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Sample records for two-directional krylov subspace

  1. An adaptation of Krylov subspace methods to path following

    Energy Technology Data Exchange (ETDEWEB)

    Walker, H.F. [Utah State Univ., Logan, UT (United States)

    1996-12-31

    Krylov subspace methods at present constitute a very well known and highly developed class of iterative linear algebra methods. These have been effectively applied to nonlinear system solving through Newton-Krylov methods, in which Krylov subspace methods are used to solve the linear systems that characterize steps of Newton`s method (the Newton equations). Here, we will discuss the application of Krylov subspace methods to path following problems, in which the object is to track a solution curve as a parameter varies. Path following methods are typically of predictor-corrector form, in which a point near the solution curve is {open_quotes}predicted{close_quotes} by some easy but relatively inaccurate means, and then a series of Newton-like corrector iterations is used to return approximately to the curve. The analogue of the Newton equation is underdetermined, and an additional linear condition must be specified to determine corrector steps uniquely. This is typically done by requiring that the steps be orthogonal to an approximate tangent direction. Augmenting the under-determined system with this orthogonality condition in a straightforward way typically works well if direct linear algebra methods are used, but Krylov subspace methods are often ineffective with this approach. We will discuss recent work in which this orthogonality condition is imposed directly as a constraint on the corrector steps in a certain way. The means of doing this preserves problem conditioning, allows the use of preconditioners constructed for the fixed-parameter case, and has certain other advantages. Experiments on standard PDE continuation test problems indicate that this approach is effective.

  2. Reduced-Rank Adaptive Filtering Using Krylov Subspace

    Directory of Open Access Journals (Sweden)

    Sergueï Burykh

    2003-01-01

    Full Text Available A unified view of several recently introduced reduced-rank adaptive filters is presented. As all considered methods use Krylov subspace for rank reduction, the approach taken in this work is inspired from Krylov subspace methods for iterative solutions of linear systems. The alternative interpretation so obtained is used to study the properties of each considered technique and to relate one reduced-rank method to another as well as to algorithms used in computational linear algebra. Practical issues are discussed and low-complexity versions are also included in our study. It is believed that the insight developed in this paper can be further used to improve existing reduced-rank methods according to known results in the domain of Krylov subspace methods.

  3. Parallelised Krylov subspace method for reactor kinetics by IQS approach

    International Nuclear Information System (INIS)

    Gupta, Anurag; Modak, R.S.; Gupta, H.P.; Kumar, Vinod; Bhatt, K.

    2005-01-01

    Nuclear reactor kinetics involves numerical solution of space-time-dependent multi-group neutron diffusion equation. Two distinct approaches exist for this purpose: the direct (implicit time differencing) approach and the improved quasi-static (IQS) approach. Both the approaches need solution of static space-energy-dependent diffusion equations at successive time-steps; the step being relatively smaller for the direct approach. These solutions are usually obtained by Gauss-Seidel type iterative methods. For a faster solution, the Krylov sub-space methods have been tried and also parallelised by many investigators. However, these studies seem to have been done only for the direct approach. In the present paper, parallelised Krylov methods are applied to the IQS approach in addition to the direct approach. It is shown that the speed-up obtained for IQS is higher than that for the direct approach. The reasons for this are also discussed. Thus, the use of IQS approach along with parallelised Krylov solvers seems to be a promising scheme

  4. Time stepping free numerical solution of linear differential equations: Krylov subspace versus waveform relaxation

    NARCIS (Netherlands)

    Bochev, Mikhail A.; Oseledets, I.V.; Tyrtyshnikov, E.E.

    2013-01-01

    The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation method based on block Krylov subspaces. Second, we compare this new implementation against Krylov subspace methods combined with the shift and invert technique.

  5. On the numerical stability analysis of pipelined Krylov subspace methods

    Czech Academy of Sciences Publication Activity Database

    Carson, E.T.; Rozložník, Miroslav; Strakoš, Z.; Tichý, P.; Tůma, M.

    submitted 2017 (2018) R&D Projects: GA ČR GA13-06684S Grant - others:GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : Krylov subspace methods * the conjugate gradient method * numerical stability * inexact computations * delay of convergence * maximal attainable accuracy * pipelined Krylov subspace methods * exascale computations

  6. Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

    Science.gov (United States)

    Freund, Roland W.

    1991-01-01

    We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  7. Matrix Krylov subspace methods for image restoration

    Directory of Open Access Journals (Sweden)

    khalide jbilou

    2015-09-01

    Full Text Available In the present paper, we consider some matrix Krylov subspace methods for solving ill-posed linear matrix equations and in those problems coming from the restoration of blurred and noisy images. Applying the well known Tikhonov regularization procedure leads to a Sylvester matrix equation depending the Tikhonov regularized parameter. We apply the matrix versions of the well known Krylov subspace methods, namely the Least Squared (LSQR and the conjugate gradient (CG methods to get approximate solutions representing the restored images. Some numerical tests are presented to show the effectiveness of the proposed methods.

  8. Krylov subspace method with communication avoiding technique for linear system obtained from electromagnetic analysis

    International Nuclear Information System (INIS)

    Ikuno, Soichiro; Chen, Gong; Yamamoto, Susumu; Itoh, Taku; Abe, Kuniyoshi; Nakamura, Hiroaki

    2016-01-01

    Krylov subspace method and the variable preconditioned Krylov subspace method with communication avoiding technique for a linear system obtained from electromagnetic analysis are numerically investigated. In the k−skip Krylov method, the inner product calculations are expanded by Krylov basis, and the inner product calculations are transformed to the scholar operations. k−skip CG method is applied for the inner-loop solver of Variable Preconditioned Krylov subspace methods, and the converged solution of electromagnetic problem is obtained using the method. (author)

  9. Excluding Noise from Short Krylov Subspace Approximations to the Truncated Singular Value Decomposition (SVD)

    Science.gov (United States)

    2017-09-27

    100 times larger for the minimal Krylov subspace. 0 5 10 15 20 25 Krylov subspace dimension 10-2 10-1 100 101 102 103 104 jjĜ ¡ 1 jj F SVD...approximation Kn (G;u(0) ) 0 5 10 15 20 25 Krylov subspace dimension 10-2 10-1 100 101 102 103 104 jjx jj fo r m in x jjĜ x ¡ bjj SVD approximation Kn (G;u(0

  10. Krylov subspace methods for the solution of large systems of ODE's

    DEFF Research Database (Denmark)

    Thomsen, Per Grove; Bjurstrøm, Nils Henrik

    1998-01-01

    In Air Pollution Modelling large systems of ODE's arise. Solving such systems may be done efficientliy by Semi Implicit Runge-Kutta methods. The internal stages may be solved using Krylov subspace methods. The efficiency of this approach is investigated and verified.......In Air Pollution Modelling large systems of ODE's arise. Solving such systems may be done efficientliy by Semi Implicit Runge-Kutta methods. The internal stages may be solved using Krylov subspace methods. The efficiency of this approach is investigated and verified....

  11. Extended Krylov subspaces approximations of matrix functions. Application to computational electromagnetics

    Energy Technology Data Exchange (ETDEWEB)

    Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)

    1996-12-31

    There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.

  12. Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method

    International Nuclear Information System (INIS)

    Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki

    2007-01-01

    The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)

  13. Krylov subspace methods for solving large unsymmetric linear systems

    International Nuclear Information System (INIS)

    Saad, Y.

    1981-01-01

    Some algorithms based upon a projection process onto the Krylov subspace K/sub m/ = Span(r 0 , Ar 0 ,...,A/sup m/-1r 0 ) are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldi's algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace K/sub m/ and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed

  14. A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

    NARCIS (Netherlands)

    Bochev, Mikhail A.

    2013-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

  15. Krylov subspace method for evaluating the self-energy matrices in electron transport calculations

    DEFF Research Database (Denmark)

    Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, D. E.

    2008-01-01

    We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite...... calculations. Numerical tests within a density functional theory framework are provided to validate the accuracy and robustness of the proposed method, which in most cases is an order of magnitude faster than conventional methods.......We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite...

  16. Residual and Backward Error Bounds in Minimum Residual Krylov Subspace Methods

    Czech Academy of Sciences Publication Activity Database

    Paige, C. C.; Strakoš, Zdeněk

    2002-01-01

    Roč. 23, č. 6 (2002), s. 1899-1924 ISSN 1064-8275 R&D Projects: GA AV ČR IAA1030103 Institutional research plan: AV0Z1030915 Keywords : linear equations * eigenproblem * large sparse matrices * iterative solutions * Krylov subspace methods * Arnoldi method * GMRES * modified Gram-Schmidt * least squares * total least squares * singular values Subject RIV: BA - General Mathematics Impact factor: 1.291, year: 2002

  17. A Krylov Subspace Method for Unstructured Mesh SN Transport Computation

    International Nuclear Information System (INIS)

    Yoo, Han Jong; Cho, Nam Zin; Kim, Jong Woon; Hong, Ser Gi; Lee, Young Ouk

    2010-01-01

    Hong, et al., have developed a computer code MUST (Multi-group Unstructured geometry S N Transport) for the neutral particle transport calculations in three-dimensional unstructured geometry. In this code, the discrete ordinates transport equation is solved by using the discontinuous finite element method (DFEM) or the subcell balance methods with linear discontinuous expansion. In this paper, the conventional source iteration in the MUST code is replaced by the Krylov subspace method to reduce computing time and the numerical test results are given

  18. On Optimal Short Recurrences for Generating Orthogonal Krylov Subspace Bases. Dedicated to Gene Golub

    Czech Academy of Sciences Publication Activity Database

    Liesen, J.; Strakoš, Zdeněk

    2008-01-01

    Roč. 50, č. 3 (2008), s. 485-503 ISSN 0036-1445 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : Krylov subspace methods * orthogonal bases * short reccurences * conjugate gradient -like methods Subject RIV: IN - Informatics, Computer Science Impact factor: 2.739, year: 2008

  19. s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lijewski, Mike [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Almgren, Ann [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Carson, Erin [Univ. of California, Berkeley, CA (United States); Knight, Nicholas [Univ. of California, Berkeley, CA (United States); Demmel, James [Univ. of California, Berkeley, CA (United States)

    2014-08-14

    Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.

  20. An efficient preconditioning technique using Krylov subspace methods for 3D characteristics solvers

    International Nuclear Information System (INIS)

    Dahmani, M.; Le Tellier, R.; Roy, R.; Hebert, A.

    2005-01-01

    The Generalized Minimal RESidual (GMRES) method, using a Krylov subspace projection, is adapted and implemented to accelerate a 3D iterative transport solver based on the characteristics method. Another acceleration technique called the self-collision rebalancing technique (SCR) can also be used to accelerate the solution or as a left preconditioner for GMRES. The GMRES method is usually used to solve a linear algebraic system (Ax=b). It uses K(r (o) ,A) as projection subspace and AK(r (o) ,A) for the orthogonalization of the residual. This paper compares the performance of these two combined methods on various problems. To implement the GMRES iterative method, the characteristics equations are derived in linear algebra formalism by using the equivalence between the method of characteristics and the method of collision probability to end up with a linear algebraic system involving fluxes and currents. Numerical results show good performance of the GMRES technique especially for the cases presenting large material heterogeneity with a scattering ratio close to 1. Similarly, the SCR preconditioning slightly increases the GMRES efficiency

  1. A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

    Science.gov (United States)

    Carpenter, Mark H.; Vuik, C.; Lucas, Peter; vanGijzen, Martin; Bijl, Hester

    2010-01-01

    A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

  2. LBAS: Lanczos Bidiagonalization with Subspace Augmentation for Discrete Inverse Problems

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Abe, Kyniyoshi

    The regularizing properties of Lanczos bidiagonalization are powerful when the underlying Krylov subspace captures the dominating components of the solution. In some applications the regularized solution can be further improved by augmenting the Krylov subspace with a low-dimensional subspace tha...

  3. Reverse time migration by Krylov subspace reduced order modeling

    Science.gov (United States)

    Basir, Hadi Mahdavi; Javaherian, Abdolrahim; Shomali, Zaher Hossein; Firouz-Abadi, Roohollah Dehghani; Gholamy, Shaban Ali

    2018-04-01

    Imaging is a key step in seismic data processing. To date, a myriad of advanced pre-stack depth migration approaches have been developed; however, reverse time migration (RTM) is still considered as the high-end imaging algorithm. The main limitations associated with the performance cost of reverse time migration are the intensive computation of the forward and backward simulations, time consumption, and memory allocation related to imaging condition. Based on the reduced order modeling, we proposed an algorithm, which can be adapted to all the aforementioned factors. Our proposed method benefit from Krylov subspaces method to compute certain mode shapes of the velocity model computed by as an orthogonal base of reduced order modeling. Reverse time migration by reduced order modeling is helpful concerning the highly parallel computation and strongly reduces the memory requirement of reverse time migration. The synthetic model results showed that suggested method can decrease the computational costs of reverse time migration by several orders of magnitudes, compared with reverse time migration by finite element method.

  4. Development of a Burnup Module DECBURN Based on the Krylov Subspace Method

    Energy Technology Data Exchange (ETDEWEB)

    Cho, J. Y.; Kim, K. S.; Shim, H. J.; Song, J. S

    2008-05-15

    This report is to develop a burnup module DECBURN that is essential for the reactor analysis and the assembly homogenization codes to trace the fuel composition change during the core burnup. The developed burnup module solves the burnup equation by the matrix exponential method based on the Krylov Subspace method. The final solution of the matrix exponential is obtained by the matrix scaling and squaring method. To develop DECBURN module, this report includes the followings as: (1) Krylov Subspace Method for Burnup Equation, (2) Manufacturing of the DECBURN module, (3) Library Structure Setup and Library Manufacturing, (4) Examination of the DECBURN module, (5) Implementation to the DeCART code and Verification. DECBURN library includes the decay constants, one-group cross section and the fission yields. Examination of the DECBURN module is performed by manufacturing a driver program, and the results of the DECBURN module is compared with those of the ORIGEN program. Also, the implemented DECBURN module to the DeCART code is applied to the LWR depletion benchmark and a OPR-1000 pin cell problem, and the solutions are compared with the HELIOS code to verify the computational soundness and accuracy. In this process, the criticality calculation method and the predictor-corrector scheme are introduced to the DeCART code for a function of the homogenization code. The examination by a driver program shows that the DECBURN module produces exactly the same solution with the ORIGEN program. DeCART code that equips the DECBURN module produces a compatible solution to the other codes for the LWR depletion benchmark. Also the multiplication factors of the DeCART code for the OPR-1000 pin cell problem agree to the HELIOS code within 100 pcm over the whole burnup steps. The multiplication factors with the criticality calculation are also compatible with the HELIOS code. These results mean that the developed DECBURN module works soundly and produces an accurate solution

  5. Time-domain simulations for metallic nano-structures - a Krylov-subspace approach beyond the limitations of FDTD

    Energy Technology Data Exchange (ETDEWEB)

    Koenig, Michael [Institut fuer Theoretische Festkoerperphysik, Universitaet Karlsruhe (Germany); Karlsruhe School of Optics and Photonics (KSOP), Universitaet Karlsruhe (Germany); Niegemann, Jens; Tkeshelashvili, Lasha; Busch, Kurt [Institut fuer Theoretische Festkoerperphysik, Universitaet Karlsruhe (Germany); DFG Forschungszentrum Center for Functional Nanostructures (CFN), Universitaet Karlsruhe (Germany); Karlsruhe School of Optics and Photonics (KSOP), Universitaet Karlsruhe (Germany)

    2008-07-01

    Numerical simulations of metallic nano-structures are crucial for the efficient design of plasmonic devices. Conventional time-domain solvers such as FDTD introduce large numerical errors especially at metallic surfaces. Our approach combines a discontinuous Galerkin method on an adaptive mesh for the spatial discretisation with a Krylov-subspace technique for the time-stepping procedure. Thus, the higher-order accuracy in both time and space is supported by unconditional stability. As illustrative examples, we compare numerical results obtained with our method against analytical reference solutions and results from FDTD calculations.

  6. Subspace orthogonalization for substructuring preconditioners for nonsymmetric systems of linear equations

    Energy Technology Data Exchange (ETDEWEB)

    Starke, G. [Universitaet Karlsruhe (Germany)

    1994-12-31

    For nonselfadjoint elliptic boundary value problems which are preconditioned by a substructuring method, i.e., nonoverlapping domain decomposition, the author introduces and studies the concept of subspace orthogonalization. In subspace orthogonalization variants of Krylov methods the computation of inner products and vector updates, and the storage of basis elements is restricted to a (presumably small) subspace, in this case the edge and vertex unknowns with respect to the partitioning into subdomains. The author investigates subspace orthogonalization for two specific iterative algorithms, GMRES and the full orthogonalization method (FOM). This is intended to eliminate certain drawbacks of the Arnoldi-based Krylov subspace methods mentioned above. Above all, the length of the Arnoldi recurrences grows linearly with the iteration index which is therefore restricted to the number of basis elements that can be held in memory. Restarts become necessary and this often results in much slower convergence. The subspace orthogonalization methods, in contrast, require the storage of only the edge and vertex unknowns of each basis element which means that one can iterate much longer before restarts become necessary. Moreover, the computation of inner products is also restricted to the edge and vertex points which avoids the disturbance of the computational flow associated with the solution of subdomain problems. The author views subspace orthogonalization as an alternative to restarting or truncating Krylov subspace methods for nonsymmetric linear systems of equations. Instead of shortening the recurrences, one restricts them to a subset of the unknowns which has to be carefully chosen in order to be able to extend this partial solution to the entire space. The author discusses the convergence properties of these iteration schemes and its advantages compared to restarted or truncated versions of Krylov methods applied to the full preconditioned system.

  7. KRYSI, Ordinary Differential Equations Solver with Sdirk Krylov Method

    International Nuclear Information System (INIS)

    Hindmarsh, A.C.; Norsett, S.P.

    2001-01-01

    1 - Description of program or function: KRYSI is a set of FORTRAN subroutines for solving ordinary differential equations initial value problems. It is suitable for both stiff and non-stiff systems. When solving the implicit stage equations in the stiff case, KRYSI uses a Krylov subspace iteration method called the SPIGMR (Scaled Preconditioned Incomplete Generalized Minimum Residual) method. No explicit Jacobian storage is required, except where used in pre- conditioning. A demonstration problem is included with a description of two pre-conditioners that are natural for its solution by KRYSI. 2 - Method of solution: KRYSI uses a three-stage, third-order singly diagonally implicit Runge-Kutta (SDIRK) method. In the stiff case, a preconditioned Krylov subspace iteration within a (so-called) inexact Newton iteration is used to solve the system of nonlinear algebraic equations

  8. Domain decomposed preconditioners with Krylov subspace methods as subdomain solvers

    Energy Technology Data Exchange (ETDEWEB)

    Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)

    1994-12-31

    Domain decomposed preconditioners for nonsymmetric partial differential equations typically require the solution of problems on the subdomains. Most implementations employ exact solvers to obtain these solutions. Consequently work and storage requirements for the subdomain problems grow rapidly with the size of the subdomain problems. Subdomain solves constitute the single largest computational cost of a domain decomposed preconditioner, and improving the efficiency of this phase of the computation will have a significant impact on the performance of the overall method. The small local memory available on the nodes of most message-passing multicomputers motivates consideration of the use of an iterative method for solving subdomain problems. For large-scale systems of equations that are derived from three-dimensional problems, memory considerations alone may dictate the need for using iterative methods for the subdomain problems. In addition to reduced storage requirements, use of an iterative solver on the subdomains allows flexibility in specifying the accuracy of the subdomain solutions. Substantial savings in solution time is possible if the quality of the domain decomposed preconditioner is not degraded too much by relaxing the accuracy of the subdomain solutions. While some work in this direction has been conducted for symmetric problems, similar studies for nonsymmetric problems appear not to have been pursued. This work represents a first step in this direction, and explores the effectiveness of performing subdomain solves using several transpose-free Krylov subspace methods, GMRES, transpose-free QMR, CGS, and a smoothed version of CGS. Depending on the difficulty of the subdomain problem and the convergence tolerance used, a reduction in solution time is possible in addition to the reduced memory requirements. The domain decomposed preconditioner is a Schur complement method in which the interface operators are approximated using interface probing.

  9. Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

    KAUST Repository

    Bisetti, Fabrizio

    2012-06-01

    Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.

  10. Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

    KAUST Repository

    Bisetti, Fabrizio

    2012-01-01

    with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix

  11. Investigating Multi-Array Antenna Signal Convergence using Wavelet Transform and Krylov Sequence

    Directory of Open Access Journals (Sweden)

    Muhammad Ahmed Sikander

    2018-01-01

    Full Text Available In the present world, wireless communication is becoming immensely popular for plethora of applications. Technology has been advancing at an accelerated rate leading to make communication reliable. Still, there are issues need to be address to minimize errors in the transmission. This research study expounds on the rapid convergence of the signal. Convergence is considered to be an important aspect in wireless communication. For rapid convergence, two ambiguities should be addressed; Eigenvalue spread and sparse identification or sparsity of the signal. Eigen value spread is defining as the ratio of minimum to maximum Eigenvalue, whereas sparsity is defining as the loosely bounded system. In this research, two of these attributes are investigated for MAA (Multi-Array Antenna signal using the cascading of Wavelet and Krylov processes. Specifically, the MAA signal is applied in the research because nowadays there are many physical hindrances in the communication path. These hurdles weaken the signal strength which in turn effects the quality of the reception. WT (Wavelet Transform is used to address the Eigenvalue problem and the Krylov sequence is used to attempt the sparse identification of the MAA signal. The results show that the convergence of the MMA signal is improved by applying Wavelet transform and Krylov Subspace.

  12. Investigating multi-array antenna signal convergence using wavelet transform and krylov sequence

    International Nuclear Information System (INIS)

    Sikander, M.A.; Hussain, R.; Hussain, R.

    2018-01-01

    In the present world, wireless communication is becoming immensely popular for plethora of applications. Technology has been advancing at an accelerated rate leading to make communication reliable. Still, there are issues need to be address to minimize errors in the transmission. This research study expounds on the rapid convergence of the signal. Convergence is considered to be an important aspect in wireless communication. For rapid convergence, two ambiguities should be addressed; Eigenvalue spread and sparse identification or sparsity of the signal. Eigen value spread is defining as the ratio of minimum to maximum Eigenvalue, whereas sparsity is defining as the loosely bounded system. In this research, two of these attributes are investigated for MAA (Multi-Array Antenna) signal using the cascading of Wavelet and Krylov processes. Specifically, the MAA signal is applied in the research because nowadays there are many physical hindrances in the communication path. These hurdles weaken the signal strength which in turn effects the quality of the reception. WT (Wavelet Transform) is used to address the Eigenvalue problem and the Krylov sequence is used to attempt the sparse identification of the MAA signal. The results show that the convergence of the MMA signal is improved by applying Wavelet transform and Krylov Subspace. (author)

  13. A fast band–Krylov eigensolver for macromolecular functional motion simulation on multicore architectures and graphics processors

    Energy Technology Data Exchange (ETDEWEB)

    Aliaga, José I., E-mail: aliaga@uji.es [Depto. Ingeniería y Ciencia de Computadores, Universitat Jaume I, Castellón (Spain); Alonso, Pedro [Departamento de Sistemas Informáticos y Computación, Universitat Politècnica de València (Spain); Badía, José M. [Depto. Ingeniería y Ciencia de Computadores, Universitat Jaume I, Castellón (Spain); Chacón, Pablo [Dept. Biological Chemical Physics, Rocasolano Physics and Chemistry Institute, CSIC, Madrid (Spain); Davidović, Davor [Rudjer Bošković Institute, Centar za Informatiku i Računarstvo – CIR, Zagreb (Croatia); López-Blanco, José R. [Dept. Biological Chemical Physics, Rocasolano Physics and Chemistry Institute, CSIC, Madrid (Spain); Quintana-Ortí, Enrique S. [Depto. Ingeniería y Ciencia de Computadores, Universitat Jaume I, Castellón (Spain)

    2016-03-15

    We introduce a new iterative Krylov subspace-based eigensolver for the simulation of macromolecular motions on desktop multithreaded platforms equipped with multicore processors and, possibly, a graphics accelerator (GPU). The method consists of two stages, with the original problem first reduced into a simpler band-structured form by means of a high-performance compute-intensive procedure. This is followed by a memory-intensive but low-cost Krylov iteration, which is off-loaded to be computed on the GPU by means of an efficient data-parallel kernel. The experimental results reveal the performance of the new eigensolver. Concretely, when applied to the simulation of macromolecules with a few thousands degrees of freedom and the number of eigenpairs to be computed is small to moderate, the new solver outperforms other methods implemented as part of high-performance numerical linear algebra packages for multithreaded architectures.

  14. A fast band–Krylov eigensolver for macromolecular functional motion simulation on multicore architectures and graphics processors

    International Nuclear Information System (INIS)

    Aliaga, José I.; Alonso, Pedro; Badía, José M.; Chacón, Pablo; Davidović, Davor; López-Blanco, José R.; Quintana-Ortí, Enrique S.

    2016-01-01

    We introduce a new iterative Krylov subspace-based eigensolver for the simulation of macromolecular motions on desktop multithreaded platforms equipped with multicore processors and, possibly, a graphics accelerator (GPU). The method consists of two stages, with the original problem first reduced into a simpler band-structured form by means of a high-performance compute-intensive procedure. This is followed by a memory-intensive but low-cost Krylov iteration, which is off-loaded to be computed on the GPU by means of an efficient data-parallel kernel. The experimental results reveal the performance of the new eigensolver. Concretely, when applied to the simulation of macromolecules with a few thousands degrees of freedom and the number of eigenpairs to be computed is small to moderate, the new solver outperforms other methods implemented as part of high-performance numerical linear algebra packages for multithreaded architectures.

  15. Krylov-Schur-Type restarts for the two-sided arnoldi method

    NARCIS (Netherlands)

    Zwaan, I.N.; Hochstenbach, M.E.

    2017-01-01

    We consider the two-sided Arnoldi method and propose a two-sided Krylov-Schurtype restarting method. We discuss the restart for standard Rayleigh-Ritz extraction as well as harmonic Rayleigh-Ritz extraction. Additionally, we provide error bounds for Ritz values and Ritz vectors in the context of

  16. An acceleration technique for 2D MOC based on Krylov subspace and domain decomposition methods

    International Nuclear Information System (INIS)

    Zhang Hongbo; Wu Hongchun; Cao Liangzhi

    2011-01-01

    Highlights: → We convert MOC into linear system solved by GMRES as an acceleration method. → We use domain decomposition method to overcome the inefficiency on large matrices. → Parallel technology is applied and a matched ray tracing system is developed. → Results show good efficiency even in large-scale and strong scattering problems. → The emphasis is that the technique is geometry-flexible. - Abstract: The method of characteristics (MOC) has great geometrical flexibility but poor computational efficiency in neutron transport calculations. The generalized minimal residual (GMRES) method, a type of Krylov subspace method, is utilized to accelerate a 2D generalized geometry characteristics solver AutoMOC. In this technique, a form of linear algebraic equation system for angular flux moments and boundary fluxes is derived to replace the conventional characteristics sweep (i.e. inner iteration) scheme, and then the GMRES method is implemented as an efficient linear system solver. This acceleration method is proved to be reliable in theory and simple for implementation. Furthermore, as introducing no restriction in geometry treatment, it is suitable for acceleration of an arbitrary geometry MOC solver. However, it is observed that the speedup decreases when the matrix becomes larger. The spatial domain decomposition method and multiprocessing parallel technology are then employed to overcome the problem. The calculation domain is partitioned into several sub-domains. For each of them, a smaller matrix is established and solved by GMRES; and the adjacent sub-domains are coupled by 'inner-edges', where the trajectory mismatches are considered adequately. Moreover, a matched ray tracing system is developed on the basis of AutoCAD, which allows a user to define the sub-domains on demand conveniently. Numerical results demonstrate that the acceleration techniques are efficient without loss of accuracy, even in the case of large-scale and strong scattering

  17. Comparison of Two-Block Decomposition Method and Chebyshev Rational Approximation Method for Depletion Calculation

    International Nuclear Information System (INIS)

    Lee, Yoon Hee; Cho, Nam Zin

    2016-01-01

    The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.

  18. Comparison of Two-Block Decomposition Method and Chebyshev Rational Approximation Method for Depletion Calculation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Yoon Hee; Cho, Nam Zin [KAERI, Daejeon (Korea, Republic of)

    2016-05-15

    The code gives inaccurate results of nuclides for evaluation of source term analysis, e.g., Sr- 90, Ba-137m, Cs-137, etc. A Krylov Subspace method was suggested by Yamamoto et al. The method is based on the projection of solution space of Bateman equation to a lower dimension of Krylov subspace. It showed good accuracy in the detailed burnup chain calculation if dimension of the Krylov subspace is high enough. In this paper, we will compare the two methods in terms of accuracy and computing time. In this paper, two-block decomposition (TBD) method and Chebyshev rational approximation method (CRAM) are compared in the depletion calculations. In the two-block decomposition method, according to the magnitude of effective decay constant, the system of Bateman equation is decomposed into short- and longlived blocks. The short-lived block is calculated by the general Bateman solution and the importance concept. Matrix exponential with smaller norm is used in the long-lived block. In the Chebyshev rational approximation, there is no decomposition of the Bateman equation system, and the accuracy of the calculation is determined by the order of expansion in the partial fraction decomposition of the rational form. The coefficients in the partial fraction decomposition are determined by a Remez-type algorithm.

  19. Newton-Krylov-Schwarz methods in unstructured grid Euler flow

    Energy Technology Data Exchange (ETDEWEB)

    Keyes, D.E. [Old Dominion Univ., Norfolk, VA (United States)

    1996-12-31

    Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton`s method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on an aerodynamic application emphasizing comparisons with a standard defect-correction approach and subdomain preconditioner consistency.

  20. LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration and Root-finding

    International Nuclear Information System (INIS)

    Hindmarsh, A.D.; Brown, P.N.

    1996-01-01

    1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, c) LSODKR includes the ability to find roots of given functions of the solution during the integration. 2 - Method of solution: Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user. 3 - Restrictions on the complexity of the problem: None

  1. Two-qubit quantum computing in a projected subspace

    International Nuclear Information System (INIS)

    Bi Qiao; Ruda, H.E.; Zhan, M.S.

