigenvalues and eigenvectors of the translation matrices of spherical waves of multiple-scattering theory

    Torrini, M.

    1983-01-01

    The exponential nature of the translation matrix G of spherical free waves has been set forth in a previous paper.The explicit expression of the exponential form of the translation matrix is given here, once the eigenvectros and the eigenvalues of G have been found. In addition, the eigenproblem relative to the matrix which transforms outgoing waves scattered by a centre in a set of spherical free waves centered at a different point is solved

  5. Genetic Algorithm Applied to the Eigenvalue Equalization Filtered-x LMS Algorithm (EE-FXLMS

    Stephan P. Lovstedt

    2008-01-01

    Full Text Available The FXLMS algorithm, used extensively in active noise control (ANC, exhibits frequency-dependent convergence behavior. This leads to degraded performance for time-varying tonal noise and noise with multiple stationary tones. Previous work by the authors proposed the eigenvalue equalization filtered-x least mean squares (EE-FXLMS algorithm. For that algorithm, magnitude coefficients of the secondary path transfer function are modified to decrease variation in the eigenvalues of the filtered-x autocorrelation matrix, while preserving the phase, giving faster convergence and increasing overall attenuation. This paper revisits the EE-FXLMS algorithm, using a genetic algorithm to find magnitude coefficients that give the least variation in eigenvalues. This method overcomes some of the problems with implementing the EE-FXLMS algorithm arising from finite resolution of sampled systems. Experimental control results using the original secondary path model, and a modified secondary path model for both the previous implementation of EE-FXLMS and the genetic algorithm implementation are compared.

  6. Hybrid subgroup decomposition method for solving fine-group eigenvalue transport problems

    Yasseri, Saam; Rahnema, Farzad

    2014-01-01

    Highlights: • An acceleration technique for solving fine-group eigenvalue transport problems. • Coarse-group quasi transport theory to solve coarse-group eigenvalue transport problems. • Consistent and inconsistent formulations for coarse-group quasi transport theory. • Computational efficiency amplified by a factor of 2 using hybrid SGD for 1D BWR problem. - Abstract: In this paper, a new hybrid method for solving fine-group eigenvalue transport problems is developed. This method extends the subgroup decomposition method to efficiently couple a new coarse-group quasi transport theory with a set of fixed-source transport decomposition sweeps to obtain the fine-group transport solution. The advantages of the quasi transport theory are its high accuracy, straight-forward implementation and numerical stability. The hybrid method is analyzed for a 1D benchmark problem characteristic of boiling water reactors (BWR). It is shown that the method reproduces the fine-group transport solution with high accuracy while increasing the computational efficiency up to 12 times compared to direct fine-group transport calculations

  7. Numerical computations of interior transmission eigenvalues for scattering objects with cavities

    Peters, Stefan; Kleefeld, Andreas

    2016-01-01

    In this article we extend the inside-outside duality for acoustic transmission eigenvalue problems by allowing scattering objects that may contain cavities. In this context we provide the functional analytical framework necessary to transfer the techniques that have been used in Kirsch and Lechleiter (2013 Inverse Problems, 29 104011) to derive the inside-outside duality. Additionally, extensive numerical results are presented to show that we are able to successfully detect interior transmission eigenvalues with the inside-outside duality approach for a variety of obstacles with and without cavities in three dimensions. In this context, we also discuss the advantages and disadvantages of the inside-outside duality approach from a numerical point of view. Furthermore we derive the integral equations necessary to extend the algorithm in Kleefeld (2013 Inverse Problems, 29 104012) to compute highly accurate interior transmission eigenvalues for scattering objects with cavities, which we will then use as reference values to examine the accuracy of the inside-outside duality algorithm. (paper)

  8. Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

    Pato, Mauricio P.; Oshanin, Gleb

    2013-03-01

    We study the probability distribution function P(β)n(w) of the Schmidt-like random variable w = x21/(∑j = 1nx2j/n), where xj, (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P(β)n(w) converges to the Marčenko-Pastur form, i.e. is defined as P_{n}^{( \\beta )}(w) \\sim \\sqrt{(4 - w)/w} for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P(β = 2)n(w) which are valid for arbitrary n and analyse their behaviour.

  9. Distribution of Schmidt-like eigenvalues for Gaussian ensembles of the random matrix theory

    Pato, Mauricio P; Oshanin, Gleb

    2013-01-01

    We study the probability distribution function P (β) n (w) of the Schmidt-like random variable w = x 2 1 /(∑ j=1 n x 2 j /n), where x j , (j = 1, 2, …, n), are unordered eigenvalues of a given n × n β-Gaussian random matrix, β being the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual (randomly chosen) eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n → ∞ and for arbitrary β the distribution P (β) n (w) converges to the Marčenko–Pastur form, i.e. is defined as P n (β) (w)∼√((4 - w)/w) for w ∈ [0, 4] and equals zero outside of the support, despite the fact that formally w is defined on the interval [0, n]. Furthermore, for Gaussian unitary ensembles (β = 2) we present exact explicit expressions for P (β=2) n (w) which are valid for arbitrary n and analyse their behaviour. (paper)

  10. Preconditioned alternating direction method of multipliers for inverse problems with constraints

    Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie

    2017-01-01

    We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method. (paper)

  11. S2SA preconditioning for the Sn equations with strictly non negative spatial discretization

    Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

    2013-01-01

    Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S n transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use a linear diffusion equation has important implications for preconditioning the S n equations with a strictly non negative spatial discretization in multiple dimensions. (authors)

  12. Rapamycin preconditioning attenuates transient focal cerebral ischemia/reperfusion injury in mice.

    Yin, Lele; Ye, Shasha; Chen, Zhen; Zeng, Yaoying

    2012-12-01

    Rapamycin, an mTOR inhibitor and immunosuppressive agent in clinic, has protective effects on traumatic brain injury and neurodegenerative diseases. But, its effects on transient focal ischemia/reperfusion disease are not very clear. In this study, we examined the effects of rapamycin preconditioning on mice treated with middle cerebral artery occlusion/reperfusion operation (MCAO/R). We found that the rapamycin preconditioning by intrahippocampal injection 20 hr before MCAO/R significantly improved the survival rate and longevity of mice. It also decreased the neurological deficit score, infracted areas and brain edema. In addition, rapamycin preconditioning decreased the production of NF-κB, TNF-α, and Bax, but not Bcl-2, an antiapoptotic protein in the ischemic area. From these results, we may conclude that rapamycin preconditioning attenuate transient focal cerebral ischemia/reperfusion injury and inhibits apoptosis induced by MCAO/R in mice.

  13. Ischemic preconditioning improves mitochondrial tolerance to experimental calcium overload.

    Crestanello, Juan A; Doliba, Nicolai M; Babsky, Andriy M; Doliba, Natalia M; Niibori, Koki; Whitman, Glenn J R; Osbakken, Mary D

    2002-04-01

    Ca(2+) overload leads to mitochondrial uncoupling, decreased ATP synthesis, and myocardial dysfunction. Pharmacologically opening of mitochondrial K(ATP) channels decreases mitochondrial Ca(2+) uptake, improving mitochondrial function during Ca(2+) overload. Ischemic preconditioning (IPC), by activating mitochondrial K(ATP) channels, may attenuate mitochondrial Ca(2+) overload and improve mitochondrial function during reperfusion. The purpose of these experiments was to study the effect of IPC (1) on mitochondrial function and (2) on mitochondrial tolerance to experimental Ca(2+) overload. Rat hearts (n = 6/group) were subjected to (a) 30 min of equilibration, 25 min of ischemia, and 30 min of reperfusion (Control) or (b) two 5-min episodes of ischemic preconditioning, 25 min of ischemia, and 30 min of reperfusion (IPC). Developed pressure (DP) was measured. Heart mitochondria were isolated at end-Equilibration (end-EQ) and at end-Reperfusion (end-RP). Mitochondrial respiratory function (state 2, oxygen consumption with substrate only; state 3, oxygen consumption stimulated by ADP; state 4, oxygen consumption after cessation of ADP phosphorylation; respiratory control index (RCI, state 3/state 4); rate of oxidative phosphorylation (ADP/Deltat), and ADP:O ratio) was measured with polarography using alpha-ketoglutarate as a substrate in the presence of different Ca(2+) concentrations (0 to 5 x 10(-7) M) to simulate Ca(2+) overload. IPC improved DP at end-RP. IPC did not improve preischemic mitochondrial respiratory function or preischemic mitochondrial response to Ca(2+) loading. IPC improved state 3, ADP/Deltat, and RCI during RP. Low Ca(2+) levels (0.5 and 1 x 10(-7) M) stimulated mitochondrial function in both groups predominantly in IPC. The Control group showed evidence of mitochondrial uncoupling at lower Ca(2+) concentrations (1 x 10(-7) M). IPC preserved state 3 at high Ca(2+) concentrations. The cardioprotective effect of IPC results, in part, from

  14. Nonlinear Preconditioning and its Application in Multicomponent Problems

    Liu, Lulu

    2015-12-07

    The Multiplicative Schwarz Preconditioned Inexact Newton (MSPIN) algorithm is presented as a complement to Additive Schwarz Preconditioned Inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. The ASPIN framework, as an option for the outermost solver, successfully handles strong nonlinearities in computational fluid dynamics, but is barely explored for the highly nonlinear models of complex multiphase flow with capillarity, heterogeneity, and complex geometry. In this dissertation, the fully implicit ASPIN method is demonstrated for a finite volume discretization based on incompressible two-phase reservoir simulators in the presence of capillary forces and gravity. Numerical experiments show that the number of global nonlinear iterations is not only scalable with respect to the number of processors, but also significantly reduced compared with the standard inexact Newton method with a backtracking technique. Moreover, the ASPIN method, in contrast with the IMPES method, saves overall execution time because of the savings in timestep size. We consider the additive and multiplicative types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Moreover, we provide the convergence analysis of the MSPIN algorithm. Under suitable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be

  15. Key cognitive preconditions for the evolution of language.

    Donald, Merlin

    2017-02-01

    Languages are socially constructed systems of expression, generated interactively in social networks, which can be assimilated by the individual brain as it develops. Languages co-evolved with culture, reflecting the changing complexity of human culture as it acquired the properties of a distributed cognitive system. Two key preconditions set the stage for the evolution of such cultures: a very general ability to rehearse and refine skills (evident early in hominin evolution in toolmaking), and the emergence of material culture as an external (to the brain) memory record that could retain and accumulate knowledge across generations. The ability to practice and rehearse skill provided immediate survival-related benefits in that it expanded the physical powers of early hominins, but the same adaptation also provided the imaginative substrate for a system of "mimetic" expression, such as found in ritual and pantomime, and in proto-words, which performed an expressive function somewhat like the home signs of deaf non-signers. The hominid brain continued to adapt to the increasing importance and complexity of culture as human interactions with material culture became more complex; above all, this entailed a gradual expansion in the integrative systems of the brain, especially those involved in the metacognitive supervision of self-performances. This supported a style of embodied mimetic imagination that improved the coordination of shared activities such as fire tending, but also in rituals and reciprocal mimetic games. The time-depth of this mimetic adaptation, and its role in both the construction and acquisition of languages, explains the importance of mimetic expression in the media, religion, and politics. Spoken language evolved out of voco-mimesis, and emerged long after the more basic abilities needed to refine skill and share intentions, probably coinciding with the common ancestor of sapient humans. Self-monitoring and self-supervised practice were necessary

  16. Opioid-induced preconditioning: recent advances and future perspectives.

    Peart, Jason N; Gross, Eric R; Gross, Garrett J

    2005-01-01

    Opioids, named by Acheson for compounds with morphine-like actions despite chemically distinct structures, have received much research interest, particularly for their central nervous system (CNS) actions involved in pain management, resulting in thousands of scientific papers focusing on their effects on the CNS and other organ systems. A more recent area which may have great clinical importance concerns the role of opioids, either endogenous or exogenous compounds, in limiting the pathogenesis of ischemia-reperfusion injury in heart and brain. The role of endogenous opioids in hibernation provides tantalizing evidence for the protective potential of opioids against ischemia or hypoxia. Mammalian hibernation, a distinct energy-conserving state, is associated with depletion of energy stores, intracellular acidosis and hypoxia, similar to those which occur during ischemia. However, despite the potentially detrimental cellular state induced with hibernation, the myocardium remains resilient for many months. What accounts for the hypoxia-tolerant state is of great interest. During hibernation, circulating levels of opioid peptides are increased dramatically, and indeed, are considered a "trigger" of hibernation. Furthermore, administration of opioid antagonists can effectively reverse hibernation in mammals. Therefore, it is not surprising that activation of opioid receptors has been demonstrated to preserve cellular status following a hypoxic insult, such as ischemia-reperfusion in many model systems including the intestine [Zhang, Y., Wu, Y.X., Hao, Y.B., Dun, Y. Yang, S.P., 2001. Role of endogenous opioid peptides in protection of ischemic preconditioning in rat small intestine. Life Sci. 68, 1013-1019], skeletal muscle [Addison, P.D., Neligan, P.C., Ashrafpour, H., Khan, A., Zhong, A., Moses, M., Forrest, C.R., Pang, C.Y., 2003. Noninvasive remote ischemic preconditioning for global protection of skeletal muscle against infarction. Am. J. Physiol. Heart Circ

  17. Function and mechanism of toll-like receptors in cerebral ischemic tolerance: from preconditioning to treatment

    Wang, Peng-Fei; Xiong, Xiao-Yi; Chen, Jing; Wang, Yan-Chun; Duan, Wei; Yang, Qing-Wu

    2015-01-01

    Increasing evidence suggests that toll-like receptors (TLRs) play an important role in cerebral ischemia-reperfusion injury. The endogenous ligands released from ischemic neurons activate the TLR signaling pathway, resulting in the production of a large number of inflammatory cytokines, thereby causing secondary inflammation damage following cerebral ischemia. However, the preconditioning for minor cerebral ischemia or the preconditioning with TLR ligands can reduce cerebral ischemic injury b...