    2002-01-01

    A formulation for performing quantum computing in a projected subspace is presented, based on the subdynamical kinetic equation (SKE) for an open quantum system. The eigenvectors of the kinetic equation are shown to remain invariant before and after interaction with the environment. However, the eigenvalues in the projected subspace exhibit a type of phase shift to the evolutionary states. This phase shift does not destroy the decoherence-free (DF) property of the subspace because the associated fidelity is 1. This permits a universal formalism to be presented--the eigenprojectors of the free part of the Hamiltonian for the system and bath may be used to construct a DF projected subspace based on the SKE. To eliminate possible phase or unitary errors induced by the change in the eigenvalues, a cancellation technique is proposed, using the adjustment of the coupling time, and applied to a two-qubit computing system. A general criteria for constructing a DF-projected subspace from the SKE is discussed. Finally, a proposal for using triangulation to realize a decoherence-free subsystem based on SKE is presented. The concrete formulation for a two-qubit model is given exactly. Our approach is general and appears to be applicable to any type of decoherence

  2. Diomres (k,m): An efficient method based on Krylov subspaces to solve big, dispersed, unsymmetrical linear systems

    Energy Technology Data Exchange (ETDEWEB)

    de la Torre Vega, E. [Instituto de Investigaciones Electricas, Cuernavaca (Mexico); Cesar Suarez Arriaga, M. [Universidad Michoacana SNH, Michoacan (Mexico)

    1995-03-01

    In geothermal simulation processes, MULKOM uses Integrated Finite Differences to solve the corresponding partial differential equations. This method requires to resolve efficiently big linear dispersed systems of non-symmetrical nature on each temporal iteration. The order of the system is usually greater than one thousand its solution could represent around 80% of CPU total calculation time. If the elapsed time solving this class of linear systems is reduced, the duration of numerical simulation decreases notably. When the matrix is big (N{ge}500) and with holes, it is inefficient to handle all the system`s elements, because it is perfectly figured out by its elements distinct of zero, quantity greatly minor than N{sup 2}. In this area, iteration methods introduce advantages with respect to gaussian elimination methods, because these last replenish matrices not having any special distribution of their non-zero elements and because they do not make use of the available solution estimations. The iterating methods of the Conjugated Gradient family, based on the subspaces of Krylov, possess the advantage of improving the convergence speed by means of preconditioning techniques. The creation of DIOMRES(k,m) method guarantees the continuous descent of the residual norm, without incurring in division by zero. This technique converges at most in N iterations if the system`s matrix is symmetrical, it does not employ too much memory to converge and updates immediately the approximation by using incomplete orthogonalization and adequate restarting. A preconditioned version of DIOMRES was applied to problems related to unsymmetrical systems with 1000 unknowns and less than five terms per equation. We found that this technique could reduce notably the time needful to find the solution without requiring memory increment. The coupling of this method to geothermal versions of MULKOM is in process.

  3. Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

    Science.gov (United States)

    Lollchund, M. R.; Dookhitram, K.; Sunhaloo, M. S.; Boojhawon, R.

    2013-04-01

    In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

  4. Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

    International Nuclear Information System (INIS)

    Lollchund, M R; Dookhitram, K; Sunhaloo, M S; Boojhawon, R

    2013-01-01

    In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

  5. Krylov Techniques for 3D Problems in Transport Theory

    International Nuclear Information System (INIS)

    Ruben Panta Pazos

    2006-01-01

    When solving integral-differential equations by means of numerical methods one has to deal with large systems of linear equations, such as happens in transport theory [10]. Many iterative techniques are now used in Transport Theory in order to solve problems of 2D and 3D dimensions. In this paper, we choose two problems to solve the following transport equation, [Equation] where x: represents the spatial variable, μ: the cosine of the angle, ψ: the angular flux, h(x, μ): is the collision frequency, k(x, μ, μ'): the scattering kernel, q(x, μ): the source. The aim of this work is the straightforward application of the Krylov spaces technique [2] to the governing equation or to its discretizations derived of the discrete ordinates method (choosing a finite number of directions and then approximating the integral term by means of a proper sum). The equation (1) can be written in functional form as [Equation] with ψ in the Hilbert space L 2 ([0,a] x [-1,1])., and q is the source function. The operator derived from a discrete ordinates scheme that approximates the operator [Equation] generates the following subspace [Equation] i.e. the subspace generated by the iterations of order 0, 1, 2,..., m-1 of the source function q. Two methods are specially outstanding, the Lanczos method to solve the problem given by equation (2) with certain boundary conditions, and the conjugate gradient method to solve the same problem with identical boundary conditions. We discuss and accelerate the basic iterative method [8]. An important conclusion is the generation of these methods to solve linear systems in Hilbert spaces, if verify the convergence conditions, which are outlined in this work. The first problem is a cubic domain with two regions, one with a source near the vertex at the origin and the shield region. In this case, the Cartesian planes (specifically 0 < x < L, 0 < y < L, 0 < z < L) are reflexive boundaries and the rest faces of the cube are vacuum boundaries. The

  6. Active Subspaces of Airfoil Shape Parameterizations

    Science.gov (United States)

    Grey, Zachary J.; Constantine, Paul G.

    2018-05-01

    Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flow field with a parameterized geometry is a popular test problem for design methodologies. We examine two particular airfoil shape parameterizations, PARSEC and CST, and study the active subspaces present in two common design quantities of interest, transonic lift and drag coefficients, under each shape parameterization. We mathematically relate the two parameterizations with a common polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical airfoil properties. In particular, we obtain and interpret a two-dimensional approximation of both transonic lift and drag, and we show how these approximation inform a multi-objective design problem.

  7. LSODKR, Stiff Ordinary Differential Equations (ODE) System Solver with Krylov Iteration with Root-finding

    International Nuclear Information System (INIS)

    Hindmarsh, A.C.; Petzold, L.R.

    2005-01-01

    1 - Description of program or function: LSODKR is a new initial value ODE solver for stiff and non-stiff systems. It is a variant of the LSODPK and LSODE solvers, intended mainly for large stiff systems. The main differences between LSODKR and LSODE are the following: a) for stiff systems, LSODKR uses a corrector iteration composed of Newton iteration and one of four preconditioned Krylov subspace iteration methods. The user must supply routines for the preconditioning operations, b) within the corrector iteration, LSODKR does automatic switching between functional (fix point) iteration and modified Newton iteration, The nonlinear iteration method-switching differs from the method-switching in LSODA and LSODAR, but provides similar savings by using the cheaper method in the non-stiff regions of the problem. c) LSODKR includes the ability to find roots of given functions of the solution during the integration. d) LSODKR also improves on the Krylov methods in LSODPK by offering the option to save and reuse the approximate Jacobian data underlying the pre-conditioner. The LSODKR source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. Integration is by Adams or BDF (Backward Differentiation Formula) methods, at user option. Corrector iteration is by Newton or fix point iteration, determined dynamically. Linear system solution is by a preconditioned Krylov iteration, selected by user from Incomplete Orthogonalization Method, Generalized Minimum Residual Method, and two variants of Preconditioned Conjugate Gradient Method. Preconditioning is to be supplied by the user

  8. Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients

    KAUST Repository

    Gao, Longfei; Calo, Victor M.

    2015-01-01

    In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved.

  9. Scalable Density-Based Subspace Clustering

    DEFF Research Database (Denmark)

    Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

    2011-01-01

    For knowledge discovery in high dimensional databases, subspace clustering detects clusters in arbitrary subspace projections. Scalability is a crucial issue, as the number of possible projections is exponential in the number of dimensions. We propose a scalable density-based subspace clustering...... method that steers mining to few selected subspace clusters. Our novel steering technique reduces subspace processing by identifying and clustering promising subspaces and their combinations directly. Thereby, it narrows down the search space while maintaining accuracy. Thorough experiments on real...... and synthetic databases show that steering is efficient and scalable, with high quality results. For future work, our steering paradigm for density-based subspace clustering opens research potential for speeding up other subspace clustering approaches as well....

  10. Efficient solution of parabolic equations by Krylov approximation methods

    Science.gov (United States)

    Gallopoulos, E.; Saad, Y.

    1990-01-01

    Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

  11. Conformal mapping and convergence of Krylov iterations

    Energy Technology Data Exchange (ETDEWEB)

    Driscoll, T.A.; Trefethen, L.N. [Cornell Univ., Ithaca, NY (United States)

    1994-12-31

    Connections between conformal mapping and matrix iterations have been known for many years. The idea underlying these connections is as follows. Suppose the spectrum of a matrix or operator A is contained in a Jordan region E in the complex plane with 0 not an element of E. Let {phi}(z) denote a conformal map of the exterior of E onto the exterior of the unit disk, with {phi}{infinity} = {infinity}. Then 1/{vert_bar}{phi}(0){vert_bar} is an upper bound for the optimal asymptotic convergence factor of any Krylov subspace iteration. This idea can be made precise in various ways, depending on the matrix iterations, on whether A is finite or infinite dimensional, and on what bounds are assumed on the non-normality of A. This paper explores these connections for a variety of matrix examples, making use of a new MATLAB Schwarz-Christoffel Mapping Toolbox developed by the first author. Unlike the earlier Fortran Schwarz-Christoffel package SCPACK, the new toolbox computes exterior as well as interior Schwarz-Christoffel maps, making it easy to experiment with spectra that are not necessarily symmetric about an axis.

  12. Estimation of direction of arrival of a moving target using subspace based approaches

    Science.gov (United States)

    Ghosh, Ripul; Das, Utpal; Akula, Aparna; Kumar, Satish; Sardana, H. K.

    2016-05-01

    In this work, array processing techniques based on subspace decomposition of signal have been evaluated for estimation of direction of arrival of moving targets using acoustic signatures. Three subspace based approaches - Incoherent Wideband Multiple Signal Classification (IWM), Least Square-Estimation of Signal Parameters via Rotation Invariance Techniques (LS-ESPRIT) and Total Least Square- ESPIRIT (TLS-ESPRIT) are considered. Their performance is compared with conventional time delay estimation (TDE) approaches such as Generalized Cross Correlation (GCC) and Average Square Difference Function (ASDF). Performance evaluation has been conducted on experimentally generated data consisting of acoustic signatures of four different types of civilian vehicles moving in defined geometrical trajectories. Mean absolute error and standard deviation of the DOA estimates w.r.t. ground truth are used as performance evaluation metrics. Lower statistical values of mean error confirm the superiority of subspace based approaches over TDE based techniques. Amongst the compared methods, LS-ESPRIT indicated better performance.

  13. A Newton-Krylov method with approximate Jacobian for implicit solution of Navier-Stokes on staggered overset-curvilinear grids with immersed boundaries

    Science.gov (United States)

    Asgharzadeh, Hafez; Borazjani, Iman

    2014-11-01

    Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.

  14. Accuracy of Two Three-Term and Three Two-Term Recurrences for Krylov Space Solvers

    Czech Academy of Sciences Publication Activity Database

    Gutknecht, M. H.; Strakoš, Zdeněk

    2000-01-01

    Roč. 22, č. 1 (2000), s. 213-229 ISSN 0895-4798 R&D Projects: GA ČR GA205/96/0921; GA AV ČR IAA2030706 Institutional research plan: AV0Z1030915 Keywords : linear system of equations * iterative method * Krylov space method * conjugate gradient method * tree-term recurrence * accuracy * roundoff Subject RIV: BA - General Mathematics Impact factor: 1.182, year: 2000

  15. Portable, parallel, reusable Krylov space codes

    Energy Technology Data Exchange (ETDEWEB)

    Smith, B.; Gropp, W. [Argonne National Lab., IL (United States)

    1994-12-31

    Krylov space accelerators are an important component of many algorithms for the iterative solution of linear systems. Each Krylov space method has it`s own particular advantages and disadvantages, therefore it is desirable to have a variety of them available all with an identical, easy to use, interface. A common complaint application programmers have with available software libraries for the iterative solution of linear systems is that they require the programmer to use the data structures provided by the library. The library is not able to work with the data structures of the application code. Hence, application programmers find themselves constantly recoding the Krlov space algorithms. The Krylov space package (KSP) is a data-structure-neutral implementation of a variety of Krylov space methods including preconditioned conjugate gradient, GMRES, BiCG-Stab, transpose free QMR and CGS. Unlike all other software libraries for linear systems that the authors are aware of, KSP will work with any application codes data structures, in Fortran or C. Due to it`s data-structure-neutral design KSP runs unchanged on both sequential and parallel machines. KSP has been tested on workstations, the Intel i860 and Paragon, Thinking Machines CM-5 and the IBM SP1.

  16. Active Subspaces for Wind Plant Surrogate Modeling

    Energy Technology Data Exchange (ETDEWEB)

    King, Ryan N [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Quick, Julian [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Dykes, Katherine L [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Adcock, Christiane [Massachusetts Institute of Technology

    2018-01-12

    Understanding the uncertainty in wind plant performance is crucial to their cost-effective design and operation. However, conventional approaches to uncertainty quantification (UQ), such as Monte Carlo techniques or surrogate modeling, are often computationally intractable for utility-scale wind plants because of poor congergence rates or the curse of dimensionality. In this paper we demonstrate that wind plant power uncertainty can be well represented with a low-dimensional active subspace, thereby achieving a significant reduction in the dimension of the surrogate modeling problem. We apply the active sub-spaces technique to UQ of plant power output with respect to uncertainty in turbine axial induction factors, and find a single active subspace direction dominates the sensitivity in power output. When this single active subspace direction is used to construct a quadratic surrogate model, the number of model unknowns can be reduced by up to 3 orders of magnitude without compromising performance on unseen test data. We conclude that the dimension reduction achieved with active subspaces makes surrogate-based UQ approaches tractable for utility-scale wind plants.

  17. Subspace System Identification of the Kalman Filter

    Directory of Open Access Journals (Sweden)

    David Di Ruscio

    2003-07-01

    Full Text Available Some proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colored inputs, proved that the subspace identification of the states only is possible if the deterministic part of the system is known or identified beforehand. However, if the inputs are white, then, it is proved that the states can be identified directly. Some alternative projection matrices which can be used to compute the extended observability matrix directly from the data are presented. Furthermore, an efficient method for computing the deterministic part of the system is presented. The closed loop subspace identification problem is also addressed and it is shown that this problem is solved and unbiased estimates are obtained by simply including a filter in the feedback. Furthermore, an algorithm for consistent closed loop subspace estimation is presented. This algorithm is using the controller parameters in order to overcome the bias problem.

  18. OpenSubspace

    DEFF Research Database (Denmark)

    Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

    2009-01-01

    Subspace clustering and projected clustering are recent research areas for clustering in high dimensional spaces. As the field is rather young, there is a lack of comparative studies on the advantages and disadvantages of the different algorithms. Part of the underlying problem is the lack...... of available open source implementations that could be used by researchers to understand, compare, and extend subspace and projected clustering algorithms. In this paper, we discuss the requirements for open source evaluation software. We propose OpenSubspace, an open source framework that meets...... these requirements. OpenSubspace integrates state-of-the-art performance measures and visualization techniques to foster research in subspace and projected clustering....

  19. Invariant subspaces

    CERN Document Server

    Radjavi, Heydar

    2003-01-01

    This broad survey spans a wealth of studies on invariant subspaces, focusing on operators on separable Hilbert space. Largely self-contained, it requires only a working knowledge of measure theory, complex analysis, and elementary functional analysis. Subjects include normal operators, analytic functions of operators, shift operators, examples of invariant subspace lattices, compact operators, and the existence of invariant and hyperinvariant subspaces. Additional chapters cover certain results on von Neumann algebras, transitive operator algebras, algebras associated with invariant subspaces,

  20. Greedy subspace clustering.

    Science.gov (United States)

    2016-09-01

    We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets ...

  1. Relevant Subspace Clustering

    DEFF Research Database (Denmark)

    Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

    2009-01-01

    Subspace clustering aims at detecting clusters in any subspace projection of a high dimensional space. As the number of possible subspace projections is exponential in the number of dimensions, the result is often tremendously large. Recent approaches fail to reduce results to relevant subspace...... clusters. Their results are typically highly redundant, i.e. many clusters are detected multiple times in several projections. In this work, we propose a novel model for relevant subspace clustering (RESCU). We present a global optimization which detects the most interesting non-redundant subspace clusters...... achieves top clustering quality while competing approaches show greatly varying performance....

  2. Newton-Krylov methods applied to nonequilibrium radiation diffusion

    International Nuclear Information System (INIS)

    Knoll, D.A.; Rider, W.J.; Olsen, G.L.

    1998-01-01

    The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton's method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton's method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step

  3. Subspace preservation, subspace locality, and gluing of completely positive maps

    International Nuclear Information System (INIS)

    Aaberg, Johan

    2004-01-01

    Three concepts concerning completely positive maps (CPMs) and trace preserving CPMs (channels) are introduced and investigated. These are named subspace preserving (SP) CPMs, subspace local (SL) channels, and gluing of CPMs. SP CPMs has, in the case of trace preserving CPMs, a simple interpretation as those which preserve probability weights on a given orthogonal sum decomposition of the Hilbert space of a quantum system. The proposed definition of subspace locality of quantum channels is an attempt to answer the question of what kind of restriction should be put on a channel, if it is to act 'locally' with respect to two 'locations', when these naturally correspond to a separation of the total Hilbert space in an orthogonal sum of subspaces, rather than a tensor product decomposition. As a description of the concept of gluings of quantum channels, consider a pair of 'evolution machines', each with the ability to evolve the internal state of a 'particle' inserted into its input. Each of these machines is characterized by a channel describing the operation the internal state has experienced when the particle is returned at the output. Suppose a particle is put in a superposition between the input of the first and the second machine. Here it is shown that the total evolution caused by a pair of such devices is not uniquely determined by the channels of the two machines. Such 'global' channels describing the machine pair are examples of gluings of the two single machine channels. Various expressions to generate the set of SP and SL channels, as well as expressions to generate the set of gluings of given channels, are deduced. We discuss conceptual aspects of the nature of these channels and the nature of the non-uniqueness of gluings

  4. Unsupervised spike sorting based on discriminative subspace learning.

    Science.gov (United States)

    Keshtkaran, Mohammad Reza; Yang, Zhi

    2014-01-01

    Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. In this paper, we present two unsupervised spike sorting algorithms based on discriminative subspace learning. The first algorithm simultaneously learns the discriminative feature subspace and performs clustering. It uses histogram of features in the most discriminative projection to detect the number of neurons. The second algorithm performs hierarchical divisive clustering that learns a discriminative 1-dimensional subspace for clustering in each level of the hierarchy until achieving almost unimodal distribution in the subspace. The algorithms are tested on synthetic and in-vivo data, and are compared against two widely used spike sorting methods. The comparative results demonstrate that our spike sorting methods can achieve substantially higher accuracy in lower dimensional feature space, and they are highly robust to noise. Moreover, they provide significantly better cluster separability in the learned subspace than in the subspace obtained by principal component analysis or wavelet transform.

  5. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

    Science.gov (United States)

    Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

    1996-01-01

    We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

  6. Newton-Krylov-Schwarz algorithms for the 2D full potential equation

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Xiao-Chuan [Univ. of Colorado, Boulder, CO (United States); Gropp, W.D. [Argonne National Lab., IL (United States); Keyes, D.E. [Old Dominion Univ. Norfolk, VA (United States)] [and others

    1996-12-31

    We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The main algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, can be made robust for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report favorable choices for numerical convergence rate and overall execution time on a distributed-memory parallel computer.

  7. Preconditioned Krylov subspace methods for eigenvalue problems

    Energy Technology Data Exchange (ETDEWEB)

    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.

  8. Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

    International Nuclear Information System (INIS)

    Zou, Ling; Zhao, Haihua; Zhang, Hongbin

    2015-01-01

    Highlights: • Using high-resolution spatial scheme in solving two-phase flow problems. • Fully implicit time integrations scheme. • Jacobian-free Newton–Krylov method. • Analytical solution for two-phase water faucet problem. - Abstract: The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists

  9. Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

    Science.gov (United States)

    Chui, Siu Lit; Lu, Ya Yan

    2004-03-01

    Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

  10. Krylov solvers for linear algebraic systems

    CERN Document Server

    Broyden, Charles George

    2004-01-01

    The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorithm and their properties, in particular their stability properties,are det

  11. Subspace confinement: how good is your qubit?

    International Nuclear Information System (INIS)

    Devitt, Simon J; Schirmer, Sonia G; Oi, Daniel K L; Cole, Jared H; Hollenberg, Lloyd C L

    2007-01-01

    The basic operating element of standard quantum computation is the qubit, an isolated two-level system that can be accurately controlled, initialized and measured. However, the majority of proposed physical architectures for quantum computation are built from systems that contain much more complicated Hilbert space structures. Hence, defining a qubit requires the identification of an appropriate controllable two-dimensional sub-system. This prompts the obvious question of how well a qubit, thus defined, is confined to this subspace, and whether we can experimentally quantify the potential leakage into states outside the qubit subspace. We demonstrate how subspace leakage can be characterized using minimal theoretical assumptions by examining the Fourier spectrum of the oscillation experiment

  12. Seismic noise attenuation using an online subspace tracking algorithm

    Science.gov (United States)

    Zhou, Yatong; Li, Shuhua; Zhang, Dong; Chen, Yangkang

    2018-02-01

    We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-the-art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVD-based singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.

  13. Geometric subspace updates with applications to online adaptive nonlinear model reduction

    DEFF Research Database (Denmark)

    Zimmermann, Ralf; Peherstorfer, Benjamin; Willcox, Karen

    2018-01-01

    In many scientific applications, including model reduction and image processing, subspaces are used as ansatz spaces for the low-dimensional approximation and reconstruction of the state vectors of interest. We introduce a procedure for adapting an existing subspace based on information from...... Estimation (GROUSE). We establish for GROUSE a closed-form expression for the residual function along the geodesic descent direction. Specific applications of subspace adaptation are discussed in the context of image processing and model reduction of nonlinear partial differential equation systems....

  14. Subspace K-means clustering.

    Science.gov (United States)

    Timmerman, Marieke E; Ceulemans, Eva; De Roover, Kim; Van Leeuwen, Karla

    2013-12-01

    To achieve an insightful clustering of multivariate data, we propose subspace K-means. Its central idea is to model the centroids and cluster residuals in reduced spaces, which allows for dealing with a wide range of cluster types and yields rich interpretations of the clusters. We review the existing related clustering methods, including deterministic, stochastic, and unsupervised learning approaches. To evaluate subspace K-means, we performed a comparative simulation study, in which we manipulated the overlap of subspaces, the between-cluster variance, and the error variance. The study shows that the subspace K-means algorithm is sensitive to local minima but that the problem can be reasonably dealt with by using partitions of various cluster procedures as a starting point for the algorithm. Subspace K-means performs very well in recovering the true clustering across all conditions considered and appears to be superior to its competitor methods: K-means, reduced K-means, factorial K-means, mixtures of factor analyzers (MFA), and MCLUST. The best competitor method, MFA, showed a performance similar to that of subspace K-means in easy conditions but deteriorated in more difficult ones. Using data from a study on parental behavior, we show that subspace K-means analysis provides a rich insight into the cluster characteristics, in terms of both the relative positions of the clusters (via the centroids) and the shape of the clusters (via the within-cluster residuals).

  15. The Detection of Subsynchronous Oscillation in HVDC Based on the Stochastic Subspace Identification Method

    Directory of Open Access Journals (Sweden)

    Chen Shi

    2014-01-01

    Full Text Available Subsynchronous oscillation (SSO usually caused by series compensation, power system stabilizer (PSS, high voltage direct current transmission (HVDC and other power electronic equipment, which will affect the safe operation of generator shafting even the system. It is very important to identify the modal parameters of SSO to take effective control strategies as well. Since the identification accuracy of traditional methods are not high enough, the stochastic subspace identification (SSI method is proposed to improve the identification accuracy of subsynchronous oscillation modal. The stochastic subspace identification method was compared with the other two methods on subsynchronous oscillation IEEE benchmark model and Xiang-Shang HVDC system model, the simulation results show that the stochastic subspace identification method has the advantages of high identification precision, high operation efficiency and strong ability of anti-noise.

  16. Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

    Czech Academy of Sciences Publication Activity Database

    Šístek, Jakub; Cirak, F.

    2015-01-01

    Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace method s Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www. science direct.com/ science /article/pii/S0045793015003023

  17. Nonlinear Krylov acceleration of reacting flow codes

    Energy Technology Data Exchange (ETDEWEB)

    Kumar, S.; Rawat, R.; Smith, P.; Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States)

    1996-12-31

    We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.

  18. Gamow state vectors as functionals over subspaces of the nuclear space

    International Nuclear Information System (INIS)

    Bohm, A.

    1979-12-01

    Exponentially decaying Gamow state vectors are obtained from S-matrix poles in the lower half of the second sheet, and are defined as functionals over a subspace of the nuclear space, PHI. Exponentially growing Gamow state vectors are obtained from S-matrix poles in the upper half of the second sheet, and are defined as functionals over another subspace of PHI. On functionals over these two subspaces the dynamical group of time development splits into two semigroups

  19. An alternative subspace approach to EEG dipole source localization

    Science.gov (United States)

    Xu, Xiao-Liang; Xu, Bobby; He, Bin

    2004-01-01

    In the present study, we investigate a new approach to electroencephalography (EEG) three-dimensional (3D) dipole source localization by using a non-recursive subspace algorithm called FINES. In estimating source dipole locations, the present approach employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of the entire estimated noise-only subspace in the case of classic MUSIC. The subspace spanned by this vector set is, in the sense of principal angle, closest to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanced accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors. The present computer simulations show, in EEG 3D dipole source localization, that compared to classic MUSIC, FINES has (1) better resolvability of two closely spaced dipolar sources and (2) better estimation accuracy of source locations. In comparison with RAP-MUSIC, FINES' performance is also better for the cases studied when the noise level is high and/or correlations among dipole sources exist.

  20. An alternative subspace approach to EEG dipole source localization

    International Nuclear Information System (INIS)

    Xu Xiaoliang; Xu, Bobby; He Bin

    2004-01-01

    In the present study, we investigate a new approach to electroencephalography (EEG) three-dimensional (3D) dipole source localization by using a non-recursive subspace algorithm called FINES. In estimating source dipole locations, the present approach employs projections onto a subspace spanned by a small set of particular vectors (FINES vector set) in the estimated noise-only subspace instead of the entire estimated noise-only subspace in the case of classic MUSIC. The subspace spanned by this vector set is, in the sense of principal angle, closest to the subspace spanned by the array manifold associated with a particular brain region. By incorporating knowledge of the array manifold in identifying FINES vector sets in the estimated noise-only subspace for different brain regions, the present approach is able to estimate sources with enhanced accuracy and spatial resolution, thus enhancing the capability of resolving closely spaced sources and reducing estimation errors. The present computer simulations show, in EEG 3D dipole source localization, that compared to classic MUSIC, FINES has (1) better resolvability of two closely spaced dipolar sources and (2) better estimation accuracy of source locations. In comparison with RAP-MUSIC, FINES' performance is also better for the cases studied when the noise level is high and/or correlations among dipole sources exist

  1. R3GMRES: including prior information in GMRES-type methods for discrete inverse problems

    DEFF Research Database (Denmark)

    Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian

    2014-01-01

    Lothar Reichel and his collaborators proposed several iterative algorithms that augment the underlying Krylov subspace with an additional low-dimensional subspace in order to produce improved regularized solutions. We take a closer look at this approach and investigate a particular Regularized Ra...

  2. Iterative Regularization with Minimum-Residual Methods

    DEFF Research Database (Denmark)

    Jensen, Toke Koldborg; Hansen, Per Christian

    2007-01-01

    subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES their success......We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov...... as regularization methods is highly problem dependent....

  3. Iterative regularization with minimum-residual methods

    DEFF Research Database (Denmark)

    Jensen, Toke Koldborg; Hansen, Per Christian

    2006-01-01

    subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES - their success......We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov...... as regularization methods is highly problem dependent....

  4. A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

    Science.gov (United States)

    Mang, Andreas; Biros, George

    2017-01-01

    We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

  5. Geometric mean for subspace selection.

    Science.gov (United States)

    Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J

    2009-02-01

    Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.

  6. Adiabatic evolution of decoherence-free subspaces and its shortcuts

    Science.gov (United States)

    Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.

    2017-10-01

    The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.

  7. INDOOR SUBSPACING TO IMPLEMENT INDOORGML FOR INDOOR NAVIGATION

    Directory of Open Access Journals (Sweden)

    H. Jung

    2015-10-01

    Full Text Available According to an increasing demand for indoor navigation, there are great attempts to develop applicable indoor network. Representation for a room as a node is not sufficient to apply complex and large buildings. As OGC established IndoorGML, subspacing to partition the space for constructing logical network is introduced. Concerning subspacing for indoor network, transition space like halls or corridors also have to be considered. This study presents the subspacing process for creating an indoor network in shopping mall. Furthermore, categorization of transition space is performed and subspacing of this space is considered. Hall and squares in mall is especially defined for subspacing. Finally, implementation of subspacing process for indoor network is presented.

  8. Indoor Subspacing to Implement Indoorgml for Indoor Navigation

    Science.gov (United States)

    Jung, H.; Lee, J.

    2015-10-01

    According to an increasing demand for indoor navigation, there are great attempts to develop applicable indoor network. Representation for a room as a node is not sufficient to apply complex and large buildings. As OGC established IndoorGML, subspacing to partition the space for constructing logical network is introduced. Concerning subspacing for indoor network, transition space like halls or corridors also have to be considered. This study presents the subspacing process for creating an indoor network in shopping mall. Furthermore, categorization of transition space is performed and subspacing of this space is considered. Hall and squares in mall is especially defined for subspacing. Finally, implementation of subspacing process for indoor network is presented.

  9. A generalized Schwinger boson mapping with a physical subspace

    International Nuclear Information System (INIS)

    Scholtz, F.G.; Geyer, H.B.

    1988-01-01

    We investigate the existence of a physical subspace for generalized Schwinger boson mappings of SO(2n+1) contains SO(2n) in view of previous observations by Marshalek and the recent construction of such a mapping and subspace for SO(8) by Kaup. It is shown that Kaup's construction can be attributed to the existence of a unique SO(8) automorphism. We proceed to construct a generalized Schwinger-type mapping for SO(2n+1) contains SO(2n) which, in contrast to a similar attempt by Yamamura and Nishiyama, indeed has a corresponding physical subspace. This new mapping includes in the special case of SO(8) the mapping by Kaup which is equivalent to the one given by Yamamura and Nishiyama for n=4. Nevertheless, we indicate the limitations of the generalized Schwinger mapping regarding its applicability to situations where one seeks to establish a direct link between phenomenological boson models and an underlying fermion microscopy. (orig.)

  10. On performance of Krylov smoothing for fully-coupled AMG preconditioners for VMS resistive MHD

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Paul T. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Shadid, John N. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States). Department of Mathematics and Statistics,; Tsuji, Paul H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2017-11-01

    Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered in an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.