  18. Effects of Ischemic Preconditioning of Different Intraoperative Ischemic Times of Vascularized Bone Graft Rabbit Models

    Ahmad Sukari Halim

    2013-11-01

    Full Text Available BackgroundIschemic preconditioning has been shown to improve the outcomes of hypoxic tolerance of the heart, brain, lung, liver, jejunum, skin, and muscle tissues. However, to date, no report of ischemic preconditioning on vascularized bone grafts has been published.MethodsSixteen rabbits were divided into four groups with ischemic times of 2, 6, 14, and 18 hours. Half of the rabbits in each group underwent ischemic preconditioning. The osteomyocutaneous flaps consisted of the tibia bone, from which the overlying muscle and skin were raised. The technique of ischemic preconditioning involved applying a vascular clamp to the pedicle for 3 cycles of 10 minutes each. The rabbits then underwent serial plain radiography and computed tomography imaging on the first, second, fourth, and sixth postoperative weeks. Following this, all of the rabbits were sacrificed and histological examinations were performed.ResultsThe results showed that for clinical analysis of the skin flaps and bone grafts, the preconditioned groups showed better survivability. In the plain radiographs, except for two non-preconditioned rabbits with intraoperative ischemic times of 6 hours, all began to show early callus formation at the fourth week. The computed tomography findings showed more callus formation in the preconditioned groups for all of the ischemic times except for the 18-hour group. The histological findings correlated with the radiological findings. There was no statistical significance in the difference between the two groups.ConclusionsIn conclusion, ischemic preconditioning improved the survivability of skin flaps and increased callus formation during the healing process of vascularized bone grafts.

  19. Brain Injury Lesion Imaging Using Preconditioned Quantitative Susceptibility Mapping without Skull Stripping.

    Soman, S; Liu, Z; Kim, G; Nemec, U; Holdsworth, S J; Main, K; Lee, B; Kolakowsky-Hayner, S; Selim, M; Furst, A J; Massaband, P; Yesavage, J; Adamson, M M; Spincemallie, P; Moseley, M; Wang, Y

    2018-04-01

    Identifying cerebral microhemorrhage burden can aid in the diagnosis and management of traumatic brain injury, stroke, hypertension, and cerebral amyloid angiopathy. MR imaging susceptibility-based methods are more sensitive than CT for detecting cerebral microhemorrhage, but methods other than quantitative susceptibility mapping provide results that vary with field strength and TE, require additional phase maps to distinguish blood from calcification, and depict cerebral microhemorrhages as bloom artifacts. Quantitative susceptibility mapping provides universal quantification of tissue magnetic property without these constraints but traditionally requires a mask generated by skull-stripping, which can pose challenges at tissue interphases. We evaluated the preconditioned quantitative susceptibility mapping MR imaging method, which does not require skull-stripping, for improved depiction of brain parenchyma and pathology. Fifty-six subjects underwent brain MR imaging with a 3D multiecho gradient recalled echo acquisition. Mask-based quantitative susceptibility mapping images were created using a commonly used mask-based quantitative susceptibility mapping method, and preconditioned quantitative susceptibility images were made using precondition-based total field inversion. All images were reviewed by a neuroradiologist and a radiology resident. Ten subjects (18%), all with traumatic brain injury, demonstrated blood products on 3D gradient recalled echo imaging. All lesions were visible on preconditioned quantitative susceptibility mapping, while 6 were not visible on mask-based quantitative susceptibility mapping. Thirty-one subjects (55%) demonstrated brain parenchyma and/or lesions that were visible on preconditioned quantitative susceptibility mapping but not on mask-based quantitative susceptibility mapping. Six subjects (11%) demonstrated pons artifacts on preconditioned quantitative susceptibility mapping and mask-based quantitative susceptibility mapping

  20. Rethinking The Going Concern Assumption As A Pre-Condition For Accounting Measurement

    Saratiel Wedzerai Musvoto; Daan G Gouws

    2011-01-01

    This study compares the principles of the going concern concept against the principles of representational measurement to determine if it is possible to establish foundations of accounting measurement with the going concern concept as a precondition. Representational measurement theory is a theory that establishes measurement in social scientific disciplines such as accounting. The going concern assumption is prescribed as one of the preconditions for measuring the attributes of the elements ...

  1. Eigenvalue Problems.

    1987-06-01

    11.55), we get (11.56) 1 bu(u - ZhU)dx < bull - hUi{ !s Ch2V(a), where C = C(aOa 1lbo,blV 0 (a),X). Next we consider I(S-Sh)uIL and Ij(T-Th)uaL2 It is...Math. Ann. 97, 711-736. Courant, R. [1943]: Variational methods for the solution of prob- .-lems of equilibrium and vibrations, Bull . Amer. Math. Soc...fournir des bornes superieures ou inferieures, C.R. Acad. Sci., Paris 235, 995-997. .V Prodi, G. (1962]: Theoremi di tipo locale per il sistema de Navier

  2. Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

    Rekab, S.; Zenine, N.

    2006-01-01

    We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

  3. Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

    Tang Wen-Lin; Tian Gui-Hua

    2011-01-01

    The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

  4. Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

    Akemann, G; Bittner, E; Lombardo, M; Markum, H; Pullirsch, R

    2004-01-01

    We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis.

  5. Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix models

    Akemann, Gernot; Bittner, Elmar; Lombardo, Maria-Paola; Markum, Harald; Pullirsch, Rainer

    2005-01-01

    We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis

  6. EFFECT OF HEAT PRECONDITIONING BY MICROWAVE HYPERTHERMIA ON HUMAN SKELETAL MUSCLE AFTER ECCENTRIC EXERCISE

    Norio Saga

    2008-03-01

    Full Text Available The purpose of this study was to clarify whether heat preconditioning results in less eccentric exercise-induced muscle damage and muscle soreness, and whether the repeated bout effect is enhanced by heat preconditioning prior to eccentric exercise. Nine untrained male volunteers aged 23 ± 3 years participated in this study. Heat preconditioning included treatment with a microwave hyperthermia unit (150 W, 20 min that was randomly applied to one of the subject's arms (MW; the other arm was used as a control (CON. One day after heat preconditioning, the subjects performed 24 maximal isokinetic eccentric contractions of the elbow flexors at 30°·s-1 (ECC1. One week after ECC1, the subjects repeated the procedure (ECC2. After each bout of exercise, maximal voluntary contraction (MVC, range of motion (ROM of the elbow joint, upper arm circumference, blood creatine kinase (CK activity and muscle soreness were measured. The subjects experienced both conditions at an interval of 3 weeks. MVC and ROM in the MW were significantly higher than those in the CON (p < 0.05 for ECC1; however, the heat preconditioning had no significant effect on upper arm circumference, blood CK activity, or muscle soreness following ECC1 and ECC2. Heat preconditioning may protect human skeletal muscle from eccentric exercise-induced muscle damage after a single bout of eccentric exercise but does not appear to promote the repeated bout effect after a second bout of eccentric exercise

  7. Prolonged preconditioning with natural honey against myocardial infarction injuries.

    Eteraf-Oskouei, Tahereh; Shaseb, Elnaz; Ghaffary, Saba; Najafi, Moslem

    2013-07-01

    Potential protective effects of prolonged preconditioning with natural honey against myocardial infarction were investigated. Male Wistar rats were pre-treated with honey (1%, 2% and 4%) for 45 days then their hearts were isolated and mounted on a Langendorff apparatus and perfused with a modified Krebs-Henseleit solution during 30 min regional ischemia fallowed by 120 min reperfusion. Two important indexes of ischemia-induced damage (infarction size and arrhythmias) were determined by computerized planimetry and ECG analysis, respectively. Honey (1% and 2%) reduced infarct size from 23±3.1% (control) to 9.7±2.4 and 9.5±2.3%, respectively (Phoney (1%) significantly reduced (PHoney (1% and 2%) also significantly decreased number of ventricular ectopic beats (VEBs). In addition, incidence and duration of reversible ventricular fibrillation (Rev VF) were lowered by honey 2% (Phoney produced significant reduction in the incidences of VT, total and Rev VF, duration and number of VT. The results showed cardioprotective effects of prolonged pre-treatment of rats with honey following myocardial infarction. Maybe, the existence of antioxidants and energy sources (glucose and fructose) in honey composition and improvement of hemodynamic functions may involve in those protective effects.

  8. Sirtinol abrogates late phase of cardiac ischemia preconditioning in rats.

    Safari, Fereshteh; Shekarforoosh, Shahnaz; Hashemi, Tahmineh; Namvar Aghdash, Simin; Fekri, Asefeh; Safari, Fatemeh

    2017-07-01

    The aim of this study was to investigate the effect of sirtinol, as an inhibitor of sirtuin NAD-dependent histone deacetylases, on myocardial ischemia reperfusion injury following early and late ischemia preconditioning (IPC). Rats underwent sustained ischemia and reperfusion (IR) alone or proceeded by early or late IPC. Sirtinol (S) was administered before IPC. Arrhythmias were evaluated based on the Lambeth model. Infarct size (IS) was measured using triphenyltetrazolium chloride staining. The transcription level of antioxidant-coding genes was assessed by real-time PCR. In early and late IPC groups, IS and the number of arrhythmia were significantly decreased (P < 0.05 and P < 0.01 vs IR, respectively). In S + early IPC, incidences of arrhythmia and IS were not different compared with the early IPC group. However, in S + late IPC the IS was different from the late IPC group (P < 0.05). In late IPC but not early IPC, transcription levels of catalase (P < 0.01) and Mn-SOD (P < 0.05) increased, although this upregulation was not significant in the S + late IPC group. Our results are consistent with the notion that different mechanisms are responsible for early and late IPC. In addition, sirtuin NAD-dependent histone deacetylases may be implicated in late IPC-induced cardioprotection.

  9. Linear multifrequency-grey acceleration recast for preconditioned Krylov iterations

    Morel, Jim E.; Brian Yang, T.-Y.; Warsa, James S.

    2007-01-01

    The linear multifrequency-grey acceleration (LMFGA) technique is used to accelerate the iterative convergence of multigroup thermal radiation diffusion calculations in high energy density simulations. Although it is effective and efficient in one-dimensional calculations, the LMFGA method has recently been observed to significantly degrade under certain conditions in multidimensional calculations with large discontinuities in material properties. To address this deficiency, we recast the LMFGA method in terms of a preconditioned system that is solved with a Krylov method (LMFGK). Results are presented demonstrating that the new LMFGK method always requires fewer iterations than the original LMFGA method. The reduction in iteration count increases with both the size of the time step and the inhomogeneity of the problem. However, for reasons later explained, the LMFGK method can cost more per iteration than the LMFGA method, resulting in lower but comparable efficiency in problems with small time steps and weak inhomogeneities. In problems with large time steps and strong inhomogeneities, the LMFGK method is significantly more efficient than the LMFGA method

  10. Cerenkov luminescence tomography based on preconditioning orthogonal matching pursuit

    Liu, Haixiao; Hu, Zhenhua; Wang, Kun; Tian, Jie; Yang, Xin

    2015-03-01

    Cerenkov luminescence imaging (CLI) is a novel optical imaging method and has been proved to be a potential substitute of the traditional radionuclide imaging such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT). This imaging method inherits the high sensitivity of nuclear medicine and low cost of optical molecular imaging. To obtain the depth information of the radioactive isotope, Cerenkov luminescence tomography (CLT) is established and the 3D distribution of the isotope is reconstructed. However, because of the strong absorption and scatter, the reconstruction of the CLT sources is always converted to an ill-posed linear system which is hard to be solved. In this work, the sparse nature of the light source was taken into account and the preconditioning orthogonal matching pursuit (POMP) method was established to effectively reduce the ill-posedness and obtain better reconstruction accuracy. To prove the accuracy and speed of this algorithm, a heterogeneous numerical phantom experiment and an in vivo mouse experiment were conducted. Both the simulation result and the mouse experiment showed that our reconstruction method can provide more accurate reconstruction result compared with the traditional Tikhonov regularization method and the ordinary orthogonal matching pursuit (OMP) method. Our reconstruction method will provide technical support for the biological application for Cerenkov luminescence.

  11. Deregulation - precondition for distributed energy in the economies in transition

    Brendow, K.