  11. Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

    Science.gov (United States)

    Banerjee, Amartya S; Lin, Lin; Suryanarayana, Phanish; Yang, Chao; Pask, John E

    2018-06-12

    We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

  12. Controllable Subspaces of Open Quantum Dynamical Systems

    International Nuclear Information System (INIS)

    Zhang Ming; Gong Erling; Xie Hongwei; Hu Dewen; Dai Hongyi

    2008-01-01

    This paper discusses the concept of controllable subspace for open quantum dynamical systems. It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable. This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable. To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.

  13. Krylov subspace acceleration of waveform relaxation

    Energy Technology Data Exchange (ETDEWEB)

    Lumsdaine, A.; Wu, Deyun [Univ. of Notre Dame, IN (United States)

    1996-12-31

    Standard solution methods for numerically solving time-dependent problems typically begin by discretizing the problem on a uniform time grid and then sequentially solving for successive time points. The initial time discretization imposes a serialization to the solution process and limits parallel speedup to the speedup available from parallelizing the problem at any given time point. This bottleneck can be circumvented by the use of waveform methods in which multiple time-points of the different components of the solution are computed independently. With the waveform approach, a problem is first spatially decomposed and distributed among the processors of a parallel machine. Each processor then solves its own time-dependent subsystem over the entire interval of interest using previous iterates from other processors as inputs. Synchronization and communication between processors take place infrequently, and communication consists of large packets of information - discretized functions of time (i.e., waveforms).

  14. Consistency Analysis of Nearest Subspace Classifier

    OpenAIRE

    Wang, Yi

    2015-01-01

    The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized to new samples. It is proved that NSS is strongly consistent under certain assumptions. For completeness, NSS is evaluated through experiments on various simulated and real data sets, in comparison with some other linear model based classifiers. It is also ...

  15. Iterative solution of linear equations in ODE codes. [Krylov subspaces

    Energy Technology Data Exchange (ETDEWEB)

    Gear, C. W.; Saad, Y.

    1981-01-01

    Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

  16. Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

    Science.gov (United States)

    Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.

    1998-01-01

    Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

  17. A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

    International Nuclear Information System (INIS)

    Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.

    2015-01-01

    We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method

  18. A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

    Energy Technology Data Exchange (ETDEWEB)

    Bakhos, Tania, E-mail: taniab@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University (United States); Saibaba, Arvind K. [Department of Electrical and Computer Engineering, Tufts University (United States); Kitanidis, Peter K. [Institute for Computational and Mathematical Engineering, Stanford University (United States); Department of Civil and Environmental Engineering, Stanford University (United States)

    2015-10-15

    We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.

  19. PRIFIRA: General regularization using prior-conditioning for fast radio interferometric imaging†

    Science.gov (United States)

    Naghibzadeh, Shahrzad; van der Veen, Alle-Jan

    2018-06-01

    Image formation in radio astronomy is a large-scale inverse problem that is inherently ill-posed. We present a general algorithmic framework based on a Bayesian-inspired regularized maximum likelihood formulation of the radio astronomical imaging problem with a focus on diffuse emission recovery from limited noisy correlation data. The algorithm is dubbed PRIor-conditioned Fast Iterative Radio Astronomy (PRIFIRA) and is based on a direct embodiment of the regularization operator into the system by right preconditioning. The resulting system is then solved using an iterative method based on projections onto Krylov subspaces. We motivate the use of a beamformed image (which includes the classical "dirty image") as an efficient prior-conditioner. Iterative reweighting schemes generalize the algorithmic framework and can account for different regularization operators that encourage sparsity of the solution. The performance of the proposed method is evaluated based on simulated one- and two-dimensional array arrangements as well as actual data from the core stations of the Low Frequency Array radio telescope antenna configuration, and compared to state-of-the-art imaging techniques. We show the generality of the proposed method in terms of regularization schemes while maintaining a competitive reconstruction quality with the current reconstruction techniques. Furthermore, we show that exploiting Krylov subspace methods together with the proper noise-based stopping criteria results in a great improvement in imaging efficiency.

  20. Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures

    National Research Council Canada - National Science Library

    Grama, Ananth; Manguoglu, Murat; Koyuturk, Mehmet; Naumov, Maxim; Sameh, Ahmed

    2008-01-01

    .... The study was motivated primarily by the lack of robustness of Krylov subspace iterative schemes with generic, black-box, pre-conditioners such as approximate (or incomplete) LU-factorizations...

  1. External Evaluation Measures for Subspace Clustering

    DEFF Research Database (Denmark)

    Günnemann, Stephan; Färber, Ines; Müller, Emmanuel

    2011-01-01

    research area of subspace clustering. We formalize general quality criteria for subspace clustering measures not yet addressed in the literature. We compare the existing external evaluation methods based on these criteria and pinpoint limitations. We propose a novel external evaluation measure which meets...

  2. Subspace learning from image gradient orientations

    NARCIS (Netherlands)

    Tzimiropoulos, Georgios; Zafeiriou, Stefanos; Pantic, Maja

    2012-01-01

    We introduce the notion of subspace learning from image gradient orientations for appearance-based object recognition. As image data is typically noisy and noise is substantially different from Gaussian, traditional subspace learning from pixel intensities fails very often to estimate reliably the

  3. Subspace Based Blind Sparse Channel Estimation

    DEFF Research Database (Denmark)

    Hayashi, Kazunori; Matsushima, Hiroki; Sakai, Hideaki

    2012-01-01

    The paper proposes a subspace based blind sparse channel estimation method using 1–2 optimization by replacing the 2–norm minimization in the conventional subspace based method by the 1–norm minimization problem. Numerical results confirm that the proposed method can significantly improve...

  4. Subspace exclusion zones for damage localization

    DEFF Research Database (Denmark)

    Bernal, Dionisio; Ulriksen, Martin Dalgaard

    2018-01-01

    , this is exploited in the context of structural damage localization to cast the Subspace Exclusion Zone (SEZ) scheme, which locates damage by reconstructing the captured field quantity shifts from analytical subspaces indexed by postulated boundaries, the so-called exclusion zones (EZs), in a model of the structure...

  5. Subspace methods for pattern recognition in intelligent environment

    CERN Document Server

    Jain, Lakhmi

    2014-01-01

    This research book provides a comprehensive overview of the state-of-the-art subspace learning methods for pattern recognition in intelligent environment. With the fast development of internet and computer technologies, the amount of available data is rapidly increasing in our daily life. How to extract core information or useful features is an important issue. Subspace methods are widely used for dimension reduction and feature extraction in pattern recognition. They transform a high-dimensional data to a lower-dimensional space (subspace), where most information is retained. The book covers a broad spectrum of subspace methods including linear, nonlinear and multilinear subspace learning methods and applications. The applications include face alignment, face recognition, medical image analysis, remote sensing image classification, traffic sign recognition, image clustering, super resolution, edge detection, multi-view facial image synthesis.

  6. Pushing Memory Bandwidth Limitations Through Efficient Implementations of Block-Krylov Space Solvers on GPUs

    Energy Technology Data Exchange (ETDEWEB)

    Clark, M. A. [NVIDIA Corp., Santa Clara; Strelchenko, Alexei [Fermilab; Vaquero, Alejandro [Utah U.; Wagner, Mathias [NVIDIA Corp., Santa Clara; Weinberg, Evan [Boston U.

    2017-10-26

    Lattice quantum chromodynamics simulations in nuclear physics have benefited from a tremendous number of algorithmic advances such as multigrid and eigenvector deflation. These improve the time to solution but do not alleviate the intrinsic memory-bandwidth constraints of the matrix-vector operation dominating iterative solvers. Batching this operation for multiple vectors and exploiting cache and register blocking can yield a super-linear speed up. Block-Krylov solvers can naturally take advantage of such batched matrix-vector operations, further reducing the iterations to solution by sharing the Krylov space between solves. However, practical implementations typically suffer from the quadratic scaling in the number of vector-vector operations. Using the QUDA library, we present an implementation of a block-CG solver on NVIDIA GPUs which reduces the memory-bandwidth complexity of vector-vector operations from quadratic to linear. We present results for the HISQ discretization, showing a 5x speedup compared to highly-optimized independent Krylov solves on NVIDIA's SaturnV cluster.

  7. On Covering Approximation Subspaces

    Directory of Open Access Journals (Sweden)

    Xun Ge

    2009-06-01

    Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.

  8. On the dimension of subspaces with bounded Schmidt rank

    International Nuclear Information System (INIS)

    Cubitt, Toby; Montanaro, Ashley; Winter, Andreas

    2008-01-01

    We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al. [e-print arXiv:quant-ph/0407049; Commun. Math. Phys., 265, 95 (2006)], which show that in large dxd-dimensional systems there exist random subspaces of dimension almost d 2 , all of whose states have entropy of entanglement at least log d-O(1). It is also a generalization of results on the dimension of completely entangled subspaces, which have connections with the construction of unextendible product bases. Here we take as entanglement measure the Schmidt rank, and determine, for every pair of local dimensions d A and d B , and every r, the largest dimension of a subspace consisting only of entangled states of Schmidt rank r or larger. This exact answer is a significant improvement on the best bounds that can be obtained using the random subspace techniques in Hayden et al. We also determine the converse: the largest dimension of a subspace with an upper bound on the Schmidt rank. Finally, we discuss the question of subspaces containing only states with Schmidt equal to r

  9. Subspace-based Inverse Uncertainty Quantification for Nuclear Data Assessment

    Energy Technology Data Exchange (ETDEWEB)

    Khuwaileh, B.A., E-mail: bakhuwai@ncsu.edu; Abdel-Khalik, H.S.

    2015-01-15

    Safety analysis and design optimization depend on the accurate prediction of various reactor attributes. Predictions can be enhanced by reducing the uncertainty associated with the attributes of interest. An inverse problem can be defined and solved to assess the sources of uncertainty, and experimental effort can be subsequently directed to further improve the uncertainty associated with these sources. In this work a subspace-based algorithm for inverse sensitivity/uncertainty quantification (IS/UQ) has been developed to enable analysts account for all sources of nuclear data uncertainties in support of target accuracy assessment-type analysis. An approximate analytical solution of the optimization problem is used to guide the search for the dominant uncertainty subspace. By limiting the search to a subspace, the degrees of freedom available for the optimization search are significantly reduced. A quarter PWR fuel assembly is modeled and the accuracy of the multiplication factor and the fission reaction rate are used as reactor attributes whose uncertainties are to be reduced. Numerical experiments are used to demonstrate the computational efficiency of the proposed algorithm. Our ongoing work is focusing on extending the proposed algorithm to account for various forms of feedback, e.g., thermal-hydraulics and depletion effects.

  10. A Rank-Constrained Matrix Representation for Hypergraph-Based Subspace Clustering

    Directory of Open Access Journals (Sweden)

    Yubao Sun

    2015-01-01

    Full Text Available This paper presents a novel, rank-constrained matrix representation combined with hypergraph spectral analysis to enable the recovery of the original subspace structures of corrupted data. Real-world data are frequently corrupted with both sparse error and noise. Our matrix decomposition model separates the low-rank, sparse error, and noise components from the data in order to enhance robustness to the corruption. In order to obtain the desired rank representation of the data within a dictionary, our model directly utilizes rank constraints by restricting the upper bound of the rank range. An alternative projection algorithm is proposed to estimate the low-rank representation and separate the sparse error from the data matrix. To further capture the complex relationship between data distributed in multiple subspaces, we use hypergraph to represent the data by encapsulating multiple related samples into one hyperedge. The final clustering result is obtained by spectral decomposition of the hypergraph Laplacian matrix. Validation experiments on the Extended Yale Face Database B, AR, and Hopkins 155 datasets show that the proposed method is a promising tool for subspace clustering.

  11. A multigrid Newton-Krylov method for flux-limited radiation diffusion

    International Nuclear Information System (INIS)

    Rider, W.J.; Knoll, D.A.; Olson, G.L.

    1998-01-01

    The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques

  12. Subspace Barzilai-Borwein Gradient Method for Large-Scale Bound Constrained Optimization

    International Nuclear Information System (INIS)

    Xiao Yunhai; Hu Qingjie

    2008-01-01

    An active set subspace Barzilai-Borwein gradient algorithm for large-scale bound constrained optimization is proposed. The active sets are estimated by an identification technique. The search direction consists of two parts: some of the components are simply defined; the other components are determined by the Barzilai-Borwein gradient method. In this work, a nonmonotone line search strategy that guarantees global convergence is used. Preliminary numerical results show that the proposed method is promising, and competitive with the well-known method SPG on a subset of bound constrained problems from CUTEr collection

  13. Kernel based subspace projection of hyperspectral images

    DEFF Research Database (Denmark)

    Larsen, Rasmus; Nielsen, Allan Aasbjerg; Arngren, Morten

    In hyperspectral image analysis an exploratory approach to analyse the image data is to conduct subspace projections. As linear projections often fail to capture the underlying structure of the data, we present kernel based subspace projections of PCA and Maximum Autocorrelation Factors (MAF...

  14. Sinusoidal Order Estimation Using Angles between Subspaces

    Directory of Open Access Journals (Sweden)

    Søren Holdt Jensen

    2009-01-01

    Full Text Available We consider the problem of determining the order of a parametric model from a noisy signal based on the geometry of the space. More specifically, we do this using the nontrivial angles between the candidate signal subspace model and the noise subspace. The proposed principle is closely related to the subspace orthogonality property known from the MUSIC algorithm, and we study its properties and compare it to other related measures. For the problem of estimating the number of complex sinusoids in white noise, a computationally efficient implementation exists, and this problem is therefore considered in detail. In computer simulations, we compare the proposed method to various well-known methods for order estimation. These show that the proposed method outperforms the other previously published subspace methods and that it is more robust to the noise being colored than the previously published methods.

  15. Subspace-based interference removal methods for a multichannel biomagnetic sensor array

    Science.gov (United States)

    Sekihara, Kensuke; Nagarajan, Srikantan S.

    2017-10-01

    Objective. In biomagnetic signal processing, the theory of the signal subspace has been applied to removing interfering magnetic fields, and a representative algorithm is the signal space projection algorithm, in which the signal/interference subspace is defined in the spatial domain as the span of signal/interference-source lead field vectors. This paper extends the notion of this conventional (spatial domain) signal subspace by introducing a new definition of signal subspace in the time domain. Approach. It defines the time-domain signal subspace as the span of row vectors that contain the source time course values. This definition leads to symmetric relationships between the time-domain and the conventional (spatial-domain) signal subspaces. As a review, this article shows that the notion of the time-domain signal subspace provides useful insights over existing interference removal methods from a unified perspective. Main results and significance. Using the time-domain signal subspace, it is possible to interpret a number of interference removal methods as the time domain signal space projection. Such methods include adaptive noise canceling, sensor noise suppression, the common temporal subspace projection, the spatio-temporal signal space separation, and the recently-proposed dual signal subspace projection. Our analysis using the notion of the time domain signal space projection reveals implicit assumptions these methods rely on, and shows that the difference between these methods results only from the manner of deriving the interference subspace. Numerical examples that illustrate the results of our arguments are provided.

  16. Different structures on subspaces of OsckM

    Directory of Open Access Journals (Sweden)

    Čomić Irena

    2013-01-01

    Full Text Available The geometry of OsckM spaces was introduced by R. Miron and Gh. Atanasiu in [6] and [7]. The theory of these spaces was developed by R. Miron and his cooperators from Romania, Japan and other countries in several books and many papers. Only some of them are mentioned in references. Here we recall the construction of adapted bases in T(OsckM and T*(OsckM, which are comprehensive with the J structure. The theory of two complementary family of subspaces is presented as it was done in [2] and [4]. The operators J,J, θ,θ, p, p* are introduced in the ambient space and subspaces. Some new relations between them are established. The action of these operators on Liouville vector fields are examined.

  17. Bio-inspired varying subspace based computational framework for a class of nonlinear constrained optimal trajectory planning problems.

    Science.gov (United States)

    Xu, Y; Li, N

    2014-09-01

    Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator-prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework.

  18. Bio-inspired varying subspace based computational framework for a class of nonlinear constrained optimal trajectory planning problems

    International Nuclear Information System (INIS)

    Xu, Y; Li, N

    2014-01-01

    Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator–prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework. (paper)

  19. Shape analysis with subspace symmetries

    KAUST Repository

    Berner, Alexander

    2011-04-01

    We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising. © 2010 The Author(s).

  20. Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation

    OpenAIRE

    Bi, Qiao; Guo, Liu; Ruda, H. E.

    2010-01-01

    A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the subspaces are just projected states which are ruled by a subdynamic kinetic equation. These projected states can be used to perform ideal quantum logical operations without decoherence.

  1. Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation

    Directory of Open Access Journals (Sweden)

    Qiao Bi

    2010-01-01

    Full Text Available A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the subspaces are just projected states which are ruled by a subdynamic kinetic equation. These projected states can be used to perform ideal quantum logical operations without decoherence.

  2. Lyapunov vectors and assimilation in the unstable subspace: theory and applications

    International Nuclear Information System (INIS)

    Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna

    2013-01-01

    Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

  3. Krylov iterative methods and synthetic acceleration for transport in binary statistical media

    International Nuclear Information System (INIS)

    Fichtl, Erin D.; Warsa, James S.; Prinja, Anil K.

    2009-01-01

    In particle transport applications there are numerous physical constructs in which heterogeneities are randomly distributed. The quantity of interest in these problems is the ensemble average of the flux, or the average of the flux over all possible material 'realizations.' The Levermore-Pomraning closure assumes Markovian mixing statistics and allows a closed, coupled system of equations to be written for the ensemble averages of the flux in each material. Generally, binary statistical mixtures are considered in which there are two (homogeneous) materials and corresponding coupled equations. The solution process is iterative, but convergence may be slow as either or both materials approach the diffusion and/or atomic mix limits. A three-part acceleration scheme is devised to expedite convergence, particularly in the atomic mix-diffusion limit where computation is extremely slow. The iteration is first divided into a series of 'inner' material and source iterations to attenuate the diffusion and atomic mix error modes separately. Secondly, atomic mix synthetic acceleration is applied to the inner material iteration and S 2 synthetic acceleration to the inner source iterations to offset the cost of doing several inner iterations per outer iteration. Finally, a Krylov iterative solver is wrapped around each iteration, inner and outer, to further expedite convergence. A spectral analysis is conducted and iteration counts and computing cost for the new two-step scheme are compared against those for a simple one-step iteration, to which a Krylov iterative method can also be applied.

  4. Enhancing Low-Rank Subspace Clustering by Manifold Regularization.

    Science.gov (United States)

    Liu, Junmin; Chen, Yijun; Zhang, JiangShe; Xu, Zongben

    2014-07-25

    Recently, low-rank representation (LRR) method has achieved great success in subspace clustering (SC), which aims to cluster the data points that lie in a union of low-dimensional subspace. Given a set of data points, LRR seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself. However, LRR only considers the global Euclidean structure, while the local manifold structure, which is often important for many real applications, is ignored. In this paper, to exploit the local manifold structure of the data, a manifold regularization characterized by a Laplacian graph has been incorporated into LRR, leading to our proposed Laplacian regularized LRR (LapLRR). An efficient optimization procedure, which is based on alternating direction method of multipliers (ADMM), is developed for LapLRR. Experimental results on synthetic and real data sets are presented to demonstrate that the performance of LRR has been enhanced by using the manifold regularization.

  5. Experimental fault-tolerant quantum cryptography in a decoherence-free subspace

    International Nuclear Information System (INIS)

    Zhang Qiang; Pan Jianwei; Yin Juan; Chen Tengyun; Lu Shan; Zhang Jun; Li Xiaoqiang; Yang Tao; Wang Xiangbin

    2006-01-01

    We experimentally implement a fault-tolerant quantum key distribution protocol with two photons in a decoherence-free subspace [Phys. Rev. A 72, 050304(R) (2005)]. It is demonstrated that our protocol can yield a good key rate even with a large bit-flip error rate caused by collective rotation, while the usual realization of the Bennett-Brassard 1984 protocol cannot produce any secure final key given the same channel. Since the experiment is performed in polarization space and does not need the calibration of a reference frame, important applications in free-space quantum communication are expected. Moreover, our method can also be used to robustly transmit an arbitrary two-level quantum state in a type of decoherence-free subspace

  6. Preconditioned Krylov and Gauss-Seidel solutions of response matrix equations

    International Nuclear Information System (INIS)

    Lewis, E.E.; Smith, M.A.; Yang, W.S.; Wollaber, A.

    2011-01-01

    The use of preconditioned Krylov methods is examined as an alternative to the partitioned matrix acceleration applied to red-black Gauss Seidel (RBGS) iteration that is presently used in the variational nodal code, VARIANT. We employ the GMRES algorithm to treat non-symmetric response matrix equations. A pre conditioner is formulated for the within-group diffusion equation which is equivalent to partitioned matrix acceleration of RBGS iterations. We employ the pre conditioner, which closely parallels two-level p multigrid, to improve RBGS and GMRES algorithms. Of the accelerated algorithms, GMRES converges with less computational effort than RBGS and therefore is chosen for further development. The p multigrid pre conditioner requires response matrices with two or more degrees of freedom (DOF) per interface that are polynomials, which are both orthogonal and hierarchical. It is therefore not directly applicable to very fine mesh calculations that are both slow to converge and that are often modeled with response matrices with only one DOF per interface. Orthogonal matrix aggregation (OMA) is introduced to circumvent this difficulty by combining N×N fine mesh response matrices with one DOF per interface into a coarse mesh response matrix with N orthogonal DOF per interface. Numerical results show that OMA used alone or in combination with p multigrid preconditioning substantially accelerates GMRES solutions. (author)

  7. Preconditioned Krylov and Gauss-Seidel solutions of response matrix equations

    Energy Technology Data Exchange (ETDEWEB)

    Lewis, E.E., E-mail: e-lewis@northwestern.edu [Department of Mechanical Engineering, Northwestern University, Evanston, IL (United States); Smith, M.A.; Yang, W.S.; Wollaber, A., E-mail: masmith@anl.gov, E-mail: wsyang@anl.gov, E-mail: wollaber@lanl.gov [Nuclear Engineering Division, Argonne National Laboratory, Argonne, IL (United States)

    2011-07-01

    The use of preconditioned Krylov methods is examined as an alternative to the partitioned matrix acceleration applied to red-black Gauss Seidel (RBGS) iteration that is presently used in the variational nodal code, VARIANT. We employ the GMRES algorithm to treat non-symmetric response matrix equations. A pre conditioner is formulated for the within-group diffusion equation which is equivalent to partitioned matrix acceleration of RBGS iterations. We employ the pre conditioner, which closely parallels two-level p multigrid, to improve RBGS and GMRES algorithms. Of the accelerated algorithms, GMRES converges with less computational effort than RBGS and therefore is chosen for further development. The p multigrid pre conditioner requires response matrices with two or more degrees of freedom (DOF) per interface that are polynomials, which are both orthogonal and hierarchical. It is therefore not directly applicable to very fine mesh calculations that are both slow to converge and that are often modeled with response matrices with only one DOF per interface. Orthogonal matrix aggregation (OMA) is introduced to circumvent this difficulty by combining N×N fine mesh response matrices with one DOF per interface into a coarse mesh response matrix with N orthogonal DOF per interface. Numerical results show that OMA used alone or in combination with p multigrid preconditioning substantially accelerates GMRES solutions. (author)

  8. Subspace methods for identification of human ankle joint stiffness.

    Science.gov (United States)

    Zhao, Y; Westwick, D T; Kearney, R E

    2011-11-01

    Joint stiffness, the dynamic relationship between the angular position of a joint and the torque acting about it, describes the dynamic, mechanical behavior of a joint during posture and movement. Joint stiffness arises from both intrinsic and reflex mechanisms, but the torques due to these mechanisms cannot be measured separately experimentally, since they appear and change together. Therefore, the direct estimation of the intrinsic and reflex stiffnesses is difficult. In this paper, we present a new, two-step procedure to estimate the intrinsic and reflex components of ankle stiffness. In the first step, a discrete-time, subspace-based method is used to estimate a state-space model for overall stiffness from the measured overall torque and then predict the intrinsic and reflex torques. In the second step, continuous-time models for the intrinsic and reflex stiffnesses are estimated from the predicted intrinsic and reflex torques. Simulations and experimental results demonstrate that the algorithm estimates the intrinsic and reflex stiffnesses accurately. The new subspace-based algorithm has three advantages over previous algorithms: 1) It does not require iteration, and therefore, will always converge to an optimal solution; 2) it provides better estimates for data with high noise or short sample lengths; and 3) it provides much more accurate results for data acquired under the closed-loop conditions, that prevail when subjects interact with compliant loads.

  9. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

    1996-12-31

    A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

  10. LogDet Rank Minimization with Application to Subspace Clustering

    Directory of Open Access Journals (Sweden)

    Zhao Kang

    2015-01-01

    Full Text Available Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose using a log-determinant (LogDet function as a smooth and closer, though nonconvex, approximation to rank for obtaining a low-rank representation in subspace clustering. Augmented Lagrange multipliers strategy is applied to iteratively optimize the LogDet-based nonconvex objective function on potentially large-scale data. By making use of the angular information of principal directions of the resultant low-rank representation, an affinity graph matrix is constructed for spectral clustering. Experimental results on motion segmentation and face clustering data demonstrate that the proposed method often outperforms state-of-the-art subspace clustering algorithms.

  11. Data-driven modeling and predictive control for boiler-turbine unit using fuzzy clustering and subspace methods.

    Science.gov (United States)

    Wu, Xiao; Shen, Jiong; Li, Yiguo; Lee, Kwang Y

    2014-05-01

    This paper develops a novel data-driven fuzzy modeling strategy and predictive controller for boiler-turbine unit using fuzzy clustering and subspace identification (SID) methods. To deal with the nonlinear behavior of boiler-turbine unit, fuzzy clustering is used to provide an appropriate division of the operation region and develop the structure of the fuzzy model. Then by combining the input data with the corresponding fuzzy membership functions, the SID method is extended to extract the local state-space model parameters. Owing to the advantages of the both methods, the resulting fuzzy model can represent the boiler-turbine unit very closely, and a fuzzy model predictive controller is designed based on this model. As an alternative approach, a direct data-driven fuzzy predictive control is also developed following the same clustering and subspace methods, where intermediate subspace matrices developed during the identification procedure are utilized directly as the predictor. Simulation results show the advantages and effectiveness of the proposed approach. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities

    International Nuclear Information System (INIS)

    Warsa, James S.; Wareing, Todd A.; Morel, Jim E.

    2004-01-01

    A loss in the effectiveness of diffusion synthetic acceleration (DSA) schemes has been observed with certain S N discretizations on two-dimensional Cartesian grids in the presence of material discontinuities. We will present more evidence supporting the conjecture that DSA effectiveness will degrade for multidimensional problems with discontinuous total cross sections, regardless of the particular physical configuration or spatial discretization. Fourier analysis and numerical experiments help us identify a set of representative problems for which established DSA schemes are ineffective, focusing on diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the S N transport equation on three-dimensional, unstructured tetrahedral meshes and look at a fully consistent and a 'partially consistent' DSA method for this discretization. The effectiveness of both methods is shown to degrade significantly. A Fourier analysis of the fully consistent DSA scheme in the limit of decreasing cell optical thickness supports the view that the DSA itself is failing when material discontinuities are present in a problem. We show that a Krylov iterative method, preconditioned with DSA, is an effective remedy that can be used to efficiently compute solutions for this class of problems. We show that as a preconditioner to the Krylov method, a partially consistent DSA method is more than adequate. In fact, it is preferable to a fully consistent method because the partially consistent method is based on a continuous finite element discretization of the diffusion equation that can be solved relatively easily. The Krylov method can be implemented in terms of the original S N source iteration coding with only slight modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration

  13. Narrowband direction of arrival estimation for antenna arrays

    CERN Document Server

    Foutz, Jeffrey

    2008-01-01

    This book provides an introduction to narrowband array signal processing, classical and subspace-based direction of arrival (DOA) estimation with an extensive discussion on adaptive direction of arrival algorithms. The book begins with a presentation of the basic theory, equations, and data models of narrowband arrays. It then discusses basic beamforming methods and describes how they relate to DOA estimation. Several of the most common classical and subspace-based direction of arrival methods are discussed. The book concludes with an introduction to subspace tracking and shows how subspace tr

  14. Monomial codes seen as invariant subspaces

    Directory of Open Access Journals (Sweden)

    García-Planas María Isabel

    2017-08-01

    Full Text Available It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field and hyperinvariant subspaces of n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible to deduce certain properties for this particular type of codes, generalizing known results on cyclic codes.

  15. Subspace-Based Holistic Registration for Low-Resolution Facial Images

    Directory of Open Access Journals (Sweden)

    Boom BJ

    2010-01-01

    Full Text Available Subspace-based holistic registration is introduced as an alternative to landmark-based face registration, which has a poor performance on low-resolution images, as obtained in camera surveillance applications. The proposed registration method finds the alignment by maximizing the similarity score between a probe and a gallery image. We use a novel probabilistic framework for both user-independent as well as user-specific face registration. The similarity is calculated using the probability that the face image is correctly aligned in a face subspace, but additionally we take the probability into account that the face is misaligned based on the residual error in the dimensions perpendicular to the face subspace. We perform extensive experiments on the FRGCv2 database to evaluate the impact that the face registration methods have on face recognition. Subspace-based holistic registration on low-resolution images can improve face recognition in comparison with landmark-based registration on high-resolution images. The performance of the tested face recognition methods after subspace-based holistic registration on a low-resolution version of the FRGC database is similar to that after manual registration.

  16. On the maximal dimension of a completely entangled subspace for ...

    Indian Academy of Sciences (India)

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

    dim S = d1d2 ...dk − (d1 +···+ dk) + k − 1, where E is the collection of all completely entangled subspaces. When H1 = H2 and k = 2 an explicit orthonormal basis of a maximal completely entangled subspace of H1 ⊗ H2 is given. We also introduce a more delicate notion of a perfectly entangled subspace for a multipartite ...

  17. Combining the CORS and BiCORSTAB Iterative Methods with MLFMA and SAI Preconditioning for Solving Large Linear Systems in Electromagnetics

    NARCIS (Netherlands)

    Carpentieri, Bruno; Jing, Yan-Fei; Huang, Ting-Zhu; Pi, Wei-Chao; Sheng, Xin-Qing

    We report on experiments with a novel family of Krylov subspace methods for solving dense, complex, non-Hermitian systems of linear equations arising from the Galerkin discretization of surface integral equation models in Electromagnetics. By some experiments on realistic radar-cross-section

  18. Preconditioning for Allen–Cahn variational inequalities with non-local constraints

    KAUST Repository

    Blank, Luise; Sarbu, Lavinia; Stoll, Martin

    2012-01-01

    -dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate

  19. Domain Decomposition for Computing Extremely Low Frequency Induced Current in the Human Body

    OpenAIRE

    Perrussel , Ronan; Voyer , Damien; Nicolas , Laurent; Scorretti , Riccardo; Burais , Noël

    2011-01-01

    International audience; Computation of electromagnetic fields in high resolution computational phantoms requires solving large linear systems. We present an application of Schwarz preconditioners with Krylov subspace methods for computing extremely low frequency induced fields in a phantom issued from the Visible Human.