    2001-01-01

    This paper holds that deregulation, i.e. restructuring, competition and privatisation, is the main precondition for a more pronounced development of distributed power (DP) in the economies in transition in central and eastern Europe. This, then, raises the question how far the electricity, gas, steam and heat generating industries have presently moved on their way towards more market-oriented frameworks, competition and private ownership. A good benchmark for measuring progress is the existence (or lack thereof), and nature, of regulatory regimes enabling fair competition among large centralised and small decentralised power, and between wholesale generators and distributors on the one hand and customers or ''autoproducers'' or power merchants on the other. The paper describes the regulatory models applied or contemplated in the winter 2000/2001 in the various countries of central and eastern Europe and identifies fifteen general issues that require attention and solution. With regard to DP, it concludes that a major upswing is unlikely to occur before 2005-2008. While technological options abound, the institutional frameworks for customer-owned competitive DP systems are only being contemplated at present and only rarely put in place.(author)

  12. FALCON Code Simulation for Verification of Fuel Preconditioning Guideline

    Lee, Hee-Hun; Kwon, Oh-Hyun; Kim, Hong-Jin; Kim, Yong-Hwan [KEPCO Nuclear Fuel Co. Ltd., Daejeon (Korea, Republic of)

    2015-10-15

    The magnitude and rate of power increases are key factors in the PCI failure process. KEPCO NF (KNF) provides operational restrictions called fuel preconditioning guideline (FPG) to mitigate PCI failures. The FPG contains recommended power maneuvering restrictions that should be followed when the KNF supplied fuel is being operated in-reactor. This guideline typically includes controlled power ramp rates, threshold power levels to initiate controlled ramp rates, and restrictions on the operating conditions that impact the potential for PCI failure. The purpose of the FPG is to allow time for stress relaxation to reduce cladding stress buildup during power maneuvers. Two general approaches have been adopted in the development of FPG to mitigate PCI failure in operating commercial reactors. The first approach relies primarily on past operational experience and power ramp test. The second one uses an analytical methodology where a figure-of-merit representative of PCI vulnerability, generally cladding hoop stress, is calculated using a fuel performance code. FALCON simulation can be the identification of a PCI limit parameter, typically cladding hoop stress, which can be used to evaluate a power maneuvering restriction on FPG. The PCI analysis is to assess the cladding hoop stress under various power ramp conditions. Startup ramp rate doesn't affect PCI failure until 50% of rated thermal power.

  13. Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

    Temel, Burcin; Mills, Greg; Metiu, Horia

    2008-03-27

    We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.

  14. Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.

    Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins

    2018-04-01

    Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.

  15. Optimal Control for the Degenerate Elliptic Logistic Equation

    Delgado, M.; Montero, J.A.; Suarez, A.

    2002-01-01

    We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results

  16. Computing eigenvalue sensitivity coefficients to nuclear data based on the CLUTCH method with RMC code

    Qiu, Yishu; She, Ding; Tang, Xiao; Wang, Kan; Liang, Jingang

    2016-01-01

    Highlights: • A new algorithm is proposed to reduce memory consumption for sensitivity analysis. • The fission matrix method is used to generate adjoint fission source distributions. • Sensitivity analysis is performed on a detailed 3D full-core benchmark with RMC. - Abstract: Recently, there is a need to develop advanced methods of computing eigenvalue sensitivity coefficients to nuclear data in the continuous-energy Monte Carlo codes. One of these methods is the iterated fission probability (IFP) method, which is adopted by most of Monte Carlo codes of having the capabilities of computing sensitivity coefficients, including the Reactor Monte Carlo code RMC. Though it is accurate theoretically, the IFP method faces the challenge of huge memory consumption. Therefore, it may sometimes produce poor sensitivity coefficients since the number of particles in each active cycle is not sufficient enough due to the limitation of computer memory capacity. In this work, two algorithms of the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method, namely, the collision-event-based algorithm (C-CLUTCH) which is also implemented in SCALE and the fission-event-based algorithm (F-CLUTCH) which is put forward in this work, are investigated and implemented in RMC to reduce memory requirements for computing eigenvalue sensitivity coefficients. While the C-CLUTCH algorithm requires to store concerning reaction rates of every collision, the F-CLUTCH algorithm only stores concerning reaction rates of every fission point. In addition, the fission matrix method is put forward to generate the adjoint fission source distribution for the CLUTCH method to compute sensitivity coefficients. These newly proposed approaches implemented in RMC code are verified by a SF96 lattice model and the MIT BEAVRS benchmark problem. The numerical results indicate the accuracy of the F-CLUTCH algorithm is the same as the C

  17. Hyperbaric oxygen preconditioning protects against traumatic brain injury at high altitude.

    Hu, S L; Hu, R; Li, F; Liu, Z; Xia, Y Z; Cui, G Y; Feng, H

    2008-01-01

    Recent studies have shown that preconditioning with hyperbaric oxygen (HBO) can reduce ischemic and hemorrhagic brain injury. We investigated effects of HBO preconditioning on traumatic brain injury (TBI) at high altitude and examined the role of matrix metalloproteinase-9 (MMP-9) in such protection. Rats were randomly divided into 3 groups: HBO preconditioning group (HBOP; n = 13), high-altitude group (HA; n = 13), and high-altitude sham operation group (HASO; n = 13). All groups were subjected to head trauma by weight-drop device, except for HASO group. HBOP rats received 5 sessions of HBO preconditioning (2.5 ATA, 100% oxygen, 1 h daily) and then were kept in hypobaric chamber at 0.6 ATA (to simulate pressure at 4000m altitude) for 3 days before operation. HA rats received control pretreatment (1 ATA, room air, 1 h daily), then followed the same procedures as HBOP group. HASO rats were subjected to skull opening only without brain injury. Twenty-four hours after TBI, 7 rats from each group were examined for neurological function and brain water content; 6 rats from each group were killed for analysis by H&E staining and immunohistochemistry. Neurological outcome in HBOP group (0.71 +/- 0.49) was better than HA group (1.57 +/- 0.53; p < 0.05). Preconditioning with HBO significantly reduced percentage of brain water content (86.24 +/- 0.52 vs. 84.60 +/- 0.37; p < 0.01). Brain morphology and structure seen by light microscopy was diminished in HA group, while fewer pathological injuries occurred in HBOP group. Compared to HA group, pretreatment with HBO significantly reduced the number of MMP-9-positive cells (92.25 +/- 8.85 vs. 74.42 +/- 6.27; p < 0.01). HBO preconditioning attenuates TBI in rats at high altitude. Decline in MMP-9 expression may contribute to HBO preconditioning-induced protection of brain tissue against TBI.