  20. Seismic noise attenuation using an online subspace tracking algorithm

    NARCIS (Netherlands)

    Zhou, Yatong; Li, Shuhua; Zhang, D.; Chen, Yangkang

    2018-01-01

    We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient

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

    Directory of Open Access Journals (Sweden)

    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.

  2. Direct lifts of coupled cell networks

    Science.gov (United States)

    Dias, A. P. S.; Moreira, C. S.

    2018-04-01

    In networks of dynamical systems, there are spaces defined in terms of equalities of cell coordinates which are flow-invariant under any dynamical system that has a form consistent with the given underlying network structure—the network synchrony subspaces. Given a network and one of its synchrony subspaces, any system with a form consistent with the network, restricted to the synchrony subspace, defines a new system which is consistent with a smaller network, called the quotient network of the original network by the synchrony subspace. Moreover, any system associated with the quotient can be interpreted as the restriction to the synchrony subspace of a system associated with the original network. We call the larger network a lift of the smaller network, and a lift can be interpreted as a result of the cellular splitting of the smaller network. In this paper, we address the question of the uniqueness in this lifting process in terms of the networks’ topologies. A lift G of a given network Q is said to be direct when there are no intermediate lifts of Q between them. We provide necessary and sufficient conditions for a lift of a general network to be direct. Our results characterize direct lifts using the subnetworks of all splitting cells of Q and of all split cells of G. We show that G is a direct lift of Q if and only if either the split subnetwork is a direct lift or consists of two copies of the splitting subnetwork. These results are then applied to the class of regular uniform networks and to the special classes of ring networks and acyclic networks. We also illustrate that one of the applications of our results is to the lifting bifurcation problem.

  3. Semitransitive subspaces of operators

    Czech Academy of Sciences Publication Activity Database

    Bernik, J.; Drnovšek, R.; Hadwin, D.; Jafarian, A.; Bukovšek, D.K.; Košir, T.; Fijavž, M.K.; Laffey, T.; Livshits, L.; Mastnak, M.; Meshulam, R.; Müller, Vladimír; Nordgren, E.; Okniński, J.; Omladič, M.; Radjavi, H.; Sourour, A.; Timoney, R.

    2006-01-01

    Roč. 15, č. 1 (2006), s. 225-238 E-ISSN 1081-3810 Institutional research plan: CEZ:AV0Z10190503 Keywords : semitransitive subspaces Subject RIV: BA - General Mathematics Impact factor: 0.322, year: 2006 http://www.math.technion.ac.il/iic/ ela

  4. Anomaly General Circulation Models.

    Science.gov (United States)

    Navarra, Antonio

    The feasibility of the anomaly model is assessed using barotropic and baroclinic models. In the barotropic case, both a stationary and a time-dependent model has been formulated and constructed, whereas only the stationary, linear case is considered in the baroclinic case. Results from the barotropic model indicate that a relation between the stationary solution and the time-averaged non-linear solution exists. The stationary linear baroclinic solution can therefore be considered with some confidence. The linear baroclinic anomaly model poses a formidable mathematical problem because it is necessary to solve a gigantic linear system to obtain the solution. A new method to find solution of large linear system, based on a projection on the Krylov subspace is shown to be successful when applied to the linearized baroclinic anomaly model. The scheme consists of projecting the original linear system on the Krylov subspace, thereby reducing the dimensionality of the matrix to be inverted to obtain the solution. With an appropriate setting of the damping parameters, the iterative Krylov method reaches a solution even using a Krylov subspace ten times smaller than the original space of the problem. This generality allows the treatment of the important problem of linear waves in the atmosphere. A larger class (nonzonally symmetric) of basic states can now be treated for the baroclinic primitive equations. These problem leads to large unsymmetrical linear systems of order 10000 and more which can now be successfully tackled by the Krylov method. The (R7) linear anomaly model is used to investigate extensively the linear response to equatorial and mid-latitude prescribed heating. The results indicate that the solution is deeply affected by the presence of the stationary waves in the basic state. The instability of the asymmetric flows, first pointed out by Simmons et al. (1983), is active also in the baroclinic case. However, the presence of baroclinic processes modifies the

  5. Adaptive Detectors for Two Types of Subspace Targets in an Inverse Gamma Textured Background

    Directory of Open Access Journals (Sweden)

    Ding Hao

    2017-06-01

    Full Text Available Considering an inverse Gamma prior distribution model for texture, the adaptive detection problems for both first order Gaussian and second order Gaussian subspace targets are researched in a compound Gaussian sea clutter. Test statistics are derived on the basis of the two-step generalized likelihood ratio test. From these tests, new adaptive detectors are proposed by substituting the covariance matrix with estimation results from the Sample Covariance Matrix (SCM, normalized SCM, and fixed point estimator. The proposed detectors consider the prior distribution model for sea clutter during the design stage, and they model parameters that match the working environment during the detection stage. Analysis and validation results indicate that the detection performance of the proposed detectors out performs existing AMF (Adaptive Matched Filter, AMF and ANMF (Adaptive Normalized Matched Filter, ANMF detectors.

  6. High resolution through-the-wall radar image based on beamspace eigenstructure subspace methods

    Science.gov (United States)

    Yoon, Yeo-Sun; Amin, Moeness G.

    2008-04-01

    Through-the-wall imaging (TWI) is a challenging problem, even if the wall parameters and characteristics are known to the system operator. Proper target classification and correct imaging interpretation require the application of high resolution techniques using limited array size. In inverse synthetic aperture radar (ISAR), signal subspace methods such as Multiple Signal Classification (MUSIC) are used to obtain high resolution imaging. In this paper, we adopt signal subspace methods and apply them to the 2-D spectrum obtained from the delay-andsum beamforming image. This is in contrast to ISAR, where raw data, in frequency and angle, is directly used to form the estimate of the covariance matrix and array response vector. Using beams rather than raw data has two main advantages, namely, it improves the signal-to-noise ratio (SNR) and can correctly image typical indoor extended targets, such as tables and cabinets, as well as point targets. The paper presents both simulated and experimental results using synthesized and real data. It compares the performance of beam-space MUSIC and Capon beamformer. The experimental data is collected at the test facility in the Radar Imaging Laboratory, Villanova University.

  7. A Kronecker product splitting preconditioner for two-dimensional space-fractional diffusion equations

    Science.gov (United States)

    Chen, Hao; Lv, Wen; Zhang, Tongtong

    2018-05-01

    We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.

  8. Domain decomposition methods and deflated Krylov subspace iterations

    NARCIS (Netherlands)

    Nabben, R.; Vuik, C.

    2006-01-01

    The balancing Neumann-Neumann (BNN) and the additive coarse grid correction (BPS) preconditioner are fast and successful preconditioners within domain decomposition methods for solving partial differential equations. For certain elliptic problems these preconditioners lead to condition numbers which

  9. Random matrix improved subspace clustering

    KAUST Repository

    Couillet, Romain; Kammoun, Abla

    2017-01-01

    This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show

  10. Persymmetric Adaptive Detectors of Subspace Signals in Homogeneous and Partially Homogeneous Clutter

    Directory of Open Access Journals (Sweden)

    Ding Hao

    2015-08-01

    Full Text Available In the field of adaptive radar detection, an effective strategy to improve the detection performance is to exploit the structural information of the covariance matrix, especially in the case of insufficient reference cells. Thus, in this study, the problem of detecting multidimensional subspace signals is discussed by considering the persymmetric structure of the clutter covariance matrix, which implies that the covariance matrix is persymmetric about its cross diagonal. Persymmetric adaptive detectors are derived on the basis of the one-step principle as well as the two-step Generalized Likelihood Ratio Test (GLRT in homogeneous and partially homogeneous clutter. The proposed detectors consider the structural information of the covariance matrix at the design stage. Simulation results suggest performance improvement compared with existing detectors when reference cells are insufficient. Moreover, the detection performance is assessed with respect to the effects of the covariance matrix, signal subspace dimension, and mismatched performance of signal subspace as well as signal fluctuations.

  11. A subspace approach to high-resolution spectroscopic imaging.

    Science.gov (United States)

    Lam, Fan; Liang, Zhi-Pei

    2014-04-01

    To accelerate spectroscopic imaging using sparse sampling of (k,t)-space and subspace (or low-rank) modeling to enable high-resolution metabolic imaging with good signal-to-noise ratio. The proposed method, called SPectroscopic Imaging by exploiting spatiospectral CorrElation, exploits a unique property known as partial separability of spectroscopic signals. This property indicates that high-dimensional spectroscopic signals reside in a very low-dimensional subspace and enables special data acquisition and image reconstruction strategies to be used to obtain high-resolution spatiospectral distributions with good signal-to-noise ratio. More specifically, a hybrid chemical shift imaging/echo-planar spectroscopic imaging pulse sequence is proposed for sparse sampling of (k,t)-space, and a low-rank model-based algorithm is proposed for subspace estimation and image reconstruction from sparse data with the capability to incorporate prior information and field inhomogeneity correction. The performance of the proposed method has been evaluated using both computer simulations and phantom studies, which produced very encouraging results. For two-dimensional spectroscopic imaging experiments on a metabolite phantom, a factor of 10 acceleration was achieved with a minimal loss in signal-to-noise ratio compared to the long chemical shift imaging experiments and with a significant gain in signal-to-noise ratio compared to the accelerated echo-planar spectroscopic imaging experiments. The proposed method, SPectroscopic Imaging by exploiting spatiospectral CorrElation, is able to significantly accelerate spectroscopic imaging experiments, making high-resolution metabolic imaging possible. Copyright © 2014 Wiley Periodicals, Inc.

  12. Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations

    NARCIS (Netherlands)

    Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der

    Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general

  13. Subspace K-means clustering

    NARCIS (Netherlands)

    Timmerman, Marieke E.; Ceulemans, Eva; De Roover, Kim; Van Leeuwen, Karla

    2013-01-01

    To achieve an insightful clustering of multivariate data, we propose subspace K-means. Its central idea is to model the centroids and cluster residuals in reduced spaces, which allows for dealing with a wide range of cluster types and yields rich interpretations of the clusters. We review the

  14. Conjunctive patches subspace learning with side information for collaborative image retrieval.

    Science.gov (United States)

    Zhang, Lining; Wang, Lipo; Lin, Weisi

    2012-08-01

    Content-Based Image Retrieval (CBIR) has attracted substantial attention during the past few years for its potential practical applications to image management. A variety of Relevance Feedback (RF) schemes have been designed to bridge the semantic gap between the low-level visual features and the high-level semantic concepts for an image retrieval task. Various Collaborative Image Retrieval (CIR) schemes aim to utilize the user historical feedback log data with similar and dissimilar pairwise constraints to improve the performance of a CBIR system. However, existing subspace learning approaches with explicit label information cannot be applied for a CIR task, although the subspace learning techniques play a key role in various computer vision tasks, e.g., face recognition and image classification. In this paper, we propose a novel subspace learning framework, i.e., Conjunctive Patches Subspace Learning (CPSL) with side information, for learning an effective semantic subspace by exploiting the user historical feedback log data for a CIR task. The CPSL can effectively integrate the discriminative information of labeled log images, the geometrical information of labeled log images and the weakly similar information of unlabeled images together to learn a reliable subspace. We formally formulate this problem into a constrained optimization problem and then present a new subspace learning technique to exploit the user historical feedback log data. Extensive experiments on both synthetic data sets and a real-world image database demonstrate the effectiveness of the proposed scheme in improving the performance of a CBIR system by exploiting the user historical feedback log data.

  15. A Poisson nonnegative matrix factorization method with parameter subspace clustering constraint for endmember extraction in hyperspectral imagery

    Science.gov (United States)

    Sun, Weiwei; Ma, Jun; Yang, Gang; Du, Bo; Zhang, Liangpei

    2017-06-01

    A new Bayesian method named Poisson Nonnegative Matrix Factorization with Parameter Subspace Clustering Constraint (PNMF-PSCC) has been presented to extract endmembers from Hyperspectral Imagery (HSI). First, the method integrates the liner spectral mixture model with the Bayesian framework and it formulates endmember extraction into a Bayesian inference problem. Second, the Parameter Subspace Clustering Constraint (PSCC) is incorporated into the statistical program to consider the clustering of all pixels in the parameter subspace. The PSCC could enlarge differences among ground objects and helps finding endmembers with smaller spectrum divergences. Meanwhile, the PNMF-PSCC method utilizes the Poisson distribution as the prior knowledge of spectral signals to better explain the quantum nature of light in imaging spectrometer. Third, the optimization problem of PNMF-PSCC is formulated into maximizing the joint density via the Maximum A Posterior (MAP) estimator. The program is finally solved by iteratively optimizing two sub-problems via the Alternating Direction Method of Multipliers (ADMM) framework and the FURTHESTSUM initialization scheme. Five state-of-the art methods are implemented to make comparisons with the performance of PNMF-PSCC on both the synthetic and real HSI datasets. Experimental results show that the PNMF-PSCC outperforms all the five methods in Spectral Angle Distance (SAD) and Root-Mean-Square-Error (RMSE), and especially it could identify good endmembers for ground objects with smaller spectrum divergences.

  16. Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

    Czech Academy of Sciences Publication Activity Database

    Hnětynková, Iveta; Plešinger, M.

    2015-01-01

    Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015

  17. A model reduction approach to numerical inversion for a parabolic partial differential equation

    International Nuclear Information System (INIS)

    Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V

    2014-01-01

    We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)

  18. A model reduction approach to numerical inversion for a parabolic partial differential equation

    Science.gov (United States)

    Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

    2014-12-01

    We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

  19. Three-Dimensional Full Core Power Calculations for Pressurized Water Reactors

    International Nuclear Information System (INIS)

    Evans, Thomas M.; Davidson, Gregory G.; Slaybaugh, Rachel N.

    2010-01-01

    We have implemented a new multilevel parallel decomposition in the Denovo discrete ordinates radiation transport code. In concert with Krylov subspace iterative solvers, the multilevel decomposition allows concurrency over energy in addition to space-angle. The original space-angle partitioning in Denovo placed an eective limit on the scalability of the transport solver that was highly dependent on the problem size. The added phase-space concurrency combined with the high-performance Krylov solvers has enabled weak scaling to 100K cores on the Jaguar XT5 supercomputer. Furthermore, the multilevel decomposition provides enough concurrency to scale to exascale computing and beyond.

  20. Quantum cloning of mixed states in symmetric subspaces

    International Nuclear Information System (INIS)

    Fan Heng

    2003-01-01

    Quantum-cloning machine for arbitrary mixed states in symmetric subspaces is proposed. This quantum-cloning machine can be used to copy part of the output state of another quantum-cloning machine and is useful in quantum computation and quantum information. The shrinking factor of this quantum cloning achieves the well-known upper bound. When the input is identical pure states, two different fidelities of this cloning machine are optimal

  1. Galerkin projection methods for solving multiple related linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Chan, T.F.; Ng, M.; Wan, W.L.

    1996-12-31

    We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.

  2. Projection methods for line radiative transfer in spherical media.

    Science.gov (United States)

    Anusha, L. S.; Nagendra, K. N.

    An efficient numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is presented for the solution of radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These methods are based on projections on the subspaces of the n dimensional Euclidean space mathbb {R}n called Krylov subspaces. The methods are shown to be faster in terms of convergence rate compared to the contemporary iterative methods such as Jacobi, Gauss-Seidel and Successive Over Relaxation (SOR).

  3. Microscopic theory of dynamical subspace for large amplitude collective motion

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

    1986-01-01

    A full quantum theory appropriate for describing large amplitude collective motion is proposed by exploiting the basic idea of the semi-classical theory so far developed within the time-depedent Hartree-Fock theory. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation specific for the collective subspace where the large amplitude collective motion is replicated as precisely as possible. As an extension of the semi-classical theory where the concept of an approximate integral surface played an important role, the collective subspace is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

  4. Proximinality in generalized direct sums

    Directory of Open Access Journals (Sweden)

    Darapaneni Narayana

    2004-01-01

    Full Text Available We consider proximinality and transitivity of proximinality for subspaces of finite codimension in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension.

  5. Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the instant code

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Yaqi; Rabiti, Cristian; Palmiotti, Giuseppe, E-mail: yaqi.wang@inl.gov, E-mail: cristian.rabiti@inl.gov, E-mail: giuseppe.palmiotti@inl.gov [Idaho National Laboratory, Idaho Falls, ID (United States)

    2011-07-01

    This paper proposes a new set of Krylov solvers, CG and GMRes, as an alternative of the Red-Black (RB) algorithm on on solving the steady-state one-speed neutron transport equation discretized with PN in angle and hybrid FEM (Finite Element Method) in space. A pre conditioner with the low-order RB iteration is designed to improve their convergence. These Krylov solvers can reduce the cost of pre-assembling the response matrices greatly. Numerical results with the INSTANT code are presented in order to show that they can be a good supplement on solving the PN-HFEM system. (author)

  6. Krylov solvers preconditioned with the low-order red-black algorithm for the PN hybrid FEM for the instant code

    International Nuclear Information System (INIS)

    Wang, Yaqi; Rabiti, Cristian; Palmiotti, Giuseppe

    2011-01-01

    This paper proposes a new set of Krylov solvers, CG and GMRes, as an alternative of the Red-Black (RB) algorithm on on solving the steady-state one-speed neutron transport equation discretized with PN in angle and hybrid FEM (Finite Element Method) in space. A pre conditioner with the low-order RB iteration is designed to improve their convergence. These Krylov solvers can reduce the cost of pre-assembling the response matrices greatly. Numerical results with the INSTANT code are presented in order to show that they can be a good supplement on solving the PN-HFEM system. (author)

  7. Tensor-GMRES method for large sparse systems of nonlinear equations

    Science.gov (United States)

    Feng, Dan; Pulliam, Thomas H.

    1994-01-01

    This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

  8. Independence and totalness of subspaces in phase space methods

    Science.gov (United States)

    Vourdas, A.

    2018-04-01

    The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

  9. On spectral subspaces and their applications to automorphism groups

    International Nuclear Information System (INIS)

    Olesen, Dorte

    1974-03-01

    An attempt is made to give a survey of the theory of spectra and spectral subspaces of group representations in an abstract Banach space setting. The theory is applied to the groups of automorphisms of operator algebras (mostly C*-algebras) and some important results of interest for mathematical physicists are proved (restrictions of the bitransposed action, spectral subspaces for the transposed action on a C*-algebra, and positive states and representations of Rsup(n)) [fr

  10. Simultaneous multislice magnetic resonance fingerprinting with low-rank and subspace modeling.

    Science.gov (United States)

    Bo Zhao; Bilgic, Berkin; Adalsteinsson, Elfar; Griswold, Mark A; Wald, Lawrence L; Setsompop, Kawin

    2017-07-01

    Magnetic resonance fingerprinting (MRF) is a new quantitative imaging paradigm that enables simultaneous acquisition of multiple magnetic resonance tissue parameters (e.g., T 1 , T 2 , and spin density). Recently, MRF has been integrated with simultaneous multislice (SMS) acquisitions to enable volumetric imaging with faster scan time. In this paper, we present a new image reconstruction method based on low-rank and subspace modeling for improved SMS-MRF. Here the low-rank model exploits strong spatiotemporal correlation among contrast-weighted images, while the subspace model captures the temporal evolution of magnetization dynamics. With the proposed model, the image reconstruction problem is formulated as a convex optimization problem, for which we develop an algorithm based on variable splitting and the alternating direction method of multipliers. The performance of the proposed method has been evaluated by numerical experiments, and the results demonstrate that the proposed method leads to improved accuracy over the conventional approach. Practically, the proposed method has a potential to allow for a 3× speedup with minimal reconstruction error, resulting in less than 5 sec imaging time per slice.

  11. Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

    Czech Academy of Sciences Publication Activity Database

    Šístek, Jakub; Cirak, F.

    2015-01-01

    Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023

  12. On Lagrange Multipliers of Trust-Region Subproblems

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

    2008-01-01

    Roč. 48, č. 4 (2008), s. 763-768 ISSN 0006-3835 R&D Projects: GA AV ČR IAA1030405 Institutional research plan: CEZ:AV0Z10300504 Keywords : unconstrained optimization * large-scale optimization * trust-region methods * conjugate gradient s * Krylov subspaces Subject RIV: BA - General Mathematics Impact factor: 0.902, year: 2008

  13. Asymptotic description of plasma turbulence: Krylov-Bogoliubov methods and quasi-particles

    International Nuclear Information System (INIS)

    Sosenko, P.P.; Bertrand, P.; Decyk, V.K.

    2001-01-01

    The asymptotic theory of charged particle motion in electromagnetic fields is developed for the general case of finite Larmor-radius effects by means of Krylov-Bogoliubov averaging method. The correspondence between the general asymptotic methods, elaborated by M. Krylov and M.Bogoliubov, the quasi-particle description and gyrokinetics is established. Such a comparison is used to shed more light on the physical sense of the reduced Poisson equation, introduced in gyrokinetics, and the particle polarization drift. It is shown that the modification of the Poisson equation in the asymptotic theory is due to the non-conservation of the magnetic moment and gyrophase trembling. it is shown that the second-order modification of the adiabatic invariant can determine the conditions of global plasma stability and introduces new nonlinear terms into the reduced Poisson equation. Such a modification is important for several plasma orderings, e.g. NHD type ordering. The feasibility of numerical simulation schemes in which the polarization drift is included into the quasi-particle equations of motion, and the Poisson equation remains unchanged is analyzed. A consistent asymptotic model is proposed in which the polarization drift is included into the quasi-particle equations of motion and the particle and quasi-particle velocities are equal. It is shown that in such models there are additional modifications of the reduced Poisson equation. The latter becomes even more complicated in contrast to earlier suggestions

  14. Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system

    KAUST Repository

    Cô rtes, A.M.A.; Coutinho, A.L.G.A.; Dalcin, L.; Calo, Victor M.

    2015-01-01

    The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.

  15. Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes system

    KAUST Repository

    Côrtes, A.M.A.

    2015-02-20

    The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity–pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise divergence-free. When applied to discretized Stokes equations, these spaces generate a symmetric and indefinite saddle-point linear system. Krylov subspace methods are usually the most efficient procedures to solve such systems. One of such methods, for symmetric systems, is the Minimum Residual Method (MINRES). However, the efficiency and robustness of Krylov subspace methods is closely tied to appropriate preconditioning strategies. For the discrete Stokes system, in particular, block-diagonal strategies provide efficient preconditioners. In this article, we compare the performance of block-diagonal preconditioners for several block choices. We verify how the eigenvalue clustering promoted by the preconditioning strategies affects MINRES convergence. We also compare the number of iterations and wall-clock timings. We conclude that among the building blocks we tested, the strategy with relaxed inner conjugate gradients preconditioned with incomplete Cholesky provided the best results.

  16. Extending the subspace hybrid method for eigenvalue problems in reactor physics calculation

    International Nuclear Information System (INIS)

    Zhang, Q.; Abdel-Khalik, H. S.

    2013-01-01

    This paper presents an innovative hybrid Monte-Carlo-Deterministic method denoted by the SUBSPACE method designed for improving the efficiency of hybrid methods for reactor analysis applications. The SUBSPACE method achieves its high computational efficiency by taking advantage of the existing correlations between desired responses. Recently, significant gains in computational efficiency have been demonstrated using this method for source driven problems. Within this work the mathematical theory behind the SUBSPACE method is introduced and extended to address core wide level k-eigenvalue problems. The method's efficiency is demonstrated based on a three-dimensional quarter-core problem, where responses are sought on the pin cell level. The SUBSPACE method is compared to the FW-CADIS method and is found to be more efficient for the utilized test problem because of the reason that the FW-CADIS method solves a forward eigenvalue problem and an adjoint fixed-source problem while the SUBSPACE method only solves an adjoint fixed-source problem. Based on the favorable results obtained here, we are confident that the applicability of Monte Carlo for large scale reactor analysis could be realized in the near future. (authors)

  17. Preconditioner considerations for an aerodynamic Newton-Krylov solver

    International Nuclear Information System (INIS)

    Chisholm, T.; Zingg, D.W.

    2003-01-01

    A fast Newton-Krylov algorithm is presented for solving the compressible Navier-Stokes equations on structured multi-block grids with application to turbulent aerodynamic flows. The one-equation Spalart-Allmaras model is used to provide the turbulent viscosity. The optimization of the algorithm is discussed. ILU(4) is suggested for a preconditioner, operating on a modified Jacobian matrix. An RCM reordering is used, with a suggested root node in the wake. The advantages of a matrix-free technique for forming matrix-vector products are shown. Three test cases are used to demonstrate convergence rates. Single-element cases are solved in less than 60 seconds on a desktop computer, while the solution of a multi-element case can be found in about 10 minutes. (author)

  18. On Investigating GMRES Convergence using Unitary Matrices

    Czech Academy of Sciences Publication Activity Database

    Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.

    2014-01-01

    Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

  19. Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

    International Nuclear Information System (INIS)

    Chen, Xudong

    2010-01-01

    This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging

  20. Margin-Wide Earthquake Subspace Scanning Along the Cascadia Subduction Zone Using the Cascadia Initiative Amphibious Dataset

    Science.gov (United States)

    Morton, E.; Bilek, S. L.; Rowe, C. A.

    2017-12-01

    Understanding the spatial extent and behavior of the interplate contact in the Cascadia Subduction Zone (CSZ) may prove pivotal to preparation for future great earthquakes, such as the M9 event of 1700. Current and historic seismic catalogs are limited in their integrity by their short duration, given the recurrence rate of great earthquakes, and by their rather high magnitude of completeness for the interplate seismic zone, due to its offshore distance from these land-based networks. This issue is addressed via the 2011-2015 Cascadia Initiative (CI) amphibious seismic array deployment, which combined coastal land seismometers with more than 60 ocean-bottom seismometers (OBS) situated directly above the presumed plate interface. We search the CI dataset for small, previously undetected interplate earthquakes to identify seismic patches on the megathrust. Using the automated subspace detection method, we search for previously undetected events. Our subspace comprises eigenvectors derived from CI OBS and on-land waveforms extracted for existing catalog events that appear to have occurred on the plate interface. Previous work focused on analysis of two repeating event clusters off the coast of Oregon spanning all 4 years of deployment. Here we expand earlier results to include detection and location analysis to the entire CSZ margin during the first year of CI deployment, with more than 200 new events detected for the central portion of the margin. Template events used for subspace scanning primarily occurred beneath the land surface along the coast, at the downdip edge of modeled high slip patches for the 1700 event, with most concentrated at the northwestern edge of the Olympic Peninsula.

  1. Subspace Correction Methods for Total Variation and $\\ell_1$-Minimization

    KAUST Repository

    Fornasier, Massimo

    2009-01-01

    This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a seminorm for a subspace. The optimization is realized by alternating minimizations of the functional on a sequence of orthogonal subspaces. On each subspace an iterative proximity-map algorithm is implemented via oblique thresholding, which is the main new tool introduced in this work. We provide convergence conditions for the algorithm in order to compute minimizers of the target energy. Analogous results are derived for a parallel variant of the algorithm. Applications are presented in domain decomposition methods for degenerate elliptic PDEs arising in total variation minimization and in accelerated sparse recovery algorithms based on 1-minimization. We include numerical examples which show e.cient solutions to classical problems in signal and image processing. © 2009 Society for Industrial and Applied Physics.

  2. A subspace preconditioning algorithm for eigenvector/eigenvalue computation

    Energy Technology Data Exchange (ETDEWEB)

    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.

  3. An angle-based subspace anomaly detection approach to high-dimensional data: With an application to industrial fault detection

    International Nuclear Information System (INIS)

    Zhang, Liangwei; Lin, Jing; Karim, Ramin

    2015-01-01

    The accuracy of traditional anomaly detection techniques implemented on full-dimensional spaces degrades significantly as dimensionality increases, thereby hampering many real-world applications. This work proposes an approach to selecting meaningful feature subspace and conducting anomaly detection in the corresponding subspace projection. The aim is to maintain the detection accuracy in high-dimensional circumstances. The suggested approach assesses the angle between all pairs of two lines for one specific anomaly candidate: the first line is connected by the relevant data point and the center of its adjacent points; the other line is one of the axis-parallel lines. Those dimensions which have a relatively small angle with the first line are then chosen to constitute the axis-parallel subspace for the candidate. Next, a normalized Mahalanobis distance is introduced to measure the local outlier-ness of an object in the subspace projection. To comprehensively compare the proposed algorithm with several existing anomaly detection techniques, we constructed artificial datasets with various high-dimensional settings and found the algorithm displayed superior accuracy. A further experiment on an industrial dataset demonstrated the applicability of the proposed algorithm in fault detection tasks and highlighted another of its merits, namely, to provide preliminary interpretation of abnormality through feature ordering in relevant subspaces. - Highlights: • An anomaly detection approach for high-dimensional reliability data is proposed. • The approach selects relevant subspaces by assessing vectorial angles. • The novel ABSAD approach displays superior accuracy over other alternatives. • Numerical illustration approves its efficacy in fault detection applications

  4. The influence of different PAST-based subspace trackers on DaPT parameter estimation

    Science.gov (United States)

    Lechtenberg, M.; Götze, J.

    2012-09-01

    In the context of parameter estimation, subspace-based methods like ESPRIT have become common. They require a subspace separation e.g. based on eigenvalue/-vector decomposition. In time-varying environments, this can be done by subspace trackers. One class of these is based on the PAST algorithm. Our non-linear parameter estimation algorithm DaPT builds on-top of the ESPRIT algorithm. Evaluation of the different variants of the PAST algorithm shows which variant of the PAST algorithm is worthwhile in the context of frequency estimation.

  5. Application of nonlinear Krylov acceleration to radiative transfer problems

    International Nuclear Information System (INIS)

    Till, A. T.; Adams, M. L.; Morel, J. E.

    2013-01-01

    The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)

  6. Metastable decoherence-free subspaces and electromagnetically induced transparency in interacting many-body systems

    DEFF Research Database (Denmark)

    Macieszczak, Katarzyna; Zhou, Yanli; Hofferberth, Sebastian

    2017-01-01

    to stationarity this leads to a slow dynamics, which renders the typical assumption of fast relaxation invalid. We derive analytically the effective nonequilibrium dynamics in the decoherence-free subspace, which features coherent and dissipative two-body interactions. We discuss the use of this scenario...