  18. Estimates of the eigenvalues of operator arising in swelling pressure model

    Kanguzhin, Baltabek; Zhapsarbayeva, Lyailya

    2016-01-01

    Swelling pressures from materials confined by structures can cause structural deformations and instability. Due to the complexity of interactions between expansive solid and solid-liquid equilibrium, the forces exerting on retaining structures from swelling are highly nonlinear. This work is our initial attempt to study a simplistic spectral problem based on the Euler-elastic beam theory and some simplistic swelling pressure model. In this work estimates of the eigenvalues of some initial/boundary value problem for nonlinear Euler-elastic beam equation are obtained.

  19. Computations of zeros of special functions and eigenvalues of differential equations by matrix method

    Miyazaki, Yoshinori

    2000-01-01

    This paper is strongly based on two powerful general theorems proved by Ikebe, et. al in 1993[15] and 1996[13], which will be referred to as Theorem A and Theorem B in this paper. They were recently published and justify the approximate computations of simple eigenvalues of infinite matrices of certain types by truncation, giving an extremely accurate error estimates. So far, they have applied to some important problems in engineering, such as computing the zeros of some special functions, an...

  20. Computation of Double Eigenvalues for Infinite Matrices of a Certain Class

    宮崎, 佳典; Yoshinori, MIYAZAKI; 静岡産業大学 国際情報学部; Faculty of Communications and Informatics, Shizuoka Sangyo University

    2001-01-01

    It has been shown that a series of three-term recurrence relations of a certain class is a powerful tool for solving zeros of some special functions and eigenvalue problems (EVPs) of certain differential equations. Such cases include: the zeros of J_v(z); the zeros of zJ′_v(z)+HJ_v(z); the EVP of the Mathieu differential equation; and the EVP of the spheroidal wave equation. Previously by the author, it was demonstrated that the three-term recurrence relations of the class may be reformulated...

  1. Third-order WKBJ eigenvalues for Lennard-Jones and Varshni V potentials

    Kesarwani, R.N.; Varshni, Y.P.

    1978-01-01

    The WKBJ method is applied to the third order for obtaining the eigenvalues for the fifth potential of Varshni, and the relevant integrals are analytically evaluated. Numerical results are obtained for the Lennard-Jones Potential, which is a special case of the Varshni V potential, and are compared to the results of Harrison and Bernstein obtained by a numerical integration of the wave equation. Error estimates are made. It is shown that for diatomic potentials, the Langer correction is not needed if the WKBJ approximation is carried to second and higher orders. (author)

  2. Positive Eigenvalues of Generalized Words in Two Hermitian Positive Definite Matrices

    Hillar, Christopher; Johnson, Charles R.

    2005-01-01

    We define a word in two positive definite (complex Hermitian) matrices $A$ and $B$ as a finite product of real powers of $A$ and $B$. The question of which words have only positive eigenvalues is addressed. This question was raised some time ago in connection with a long-standing problem in theoretical physics, and it was previously approached by the authors for words in two real positive definite matrices with positive integral exponents. A large class of words that do guarantee positive eig...

  3. The numerical analysis of eigenvalue problem solutions in the multigroup diffusion theory

    Woznick, Z.I.

    1994-01-01

    In this paper a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations is described. Usually the solution method is based on the system of inner and outer iterations. The presented matrix formalism allows us to visualize clearly, how the used matrix splitting influences the structure of the matrix in an eigenvalue problem to be solved as well as the independence between inner and outer iterations within global iterations. To keep the page limit, the present version of the paper consists only with first three of five sections given in the original paper under the same title (which will be published soon). (author). 13 refs

  4. The Application of Vector Fitting to Eigenvalue-based Harmonic Stability Analysis

    Dowlatabadi, Mohammadkazem Bakhshizadeh; Yoon, Changwoo; Hjerrild, Jesper

    2017-01-01

    Participation factor analysis is an interesting feature of the eigenvalue-based stability analysis in a power system, which enables the developers to identify the problematic elements in a multi-vendor project like in an offshore wind power plant. However, this method needs a full state space model...... of the elements that is not always possible to have in a competitive world due to confidentiality. In this paper, by using an identification method, the state space models for power converters are extracted from the provided data by the suppliers. Some uncertainties in the identification process are also...

  5. Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

    Xuqing Zhang

    2013-01-01

    Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

  6. Computation of dominant eigenvalues and eigenvectors: A comparative study of algorithms

    Nightingale, M.P.; Viswanath, V.S.; Mueller, G.

    1993-01-01

    We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices---the modified Lanczoes method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods

  7. POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

    FAOUZI HADDOUCHI

    2015-11-01

    Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

  8. Preconditioning with endoplasmic reticulum stress ameliorates endothelial cell inflammation.

    Leonard, Antony; Paton, Adrienne W; El-Quadi, Monaliza; Paton, James C; Fazal, Fabeha

    2014-01-01

    Endoplasmic Reticulum (ER) stress, caused by disturbance in ER homeostasis, has been implicated in several pathological conditions such as ischemic injury, neurodegenerative disorders, metabolic diseases and more recently in inflammatory conditions. Our present study aims at understanding the role of ER stress in endothelial cell (EC) inflammation, a critical event in the pathogenesis of acute lung injury (ALI). We found that preconditioning human pulmonary artery endothelial cells (HPAEC) to ER stress either by depleting ER chaperone and signaling regulator BiP using siRNA, or specifically cleaving (inactivating) BiP using subtilase cytotoxin (SubAB), alleviates EC inflammation. The two approaches adopted to abrogate BiP function induced ATF4 protein expression and the phosphorylation of eIF2α, both markers of ER stress, which in turn resulted in blunting the activation of NF-κB, and restoring endothelial barrier integrity. Pretreatment of HPAEC with BiP siRNA inhibited thrombin-induced IκBα degradation and its resulting downstream signaling pathway involving NF-κB nuclear translocation, DNA binding, phosphorylation at serine536, transcriptional activation and subsequent expression of adhesion molecules. However, TNFα-mediated NF-κB signaling was unaffected upon BiP knockdown. In an alternative approach, SubAB-mediated inactivation of NF-κB was independent of IκBα degradation. Mechanistic analysis revealed that pretreatment of EC with SubAB interfered with the binding of the liberated NF-κB to the DNA, thereby resulting in reduced expression of adhesion molecules, cytokines and chemokines. In addition, both knockdown and inactivation of BiP stimulated actin cytoskeletal reorganization resulting in restoration of endothelial permeability. Together our studies indicate that BiP plays a central role in EC inflammation and injury via its action on NF-κB activation and regulation of vascular permeability.

  9. Preconditioning of Interplanetary Space Due to Transient CME Disturbances

    Temmer, M.; Reiss, M. A.; Hofmeister, S. J.; Veronig, A. M.; Nikolic, L.