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

    International Nuclear Information System (INIS)

    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)

  8. DETECTION OF CHANGES OF THE SYSTEM TECHNICAL STATE USING STOCHASTIC SUBSPACE OBSERVATION METHOD

    Directory of Open Access Journals (Sweden)

    Andrzej Puchalski

    2014-03-01

    Full Text Available System diagnostics based on vibroacoustics signals, carried out by means of stochastic subspace methods was undertaken in the hereby paper. Subspace methods are the ones based on numerical linear algebra tools. The considered solutions belong to diagnostic methods according to data, leading to the generation of residuals allowing failure recognition of elements and assemblies in machines and devices. The algorithm of diagnostics according to the subspace observation method was applied – in the paper – for the estimation of the valve system of the spark ignition engine.

  9. Hybrid parallelization of the XTOR-2F code for the simulation of two-fluid MHD instabilities in tokamaks

    Science.gov (United States)

    Marx, Alain; Lütjens, Hinrich

    2017-03-01

    A hybrid MPI/OpenMP parallel version of the XTOR-2F code [Lütjens and Luciani, J. Comput. Phys. 229 (2010) 8130] solving the two-fluid MHD equations in full tokamak geometry by means of an iterative Newton-Krylov matrix-free method has been developed. The present work shows that the code has been parallelized significantly despite the numerical profile of the problem solved by XTOR-2F, i.e. a discretization with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner at every Krylov iteration of the solver. The execution time of the parallelized version is an order of magnitude smaller than the sequential one for low resolution cases, with an increasing speedup when the discretization mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.

  10. Closed and Open Loop Subspace System Identification of the Kalman Filter

    Directory of Open Access Journals (Sweden)

    David Di Ruscio

    2009-04-01

    Full Text Available Some methods for consistent closed loop subspace system identification presented in the literature are analyzed and compared to a recently published subspace algorithm for both open as well as for closed loop data, the DSR_e algorithm. Some new variants of this algorithm are presented and discussed. Simulation experiments are included in order to illustrate if the algorithms are variance efficient or not.

  11. Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion

    International Nuclear Information System (INIS)

    Mousseau, V.A.; Knoll, D.A.; Rider, W.J.

    2000-01-01

    An algorithm is presented for the solution of the time dependent reaction-diffusion systems which arise in non-equilibrium radiation diffusion applications. This system of nonlinear equations is solved by coupling three numerical methods, Jacobian-free Newton-Krylov, operator splitting, and multigrid linear solvers. An inexact Newton's method is used to solve the system of nonlinear equations. Since building the Jacobian matrix for problems of interest can be challenging, the authors employ a Jacobian-free implementation of Newton's method, where the action of the Jacobian matrix on a vector is approximated by a first order Taylor series expansion. Preconditioned generalized minimal residual (PGMRES) is the Krylov method used to solve the linear systems that come from the iterations of Newton's method. The preconditioner in this solution method is constructed using a physics-based divide and conquer approach, often referred to as operator splitting. This solution procedure inverts the scalar elliptic systems that make up the preconditioner using simple multigrid methods. The preconditioner also addresses the strong coupling between equations with local 2 x 2 block solves. The intra-cell coupling is applied after the inter-cell coupling has already been addressed by the elliptic solves. Results are presented using this solution procedure that demonstrate its efficiency while incurring minimal memory requirements

  12. Numerical Validation of the Delaunay Normalization and the Krylov-Bogoliubov-Mitropolsky Method

    Directory of Open Access Journals (Sweden)

    David Ortigosa

    2014-01-01

    Full Text Available A scalable second-order analytical orbit propagator programme based on modern and classical perturbation methods is being developed. As a first step in the validation and verification of part of our orbit propagator programme, we only consider the perturbation produced by zonal harmonic coefficients in the Earth’s gravity potential, so that it is possible to analyze the behaviour of the mathematical expressions involved in Delaunay normalization and the Krylov-Bogoliubov-Mitropolsky method in depth and determine their limits.

  13. Model Reduction using Vorobyev Moment Problem

    Czech Academy of Sciences Publication Activity Database

    Strakoš, Zdeněk

    2009-01-01

    Roč. 51, č. 3 (2009), s. 363-379 ISSN 1017-1398 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : matching moments * model reduction * Krylov subspace methods * conjugate gradient method * Lanczos method * Arnoldi method * Gauss-Christoffel quadrature * scattering amplitude Subject RIV: BA - General Mathematics Impact factor: 0.716, year: 2009

  14. Preconditioner Updates Applied to CFD Model Problems

    Czech Academy of Sciences Publication Activity Database

    Birken, P.; Duintjer Tebbens, Jurjen; Meister, A.; Tůma, Miroslav

    2008-01-01

    Roč. 58, č. 11 (2008), s. 1628-1641 ISSN 0168-9274 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB100300703 Institutional research plan: CEZ:AV0Z10300504 Keywords : finite volume methods * update preconditioning * Krylov subspace methods * Euler equations * conservation laws Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2008

  15. Subspace Arrangement Codes and Cryptosystems

    Science.gov (United States)

    2011-05-09

    Signature Date Acceptance for the Trident Scholar Committee Professor Carl E. Wick Associate Director of Midshipmen Research Signature Date SUBSPACE...Professor William Traves. I also thank Professor Carl Wick and the Trident Scholar Committee for providing me with the opportunity to conduct this... Sagan . Why the characteristic polynomial factors. Bulletin of the American Mathematical Society, 36(2):113–133, February 1999. [16] Karen E. Smith

  16. Detecting anomalies in crowded scenes via locality-constrained affine subspace coding

    Science.gov (United States)

    Fan, Yaxiang; Wen, Gongjian; Qiu, Shaohua; Li, Deren

    2017-07-01

    Video anomaly event detection is the process of finding an abnormal event deviation compared with the majority of normal or usual events. The main challenges are the high structure redundancy and the dynamic changes in the scenes that are in surveillance videos. To address these problems, we present a framework for anomaly detection and localization in videos that is based on locality-constrained affine subspace coding (LASC) and a model updating procedure. In our algorithm, LASC attempts to reconstruct the test sample by its top-k nearest subspaces, which are obtained by segmenting the normal samples space using a clustering method. A sample with a large reconstruction cost is detected as abnormal by setting a threshold. To adapt to the scene changes over time, a model updating strategy is proposed. We experiment on two public datasets: the UCSD dataset and the Avenue dataset. The results demonstrate that our method achieves competitive performance at a 700 fps on a single desktop PC.

  17. Robust subspace estimation using low-rank optimization theory and applications

    CERN Document Server

    Oreifej, Omar

    2014-01-01

    Various fundamental applications in computer vision and machine learning require finding the basis of a certain subspace. Examples of such applications include face detection, motion estimation, and activity recognition. An increasing interest has been recently placed on this area as a result of significant advances in the mathematics of matrix rank optimization. Interestingly, robust subspace estimation can be posed as a low-rank optimization problem, which can be solved efficiently using techniques such as the method of Augmented Lagrange Multiplier. In this book,?the authors?discuss fundame

  18. Random matrix improved subspace clustering

    KAUST Repository

    Couillet, Romain

    2017-03-06

    This article introduces a spectral method for statistical subspace clustering. The method is built upon standard kernel spectral clustering techniques, however carefully tuned by theoretical understanding arising from random matrix findings. We show in particular that our method provides high clustering performance while standard kernel choices provably fail. An application to user grouping based on vector channel observations in the context of massive MIMO wireless communication networks is provided.

  19. Counting Subspaces of a Finite Vector Space

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 11. Counting Subspaces of a Finite Vector Space – 1. Amritanshu Prasad. General Article Volume 15 Issue 11 November 2010 pp 977-987. Fulltext. Click here to view fulltext PDF. Permanent link:

  20. Roller Bearing Monitoring by New Subspace-Based Damage Indicator

    Directory of Open Access Journals (Sweden)

    G. Gautier

    2015-01-01

    Full Text Available A frequency-band subspace-based damage identification method for fault diagnosis in roller bearings is presented. Subspace-based damage indicators are obtained by filtering the vibration data in the frequency range where damage is likely to occur, that is, around the bearing characteristic frequencies. The proposed method is validated by considering simulated data of a damaged bearing. Also, an experimental case is considered which focuses on collecting the vibration data issued from a run-to-failure test. It is shown that the proposed method can detect bearing defects and, as such, it appears to be an efficient tool for diagnosis purpose.

  1. On the Convergence of Q-OR and Q-MR Krylov Methods for Solving Nonsymmetric Linear Systems

    Czech Academy of Sciences Publication Activity Database

    Duintjer Tebbens, Jurjen; Meurant, G.

    2016-01-01

    Roč. 56, č. 1 (2016), s. 77-97 ISSN 0006-3835 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : Krylov method * Q-OR method * Q-MR method * BiCG * QMR * CMRH * eigenvalue influence * prescribed convergence Subject RIV: BA - General Mathematics Impact factor: 1.670, year: 2016

  2. Structured Kernel Subspace Learning for Autonomous Robot Navigation.

    Science.gov (United States)

    Kim, Eunwoo; Choi, Sungjoon; Oh, Songhwai

    2018-02-14

    This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for predicting the motion of a pedestrian and controlling a robot to avoid incoming pedestrians, it is still difficult to safely navigate in a dynamic environment due to challenges, such as the varying quality and complexity of training data with unwanted noises. This paper addresses these challenges simultaneously by proposing a robust kernel subspace learning algorithm based on the recent advances in nuclear-norm and l 1 -norm minimization. We model the motion of a pedestrian and the robot controller using Gaussian processes. The proposed method efficiently approximates a kernel matrix used in Gaussian process regression by learning low-rank structured matrix (with symmetric positive semi-definiteness) to find an orthogonal basis, which eliminates the effects of erroneous and inconsistent data. Based on structured kernel subspace learning, we propose a robust motion model and motion controller for safe navigation in dynamic environments. We evaluate the proposed robust kernel learning in various tasks, including regression, motion prediction, and motion control problems, and demonstrate that the proposed learning-based systems are robust against outliers and outperform existing regression and navigation methods.

  3. A Subspace Approach to the Structural Decomposition and Identification of Ankle Joint Dynamic Stiffness.

    Science.gov (United States)

    Jalaleddini, Kian; Tehrani, Ehsan Sobhani; Kearney, Robert E

    2017-06-01

    The purpose of this paper is to present a structural decomposition subspace (SDSS) method for decomposition of the joint torque to intrinsic, reflexive, and voluntary torques and identification of joint dynamic stiffness. First, it formulates a novel state-space representation for the joint dynamic stiffness modeled by a parallel-cascade structure with a concise parameter set that provides a direct link between the state-space representation matrices and the parallel-cascade parameters. Second, it presents a subspace method for the identification of the new state-space model that involves two steps: 1) the decomposition of the intrinsic and reflex pathways and 2) the identification of an impulse response model of the intrinsic pathway and a Hammerstein model of the reflex pathway. Extensive simulation studies demonstrate that SDSS has significant performance advantages over some other methods. Thus, SDSS was more robust under high noise conditions, converging where others failed; it was more accurate, giving estimates with lower bias and random errors. The method also worked well in practice and yielded high-quality estimates of intrinsic and reflex stiffnesses when applied to experimental data at three muscle activation levels. The simulation and experimental results demonstrate that SDSS accurately decomposes the intrinsic and reflex torques and provides accurate estimates of physiologically meaningful parameters. SDSS will be a valuable tool for studying joint stiffness under functionally important conditions. It has important clinical implications for the diagnosis, assessment, objective quantification, and monitoring of neuromuscular diseases that change the muscle tone.

  4. Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Ling; Zhao, Haihua; Zhang, Hongbin

    2016-04-01

    The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integration methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.

  5. Integrated Phoneme Subspace Method for Speech Feature Extraction

    Directory of Open Access Journals (Sweden)

    Park Hyunsin

    2009-01-01

    Full Text Available Speech feature extraction has been a key focus in robust speech recognition research. In this work, we discuss data-driven linear feature transformations applied to feature vectors in the logarithmic mel-frequency filter bank domain. Transformations are based on principal component analysis (PCA, independent component analysis (ICA, and linear discriminant analysis (LDA. Furthermore, this paper introduces a new feature extraction technique that collects the correlation information among phoneme subspaces and reconstructs feature space for representing phonemic information efficiently. The proposed speech feature vector is generated by projecting an observed vector onto an integrated phoneme subspace (IPS based on PCA or ICA. The performance of the new feature was evaluated for isolated word speech recognition. The proposed method provided higher recognition accuracy than conventional methods in clean and reverberant environments.

  6. Outlier Ranking via Subspace Analysis in Multiple Views of the Data

    DEFF Research Database (Denmark)

    Muller, Emmanuel; Assent, Ira; Iglesias, Patricia

    2012-01-01

    , a novel outlier ranking concept. Outrank exploits subspace analysis to determine the degree of outlierness. It considers different subsets of the attributes as individual outlier properties. It compares clustered regions in arbitrary subspaces and derives an outlierness score for each object. Its...... principled integration of multiple views into an outlierness measure uncovers outliers that are not detectable in the full attribute space. Our experimental evaluation demonstrates that Outrank successfully determines a high quality outlier ranking, and outperforms state-of-the-art outlierness measures....

  7. Quantum Zeno subspaces induced by temperature

    Energy Technology Data Exchange (ETDEWEB)

    Militello, B.; Scala, M.; Messina, A. [Dipartimento di Fisica dell' Universita di Palermo, Via Archirafi 36, I-90123 Palermo (Italy)

    2011-08-15

    We discuss the partitioning of the Hilbert space of a quantum system induced by the interaction with another system at thermal equilibrium, showing that the higher the temperature the more effective is the formation of Zeno subspaces. We show that our analysis keeps its validity even in the case of interaction with a bosonic reservoir, provided appropriate limitations of the relevant bandwidth.

  8. Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

    International Nuclear Information System (INIS)

    Vourdas, A.

    2014-01-01

    The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H 1 ,H 2 ), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H 1 ),P(H 2 ), to the subspaces H 1 , H 2 . As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities

  9. Improved Stochastic Subspace System Identification for Structural Health Monitoring

    Science.gov (United States)

    Chang, Chia-Ming; Loh, Chin-Hsiung

    2015-07-01

    Structural health monitoring acquires structural information through numerous sensor measurements. Vibrational measurement data render the dynamic characteristics of structures to be extracted, in particular of the modal properties such as natural frequencies, damping, and mode shapes. The stochastic subspace system identification has been recognized as a power tool which can present a structure in the modal coordinates. To obtain qualitative identified data, this tool needs to spend computational expense on a large set of measurements. In study, a stochastic system identification framework is proposed to improve the efficiency and quality of the conventional stochastic subspace system identification. This framework includes 1) measured signal processing, 2) efficient space projection, 3) system order selection, and 4) modal property derivation. The measured signal processing employs the singular spectrum analysis algorithm to lower the noise components as well as to present a data set in a reduced dimension. The subspace is subsequently derived from the data set presented in a delayed coordinate. With the proposed order selection criteria, the number of structural modes is determined, resulting in the modal properties. This system identification framework is applied to a real-world bridge for exploring the feasibility in real-time applications. The results show that this improved system identification method significantly decreases computational time, while qualitative modal parameters are still attained.

  10. Subspace in Linear Algebra: Investigating Students' Concept Images and Interactions with the Formal Definition

    Science.gov (United States)

    Wawro, Megan; Sweeney, George F.; Rabin, Jeffrey M.

    2011-01-01

    This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

  11. Performance Analysis of Blind Subspace-Based Signature Estimation Algorithms for DS-CDMA Systems with Unknown Correlated Noise

    Science.gov (United States)

    Zarifi, Keyvan; Gershman, Alex B.

    2006-12-01

    We analyze the performance of two popular blind subspace-based signature waveform estimation techniques proposed by Wang and Poor and Buzzi and Poor for direct-sequence code division multiple-access (DS-CDMA) systems with unknown correlated noise. Using the first-order perturbation theory, analytical expressions for the mean-square error (MSE) of these algorithms are derived. We also obtain simple high SNR approximations of the MSE expressions which explicitly clarify how the performance of these techniques depends on the environmental parameters and how it is related to that of the conventional techniques that are based on the standard white noise assumption. Numerical examples further verify the consistency of the obtained analytical results with simulation results.

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

    Czech Academy of Sciences Publication Activity Database

    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

  13. KIOPS: A fast adaptive Krylov subspace solver for exponential integrators

    OpenAIRE

    Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya

    2018-01-01

    This paper presents a new algorithm KIOPS for computing linear combinations of $\\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no information about the spectrum or norm of the Jacobian matrix is known \\textit{a priori}. We first show that such problems can be solved efficiently by computing a single exponential of a modified matrix. Then our approach is to compute an appropriate basis for ...

  14. Lattice QCD computations: Recent progress with modern Krylov subspace methods

    Energy Technology Data Exchange (ETDEWEB)

    Frommer, A. [Bergische Universitaet GH Wuppertal (Germany)

    1996-12-31

    Quantum chromodynamics (QCD) is the fundamental theory of the strong interaction of matter. In order to compare the theory with results from experimental physics, the theory has to be reformulated as a discrete problem of lattice gauge theory using stochastic simulations. The computational challenge consists in solving several hundreds of very large linear systems with several right hand sides. A considerable part of the world`s supercomputer time is spent in such QCD calculations. This paper presents results on solving systems for the Wilson fermions. Recent progress is reviewed on algorithms obtained in cooperation with partners from theoretical physics.

  15. Parallel algorithms for unconstrained optimization by multisplitting with inexact subspace search - the abstract

    Energy Technology Data Exchange (ETDEWEB)

    Renaut, R.; He, Q. [Arizona State Univ., Tempe, AZ (United States)

    1994-12-31

    In a new parallel iterative algorithm for unconstrained optimization by multisplitting is proposed. In this algorithm the original problem is split into a set of small optimization subproblems which are solved using well known sequential algorithms. These algorithms are iterative in nature, e.g. DFP variable metric method. Here the authors use sequential algorithms based on an inexact subspace search, which is an extension to the usual idea of an inexact fine search. Essentially the idea of the inexact line search for nonlinear minimization is that at each iteration the authors only find an approximate minimum in the line search direction. Hence by inexact subspace search, they mean that, instead of finding the minimum of the subproblem at each interation, they do an incomplete down hill search to give an approximate minimum. Some convergence and numerical results for this algorithm will be presented. Further, the original theory will be generalized to the situation with a singular Hessian. Applications for nonlinear least squares problems will be presented. Experimental results will be presented for implementations on an Intel iPSC/860 Hypercube with 64 nodes as well as on the Intel Paragon.

  16. Random Subspace Aggregation for Cancer Prediction with Gene Expression Profiles

    Directory of Open Access Journals (Sweden)

    Liying Yang

    2016-01-01

    Full Text Available Background. Precisely predicting cancer is crucial for cancer treatment. Gene expression profiles make it possible to analyze patterns between genes and cancers on the genome-wide scale. Gene expression data analysis, however, is confronted with enormous challenges for its characteristics, such as high dimensionality, small sample size, and low Signal-to-Noise Ratio. Results. This paper proposes a method, termed RS_SVM, to predict gene expression profiles via aggregating SVM trained on random subspaces. After choosing gene features through statistical analysis, RS_SVM randomly selects feature subsets to yield random subspaces and training SVM classifiers accordingly and then aggregates SVM classifiers to capture the advantage of ensemble learning. Experiments on eight real gene expression datasets are performed to validate the RS_SVM method. Experimental results show that RS_SVM achieved better classification accuracy and generalization performance in contrast with single SVM, K-nearest neighbor, decision tree, Bagging, AdaBoost, and the state-of-the-art methods. Experiments also explored the effect of subspace size on prediction performance. Conclusions. The proposed RS_SVM method yielded superior performance in analyzing gene expression profiles, which demonstrates that RS_SVM provides a good channel for such biological data.

  17. Boundary regularity of Nevanlinna domains and univalent functions in model subspaces

    International Nuclear Information System (INIS)

    Baranov, Anton D; Fedorovskiy, Konstantin Yu

    2011-01-01

    In the paper we study boundary regularity of Nevanlinna domains, which have appeared in problems of uniform approximation by polyanalytic polynomials. A new method for constructing Nevanlinna domains with essentially irregular nonanalytic boundaries is suggested; this method is based on finding appropriate univalent functions in model subspaces, that is, in subspaces of the form K Θ =H 2 ominus ΘH 2 , where Θ is an inner function. To describe the irregularity of the boundaries of the domains obtained, recent results by Dolzhenko about boundary regularity of conformal mappings are used. Bibliography: 18 titles.

  18. Sparse subspace clustering for data with missing entries and high-rank matrix completion.

    Science.gov (United States)

    Fan, Jicong; Chow, Tommy W S

    2017-09-01

    Many methods have recently been proposed for subspace clustering, but they are often unable to handle incomplete data because of missing entries. Using matrix completion methods to recover missing entries is a common way to solve the problem. Conventional matrix completion methods require that the matrix should be of low-rank intrinsically, but most matrices are of high-rank or even full-rank in practice, especially when the number of subspaces is large. In this paper, a new method called Sparse Representation with Missing Entries and Matrix Completion is proposed to solve the problems of incomplete-data subspace clustering and high-rank matrix completion. The proposed algorithm alternately computes the matrix of sparse representation coefficients and recovers the missing entries of a data matrix. The proposed algorithm recovers missing entries through minimizing the representation coefficients, representation errors, and matrix rank. Thorough experimental study and comparative analysis based on synthetic data and natural images were conducted. The presented results demonstrate that the proposed algorithm is more effective in subspace clustering and matrix completion compared with other existing methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

  19. Linear systems solvers - recent developments and implications for lattice computations

    International Nuclear Information System (INIS)

    Frommer, A.

    1996-01-01

    We review the numerical analysis' understanding of Krylov subspace methods for solving (non-hermitian) systems of equations and discuss its implications for lattice gauge theory computations using the example of the Wilson fermion matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES are close to optimal for the Wilson fermion matrix. Consequently, preconditioning appears to be the crucial issue for further improvements. (orig.)

  20. Subspace identification of distributed clusters of homogeneous systems

    NARCIS (Netherlands)

    Yu, C.; Verhaegen, M.H.G.

    2017-01-01

    This note studies the identification of a network comprised of interconnected clusters of LTI systems. Each cluster consists of homogeneous dynamical systems, and its interconnections with the rest of the network are unmeasurable. A subspace identification method is proposed for identifying a single

  1. CLAss-Specific Subspace Kernel Representations and Adaptive Margin Slack Minimization for Large Scale Classification.

    Science.gov (United States)

    Yu, Yinan; Diamantaras, Konstantinos I; McKelvey, Tomas; Kung, Sun-Yuan

    2018-02-01

    In kernel-based classification models, given limited computational power and storage capacity, operations over the full kernel matrix becomes prohibitive. In this paper, we propose a new supervised learning framework using kernel models for sequential data processing. The framework is based on two components that both aim at enhancing the classification capability with a subset selection scheme. The first part is a subspace projection technique in the reproducing kernel Hilbert space using a CLAss-specific Subspace Kernel representation for kernel approximation. In the second part, we propose a novel structural risk minimization algorithm called the adaptive margin slack minimization to iteratively improve the classification accuracy by an adaptive data selection. We motivate each part separately, and then integrate them into learning frameworks for large scale data. We propose two such frameworks: the memory efficient sequential processing for sequential data processing and the parallelized sequential processing for distributed computing with sequential data acquisition. We test our methods on several benchmark data sets and compared with the state-of-the-art techniques to verify the validity of the proposed techniques.

  2. Subspace based adaptive denoising of surface EMG from neurological injury patients

    Science.gov (United States)

    Liu, Jie; Ying, Dongwen; Zev Rymer, William; Zhou, Ping

    2014-10-01

    Objective: After neurological injuries such as spinal cord injury, voluntary surface electromyogram (EMG) signals recorded from affected muscles are often corrupted by interferences, such as spurious involuntary spikes and background noises produced by physiological and extrinsic/accidental origins, imposing difficulties for signal processing. Conventional methods did not well address the problem caused by interferences. It is difficult to mitigate such interferences using conventional methods. The aim of this study was to develop a subspace-based denoising method to suppress involuntary background spikes contaminating voluntary surface EMG recordings. Approach: The Karhunen-Loeve transform was utilized to decompose a noisy signal into a signal subspace and a noise subspace. An optimal estimate of EMG signal is derived from the signal subspace and the noise power. Specifically, this estimator is capable of making a tradeoff between interference reduction and signal distortion. Since the estimator partially relies on the estimate of noise power, an adaptive method was presented to sequentially track the variation of interference power. The proposed method was evaluated using both semi-synthetic and real surface EMG signals. Main results: The experiments confirmed that the proposed method can effectively suppress interferences while keep the distortion of voluntary EMG signal in a low level. The proposed method can greatly facilitate further signal processing, such as onset detection of voluntary muscle activity. Significance: The proposed method can provide a powerful tool for suppressing background spikes and noise contaminating voluntary surface EMG signals of paretic muscles after neurological injuries, which is of great importance for their multi-purpose applications.

  3. Noise-robust unsupervised spike sorting based on discriminative subspace learning with outlier handling.

    Science.gov (United States)

    Keshtkaran, Mohammad Reza; Yang, Zhi

    2017-06-01

    Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. Most of the feature extraction and dimensionality reduction techniques that have been used for spike sorting give a projection subspace which is not necessarily the most discriminative one. Therefore, the clusters which appear inherently separable in some discriminative subspace may overlap if projected using conventional feature extraction approaches leading to a poor sorting accuracy especially when the noise level is high. In this paper, we propose a noise-robust and unsupervised spike sorting algorithm based on learning discriminative spike features for clustering. The proposed algorithm uses discriminative subspace learning to extract low dimensional and most discriminative features from the spike waveforms and perform clustering with automatic detection of the number of the clusters. The core part of the algorithm involves iterative subspace selection using linear discriminant analysis and clustering using Gaussian mixture model with outlier detection. A statistical test in the discriminative subspace is proposed to automatically detect the number of the clusters. Comparative results on publicly available simulated and real in vivo datasets demonstrate that our algorithm achieves substantially improved cluster distinction leading to higher sorting accuracy and more reliable detection of clusters which are highly overlapping and not detectable using conventional feature extraction techniques such as principal component analysis or wavelets. By providing more accurate information about the activity of more number of individual neurons with high robustness to neural noise and outliers, the proposed unsupervised spike sorting algorithm facilitates more detailed and accurate analysis of single- and multi-unit activities in neuroscience and brain machine interface studies.

  4. Noise-robust unsupervised spike sorting based on discriminative subspace learning with outlier handling

    Science.gov (United States)

    Keshtkaran, Mohammad Reza; Yang, Zhi

    2017-06-01

    Objective. Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. Most of the feature extraction and dimensionality reduction techniques that have been used for spike sorting give a projection subspace which is not necessarily the most discriminative one. Therefore, the clusters which appear inherently separable in some discriminative subspace may overlap if projected using conventional feature extraction approaches leading to a poor sorting accuracy especially when the noise level is high. In this paper, we propose a noise-robust and unsupervised spike sorting algorithm based on learning discriminative spike features for clustering. Approach. The proposed algorithm uses discriminative subspace learning to extract low dimensional and most discriminative features from the spike waveforms and perform clustering with automatic detection of the number of the clusters. The core part of the algorithm involves iterative subspace selection using linear discriminant analysis and clustering using Gaussian mixture model with outlier detection. A statistical test in the discriminative subspace is proposed to automatically detect the number of the clusters. Main results. Comparative results on publicly available simulated and real in vivo datasets demonstrate that our algorithm achieves substantially improved cluster distinction leading to higher sorting accuracy and more reliable detection of clusters which are highly overlapping and not detectable using conventional feature extraction techniques such as principal component analysis or wavelets. Significance. By providing more accurate information about the activity of more number of individual neurons with high robustness to neural noise and outliers, the proposed unsupervised spike sorting algorithm facilitates more detailed and accurate analysis of single- and multi-unit activities in neuroscience and brain machine interface studies.

  5. MULTI-LABEL ASRS DATASET CLASSIFICATION USING SEMI-SUPERVISED SUBSPACE CLUSTERING

    Data.gov (United States)

    National Aeronautics and Space Administration — MULTI-LABEL ASRS DATASET CLASSIFICATION USING SEMI-SUPERVISED SUBSPACE CLUSTERING MOHAMMAD SALIM AHMED, LATIFUR KHAN, NIKUNJ OZA, AND MANDAVA RAJESWARI Abstract....

  6. GPGPU accelerated Krylov methods for compact modeling of on-chip passive integrated structures within the Chameleon-RF workflow

    Directory of Open Access Journals (Sweden)

    Sebastian Gim

    2012-11-01

    Full Text Available Continued device scaling into the nanometer region and high frequencies of operation well into the multi-GHz region has given rise to new effects that previously had negligible impact but now present greater challenges and unprecedented complexity to designing successful mixed-signal silicon. The Chameleon-RF project was conceived to address these challenges. Creative use of domain decomposition, multi grid techniques or reduced order modeling techniques (ROM can be selectively applied at all levels of the process to efficiently prune down degrees of freedom (DoFs. However, the simulation of complex systems within a reasonable amount of time remains a computational challenge. This paper presents work done in the incorporation of GPGPU technology to accelerate Krylov based algorithms used for compact modeling of on-chip passive integrated structures within the workflow of the Chameleon-RF project. Based upon insight gained from work done above, a novel GPGPU accelerated algorithm was developed for the Krylov ROM (kROM methods and is described here for the benefit of the wider community.

  7. Linear Subspace Ranking Hashing for Cross-Modal Retrieval.

    Science.gov (United States)

    Li, Kai; Qi, Guo-Jun; Ye, Jun; Hua, Kien A

    2017-09-01

    Hashing has attracted a great deal of research in recent years due to its effectiveness for the retrieval and indexing of large-scale high-dimensional multimedia data. In this paper, we propose a novel ranking-based hashing framework that maps data from different modalities into a common Hamming space where the cross-modal similarity can be measured using Hamming distance. Unlike existing cross-modal hashing algorithms where the learned hash functions are binary space partitioning functions, such as the sign and threshold function, the proposed hashing scheme takes advantage of a new class of hash functions closely related to rank correlation measures which are known to be scale-invariant, numerically stable, and highly nonlinear. Specifically, we jointly learn two groups of linear subspaces, one for each modality, so that features' ranking orders in different linear subspaces maximally preserve the cross-modal similarities. We show that the ranking-based hash function has a natural probabilistic approximation which transforms the original highly discontinuous optimization problem into one that can be efficiently solved using simple gradient descent algorithms. The proposed hashing framework is also flexible in the sense that the optimization procedures are not tied up to any specific form of loss function, which is typical for existing cross-modal hashing methods, but rather we can flexibly accommodate different loss functions with minimal changes to the learning steps. We demonstrate through extensive experiments on four widely-used real-world multimodal datasets that the proposed cross-modal hashing method can achieve competitive performance against several state-of-the-arts with only moderate training and testing time.

  8. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

    Science.gov (United States)

    Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

    2016-01-01

    In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite

  9. Subspace-based analysis of the ERT inverse problem

    Science.gov (United States)

    Ben Hadj Miled, Mohamed Khames; Miller, Eric L.

    2004-05-01

    In a previous work, we proposed a source-type formulation to the electrical resistance tomography (ERT) problem. Specifically, we showed that inhomogeneities in the medium can be viewed as secondary sources embedded in the homogeneous background medium and located at positions associated with variation in electrical conductivity. Assuming a piecewise constant conductivity distribution, the support of equivalent sources is equal to the boundary of the inhomogeneity. The estimation of the anomaly shape takes the form of an inverse source-type problem. In this paper, we explore the use of subspace methods to localize the secondary equivalent sources associated with discontinuities in the conductivity distribution. Our first alternative is the multiple signal classification (MUSIC) algorithm which is commonly used in the localization of multiple sources. The idea is to project a finite collection of plausible pole (or dipole) sources onto an estimated signal subspace and select those with largest correlations. In ERT, secondary sources are excited simultaneously but in different ways, i.e. with distinct amplitude patterns, depending on the locations and amplitudes of primary sources. If the number of receivers is "large enough", different source configurations can lead to a set of observation vectors that span the data subspace. However, since sources that are spatially close to each other have highly correlated signatures, seperation of such signals becomes very difficult in the presence of noise. To overcome this problem we consider iterative MUSIC algorithms like R-MUSIC and RAP-MUSIC. These recursive algorithms pose a computational burden as they require multiple large combinatorial searches. Results obtained with these algorithms using simulated data of different conductivity patterns are presented.

  10. Evaluating Clustering in Subspace Projections of High Dimensional Data

    DEFF Research Database (Denmark)

    Müller, Emmanuel; Günnemann, Stephan; Assent, Ira

    2009-01-01

    Clustering high dimensional data is an emerging research field. Subspace clustering or projected clustering group similar objects in subspaces, i.e. projections, of the full space. In the past decade, several clustering paradigms have been developed in parallel, without thorough evaluation...... and comparison between these paradigms on a common basis. Conclusive evaluation and comparison is challenged by three major issues. First, there is no ground truth that describes the "true" clusters in real world data. Second, a large variety of evaluation measures have been used that reflect different aspects...... of the clustering result. Finally, in typical publications authors have limited their analysis to their favored paradigm only, while paying other paradigms little or no attention. In this paper, we take a systematic approach to evaluate the major paradigms in a common framework. We study representative clustering...

  11. On the Worst-Case Convergence of MR and CG for Symmetric Positive Definite Tridiagonal Toeplitz Matrices

    Czech Academy of Sciences Publication Activity Database

    Liesen, J.; Tichý, Petr

    2005-01-01

    Roč. 20, - (2005), s. 180-197 ISSN 1068-9613 R&D Projects: GA AV ČR(CZ) KJB1030306 Institutional research plan: CEZ:AV0Z10300504 Keywords : Krylov subspace methods * conjugate gradient method * minimal residual method * convergence analysis * tridiagonal Toeplitz matrices * Poisson equation Subject RIV: BA - General Mathematics Impact factor: 0.608, year: 2005 http://etna.mcs.kent.edu/volumes/2001-2010/vol20/abstract.php?vol=20&pages=180-197

  12. Independent Subspace Analysis of the Sea Surface Temperature Variability: Non-Gaussian Sources and Sensitivity to Sampling and Dimensionality

    Directory of Open Access Journals (Sweden)

    Carlos A. L. Pires

    2017-01-01

    Full Text Available We propose an expansion of multivariate time-series data into maximally independent source subspaces. The search is made among rotations of prewhitened data which maximize non-Gaussianity of candidate sources. We use a tensorial invariant approximation of the multivariate negentropy in terms of a linear combination of squared coskewness and cokurtosis. By solving a high-order singular value decomposition problem, we extract the axes associated with most non-Gaussianity. Moreover, an estimate of the Gaussian subspace is provided by the trailing singular vectors. The independent subspaces are obtained through the search of “quasi-independent” components within the estimated non-Gaussian subspace, followed by the identification of groups with significant joint negentropies. Sources result essentially from the coherency of extremes of the data components. The method is then applied to the global sea surface temperature anomalies, equatorward of 65°, after being tested with non-Gaussian surrogates consistent with the data anomalies. The main emerging independent components and subspaces, supposedly generated by independent forcing, include different variability modes, namely, The East-Pacific, the Central Pacific, and the Atlantic Niños, the Atlantic Multidecadal Oscillation, along with the subtropical dipoles in the Indian, South Pacific, and South-Atlantic oceans. Benefits and usefulness of independent subspaces are then discussed.

  13. Central subspace dimensionality reduction using covariance operators.

    Science.gov (United States)

    Kim, Minyoung; Pavlovic, Vladimir

    2011-04-01

    We consider the task of dimensionality reduction informed by real-valued multivariate labels. The problem is often treated as Dimensionality Reduction for Regression (DRR), whose goal is to find a low-dimensional representation, the central subspace, of the input data that preserves the statistical correlation with the targets. A class of DRR methods exploits the notion of inverse regression (IR) to discover central subspaces. Whereas most existing IR techniques rely on explicit output space slicing, we propose a novel method called the Covariance Operator Inverse Regression (COIR) that generalizes IR to nonlinear input/output spaces without explicit target slicing. COIR's unique properties make DRR applicable to problem domains with high-dimensional output data corrupted by potentially significant amounts of noise. Unlike recent kernel dimensionality reduction methods that employ iterative nonconvex optimization, COIR yields a closed-form solution. We also establish the link between COIR, other DRR techniques, and popular supervised dimensionality reduction methods, including canonical correlation analysis and linear discriminant analysis. We then extend COIR to semi-supervised settings where many of the input points lack their labels. We demonstrate the benefits of COIR on several important regression problems in both fully supervised and semi-supervised settings.

  14. Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

    Science.gov (United States)

    Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

    2016-01-01

    In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740

  15. Active Subspace Methods for Data-Intensive Inverse Problems

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Qiqi [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

    2017-04-27

    The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.

  16. Comparison Study of Subspace Identification Methods Applied to Flexible Structures

    Science.gov (United States)

    Abdelghani, M.; Verhaegen, M.; Van Overschee, P.; De Moor, B.

    1998-09-01

    In the past few years, various time domain methods for identifying dynamic models of mechanical structures from modal experimental data have appeared. Much attention has been given recently to so-called subspace methods for identifying state space models. This paper presents a detailed comparison study of these subspace identification methods: the eigensystem realisation algorithm with observer/Kalman filter Markov parameters computed from input/output data (ERA/OM), the robust version of the numerical algorithm for subspace system identification (N4SID), and a refined version of the past outputs scheme of the multiple-output error state space (MOESP) family of algorithms. The comparison is performed by simulating experimental data using the five mode reduced model of the NASA Mini-Mast structure. The general conclusion is that for the case of white noise excitations as well as coloured noise excitations, the N4SID/MOESP algorithms perform equally well but give better results (improved transfer function estimates, improved estimates of the output) compared to the ERA/OM algorithm. The key computational step in the three algorithms is the approximation of the extended observability matrix of the system to be identified, for N4SID/MOESP, or of the observer for the system to be identified, for the ERA/OM. Furthermore, the three algorithms only require the specification of one dimensioning parameter.

  17. Experimental Study of Generalized Subspace Filters for the Cocktail Party Situation

    DEFF Research Database (Denmark)

    Christensen, Knud Bank; Christensen, Mads Græsbøll; Boldt, Jesper B.

    2016-01-01

    This paper investigates the potential performance of generalized subspace filters for speech enhancement in cocktail party situations with very poor signal/noise ratio, e.g. down to -15 dB. Performance metrics output signal/noise ratio, signal/ distortion ratio, speech quality rating and speech...... intelligibility rating are mapped as functions of two algorithm parameters, revealing clear trade-off options between noise, distortion and subjective performances and a recommended choice of trade-off. Given sufficiently good noise statistics, SNR improvements around 20 dB as well as PESQ quality and STOI...

  18. Experimental Comparison of Signal Subspace Based Noise Reduction Methods

    DEFF Research Database (Denmark)

    Hansen, Peter Søren Kirk; Hansen, Per Christian; Hansen, Steffen Duus

    1999-01-01

    The signal subspace approach for non-parametric speech enhancement is considered. Several algorithms have been proposed in the literature but only partly analyzed. Here, the different algorithms are compared, and the emphasis is put onto the limiting factors and practical behavior of the estimators...

  19. The importance of Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov

    Science.gov (United States)

    Sharkov, N. A.; Sharkova, O. A.

    2018-05-01

    The paper identifies the importance of the Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov and for the modern knowledge in survivability and safety of ships. The works by Leonard Euler "Marine Science" and "The Moon Motion New Theory" are discussed.

  20. Quantum theory of dynamical collective subspace for large-amplitude collective motion

    International Nuclear Information System (INIS)

    Sakata, Fumihiko; Marumori, Toshio; Ogura, Masanori.

    1986-03-01

    By placing emphasis on conceptual correspondence to the ''classical'' theory which has been developed within the framework of the time-dependent Hartree-Fock theory, a full quantum theory appropriate for describing large-amplitude collective motion is proposed. A central problem of the quantum theory is how to determine an optimal representation called a dynamical representation; the representation is specific for the collective subspace where the large-amplitude collective motion is replicated as satisfactorily as possible. As an extension of the classical theory where the concept of an approximate integral surface plays an important role, the dynamical representation is properly characterized by introducing a concept of an approximate invariant subspace of the Hamiltonian. (author)

  1. Robust Adaptive Beamforming with Sensor Position Errors Using Weighted Subspace Fitting-Based Covariance Matrix Reconstruction.

    Science.gov (United States)

    Chen, Peng; Yang, Yixin; Wang, Yong; Ma, Yuanliang

    2018-05-08

    When sensor position errors exist, the performance of recently proposed interference-plus-noise covariance matrix (INCM)-based adaptive beamformers may be severely degraded. In this paper, we propose a weighted subspace fitting-based INCM reconstruction algorithm to overcome sensor displacement for linear arrays. By estimating the rough signal directions, we construct a novel possible mismatched steering vector (SV) set. We analyze the proximity of the signal subspace from the sample covariance matrix (SCM) and the space spanned by the possible mismatched SV set. After solving an iterative optimization problem, we reconstruct the INCM using the estimated sensor position errors. Then we estimate the SV of the desired signal by solving an optimization problem with the reconstructed INCM. The main advantage of the proposed algorithm is its robustness against SV mismatches dominated by unknown sensor position errors. Numerical examples show that even if the position errors are up to half of the assumed sensor spacing, the output signal-to-interference-plus-noise ratio is only reduced by 4 dB. Beam patterns plotted using experiment data show that the interference suppression capability of the proposed beamformer outperforms other tested beamformers.

  2. The BL-QMR algorithm for non-Hermitian linear systems with multiple right-hand sides

    Energy Technology Data Exchange (ETDEWEB)

    Freund, R.W. [AT& T Bell Labs., Murray Hill, NJ (United States)

    1996-12-31

    Many applications require the solution of multiple linear systems that have the same coefficient matrix, but differ in their right-hand sides. Instead of applying an iterative method to each of these systems individually, it is potentially much more efficient to employ a block version of the method that generates iterates for all the systems simultaneously. However, it is quite intricate to develop robust and efficient block iterative methods. In particular, a key issue in the design of block iterative methods is the need for deflation. The iterates for the different systems that are produced by a block method will, in general, converge at different stages of the block iteration. An efficient and robust block method needs to be able to detect and then deflate converged systems. Each such deflation reduces the block size, and thus the block method needs to be able to handle varying block sizes. For block Krylov-subspace methods, deflation is also crucial in order to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences. An added difficulty arises for Lanczos-type block methods for non-Hermitian systems, since they involve two different block Krylov sequences. In these methods, deflation can now occur independently in both sequences, and consequently, the block sizes in the two sequences may become different in the course of the iteration, even though they were identical at the beginning. We present a block version of Freund and Nachtigal`s quasi-minimal residual method for the solution of non-Hermitian linear systems with single right-hand sides.

  3. Subspace Correction Methods for Total Variation and $\\ell_1$-Minimization

    KAUST Repository

    Fornasier, Massimo; Schö nlieb, Carola-Bibiane

    2009-01-01

    This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a seminorm for a subspace. The optimization is realized by alternating minimizations of the functional on a

  4. Stochastic estimation of nuclear level density in the nuclear shell model: An application to parity-dependent level density in 58Ni

    Directory of Open Access Journals (Sweden)

    Noritaka Shimizu

    2016-02-01

    Full Text Available We introduce a novel method to obtain level densities in large-scale shell-model calculations. Our method is a stochastic estimation of eigenvalue count based on a shifted Krylov-subspace method, which enables us to obtain level densities of huge Hamiltonian matrices. This framework leads to a successful description of both low-lying spectroscopy and the experimentally observed equilibration of Jπ=2+ and 2− states in 58Ni in a unified manner.

  5. Breaking of separability condition for dynamical collective subspace; Onset of quantum chaos in large-amplitude collective motion

    Energy Technology Data Exchange (ETDEWEB)

    Sakata, Fumihiko [Tokyo Univ., Tanashi (Japan). Inst. for Nuclear Study; Yamamoto, Yoshifumi; Marumori, Toshio; Iida, Shinji; Tsukuma, Hidehiko

    1989-11-01

    It is the purpose of the present paper to study 'global structure' of the state space of an N-body interacting fermion system, which exhibits regular, transient and stochastic phases depending on strength of the interaction. An optimum representation called a dynamical representation plays an essential role in this investigation. The concept of the dynamical representation has been introduced in the quantum theory of dynamical subspace in our previous paper, in order to determine self-consistently an optimum collective subspace as well as an optimum collective Hamiltonian. In the theory, furthermore, dynamical conditions called separability and stability conditions have been provided in order to identify the optimum collective subspace as an approximate invariant subspace of the Hamiltonian. Physical meaning of these conditions are clarified from a viewpoint to relate breaking of them with bifurcation of the collectivity and an onset of quantum chaos from the regular collective motion, by illustrating the general idea with numerical results obtained for a simple soluble model. It turns out that the onset of the stochastic phase is associated with dissolution of the quantum numbers to specify the collective subspace and this dissolution is induced by the breaking of the separability condition in the dynamical representation. (author).

  6. Subspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Jensen, Søren Holdt

    We survey the definitions and use of rank-revealing matrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both...... diagonal (eigenvalue and singular value) decompositions and rank-revealing triangular decompositions (ULV, URV, VSV, ULLV and ULLIV). In addition we show how the subspace-based algorithms can be evaluated and compared by means of simple FIR filter interpretations. The algorithms are illustrated...... with working Matlab code and applications in speech processing....

  7. A Comparative Study for Orthogonal Subspace Projection and Constrained Energy Minimization

    National Research Council Canada - National Science Library

    Du, Qian; Ren, Hsuan; Chang, Chein-I

    2003-01-01

    ...: orthogonal subspace projection (OSP) and constrained energy minimization (CEM). It is shown that they are closely related and essentially equivalent provided that the noise is white with large SNR...

  8. Using CUDA Technology for Defining the Stiffness Matrix in the Subspace of Eigenvectors

    Directory of Open Access Journals (Sweden)

    Yu. V. Berchun

    2015-01-01

    Full Text Available The aim is to improve the performance of solving a problem of deformable solid mechanics through the use of GPGPU. The paper describes technologies for computing systems using both a central and a graphics processor and provides motivation for using CUDA technology as the efficient one.The paper also analyses methods to solve the problem of defining natural frequencies and design waveforms, i.e. an iteration method in the subspace. The method includes several stages. The paper considers the most resource-hungry stage, which defines the stiffness matrix in the subspace of eigenforms and gives the mathematical interpretation of this stage.The GPU choice as a computing device is justified. The paper presents an algorithm for calculating the stiffness matrix in the subspace of eigenforms taking into consideration the features of input data. The global stiffness matrix is very sparse, and its size can reach tens of millions. Therefore, it is represented as a set of the stiffness matrices of the single elements of a model. The paper analyses methods of data representation in the software and selects the best practices for GPU computing.It describes the software implementation using CUDA technology to calculate the stiffness matrix in the subspace of eigenforms. Due to the input data nature, it is impossible to use the universal libraries of matrix computations (cuSPARSE and cuBLAS for loading the GPU. For efficient use of GPU resources in the software implementation, the stiffness matrices of elements are built in the block matrices of a special form. The advantages of using shared memory in GPU calculations are described.The transfer to the GPU computations allowed a twentyfold increase in performance (as compared to the multithreaded CPU-implementation on the model of middle dimensions (degrees of freedom about 2 million. Such an acceleration of one stage speeds up defining the natural frequencies and waveforms by the iteration method in a subspace

  9. N-screen aware multicriteria hybrid recommender system using weight based subspace clustering.

    Science.gov (United States)

    Ullah, Farman; Sarwar, Ghulam; Lee, Sungchang

    2014-01-01

    This paper presents a recommender system for N-screen services in which users have multiple devices with different capabilities. In N-screen services, a user can use various devices in different locations and time and can change a device while the service is running. N-screen aware recommendation seeks to improve the user experience with recommended content by considering the user N-screen device attributes such as screen resolution, media codec, remaining battery time, and access network and the user temporal usage pattern information that are not considered in existing recommender systems. For N-screen aware recommendation support, this work introduces a user device profile collaboration agent, manager, and N-screen control server to acquire and manage the user N-screen devices profile. Furthermore, a multicriteria hybrid framework is suggested that incorporates the N-screen devices information with user preferences and demographics. In addition, we propose an individual feature and subspace weight based clustering (IFSWC) to assign different weights to each subspace and each feature within a subspace in the hybrid framework. The proposed system improves the accuracy, precision, scalability, sparsity, and cold start issues. The simulation results demonstrate the effectiveness and prove the aforementioned statements.

  10. Geodesic Flow Kernel Support Vector Machine for Hyperspectral Image Classification by Unsupervised Subspace Feature Transfer

    Directory of Open Access Journals (Sweden)

    Alim Samat

    2016-03-01

    Full Text Available In order to deal with scenarios where the training data, used to deduce a model, and the validation data have different statistical distributions, we study the problem of transformed subspace feature transfer for domain adaptation (DA in the context of hyperspectral image classification via a geodesic Gaussian flow kernel based support vector machine (GFKSVM. To show the superior performance of the proposed approach, conventional support vector machines (SVMs and state-of-the-art DA algorithms, including information-theoretical learning of discriminative cluster for domain adaptation (ITLDC, joint distribution adaptation (JDA, and joint transfer matching (JTM, are also considered. Additionally, unsupervised linear and nonlinear subspace feature transfer techniques including principal component analysis (PCA, randomized nonlinear principal component analysis (rPCA, factor analysis (FA and non-negative matrix factorization (NNMF are investigated and compared. Experiments on two real hyperspectral images show the cross-image classification performances of the GFKSVM, confirming its effectiveness and suitability when applied to hyperspectral images.

  11. Fast regularizing sequential subspace optimization in Banach spaces

    International Nuclear Information System (INIS)

    Schöpfer, F; Schuster, T

    2009-01-01

    We are concerned with fast computations of regularized solutions of linear operator equations in Banach spaces in case only noisy data are available. To this end we modify recently developed sequential subspace optimization methods in such a way that the therein employed Bregman projections onto hyperplanes are replaced by Bregman projections onto stripes whose width is in the order of the noise level

  12. Lie n-derivations on 7 -subspace lattice algebras

    Indian Academy of Sciences (India)

    all x ∈ K and all A ∈ Alg L. Based on this result, a complete characterization of linear n-Lie derivations on Alg L is obtained. Keywords. J -subspace lattice algebras; Lie derivations; Lie n-derivations; derivations. 2010 Mathematics Subject Classification. 47B47, 47L35. 1. Introduction. Let A be an algebra. Recall that a linear ...

  13. Parallel computing techniques for rotorcraft aerodynamics

    Science.gov (United States)

    Ekici, Kivanc

    The modification of unsteady three-dimensional Navier-Stokes codes for application on massively parallel and distributed computing environments is investigated. The Euler/Navier-Stokes code TURNS (Transonic Unsteady Rotor Navier-Stokes) was chosen as a test bed because of its wide use by universities and industry. For the efficient implementation of TURNS on parallel computing systems, two algorithmic changes are developed. First, main modifications to the implicit operator, Lower-Upper Symmetric Gauss Seidel (LU-SGS) originally used in TURNS, is performed. Second, application of an inexact Newton method, coupled with a Krylov subspace iterative method (Newton-Krylov method) is carried out. Both techniques have been tried previously for the Euler equations mode of the code. In this work, we have extended the methods to the Navier-Stokes mode. Several new implicit operators were tried because of convergence problems of traditional operators with the high cell aspect ratio (CAR) grids needed for viscous calculations on structured grids. Promising results for both Euler and Navier-Stokes cases are presented for these operators. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. The parallel implicit operators used in the previous step are employed as preconditioners and the results are compared. The Message Passing Interface (MPI) protocol has been used because of its portability to various parallel architectures. It should be noted that the proposed methodology is general and can be applied to several other CFD codes (e.g. OVERFLOW).

  14. Linear multifrequency-grey acceleration recast for preconditioned Krylov iterations

    International Nuclear Information System (INIS)

    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

  15. Recursive subspace identification for in flight modal analysis of airplanes

    OpenAIRE

    De Cock , Katrien; Mercère , Guillaume; De Moor , Bart

    2006-01-01

    International audience; In this paper recursive subspace identification algorithms are applied to track the modal parameters of airplanes on-line during test flights. The ability to track changes in the damping ratios and the influence of the forgetting factor are studied through simulations.

  16. Novel algorithm of large-scale simultaneous linear equations

    International Nuclear Information System (INIS)

    Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L

    2010-01-01

    We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.

  17. Recursive Subspace Identification of AUV Dynamic Model under General Noise Assumption

    Directory of Open Access Journals (Sweden)

    Zheping Yan

    2014-01-01

    Full Text Available A recursive subspace identification algorithm for autonomous underwater vehicles (AUVs is proposed in this paper. Due to the advantages at handling nonlinearities and couplings, the AUV model investigated here is for the first time constructed as a Hammerstein model with nonlinear feedback in the linear part. To better take the environment and sensor noises into consideration, the identification problem is concerned as an errors-in-variables (EIV one which means that the identification procedure is under general noise assumption. In order to make the algorithm recursively, propagator method (PM based subspace approach is extended into EIV framework to form the recursive identification method called PM-EIV algorithm. With several identification experiments carried out by the AUV simulation platform, the proposed algorithm demonstrates its effectiveness and feasibility.

  18. Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to the Sn Equations with Highly Forward-Peaked Scattering

    Science.gov (United States)

    Turcksin, Bruno; Ragusa, Jean C.; Morel, Jim E.

    2012-01-01

    It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.

  19. Intrinsic Grassmann Averages for Online Linear and Robust Subspace Learning

    DEFF Research Database (Denmark)

    Chakraborty, Rudrasis; Hauberg, Søren; Vemuri, Baba C.

    2017-01-01

    Principal Component Analysis (PCA) is a fundamental method for estimating a linear subspace approximation to high-dimensional data. Many algorithms exist in literature to achieve a statistically robust version of PCA called RPCA. In this paper, we present a geometric framework for computing the p...

  20. Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

    KAUST Repository

    Pavarino, L.F.; Scacchi, S.; Zampini, Stefano

    2015-01-01

    The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

  1. Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

    KAUST Repository

    Pavarino, L.F.

    2015-07-18

    The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

  2. Mitigating Wind Induced Noise in Outdoor Microphone Signals Using a Singular Spectral Subspace Method

    Directory of Open Access Journals (Sweden)

    Omar Eldwaik

    2018-01-01

    Full Text Available Wind induced noise is one of the major concerns of outdoor acoustic signal acquisition. It affects many field measurement and audio recording scenarios. Filtering such noise is known to be difficult due to its broadband and time varying nature. In this paper, a new method to mitigate wind induced noise in microphone signals is developed. Instead of applying filtering techniques, wind induced noise is statistically separated from wanted signals in a singular spectral subspace. The paper is presented in the context of handling microphone signals acquired outdoor for acoustic sensing and environmental noise monitoring or soundscapes sampling. The method includes two complementary stages, namely decomposition and reconstruction. The first stage decomposes mixed signals in eigen-subspaces, selects and groups the principal components according to their contributions to wind noise and wanted signals in the singular spectrum domain. The second stage reconstructs the signals in the time domain, resulting in the separation of wind noise and wanted signals. Results show that microphone wind noise is separable in the singular spectrum domain evidenced by the weighted correlation. The new method might be generalized to other outdoor sound acquisition applications.

  3. Von Neumann algebras as complemented subspaces of B(H)

    DEFF Research Database (Denmark)

    Christensen, Erik; Wang, Liguang

    2014-01-01

    Let M be a von Neumann algebra of type II1 which is also a complemented subspace of B( H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented factor of type II1 on a Hilbert space H, then M is injective...

  4. Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals

    International Nuclear Information System (INIS)

    Baranov, Anton D

    2009-01-01

    We study properties of the embedding operators of model subspaces K p Θ (defined by inner functions) in the Hardy space H p (coinvariant subspaces of the shift operator). We find a criterion for the embedding of K p Θ in L p (μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in K p Θ . We investigate measures μ such that the embedding operator belongs to some Schatten-von Neumann ideal.

  5. Ordering sparse matrices for cache-based systems

    International Nuclear Information System (INIS)

    Biswas, Rupak; Oliker, Leonid

    2001-01-01

    The Conjugate Gradient (CG) algorithm is the oldest and best-known Krylov subspace method used to solve sparse linear systems. Most of the coating-point operations within each CG iteration is spent performing sparse matrix-vector multiplication (SPMV). We examine how various ordering and partitioning strategies affect the performance of CG and SPMV when different programming paradigms are used on current commercial cache-based computers. However, a multithreaded implementation on the cacheless Cray MTA demonstrates high efficiency and scalability without any special ordering or partitioning

  6. On Efficient Numerical Approximation of the Bilinear Form c* A(-1)b

    Czech Academy of Sciences Publication Activity Database

    Strakoš, Z.; Tichý, Petr

    2011-01-01

    Roč. 33, č. 2 (2011), s. 565-587 ISSN 1064-8275 R&D Projects: GA AV ČR IAA100300802 Grant - others:GA ČR(CZ) GA201/09/0917; GA AV ČR(CZ) M100300901 Program:GA Institutional research plan: CEZ:AV0Z10300504 Keywords : bilinear forms * scattering amplitude * method of moments * Krylov subspace methods * conjugate gradient method * biconjugate gradient method * Lanczos algorithm * Arnoldi algorithm * Gauss-Christoffel quadrature * model reduction Subject RIV: BA - General Mathematics Impact factor: 1.569, year: 2011

  7. Application of Earthquake Subspace Detectors at Kilauea and Mauna Loa Volcanoes, Hawai`i

    Science.gov (United States)

    Okubo, P.; Benz, H.; Yeck, W.

    2016-12-01

    Recent studies have demonstrated the capabilities of earthquake subspace detectors for detailed cataloging and tracking of seismicity in a number of regions and settings. We are exploring the application of subspace detectors at the United States Geological Survey's Hawaiian Volcano Observatory (HVO) to analyze seismicity at Kilauea and Mauna Loa volcanoes. Elevated levels of microseismicity and occasional swarms of earthquakes associated with active volcanism here present cataloging challenges due the sheer numbers of earthquakes and an intrinsically low signal-to-noise environment featuring oceanic microseism and volcanic tremor in the ambient seismic background. With high-quality continuous recording of seismic data at HVO, we apply subspace detectors (Harris and Dodge, 2011, Bull. Seismol. Soc. Am., doi: 10.1785/0120100103) during intervals of noteworthy seismicity. Waveform templates are drawn from Magnitude 2 and larger earthquakes within clusters of earthquakes cataloged in the HVO seismic database. At Kilauea, we focus on seismic swarms in the summit caldera region where, despite continuing eruptions from vents in the summit region and in the east rift zone, geodetic measurements reflect a relatively inflated volcanic state. We also focus on seismicity beneath and adjacent to Mauna Loa's summit caldera that appears to be associated with geodetic expressions of gradual volcanic inflation, and where precursory seismicity clustered prior to both Mauna Loa's most recent eruptions in 1975 and 1984. We recover several times more earthquakes with the subspace detectors - down to roughly 2 magnitude units below the templates, based on relative amplitudes - compared to the numbers of cataloged earthquakes. The increased numbers of detected earthquakes in these clusters, and the ability to associate and locate them, allow us to infer details of the spatial and temporal distributions and possible variations in stresses within these key regions of the volcanoes.

  8. Discrete-State Stochastic Models of Calcium-Regulated Calcium Influx and Subspace Dynamics Are Not Well-Approximated by ODEs That Neglect Concentration Fluctuations

    Science.gov (United States)

    Weinberg, Seth H.; Smith, Gregory D.

    2012-01-01

    Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result that accounts for the small subspace volume) with the corresponding deterministic model (an approximation that assumes large system size). When subspace calcium did not regulate calcium influx, the deterministic and stochastic descriptions agreed. However, when calcium binding altered channel activity in the model, the continuous deterministic description often deviated significantly from the discrete stochastic model, unless the subspace volume is unrealistically large and/or the kinetics of the calcium binding are sufficiently fast. This principle was also demonstrated using a physiologically realistic model of calmodulin regulation of L-type calcium channels introduced by Yue and coworkers. PMID:23509597

  9. Hankel Matrix Correlation Function-Based Subspace Identification Method for UAV Servo System

    Directory of Open Access Journals (Sweden)

    Minghong She

    2018-01-01

    Full Text Available For the identification problem of closed-loop subspace model, we propose a zero space projection method based on the estimation of correlation function to fill the block Hankel matrix of identification model by combining the linear algebra with geometry. By using the same projection of related data in time offset set and LQ decomposition, the multiplication operation of projection is achieved and dynamics estimation of the unknown equipment system model is obtained. Consequently, we have solved the problem of biased estimation caused when the open-loop subspace identification algorithm is applied to the closed-loop identification. A simulation example is given to show the effectiveness of the proposed approach. In final, the practicability of the identification algorithm is verified by hardware test of UAV servo system in real environment.