    2017-01-01

    Interplanetary space is characteristically structured mainly by high-speed solar wind streams emanating from coronal holes and transient disturbances such as coronal mass ejections (CMEs). While high-speed solar wind streams pose a continuous outflow, CMEs abruptly disrupt the rather steady structure, causing large deviations from the quiet solar wind conditions. For the first time, we give a quantification of the duration of disturbed conditions (preconditioning) for interplanetary space caused by CMEs. To this aim, we investigate the plasma speed component of the solar wind and the impact of in situ detected interplanetary CMEs (ICMEs), compared to different background solar wind models (ESWF, WSA, persistence model) for the time range 2011–2015. We quantify in terms of standard error measures the deviations between modeled background solar wind speed and observed solar wind speed. Using the mean absolute error, we obtain an average deviation for quiet solar activity within a range of 75.1–83.1 km s −1 . Compared to this baseline level, periods within the ICME interval showed an increase of 18%–32% above the expected background, and the period of two days after the ICME displayed an increase of 9%–24%. We obtain a total duration of enhanced deviations over about three and up to six days after the ICME start, which is much longer than the average duration of an ICME disturbance itself (∼1.3 days), concluding that interplanetary space needs ∼2–5 days to recover from the impact of ICMEs. The obtained results have strong implications for studying CME propagation behavior and also for space weather forecasting.

  10. Preconditioning of Interplanetary Space Due to Transient CME Disturbances

    Temmer, M.; Reiss, M. A.; Hofmeister, S. J.; Veronig, A. M. [Institute of Physics, University of Graz, Universitätsplatz 5/II, A-8010 Graz (Austria); Nikolic, L., E-mail: manuela.temmer@uni-graz.at [Canadian Hazards Information Service, Natural Resources Canada, 2617 Anderson Road, Ottawa, Ontario K1A 0Y3 (Canada)

    2017-02-01

    Interplanetary space is characteristically structured mainly by high-speed solar wind streams emanating from coronal holes and transient disturbances such as coronal mass ejections (CMEs). While high-speed solar wind streams pose a continuous outflow, CMEs abruptly disrupt the rather steady structure, causing large deviations from the quiet solar wind conditions. For the first time, we give a quantification of the duration of disturbed conditions (preconditioning) for interplanetary space caused by CMEs. To this aim, we investigate the plasma speed component of the solar wind and the impact of in situ detected interplanetary CMEs (ICMEs), compared to different background solar wind models (ESWF, WSA, persistence model) for the time range 2011–2015. We quantify in terms of standard error measures the deviations between modeled background solar wind speed and observed solar wind speed. Using the mean absolute error, we obtain an average deviation for quiet solar activity within a range of 75.1–83.1 km s{sup −1}. Compared to this baseline level, periods within the ICME interval showed an increase of 18%–32% above the expected background, and the period of two days after the ICME displayed an increase of 9%–24%. We obtain a total duration of enhanced deviations over about three and up to six days after the ICME start, which is much longer than the average duration of an ICME disturbance itself (∼1.3 days), concluding that interplanetary space needs ∼2–5 days to recover from the impact of ICMEs. The obtained results have strong implications for studying CME propagation behavior and also for space weather forecasting.

  11. Angiotensin II Removes Kidney Resistance Conferred by Ischemic Preconditioning

    Hee-Seong Jang

    2014-01-01

    Full Text Available Ischemic preconditioning (IPC by ischemia/reperfusion (I/R renders resistance to the kidney. Strong IPC triggers kidney fibrosis, which is involved in angiotensin II (AngII and its type 1 receptor (AT1R signaling. Here, we investigated the role of AngII/AT1R signal pathway in the resistance of IPC kidneys to subsequent I/R injury. IPC of kidneys was generated by 30 minutes of bilateral renal ischemia and 8 days of reperfusion. Sham-operation was performed to generate control (non-IPC mice. To examine the roles of AngII and AT1R in IPC kidneys to subsequent I/R, IPC kidneys were subjected to either 30 minutes of bilateral kidney ischemia or sham-operation following treatment with AngII, losartan (AT1R blocker, or AngII plus losartan. IPC kidneys showed fibrotic changes, decreased AngII, and increased AT1R expression. I/R dramatically increased plasma creatinine concentrations in non-IPC mice, but not in IPC mice. AngII treatment in IPC mice resulted in enhanced morphological damage, oxidative stress, and inflammatory responses, with functional impairment, whereas losartan treatment reversed these effects. However, AngII treatment in non-IPC mice did not change I/R-induced injury. AngII abolished the resistance of IPC kidneys to subsequent I/R via the enhancement of oxidative stress and inflammatory responses, suggesting that the AngII/AT1R signaling pathway is associated with outcome in injury-experienced kidney.

  12. Two-group k-eigenvalue benchmark calculations for planar geometry transport in a binary stochastic medium

    Davis, I.M.; Palmer, T.S.

    2005-01-01

    Benchmark calculations are performed for neutron transport in a two material (binary) stochastic multiplying medium. Spatial, angular, and energy dependence are included. The problem considered is based on a fuel assembly of a common pressurized water reactor. The mean chord length through the assembly is determined and used as the planar geometry system length. According to assumed or calculated material distributions, this system length is populated with alternating fuel and moderator segments of random size. Neutron flux distributions are numerically computed using a discretized form of the Boltzmann transport equation employing diffusion synthetic acceleration. Average quantities (group fluxes and k-eigenvalue) and variances are calculated from an ensemble of realizations of the mixing statistics. The effects of varying two parameters in the fuel, two different boundary conditions, and three different sets of mixing statistics are assessed. A probability distribution function (PDF) of the k-eigenvalue is generated and compared with previous research. Atomic mix solutions are compared with these benchmark ensemble average flux and k-eigenvalue solutions. Mixing statistics with large standard deviations give the most widely varying ensemble solutions of the flux and k-eigenvalue. The shape of the k-eigenvalue PDF qualitatively agrees with previous work. Its overall shape is independent of variations in fuel cross-sections for the problems considered, but its width is impacted by these variations. Statistical distributions with smaller standard deviations alter the shape of this PDF toward a normal distribution. The atomic mix approximation yields large over-predictions of the ensemble average k-eigenvalue and under-predictions of the flux. Qualitatively correct flux shapes are obtained in some cases. These benchmark calculations indicate that a model which includes higher statistical moments of the mixing statistics is needed for accurate predictions of binary

  13. The remote ischemic preconditioning algorithm: effect of number of cycles, cycle duration and effector organ mass on efficacy of protection.

    Johnsen, Jacob; Pryds, Kasper; Salman, Rasha; Løfgren, Bo; Kristiansen, Steen Buus; Bøtker, Hans Erik

    2016-03-01

    Remote ischemic preconditioning (rIPC), induced by cycles of transient limb ischemia and reperfusion (IR), is cardioprotective. The optimal rIPC-algorithm is not established. We investigated the effect of cycle numbers and ischemia duration within each rIPC-cycle and the influence of effector organ mass on the efficacy of cardioprotection. Furthermore, the duration of the early phase of protection by rIPC was investigated. Using a tourniquet tightened at the inguinal level, we subjected C57Bl/6NTac mice to intermittent hind-limb ischemia and reperfusion. The rIPC-protocols consisted of (I) two, four, six or eight cycles, (II) 2, 5 or 10 min of ischemia in each cycle, (III) single or two hind-limb occlusions and (IV) 0.5, 1.5, 2.0 or 2.5 h intervals from rIPC to index cardiac ischemia. All rIPC algorithms were followed by 5 min of reperfusion. The hearts were subsequently exposed to 25 min of global ischemia and 60 min of reperfusion in an ex vivo Langendorff model. Cardioprotection was evaluated by infarct size and post-ischemic hemodynamic recovery. Four to six rIPC cycles yielded significant cardioprotection with no further protection by eight cycles. Ischemic cycles lasting 2 min offered the same protection as cycles of 5 min ischemia, whereas prolonged cycles lasting 10 min abrogated protection. One and two hind-limb preconditioning were equally protective. In our mouse model, the duration of protection by rIPC was 1.5 h. These findings indicate that the number and duration of cycles rather than the tissue mass exposed to rIPC determines the efficacy of rIPC.

  14. Hypoxia-preconditioned mesenchymal stem cells ameliorate ischemia/reperfusion-induced lung injury.

    Yung-Yang Liu

    Full Text Available Hypoxia preconditioning has been proven to be an effective method to enhance the therapeutic action of mesenchymal stem cells (MSCs. However, the beneficial effects of hypoxic MSCs in ischemia/reperfusion (I/R lung injury have yet to be investigated. In this study, we hypothesized that the administration of hypoxic MSCs would have a positive therapeutic impact on I/R lung injury at molecular, cellular, and functional levels.I/R lung injury was induced in isolated and perfused rat lungs. Hypoxic MSCs were administered in perfusate at a low (2.5×105 cells and high (1×106 cells dose. Rats ventilated with a low tidal volume of 6 ml/kg served as controls. Hemodynamics, lung injury indices, inflammatory responses and activation of apoptotic pathways were determined.I/R induced permeability pulmonary edema with capillary leakage and increased levels of reactive oxygen species (ROS, pro-inflammatory cytokines, adhesion molecules, cytosolic cytochrome C, and activated MAPK, NF-κB, and apoptotic pathways. The administration of a low dose of hypoxic MSCs effectively attenuated I/R pathologic lung injury score by inhibiting inflammatory responses associated with the generation of ROS and anti-apoptosis effect, however this effect was not observed with a high dose of hypoxic MSCs. Mechanistically, a low dose of hypoxic MSCs down-regulated P38 MAPK and NF-κB signaling but upregulated glutathione, prostaglandin E2, IL-10, mitochondrial cytochrome C and Bcl-2. MSCs infused at a low dose migrated into interstitial and alveolar spaces and bronchial trees, while MSCs infused at a high dose aggregated in the microcirculation and induced pulmonary embolism.Hypoxic MSCs can quickly migrate into extravascular lung tissue and adhere to other inflammatory or structure cells and attenuate I/R lung injury through anti-oxidant, anti-inflammatory and anti-apoptotic mechanisms. However, the dose of MSCs needs to be optimized to prevent pulmonary embolism and thrombosis.

  15. Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

    Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

    2003-09-01

    Multiconjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wave-front control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10-2 Hz, i.e., 4-5 orders of magnitude lower than the typical 103 Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

  16. Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach.

    Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M; El Fakhri, Georges

    2013-10-01

    Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach. Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach. At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG. The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.

  17. Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics.

    Gilles, Luc; Ellerbroek, Brent L; Vogel, Curtis R

    2003-09-10

    Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.

  18. Integrity of Cerebellar Fastigial Nucleus Intrinsic Neurons Is Critical for the Global Ischemic Preconditioning

    Eugene V. Golanov

    2017-09-01

    Full Text Available Excitation of intrinsic neurons of cerebellar fastigial nucleus (FN renders brain tolerant to local and global ischemia. This effect reaches a maximum 72 h after the stimulation and lasts over 10 days. Comparable neuroprotection is observed following sublethal global brain ischemia, a phenomenon known as preconditioning. We hypothesized that FN may participate in the mechanisms of ischemic preconditioning as a part of the intrinsic neuroprotective mechanism. To explore potential significance of FN neurons in brain ischemic tolerance we lesioned intrinsic FN neurons with excitotoxin ibotenic acid five days before exposure to 20 min four-vessel occlusion (4-VO global ischemia while analyzing neuronal damage in Cornu Ammoni area 1 (CA1 hippocampal area one week later. In FN-lesioned animals, loss of CA1 cells was higher by 22% compared to control (phosphate buffered saline (PBS-injected animals. Moreover, lesion of FN neurons increased morbidity following global ischemia by 50%. Ablation of FN neurons also reversed salvaging effects of five-minute ischemic preconditioning on CA1 neurons and morbidity, while ablation of cerebellar dentate nucleus neurons did not change effect of ischemic preconditioning. We conclude that FN is an important part of intrinsic neuroprotective system, which participates in ischemic preconditioning and may participate in naturally occurring neuroprotection, such as “diving response”.

  19. Time-domain full waveform inversion using the gradient preconditioning based on transmitted waves energy

    Zhang, Xiao-bo

    2017-06-01

    The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge storage consumption in the gradient preconditioning algorithms based on Hessian matrices in time-domain full waveform inversion (FWI), but the accuracy is affected by the energy of reflected waves when strong reflectors are present in velocity model. To address this problem, we propose a gradient preconditioning method, which scales the gradient based on the energy of the “approximated transmitted wavefield” simulated by the nonreflecting acoustic wave equation. The method does not require computing or storing the Hessian matrix or its inverse. Furthermore, it can effectively eliminate the effects caused by geometric diffusion and non-uniformity illumination on gradient. The results of model experiments confirm that the time-domain FWI using the gradient preconditioning based on transmitted waves energy can achieve higher inversion precision for high-velocity body and the deep strata below when compared with using the gradient preconditioning based on seismic waves energy.

  20. Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

    Hejranfar, Kazem; Parseh, Kaveh

    2017-09-01

    The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.