  10. A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

    Science.gov (United States)

    Asgharzadeh, Hafez; Borazjani, Iman

    2017-02-15

    The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the

  11. A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

    Science.gov (United States)

    Asgharzadeh, Hafez; Borazjani, Iman

    2016-01-01

    The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the

  12. Stable reduced-order models of generalized dynamical systems using coordinate-transformed Arnoldi algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Silveira, L.M.; Kamon, M.; Elfadel, I.; White, J. [Massachusetts Inst. of Technology, Cambridge, MA (United States)

    1996-12-31

    Model order reduction based on Krylov subspace iterative methods has recently emerged as a major tool for compressing the number of states in linear models used for simulating very large physical systems (VLSI circuits, electromagnetic interactions). There are currently two main methods for accomplishing such a compression: one is based on the nonsymmetric look-ahead Lanczos algorithm that gives a numerically stable procedure for finding Pade approximations, while the other is based on a less well characterized Arnoldi algorithm. In this paper, we show that for certain classes of generalized state-space systems, the reduced-order models produced by a coordinate-transformed Arnoldi algorithm inherit the stability of the original system. Complete Proofs of our results will be given in the final paper.

  13. Application of spectral Lanczos decomposition method to large scale problems arising geophysics

    Energy Technology Data Exchange (ETDEWEB)

    Tamarchenko, T. [Western Atlas Logging Services, Houston, TX (United States)

    1996-12-31

    This paper presents an application of Spectral Lanczos Decomposition Method (SLDM) to numerical modeling of electromagnetic diffusion and elastic waves propagation in inhomogeneous media. SLDM approximates an action of a matrix function as a linear combination of basis vectors in Krylov subspace. I applied the method to model electromagnetic fields in three-dimensions and elastic waves in two dimensions. The finite-difference approximation of the spatial part of differential operator reduces the initial boundary-value problem to a system of ordinary differential equations with respect to time. The solution to this system requires calculating exponential and sine/cosine functions of the stiffness matrices. Large scale numerical examples are in a good agreement with the theoretical error bounds and stability estimates given by Druskin, Knizhnerman, 1987.

  14. Index Formulae for Subspaces of Kreĭn Spaces

    NARCIS (Netherlands)

    Dijksma, Aad; Gheondea, Aurelian

    1996-01-01

    For a subspace S of a Kreĭn space K and an arbitrary fundamental decomposition K = K-[+]K+ of K, we prove the index formula κ-(S) + dim(S⊥ ∩ K+) = κ+(S⊥) + dim(S ∩ K-), where κ±(S) stands for the positive/negative signature of S. The difference dim(S ∩ K-) - dim(S⊥ ∩ K+), provided it is well

  15. Visual tracking based on the sparse representation of the PCA subspace

    Science.gov (United States)

    Chen, Dian-bing; Zhu, Ming; Wang, Hui-li

    2017-09-01

    We construct a collaborative model of the sparse representation and the subspace representation. First, we represent the tracking target in the principle component analysis (PCA) subspace, and then we employ an L 1 regularization to restrict the sparsity of the residual term, an L 2 regularization term to restrict the sparsity of the representation coefficients, and an L 2 norm to restrict the distance between the reconstruction and the target. Then we implement the algorithm in the particle filter framework. Furthermore, an iterative method is presented to get the global minimum of the residual and the coefficients. Finally, an alternative template update scheme is adopted to avoid the tracking drift which is caused by the inaccurate update. In the experiment, we test the algorithm on 9 sequences, and compare the results with 5 state-of-art methods. According to the results, we can conclude that our algorithm is more robust than the other methods.

  16. Cumulant-Based Coherent Signal Subspace Method for Bearing and Range Estimation

    Directory of Open Access Journals (Sweden)

    Bourennane Salah

    2007-01-01

    Full Text Available A new method for simultaneous range and bearing estimation for buried objects in the presence of an unknown Gaussian noise is proposed. This method uses the MUSIC algorithm with noise subspace estimated by using the slice fourth-order cumulant matrix of the received data. The higher-order statistics aim at the removal of the additive unknown Gaussian noise. The bilinear focusing operator is used to decorrelate the received signals and to estimate the coherent signal subspace. A new source steering vector is proposed including the acoustic scattering model at each sensor. Range and bearing of the objects at each sensor are expressed as a function of those at the first sensor. This leads to the improvement of object localization anywhere, in the near-field or in the far-field zone of the sensor array. Finally, the performances of the proposed method are validated on data recorded during experiments in a water tank.

  17. On the Kalman Filter error covariance collapse into the unstable subspace

    Directory of Open Access Journals (Sweden)

    A. Trevisan

    2011-03-01

    Full Text Available When the Extended Kalman Filter is applied to a chaotic system, the rank of the error covariance matrices, after a sufficiently large number of iterations, reduces to N+ + N0 where N+ and N0 are the number of positive and null Lyapunov exponents. This is due to the collapse into the unstable and neutral tangent subspace of the solution of the full Extended Kalman Filter. Therefore the solution is the same as the solution obtained by confining the assimilation to the space spanned by the Lyapunov vectors with non-negative Lyapunov exponents. Theoretical arguments and numerical verification are provided to show that the asymptotic state and covariance estimates of the full EKF and of its reduced form, with assimilation in the unstable and neutral subspace (EKF-AUS are the same. The consequences of these findings on applications of Kalman type Filters to chaotic models are discussed.

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

    Czech Academy of Sciences Publication Activity Database

    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

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

    Czech Academy of Sciences Publication Activity Database

    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

  20. Preconditioning for Allen–Cahn variational inequalities with non-local constraints

    KAUST Repository

    Blank, Luise

    2012-06-01

    The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach. © 2012 Elsevier Inc.

  1. Quantum Gate Operations in Decoherence-Free Subspace with Superconducting Charge Qubits inside a Cavity

    International Nuclear Information System (INIS)

    Yi-Min, Wang; Yan-Li, Zhou; Lin-Mei, Liang; Cheng-Zu, Li

    2009-01-01

    We propose a feasible scheme to achieve universal quantum gate operations in decoherence-free subspace with superconducting charge qubits placed in a microwave cavity. Single-logic-qubit gates can be realized with cavity assisted interaction, which possesses the advantages of unconventional geometric gate operation. The two-logic-qubit controlled-phase gate between subsystems can be constructed with the help of a variable electrostatic transformer. The collective decoherence can be successfully avoided in our well-designed system. Moreover, GHZ state for logical qubits can also be easily produced in this system

  2. Curve Evolution in Subspaces and Exploring the Metameric Class of Histogram of Gradient Orientation based Features using Nonlinear Projection Methods

    DEFF Research Database (Denmark)

    Tatu, Aditya Jayant

    This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods. Curve evolution is a well known method used in various applications like...... tracking interfaces, active contour based segmentation methods and others. It can also be used to study shape spaces, as deforming a shape can be thought of as evolving its boundary curve. During curve evolution a curve traces out a path in the infinite dimensional space of curves. Due to application...... specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined...

  3. Quantum computation via local control theory: Direct sum vs. direct product Hilbert spaces

    International Nuclear Information System (INIS)

    Sklarz, Shlomo E.; Tannor, David J.

    2006-01-01

    The central objective in any quantum computation is the creation of a desired unitary transformation; the mapping that this unitary transformation produces between the input and output states is identified with the computation. In [S.E. Sklarz, D.J. Tannor, arXiv:quant-ph/0404081 (submitted to PRA) (2004)] it was shown that local control theory can be used to calculate fields that will produce such a desired unitary transformation. In contrast with previous strategies for quantum computing based on optimal control theory, the local control scheme maintains the system within the computational subspace at intermediate times, thereby avoiding unwanted decay processes. In [S.E. Sklarz et al.], the structure of the Hilbert space had a direct sum structure with respect to the computational register and the mediating states. In this paper, we extend the formalism to the important case of a direct product Hilbert space. The final equations for the control algorithm for the two cases are remarkably similar in structure, despite the fact that the derivations are completely different and that in one case the dynamics is in a Hilbert space and in the other case the dynamics is in a Liouville space. As shown in [S.E. Sklarz et al.], the direct sum implementation leads to a computational mechanism based on virtual transitions, and can be viewed as an extension of the principles of Stimulated Raman Adiabatic Passage from state manipulation to evolution operator manipulation. The direct product implementation developed here leads to the intriguing concept of virtual entanglement - computation that exploits second-order transitions that pass through entangled states but that leaves the subsystems nearly separable at all intermediate times. Finally, we speculate on a connection between the algorithm developed here and the concept of decoherence free subspaces

  4. EVD Dualdating Based Online Subspace Learning

    Directory of Open Access Journals (Sweden)

    Bo Jin

    2014-01-01

    Full Text Available Conventional incremental PCA methods usually only discuss the situation of adding samples. In this paper, we consider two different cases: deleting samples and simultaneously adding and deleting samples. To avoid the NP-hard problem of downdating SVD without right singular vectors and specific position information, we choose to use EVD instead of SVD, which is used by most IPCA methods. First, we propose an EVD updating and downdating algorithm, called EVD dualdating, which permits simultaneous arbitrary adding and deleting operation, via transforming the EVD of the covariance matrix into a SVD updating problem plus an EVD of a small autocorrelation matrix. A comprehensive analysis is delivered to express the essence, expansibility, and computation complexity of EVD dualdating. A mathematical theorem proves that if the whole data matrix satisfies the low-rank-plus-shift structure, EVD dualdating is an optimal rank-k estimator under the sequential environment. A selection method based on eigenvalues is presented to determine the optimal rank k of the subspace. Then, we propose three incremental/decremental PCA methods: EVDD-IPCA, EVDD-DPCA, and EVDD-IDPCA, which are adaptive to the varying mean. Finally, plenty of comparative experiments demonstrate that EVDD-based methods outperform conventional incremental/decremental PCA methods in both efficiency and accuracy.

  5. Bi Sparsity Pursuit: A Paradigm for Robust Subspace Recovery

    Science.gov (United States)

    2016-09-27

    Bian, Student Member, IEEE, and Hamid Krim, Fellow, IEEE Abstract The success of sparse models in computer vision and machine learning is due to the...16. SECURITY CLASSIFICATION OF: The success of sparse models in computer vision and machine learning is due to the fact that, high dimensional data...vision and machine learning is due to the fact that, high dimensional data is distributed in a union of low dimensional subspaces in many real-world

  6. View subspaces for indexing and retrieval of 3D models

    Science.gov (United States)

    Dutagaci, Helin; Godil, Afzal; Sankur, Bülent; Yemez, Yücel

    2010-02-01

    View-based indexing schemes for 3D object retrieval are gaining popularity since they provide good retrieval results. These schemes are coherent with the theory that humans recognize objects based on their 2D appearances. The viewbased techniques also allow users to search with various queries such as binary images, range images and even 2D sketches. The previous view-based techniques use classical 2D shape descriptors such as Fourier invariants, Zernike moments, Scale Invariant Feature Transform-based local features and 2D Digital Fourier Transform coefficients. These methods describe each object independent of others. In this work, we explore data driven subspace models, such as Principal Component Analysis, Independent Component Analysis and Nonnegative Matrix Factorization to describe the shape information of the views. We treat the depth images obtained from various points of the view sphere as 2D intensity images and train a subspace to extract the inherent structure of the views within a database. We also show the benefit of categorizing shapes according to their eigenvalue spread. Both the shape categorization and data-driven feature set conjectures are tested on the PSB database and compared with the competitor view-based 3D shape retrieval algorithms.

  7. Beamforming using subspace estimation from a diagonally averaged sample covariance.

    Science.gov (United States)

    Quijano, Jorge E; Zurk, Lisa M

    2017-08-01

    The potential benefit of a large-aperture sonar array for high resolution target localization is often challenged by the lack of sufficient data required for adaptive beamforming. This paper introduces a Toeplitz-constrained estimator of the clairvoyant signal covariance matrix corresponding to multiple far-field targets embedded in background isotropic noise. The estimator is obtained by averaging along subdiagonals of the sample covariance matrix, followed by covariance extrapolation using the method of maximum entropy. The sample covariance is computed from limited data snapshots, a situation commonly encountered with large-aperture arrays in environments characterized by short periods of local stationarity. Eigenvectors computed from the Toeplitz-constrained covariance are used to construct signal-subspace projector matrices, which are shown to reduce background noise and improve detection of closely spaced targets when applied to subspace beamforming. Monte Carlo simulations corresponding to increasing array aperture suggest convergence of the proposed projector to the clairvoyant signal projector, thereby outperforming the classic projector obtained from the sample eigenvectors. Beamforming performance of the proposed method is analyzed using simulated data, as well as experimental data from the Shallow Water Array Performance experiment.

  8. A frequency domain subspace algorithm for mixed causal, anti-causal LTI systems

    NARCIS (Netherlands)

    Fraanje, Rufus; Verhaegen, Michel; Verdult, Vincent; Pintelon, Rik

    2003-01-01

    The paper extends the subspacc identification method to estimate state-space models from frequency response function (FRF) samples, proposed by McKelvey et al. (1996) for mixed causal/anti-causal systems, and shows that other frequency domain subspace algorithms can be extended similarly. The method

  9. Expedited Holonomic Quantum Computation via Net Zero-Energy-Cost Control in Decoherence-Free Subspace.

    Science.gov (United States)

    Pyshkin, P V; Luo, Da-Wei; Jing, Jun; You, J Q; Wu, Lian-Ao

    2016-11-25

    Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. This control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an expedited holonomic quantum computation protocol.

  10. Kernel based subspace projection of near infrared hyperspectral images of maize kernels

    DEFF Research Database (Denmark)

    Larsen, Rasmus; Arngren, Morten; Hansen, Per Waaben

    2009-01-01

    In this paper we present an exploratory analysis of hyper- spectral 900-1700 nm images of maize kernels. The imaging device is a line scanning hyper spectral camera using a broadband NIR illumi- nation. In order to explore the hyperspectral data we compare a series of subspace projection methods ......- tor transform outperform the linear methods as well as kernel principal components in producing interesting projections of the data.......In this paper we present an exploratory analysis of hyper- spectral 900-1700 nm images of maize kernels. The imaging device is a line scanning hyper spectral camera using a broadband NIR illumi- nation. In order to explore the hyperspectral data we compare a series of subspace projection methods...... including principal component analysis and maximum autocorrelation factor analysis. The latter utilizes the fact that interesting phenomena in images exhibit spatial autocorrelation. However, linear projections often fail to grasp the underlying variability on the data. Therefore we propose to use so...

  11. Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

    International Nuclear Information System (INIS)

    Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long

    2014-01-01

    In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)

  12. Some observations on weighted GMRES

    KAUST Repository

    Güttel, Stefan

    2014-01-10

    We investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used. © 2014 Springer Science+Business Media New York.

  13. Some observations on weighted GMRES

    KAUST Repository

    Gü ttel, Stefan; Pestana, Jennifer

    2014-01-01

    We investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used. © 2014 Springer Science+Business Media New York.

  14. REVIEW APPROACHES ECONOMIC DEVELOPMENT OF THE TERRITORY OF THE ARCTIC ZONE OF THE RUSSIAN FEDERATION, PRESENTED IN THE FORM OF TARGET SUBSPACE

    Directory of Open Access Journals (Sweden)

    N. I. Didenko

    2015-01-01

    Full Text Available This paper presents a conceptual idea of the organization of management of development of the Arctic area of the Russian Federation in the form of a set of target subspace. Among the possible types of target subspace comprising the Arctic zone of the Russian Federation, allocated seven subspace: basic city mobile Camps, site production of mineral resources, recreational area, fishing area, the Northern Sea Route, infrastructure protection safe existence in the Arctic. The task of determining the most appropriate theoretical approach for the development of each target subspaces. To this end, the theoretical approaches of economic growth and development of the theory of "economic base» (Economic Base Theory; resource theory (Staple Theory; Theory sectors (Sector Theory; theory of growth poles (Growth Pole Theory; neoclassical theory (Neoclassical Growth Theory; theory of inter-regional trade (Interregional Trade Theory; theory of the commodity cycle; entrepreneurial theory (Entrepreneurship Theories.

  15. Two-Dimensional DOA Estimation in Compressed Sensing with Compressive-Reduced Dimension-lp-MUSIC

    Directory of Open Access Journals (Sweden)

    Weijian Si

    2015-01-01

    Full Text Available This paper presents a novel two-dimensional (2D direction of arrival (DOA estimation method in compressed sensing (CS to remove the estimation failure problem and achieve superior performance. The proposed method separates the steering vector into two parts to construct two corresponding noise subspaces by introducing electric angles. Then, electric angles are estimated based on the constructed noise subspaces. In order to estimate the azimuth and elevation angles in terms of estimates of electric angles, arc-tangent operations are exploited. The arc-tangent is a one-to-one function and allows the value of the argument to be larger than unity so that the proposed method never fails. The proposed method can avoid pair matching to reduce the computational complexity and extend the number of snapshots to improve performance. Simulation results show that the proposed method can avoid estimation failure occurrence and has superior performance as compared to existing methods.

  16. On the selection of user-defined parameters in data-driven stochastic subspace identification

    Science.gov (United States)

    Priori, C.; De Angelis, M.; Betti, R.

    2018-02-01

    The paper focuses on the time domain output-only technique called Data-Driven Stochastic Subspace Identification (DD-SSI); in order to identify modal models (frequencies, damping ratios and mode shapes), the role of its user-defined parameters is studied, and rules to determine their minimum values are proposed. Such investigation is carried out using, first, the time histories of structural responses to stationary excitations, with a large number of samples, satisfying the hypothesis on the input imposed by DD-SSI. Then, the case of non-stationary seismic excitations with a reduced number of samples is considered. In this paper, partitions of the data matrix different from the one proposed in the SSI literature are investigated, together with the influence of different choices of the weighting matrices. The study is carried out considering two different applications: (1) data obtained from vibration tests on a scaled structure and (2) in-situ tests on a reinforced concrete building. Referring to the former, the identification of a steel frame structure tested on a shaking table is performed using its responses in terms of absolute accelerations to a stationary (white noise) base excitation and to non-stationary seismic excitations of low intensity. Black-box and modal models are identified in both cases and the results are compared with those from an input-output subspace technique. With regards to the latter, the identification of a complex hospital building is conducted using data obtained from ambient vibration tests.

  17. Code subspaces for LLM geometries

    Science.gov (United States)

    Berenstein, David; Miller, Alexandra

    2018-03-01

    We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.

  18. Modal–Physical Hybrid System Identification of High-rise Building via Subspace and Inverse-Mode Methods

    Directory of Open Access Journals (Sweden)

    Kohei Fujita

    2017-08-01

    Full Text Available A system identification (SI problem of high-rise buildings is investigated under restricted data environments. The shear and bending stiffnesses of a shear-bending model (SB model representing the high-rise buildings are identified via the smart combination of the subspace and inverse-mode methods. Since the shear and bending stiffnesses of the SB model can be identified in the inverse-mode method by using the lowest mode of horizontal displacements and floor rotation angles, the lowest mode of the objective building is identified first by using the subspace method. Identification of the lowest mode is performed by using the amplitude of transfer functions derived in the subspace method. Considering the resolution in measuring the floor rotation angles in lower stories, floor rotation angles in most stories are predicted from the floor rotation angle at the top floor. An empirical equation of floor rotation angles is proposed by investigating those for various building models. From the viewpoint of application of the present SI method to practical situations, a non-simultaneous measurement system is also proposed. In order to investigate the reliability and accuracy of the proposed SI method, a 10-story building frame subjected to micro-tremor is examined.

  19. Uncertainty calculation for modal parameters used with stochastic subspace identification: an application to a bridge structure

    Science.gov (United States)

    Hsu, Wei-Ting; Loh, Chin-Hsiung; Chao, Shu-Hsien

    2015-03-01

    Stochastic subspace identification method (SSI) has been proven to be an efficient algorithm for the identification of liner-time-invariant system using multivariate measurements. Generally, the estimated modal parameters through SSI may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, finite number of data samples etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the stabilization diagram can help users to identify the correct model, i.e. through removing the spurious modes. Modal parameters are estimated at successive model orders where the physical modes of the system are extracted and separated from the spurious modes. Besides, an uncertainty computation scheme was derived for the calculation of uncertainty bounds for modal parameters at some given model order. The uncertainty bounds of damping ratios are particularly interesting, as the estimation of damping ratios are difficult to obtain. In this paper, an automated stochastic subspace identification algorithm is addressed. First, the identification of modal parameters through covariance-driven stochastic subspace identification from the output-only measurements is used for discussion. A systematic way of investigation on the criteria for the stabilization diagram is presented. Secondly, an automated algorithm of post-processing on stabilization diagram is demonstrated. Finally, the computation of uncertainty bounds for each mode with all model order in the stabilization diagram is utilized to determine system natural frequencies and damping ratios. Demonstration of this study on the system identification of a three-span steel bridge under operation condition is presented. It is shown that the proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance the robustness and reliability in structural health monitoring.

  20. Invariant subspaces in some function spaces on symmetric spaces. II

    International Nuclear Information System (INIS)

    Platonov, S S

    1998-01-01

    Let G be a semisimple connected Lie group with finite centre, K a maximal compact subgroup of G, and M=G/K a Riemannian symmetric space of non-compact type. We study the problem of describing the structure of closed linear subspaces in various function spaces on M that are invariant under the quasiregular representation of the group G. We consider the case when M is a symplectic symmetric space of rank 1

  1. Fast solution of Cahn–Hilliard variational inequalities using implicit time discretization and finite elements

    KAUST Repository

    Bosch, Jessica

    2014-04-01

    We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach. © 2014 Elsevier Inc.

  2. 2nd International Workshop on the Numerical Solution of Markov Chains

    CERN Document Server

    1995-01-01

    Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.

  3. Nonlinear acceleration of SN transport calculations

    Energy Technology Data Exchange (ETDEWEB)

    Fichtl, Erin D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Calef, Matthew T [Los Alamos National Laboratory

    2010-12-20

    The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

  4. Nonlinear acceleration of S_n transport calculations

    International Nuclear Information System (INIS)

    Fichtl, Erin D.; Warsa, James S.; Calef, Matthew T.

    2011-01-01

    The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we employ a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application. (author)

  5. Investigation of the stochastic subspace identification method for on-line wind turbine tower monitoring

    Science.gov (United States)

    Dai, Kaoshan; Wang, Ying; Lu, Wensheng; Ren, Xiaosong; Huang, Zhenhua

    2017-04-01

    Structural health monitoring (SHM) of wind turbines has been applied in the wind energy industry to obtain their real-time vibration parameters and to ensure their optimum performance. For SHM, the accuracy of its results and the efficiency of its measurement methodology and data processing algorithm are the two major concerns. Selection of proper measurement parameters could improve such accuracy and efficiency. The Stochastic Subspace Identification (SSI) is a widely used data processing algorithm for SHM. This research discussed the accuracy and efficiency of SHM using SSI method to identify vibration parameters of on-line wind turbine towers. Proper measurement parameters, such as optimum measurement duration, are recommended.

  6. Improving the Communication Pattern in Matrix-Vector Operations for Large Scale-Free Graphs by Disaggregation

    Energy Technology Data Exchange (ETDEWEB)

    Kuhlemann, Verena [Emory Univ., Atlanta, GA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2013-10-28

    Matrix-vector multiplication is the key operation in any Krylov-subspace iteration method. We are interested in Krylov methods applied to problems associated with the graph Laplacian arising from large scale-free graphs. Furthermore, computations with graphs of this type on parallel distributed-memory computers are challenging. This is due to the fact that scale-free graphs have a degree distribution that follows a power law, and currently available graph partitioners are not efficient for such an irregular degree distribution. The lack of a good partitioning leads to excessive interprocessor communication requirements during every matrix-vector product. Here, we present an approach to alleviate this problem based on embedding the original irregular graph into a more regular one by disaggregating (splitting up) vertices in the original graph. The matrix-vector operations for the original graph are performed via a factored triple matrix-vector product involving the embedding graph. And even though the latter graph is larger, we are able to decrease the communication requirements considerably and improve the performance of the matrix-vector product.

  7. NITSOL: A Newton iterative solver for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)

    1996-12-31

    Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.

  8. Projected Gauss-Seidel subspace minimization method for interactive rigid body dynamics

    DEFF Research Database (Denmark)

    Silcowitz-Hansen, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

    2010-01-01

    artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We formulate the contact force problem as a nonlinear complementarity problem, and discretize the problem to derive the Projected Gauss–Seidel method. We combine the Projected Gauss......–Seidel method with a subspace minimization method. Our new method shows improved qualities and superior convergence properties for specific configurations....

  9. Visual characterization and diversity quantification of chemical libraries: 2. Analysis and selection of size-independent, subspace-specific diversity indices.

    Science.gov (United States)

    Colliandre, Lionel; Le Guilloux, Vincent; Bourg, Stephane; Morin-Allory, Luc

    2012-02-27

    High Throughput Screening (HTS) is a standard technique widely used to find hit compounds in drug discovery projects. The high costs associated with such experiments have highlighted the need to carefully design screening libraries in order to avoid wasting resources. Molecular diversity is an established concept that has been used to this end for many years. In this article, a new approach to quantify the molecular diversity of screening libraries is presented. The approach is based on the Delimited Reference Chemical Subspace (DRCS) methodology, a new method that can be used to delimit the densest subspace spanned by a reference library in a reduced 2D continuous space. A total of 22 diversity indices were implemented or adapted to this methodology, which is used here to remove outliers and obtain a relevant cell-based partition of the subspace. The behavior of these indices was assessed and compared in various extreme situations and with respect to a set of theoretical rules that a diversity function should satisfy when libraries of different sizes have to be compared. Some gold standard indices are found inappropriate in such a context, while none of the tested indices behave perfectly in all cases. Five DRCS-based indices accounting for different aspects of diversity were finally selected, and a simple framework is proposed to use them effectively. Various libraries have been profiled with respect to more specific subspaces, which further illustrate the interest of the method.

  10. Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

    Directory of Open Access Journals (Sweden)

    Yizhe Wang

    2018-01-01

    Full Text Available Active flutter suppression and subspace identification for a flexible wing model using micro fiber composite actuator were experimentally studied in a low speed wind tunnel. NACA0006 thin airfoil model was used for the experimental object to verify the performance of identification algorithm and designed controller. The equation of the fluid, vibration, and piezoelectric coupled motion was theoretically analyzed and experimentally identified under the open-loop and closed-loop condition by subspace method for controller design. A robust pole placement algorithm in terms of linear matrix inequality that accommodates the model uncertainty caused by identification deviation and flow speed variation was utilized to stabilize the divergent aeroelastic system. For further enlarging the flutter envelope, additional controllers were designed subject to the models beyond the flutter speed. Wind speed was measured online as the decision parameter of switching between the controllers. To ensure the stability of arbitrary switching, Common Lyapunov function method was applied to design the robust pole placement controllers for different models to ensure that the closed-loop system shared a common Lyapunov function. Wind tunnel result showed that the designed controllers could stabilize the time varying aeroelastic system over a wide range under arbitrary switching.

  11. An Improved EMD-Based Dissimilarity Metric for Unsupervised Linear Subspace Learning

    Directory of Open Access Journals (Sweden)

    Xiangchun Yu

    2018-01-01

    Full Text Available We investigate a novel way of robust face image feature extraction by adopting the methods based on Unsupervised Linear Subspace Learning to extract a small number of good features. Firstly, the face image is divided into blocks with the specified size, and then we propose and extract pooled Histogram of Oriented Gradient (pHOG over each block. Secondly, an improved Earth Mover’s Distance (EMD metric is adopted to measure the dissimilarity between blocks of one face image and the corresponding blocks from the rest of face images. Thirdly, considering the limitations of the original Locality Preserving Projections (LPP, we proposed the Block Structure LPP (BSLPP, which effectively preserves the structural information of face images. Finally, an adjacency graph is constructed and a small number of good features of a face image are obtained by methods based on Unsupervised Linear Subspace Learning. A series of experiments have been conducted on several well-known face databases to evaluate the effectiveness of the proposed algorithm. In addition, we construct the noise, geometric distortion, slight translation, slight rotation AR, and Extended Yale B face databases, and we verify the robustness of the proposed algorithm when faced with a certain degree of these disturbances.

  12. Structural damage diagnosis based on on-line recursive stochastic subspace identification

    International Nuclear Information System (INIS)

    Loh, Chin-Hsiung; Weng, Jian-Huang; Liu, Yi-Cheng; Lin, Pei-Yang; Huang, Shieh-Kung

    2011-01-01

    This paper presents a recursive stochastic subspace identification (RSSI) technique for on-line and almost real-time structural damage diagnosis using output-only measurements. Through RSSI the time-varying natural frequencies of a system can be identified. To reduce the computation time in conducting LQ decomposition in RSSI, the Givens rotation as well as the matrix operation appending a new data set are derived. The relationship between the size of the Hankel matrix and the data length in each shifting moving window is examined so as to extract the time-varying features of the system without loss of generality and to establish on-line and almost real-time system identification. The result from the RSSI technique can also be applied to structural damage diagnosis. Off-line data-driven stochastic subspace identification was used first to establish the system matrix from the measurements of an undamaged (reference) case. Then the RSSI technique incorporating a Kalman estimator is used to extract the dynamic characteristics of the system through continuous monitoring data. The predicted residual error is defined as a damage feature and through the outlier statistics provides an indicator of damage. Verification of the proposed identification algorithm by using the bridge scouring test data and white noise response data of a reinforced concrete frame structure is conducted

  13. A new efficient method for the calculation of interior eigenpairs and its application to vibrational structure problems

    Science.gov (United States)

    Petrenko, Taras; Rauhut, Guntram

    2017-03-01

    Vibrational configuration interaction theory is a common method for calculating vibrational levels and associated IR and Raman spectra of small and medium-sized molecules. When combined with appropriate configuration selection procedures, the method allows the treatment of configuration spaces with up to 1010 configurations. In general, this approach pursues the construction of the eigenstates with significant contributions of physically relevant configurations. The corresponding eigenfunctions are evaluated in the subspace of selected configurations. However, it can easily reach the dimension which is not tractable for conventional eigenvalue solvers. Although Davidson and Lanczos methods are the methods of choice for calculating exterior eigenvalues, they usually fall into stagnation when applied to interior states. The latter are commonly treated by the Jacobi-Davidson method. This approach in conjunction with matrix factorization for solving the correction equation (CE) is prohibitive for larger problems, and it has limited efficiency if the solution of the CE is based on Krylov's subspace algorithms. We propose an iterative subspace method that targets the eigenvectors with significant contributions to a given reference vector and is based on the optimality condition for the residual norm corresponding to the error in the solution vector. The subspace extraction and expansion are modified according to these principles which allow very efficient calculation of interior vibrational states with a strong multireference character in different vibrational structure problems. The convergence behavior of the method and its performance in comparison with the aforementioned algorithms are investigated in a set of benchmark calculations.

  14. Subspace-Based Noise Reduction for Speech Signals via Diagonal and Triangular Matrix Decompositions

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Jensen, Søren Holdt

    2007-01-01

    We survey the definitions and use of rank-revealing matrix decompositions in single-channel noise reduction algorithms for speech signals. Our algorithms are based on the rank-reduction paradigm and, in particular, signal subspace techniques. The focus is on practical working algorithms, using both...... with working Matlab code and applications in speech processing....

  15. Banach C*-algebras not containing a subspace isomorphic to C0

    International Nuclear Information System (INIS)

    Basit, B.

    1989-09-01

    If X is a locally Hausdorff space and C 0 (X) the Banach algebra of continuous functions defined on X vanishing at infinity, we showed that a subalgebra A of C 0 (X) is finite dimensional if it does not contain a subspace isomorphic to the Banach space C 0 of convergent to zero complex sequences. In this paper we extend this result to noncommutative Banach C*-algebras and Banach* algebras. 10 refs

  16. Perturbation for Frames for a Subspace of a Hilbert Space

    DEFF Research Database (Denmark)

    Christensen, Ole; deFlicht, C.; Lennard, C.

    1997-01-01

    We extend a classical result stating that a sufficiently small perturbation$\\{ g_i \\}$ of a Riesz sequence $\\{ f_i \\}$ in a Hilbert space $H$ is again a Riesz sequence. It turns out that the analog result for a frame does not holdunless the frame is complete. However, we are able to prove a very...... similarresult for frames in the case where the gap between the subspaces$\\overline{span} \\{f_i \\}$ and $\\overline{span} \\{ g_i \\}$ is small enough. We give a geometric interpretation of the result....

  17. Decomposition of Near-Infrared Spectroscopy Signals Using Oblique Subspace Projections: Applications in Brain Hemodynamic Monitoring

    Directory of Open Access Journals (Sweden)

    Alexander Caicedo

    2016-11-01

    Full Text Available Clinical data is comprised by a large number of synchronously collected biomedical signals that are measured at different locations. Deciphering the interrelationships of these signals can yield important information about their dependence providing some useful clinical diagnostic data. For instance, by computing the coupling between Near-Infrared Spectroscopy signals (NIRS and systemic variables the status of the hemodynamic regulation mechanisms can be assessed. In this paper we introduce an algorithm for the decomposition of NIRS signals into additive components. The algorithm, SIgnal DEcomposition base on Obliques Subspace Projections (SIDE-ObSP, assumes that the measured NIRS signal is a linear combination of the systemic measurements, following the linear regression model y = Ax + _. SIDE-ObSP decomposes the output such that, each component in the decomposition represents the sole linear influence of one corresponding regressor variable. This decomposition scheme aims at providing a better understanding of the relation between NIRS and systemic variables, and to provide a framework for the clinical interpretation of regression algorithms, thereby, facilitating their introduction into clinical practice. SIDE-ObSP combines oblique subspace projections (ObSP with the structure of a mean average system in order to define adequate signal subspaces. To guarantee smoothness in the estimated regression parameters, as observed in normal physiological processes, we impose a Tikhonov regularization using a matrix differential operator. We evaluate the performance of SIDE-ObSP by using a synthetic dataset, and present two case studies in the field of cerebral hemodynamics monitoring using NIRS. In addition, we compare the performance of this method with other system identification techniques. In the first case study data from 20 neonates during the first three days of life was used, here SIDE-ObSP decoupled the influence of changes in arterial oxygen

  18. Decomposition of Near-Infrared Spectroscopy Signals Using Oblique Subspace Projections: Applications in Brain Hemodynamic Monitoring.

    Science.gov (United States)

    Caicedo, Alexander; Varon, Carolina; Hunyadi, Borbala; Papademetriou, Maria; Tachtsidis, Ilias; Van Huffel, Sabine

    2016-01-01

    Clinical data is comprised by a large number of synchronously collected biomedical signals that are measured at different locations. Deciphering the interrelationships of these signals can yield important information about their dependence providing some useful clinical diagnostic data. For instance, by computing the coupling between Near-Infrared Spectroscopy signals (NIRS) and systemic variables the status of the hemodynamic regulation mechanisms can be assessed. In this paper we introduce an algorithm for the decomposition of NIRS signals into additive components. The algorithm, SIgnal DEcomposition base on Obliques Subspace Projections (SIDE-ObSP), assumes that the measured NIRS signal is a linear combination of the systemic measurements, following the linear regression model y = Ax + ϵ . SIDE-ObSP decomposes the output such that, each component in the decomposition represents the sole linear influence of one corresponding regressor variable. This decomposition scheme aims at providing a better understanding of the relation between NIRS and systemic variables, and to provide a framework for the clinical interpretation of regression algorithms, thereby, facilitating their introduction into clinical practice. SIDE-ObSP combines oblique subspace projections (ObSP) with the structure of a mean average system in order to define adequate signal subspaces. To guarantee smoothness in the estimated regression parameters, as observed in normal physiological processes, we impose a Tikhonov regularization using a matrix differential operator. We evaluate the performance of SIDE-ObSP by using a synthetic dataset, and present two case studies in the field of cerebral hemodynamics monitoring using NIRS. In addition, we compare the performance of this method with other system identification techniques. In the first case study data from 20 neonates during the first 3 days of life was used, here SIDE-ObSP decoupled the influence of changes in arterial oxygen saturation from the

  19. Development of Subspace-based Hybrid Monte Carlo-Deterministric Algorithms for Reactor Physics Calculations

    International Nuclear Information System (INIS)

    Abdel-Khalik, Hany S.; Zhang, Qiong

    2014-01-01

    The development of hybrid Monte-Carlo-Deterministic (MC-DT) approaches, taking place over the past few decades, have primarily focused on shielding and detection applications where the analysis requires a small number of responses, i.e. at the detector locations(s). This work further develops a recently introduced global variance reduction approach, denoted by the SUBSPACE approach is designed to allow the use of MC simulation, currently limited to benchmarking calculations, for routine engineering calculations. By way of demonstration, the SUBSPACE approach is applied to assembly level calculations used to generate the few-group homogenized cross-sections. These models are typically expensive and need to be executed in the order of 10 3 - 10 5 times to properly characterize the few-group cross-sections for downstream core-wide calculations. Applicability to k-eigenvalue core-wide models is also demonstrated in this work. Given the favorable results obtained in this work, we believe the applicability of the MC method for reactor analysis calculations could be realized in the near future.

  20. Subspace Dimensionality: A Tool for Automated QC in Seismic Array Processing

    Science.gov (United States)

    Rowe, C. A.; Stead, R. J.; Begnaud, M. L.

    2013-12-01

    Because of the great resolving power of seismic arrays, the application of automated processing to array data is critically important in treaty verification work. A significant problem in array analysis is the inclusion of bad sensor channels in the beamforming process. We are testing an approach to automated, on-the-fly quality control (QC) to aid in the identification of poorly performing sensor channels prior to beam-forming in routine event detection or location processing. The idea stems from methods used for large computer servers, when monitoring traffic at enormous numbers of nodes is impractical on a node-by node basis, so the dimensionality of the node traffic is instead monitoried for anomalies that could represent malware, cyber-attacks or other problems. The technique relies upon the use of subspace dimensionality or principal components of the overall system traffic. The subspace technique is not new to seismology, but its most common application has been limited to comparing waveforms to an a priori collection of templates for detecting highly similar events in a swarm or seismic cluster. In the established template application, a detector functions in a manner analogous to waveform cross-correlation, applying a statistical test to assess the similarity of the incoming data stream to known templates for events of interest. In our approach, we seek not to detect matching signals, but instead, we examine the signal subspace dimensionality in much the same way that the method addresses node traffic anomalies in large computer systems. Signal anomalies recorded on seismic arrays affect the dimensional structure of the array-wide time-series. We have shown previously that this observation is useful in identifying real seismic events, either by looking at the raw signal or derivatives thereof (entropy, kurtosis), but here we explore the effects of malfunctioning channels on the dimension of the data and its derivatives, and how to leverage this effect for

  1. Improved magnetic resonance fingerprinting reconstruction with low-rank and subspace modeling.

    Science.gov (United States)

    Zhao, Bo; Setsompop, Kawin; Adalsteinsson, Elfar; Gagoski, Borjan; Ye, Huihui; Ma, Dan; Jiang, Yun; Ellen Grant, P; Griswold, Mark A; Wald, Lawrence L

    2018-02-01

    This article introduces a constrained imaging method based on low-rank and subspace modeling to improve the accuracy and speed of MR fingerprinting (MRF). A new model-based imaging method is developed for MRF to reconstruct high-quality time-series images and accurate tissue parameter maps (e.g., T 1 , T 2 , and spin density maps). Specifically, the proposed method exploits low-rank approximations of MRF time-series images, and further enforces temporal subspace constraints to capture magnetization dynamics. This allows the time-series image reconstruction problem to be formulated as a simple linear least-squares problem, which enables efficient computation. After image reconstruction, tissue parameter maps are estimated via dictionary-based pattern matching, as in the conventional approach. The effectiveness of the proposed method was evaluated with in vivo experiments. Compared with the conventional MRF reconstruction, the proposed method reconstructs time-series images with significantly reduced aliasing artifacts and noise contamination. Although the conventional approach exhibits some robustness to these corruptions, the improved time-series image reconstruction in turn provides more accurate tissue parameter maps. The improvement is pronounced especially when the acquisition time becomes short. The proposed method significantly improves the accuracy of MRF, and also reduces data acquisition time. Magn Reson Med 79:933-942, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

  2. A Framework for Evaluation and Exploration of Clustering Algorithms in Subspaces of High Dimensional Databases

    DEFF Research Database (Denmark)

    Müller, Emmanuel; Assent, Ira; Günnemann, Stephan

    2011-01-01

    comparative studies on the advantages and disadvantages of the different algorithms exist. Part of the underlying problem is the lack of available open source implementations that could be used by researchers to understand, compare, and extend subspace and projected clustering algorithms. In this work, we...

  3. Gene selection for microarray data classification via subspace learning and manifold regularization.

    Science.gov (United States)

    Tang, Chang; Cao, Lijuan; Zheng, Xiao; Wang, Minhui

    2017-12-19

    With the rapid development of DNA microarray technology, large amount of genomic data has been generated. Classification of these microarray data is a challenge task since gene expression data are often with thousands of genes but a small number of samples. In this paper, an effective gene selection method is proposed to select the best subset of genes for microarray data with the irrelevant and redundant genes removed. Compared with original data, the selected gene subset can benefit the classification task. We formulate the gene selection task as a manifold regularized subspace learning problem. In detail, a projection matrix is used to project the original high dimensional microarray data into a lower dimensional subspace, with the constraint that the original genes can be well represented by the selected genes. Meanwhile, the local manifold structure of original data is preserved by a Laplacian graph regularization term on the low-dimensional data space. The projection matrix can serve as an importance indicator of different genes. An iterative update algorithm is developed for solving the problem. Experimental results on six publicly available microarray datasets and one clinical dataset demonstrate that the proposed method performs better when compared with other state-of-the-art methods in terms of microarray data classification. Graphical Abstract The graphical abstract of this work.

  4. Code Coupling via Jacobian-Free Newton-Krylov Algorithms with Application to Magnetized Fluid Plasma and Kinetic Neutral Models

    Energy Technology Data Exchange (ETDEWEB)

    Joseph, Ilon [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2014-05-27

    Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for solving the problem of coupling codes that address dfferent physics models. As communication capability between individual submodules varies, different choices of coupling algorithms are required. The more communication that is available, the more possible it becomes to exploit the simple sparsity pattern of the Jacobian, albeit of a large system. The less communication that is available, the more dense the Jacobian matrices become and new types of preconditioners must be sought to efficiently take large time steps. In general, methods that use constrained or reduced subsystems can offer a compromise in complexity. The specific problem of coupling a fluid plasma code to a kinetic neutrals code is discussed as an example.

  5. Robust adaptive subspace detection in impulsive noise

    KAUST Repository

    Ben Atitallah, Ismail

    2016-09-13

    This paper addresses the design of the Adaptive Subspace Matched Filter (ASMF) detector in the presence of compound Gaussian clutters and a mismatch in the steering vector. In particular, we consider the case wherein the ASMF uses the regularized Tyler estimator (RTE) to estimate the clutter covariance matrix. Under this setting, a major question that needs to be addressed concerns the setting of the threshold and the regularization parameter. To answer this question, we consider the regime in which the number of observations used to estimate the RTE and their dimensions grow large together. Recent results from random matrix theory are then used in order to approximate the false alarm and detection probabilities by deterministic quantities. The latter are optimized in order to maximize an upper bound on the asymptotic detection probability while keeping the asymptotic false alarm probability at a fixed rate. © 2016 IEEE.

  6. Robust adaptive subspace detection in impulsive noise

    KAUST Repository

    Ben Atitallah, Ismail; Kammoun, Abla; Alouini, Mohamed-Slim; Al-Naffouri, Tareq Y.

    2016-01-01

    This paper addresses the design of the Adaptive Subspace Matched Filter (ASMF) detector in the presence of compound Gaussian clutters and a mismatch in the steering vector. In particular, we consider the case wherein the ASMF uses the regularized Tyler estimator (RTE) to estimate the clutter covariance matrix. Under this setting, a major question that needs to be addressed concerns the setting of the threshold and the regularization parameter. To answer this question, we consider the regime in which the number of observations used to estimate the RTE and their dimensions grow large together. Recent results from random matrix theory are then used in order to approximate the false alarm and detection probabilities by deterministic quantities. The latter are optimized in order to maximize an upper bound on the asymptotic detection probability while keeping the asymptotic false alarm probability at a fixed rate. © 2016 IEEE.

  7. Practical Low Data-Complexity Subspace-Trail Cryptanalysis of Round-Reduced PRINCE

    DEFF Research Database (Denmark)

    Grassi, Lorenzo; Rechberger, Christian

    2016-01-01

    Subspace trail cryptanalysis is a very recent new cryptanalysis technique, and includes differential, truncated differential, impossible differential, and integral attacks as special cases. In this paper, we consider PRINCE, a widely analyzed block cipher proposed in 2012. After the identification......-plaintext category. The attacks have been verified using a C implementation. Of independent interest, we consider a variant of PRINCE in which ShiftRows and MixLayer operations are exchanged in position. In particular, our result shows that the position of ShiftRows and MixLayer operations influences the security...

  8. Random subspaces for encryption based on a private shared Cartesian frame

    International Nuclear Information System (INIS)

    Bartlett, Stephen D.; Hayden, Patrick; Spekkens, Robert W.

    2005-01-01

    A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities

  9. Combined incomplete LU and strongly implicit procedure preconditioning

    Energy Technology Data Exchange (ETDEWEB)

    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.

  10. Single and multiple object tracking using log-euclidean Riemannian subspace and block-division appearance model.

    Science.gov (United States)

    Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei

    2012-12-01

    Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.

  11. A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification

    Energy Technology Data Exchange (ETDEWEB)

    Schunert, Sebastian; Wang, Congjian; Wang, Yaqi; Kong, Fande; Ortensi, Javier; Baker, Benjamin; Gleicher, Frederick; DeHart, Mark; Martineau, Richard

    2017-04-01

    Rattlesnake and MAMMOTH are the designated TREAT analysis tools currently being developed at the Idaho National Laboratory. Concurrent with development of the multi-physics, multi-scale capabilities, sensitivity analysis and uncertainty quantification (SA/UQ) capabilities are required for predicitive modeling of the TREAT reactor. For steady-state SA/UQ, that is essential for setting initial conditions for the transients, generalized perturbation theory (GPT) will be used. This work describes the implementation of a PETSc based solver for the generalized adjoint equations that constitute a inhomogeneous, rank deficient problem. The standard approach is to use an outer iteration strategy with repeated removal of the fundamental mode contamination. The described GPT algorithm directly solves the GPT equations without the need of an outer iteration procedure by using Krylov subspaces that are orthogonal to the operator’s nullspace. Three test problems are solved and provide sufficient verification for the Rattlesnake’s GPT capability. We conclude with a preliminary example evaluating the impact of the Boron distribution in the TREAT reactor using perturbation theory.

  12. Rank-defective millimeter-wave channel estimation based on subspace-compressive sensing

    Directory of Open Access Journals (Sweden)

    Majid Shakhsi Dastgahian

    2016-11-01

    Full Text Available Millimeter-wave communication (mmWC is considered as one of the pioneer candidates for 5G indoor and outdoor systems in E-band. To subdue the channel propagation characteristics in this band, high dimensional antenna arrays need to be deployed at both the base station (BS and mobile sets (MS. Unlike the conventional MIMO systems, Millimeter-wave (mmW systems lay away to employ the power predatory equipment such as ADC or RF chain in each branch of MIMO system because of hardware constraints. Such systems leverage to the hybrid precoding (combining architecture for downlink deployment. Because there is a large array at the transceiver, it is impossible to estimate the channel by conventional methods. This paper develops a new algorithm to estimate the mmW channel by exploiting the sparse nature of the channel. The main contribution is the representation of a sparse channel model and the exploitation of a modified approach based on Multiple Measurement Vector (MMV greedy sparse framework and subspace method of Multiple Signal Classification (MUSIC which work together to recover the indices of non-zero elements of an unknown channel matrix when the rank of the channel matrix is defected. In practical rank-defective channels, MUSIC fails, and we need to propose new extended MUSIC approaches based on subspace enhancement to compensate the limitation of MUSIC. Simulation results indicate that our proposed extended MUSIC algorithms will have proper performances and moderate computational speeds, and that they are even able to work in channels with an unknown sparsity level.

  13. Consistency analysis of subspace identification methods based on a linear regression approach

    DEFF Research Database (Denmark)

    Knudsen, Torben

    2001-01-01

    In the literature results can be found which claim consistency for the subspace method under certain quite weak assumptions. Unfortunately, a new result gives a counter example showing inconsistency under these assumptions and then gives new more strict sufficient assumptions which however does n...... not include important model structures as e.g. Box-Jenkins. Based on a simple least squares approach this paper shows the possible inconsistency under the weak assumptions and develops only slightly stricter assumptions sufficient for consistency and which includes any model structure...

  14. Damage location and quantification of a pretensioned concrete beam using stochastic subspace identification

    Science.gov (United States)

    Cancelli, Alessandro; Micheli, Laura; Laflamme, Simon; Alipour, Alice; Sritharan, Sri; Ubertini, Filippo

    2017-04-01

    Stochastic subspace identification (SSID) is a first-order linear system identification technique enabling modal analysis through the time domain. Research in the field of structural health monitoring has demonstrated that SSID can be used to successfully retrieve modal properties, including modal damping ratios, using output-only measurements. In this paper, the utilization of SSID for indirectly retrieving structures' stiffness matrix was investigated, through the study of a simply supported reinforced concrete beam subjected to dynamic loads. Hence, by introducing a physical model of the structure, a second-order identification method is achieved. The reconstruction is based on system condensation methods, which enables calculation of reduced order stiffness, damping, and mass matrices for the structural system. The methods compute the reduced order matrices directly from the modal properties, obtained through the use of SSID. Lastly, the reduced properties of the system are used to reconstruct the stiffness matrix of the beam. The proposed approach is first verified through numerical simulations and then validated using experimental data obtained from a full-scale reinforced concrete beam that experienced progressive damage. Results show that the SSID technique can be used to diagnose, locate, and quantify damage through the reconstruction of the stiffness matrix.

  15. Towards automatic music transcription: note extraction based on independent subspace analysis

    Science.gov (United States)

    Wellhausen, Jens; Hoynck, Michael

    2005-01-01

    Due to the increasing amount of music available electronically the need of automatic search, retrieval and classification systems for music becomes more and more important. In this paper an algorithm for automatic transcription of polyphonic piano music into MIDI data is presented, which is a very interesting basis for database applications, music analysis and music classification. The first part of the algorithm performs a note accurate temporal audio segmentation. In the second part, the resulting segments are examined using Independent Subspace Analysis to extract sounding notes. Finally, the results are used to build a MIDI file as a new representation of the piece of music which is examined.

  16. Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz

    KAUST Repository

    Yuan, Xuefei

    2012-07-01

    Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.

  17. Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz

    KAUST Repository

    Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E.

    2012-01-01

    Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of . r-refinement adaptive grids obtained from solving a single Monge-Ampère (MA) equation addresses the high-resolution requirements near the . x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated. © 2012 Elsevier Inc.

  18. On optimal improvements of classical iterative schemes for Z-matrices

    Science.gov (United States)

    Noutsos, D.; Tzoumas, M.

    2006-04-01

    Many researchers have considered preconditioners, applied to linear systems, whose matrix coefficient is a Z- or an M-matrix, that make the associated Jacobi and Gauss-Seidel methods converge asymptotically faster than the unpreconditioned ones. Such preconditioners are chosen so that they eliminate the off-diagonal elements of the same column or the elements of the first upper diagonal [Milaszewicz, LAA 93 (1987) 161-170], Gunawardena et al. [LAA 154-156 (1991) 123-143]. In this work we generalize the previous preconditioners to obtain optimal methods. "Good" Jacobi and Gauss-Seidel algorithms are given and preconditioners, that eliminate more than one entry per row, are also proposed and analyzed. Moreover, the behavior of the above preconditioners to the Krylov subspace methods is studied.

  19. Data-Driven Predictive Direct Load Control of Refrigeration Systems

    DEFF Research Database (Denmark)

    Shafiei, Seyed Ehsan; Knudsen, Torben; Wisniewski, Rafal

    2015-01-01

    A predictive control using subspace identification is applied for the smart grid integration of refrigeration systems under a direct load control scheme. A realistic demand response scenario based on regulation of the electrical power consumption is considered. A receding horizon optimal control...... is proposed to fulfil two important objectives: to secure high coefficient of performance and to participate in power consumption management. Moreover, a new method for design of input signals for system identification is put forward. The control method is fully data driven without an explicit use of model...... against real data. The performance improvement results in a 22% reduction in the energy consumption. A comparative simulation is accomplished showing the superiority of the method over the existing approaches in terms of the load following performance....

  20. A Comfort-Aware Energy Efficient HVAC System Based on the Subspace Identification Method

    Directory of Open Access Journals (Sweden)

    O. Tsakiridis

    2016-01-01

    Full Text Available A proactive heating method is presented aiming at reducing the energy consumption in a HVAC system while maintaining the thermal comfort of the occupants. The proposed technique fuses time predictions for the zones’ temperatures, based on a deterministic subspace identification method, and zones’ occupancy predictions, based on a mobility model, in a decision scheme that is capable of regulating the balance between the total energy consumed and the total discomfort cost. Simulation results for various occupation-mobility models demonstrate the efficiency of the proposed technique.

  1. Robust Quantum Secure Direct Communication over Collective Rotating Channel

    International Nuclear Information System (INIS)

    Qin Sujuan; Gao Fei; Wen Qiaoyan; Zhu Fuchen

    2010-01-01

    A quantum secure direct communication protocol over a collective rotating channel is proposed. The protocol encodes logical bits in noiseless subspaces, and so it can function over a quantum channel subjected to an arbitrary degree of collective rotating noise. Although entangled states are used, both the sender and receiver are only required to perform single-particle product measurement or Pauli operations. The protocol is feasible with present-day technique. (general)

  2. Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach.

    Directory of Open Access Journals (Sweden)

    Ulf Hensen

    Full Text Available We develop a general minimally coupled subspace approach (MCSA to compute absolute entropies of macromolecules, such as proteins, from computer generated canonical ensembles. Our approach overcomes limitations of current estimates such as the quasi-harmonic approximation which neglects non-linear and higher-order correlations as well as multi-minima characteristics of protein energy landscapes. Here, Full Correlation Analysis, adaptive kernel density estimation, and mutual information expansions are combined and high accuracy is demonstrated for a number of test systems ranging from alkanes to a 14 residue peptide. We further computed the configurational entropy for the full 67-residue cofactor of the TATA box binding protein illustrating that MCSA yields improved results also for large macromolecular systems.

  3. Face recognition based on two-dimensional discriminant sparse preserving projection

    Science.gov (United States)

    Zhang, Dawei; Zhu, Shanan

    2018-04-01

    In this paper, a supervised dimensionality reduction algorithm named two-dimensional discriminant sparse preserving projection (2DDSPP) is proposed for face recognition. In order to accurately model manifold structure of data, 2DDSPP constructs within-class affinity graph and between-class affinity graph by the constrained least squares (LS) and l1 norm minimization problem, respectively. Based on directly operating on image matrix, 2DDSPP integrates graph embedding (GE) with Fisher criterion. The obtained projection subspace preserves within-class neighborhood geometry structure of samples, while keeping away samples from different classes. The experimental results on the PIE and AR face databases show that 2DDSPP can achieve better recognition performance.

  4. Similarity measurement method of high-dimensional data based on normalized net lattice subspace

    Institute of Scientific and Technical Information of China (English)

    Li Wenfa; Wang Gongming; Li Ke; Huang Su

    2017-01-01

    The performance of conventional similarity measurement methods is affected seriously by the curse of dimensionality of high-dimensional data.The reason is that data difference between sparse and noisy dimensionalities occupies a large proportion of the similarity, leading to the dissimilarities between any results.A similarity measurement method of high-dimensional data based on normalized net lattice subspace is proposed.The data range of each dimension is divided into several intervals, and the components in different dimensions are mapped onto the corresponding interval.Only the component in the same or adjacent interval is used to calculate the similarity.To validate this meth-od, three data types are used, and seven common similarity measurement methods are compared. The experimental result indicates that the relative difference of the method is increasing with the di-mensionality and is approximately two or three orders of magnitude higher than the conventional method.In addition, the similarity range of this method in different dimensions is [0, 1], which is fit for similarity analysis after dimensionality reduction.

  5. Fault Detection for Industrial Processes

    Directory of Open Access Journals (Sweden)

    Yingwei Zhang

    2012-01-01

    Full Text Available A new fault-relevant KPCA algorithm is proposed. Then the fault detection approach is proposed based on the fault-relevant KPCA algorithm. The proposed method further decomposes both the KPCA principal space and residual space into two subspaces. Compared with traditional statistical techniques, the fault subspace is separated based on the fault-relevant influence. This method can find fault-relevant principal directions and principal components of systematic subspace and residual subspace for process monitoring. The proposed monitoring approach is applied to Tennessee Eastman process and penicillin fermentation process. The simulation results show the effectiveness of the proposed method.

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

    Czech Academy of Sciences Publication Activity Database

    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

  7. Model reduction and frequency residuals for a robust estimation of nonlinearities in subspace identification

    Science.gov (United States)

    De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.

    2017-09-01

    The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.

  8. Performance of the discrete ordinates method-like neutron transport computation with equivalent group condensation and angle-collapsing

    International Nuclear Information System (INIS)

    Yoo, Han Jong; Won, Jong Hyuck; Cho, Nam Zin

    2011-01-01

    In computational studies of neutron transport equations, the fine-group to few-group condensation procedure leads to equivalent total cross section that becomes angle dependent. The difficulty of this angle dependency has been traditionally treated by consistent P or extended transport approximation in the literature. In a previous study, we retained the angle dependency of the total cross section and applied directly to the discrete ordinates equation, with additional concept of angle-collapsing, and tested in a one-dimensional slab problem. In this study, we provide further results of this discrete ordinates-like method in comparison with the typical traditional methods. In addition, IRAM acceleration (based on Krylov subspace method) is tested for the purpose of further reducing the computational burden of few-group calculation. From the test results, it is ascertained that the angle-dependent total cross section with angle-collapsing gives excellent estimation of k_e_f_f and flux distribution and that IRAM acceleration effectively reduces the number of outer iterations. However, since IRAM requires sufficient convergence in inner iterations, speedup in total computer time is not significant for problems with upscattering. (author)

  9. Power flow prediction in vibrating systems via model reduction

    Science.gov (United States)

    Li, Xianhui

    This dissertation focuses on power flow prediction in vibrating systems. Reduced order models (ROMs) are built based on rational Krylov model reduction which preserve power flow information in the original systems over a specified frequency band. Stiffness and mass matrices of the ROMs are obtained by projecting the original system matrices onto the subspaces spanned by forced responses. A matrix-free algorithm is designed to construct ROMs directly from the power quantities at selected interpolation frequencies. Strategies for parallel implementation of the algorithm via message passing interface are proposed. The quality of ROMs is iteratively refined according to the error estimate based on residual norms. Band capacity is proposed to provide a priori estimate of the sizes of good quality ROMs. Frequency averaging is recast as ensemble averaging and Cauchy distribution is used to simplify the computation. Besides model reduction for deterministic systems, details of constructing ROMs for parametric and nonparametric random systems are also presented. Case studies have been conducted on testbeds from Harwell-Boeing collections. Input and coupling power flow are computed for the original systems and the ROMs. Good agreement is observed in all cases.

  10. Coherent effects on two-photon correlation and directional emission of two two-level atoms

    International Nuclear Information System (INIS)

    Ooi, C. H. Raymond; Kim, Byung-Gyu; Lee, Hai-Woong

    2007-01-01

    Sub- and superradiant dynamics of spontaneously decaying atoms are manifestations of collective many-body systems. We study the internal dynamics and the radiation properties of two atoms in free space. Interesting results are obtained when the atoms are separated by less than half a wavelength of the atomic transition, where the dipole-dipole interaction gives rise to new coherent effects, such as (a) coherence between two intermediate collective states, (b) oscillations in the two-photon correlation G (2) , (c) emission of two photons by one atom, and (d) the loss of directional correlation. We compare the population dynamics during the two-photon emission process with the dynamics of single-photon emission in the cases of a Λ and a V scheme. We compute the temporal correlation and angular correlation of two successively emitted photons using the G (2) for different values of atomic separation. We find antibunching when the atomic separation is a quarter wavelength λ/4. Oscillations in the temporal correlation provide a useful feature for measuring subwavelength atomic separation. Strong directional correlation between two emitted photons is found for atomic separation larger than a wavelength. We also compare the directionality of a photon spontaneously emitted by the two atoms prepared in phased-symmetric and phased-antisymmetric entangled states vertical bar ±> k 0 =e ik 0 ·r 1 vertical bar a 1 ,b 2 >±e ik 0 ·r 2 vertical bar b 1 ,a 2 > by a laser pulse with wave vector k 0 . Photon emission is directionally suppressed along k 0 for the phased-antisymmetric state. The directionality ceases for interatomic distances less than λ/2

  11. Direction of Arrival Estimation Accuracy Enhancement via Using Displacement Invariance Technique

    Directory of Open Access Journals (Sweden)

    Youssef Fayad

    2015-01-01

    Full Text Available A new algorithm for improving Direction of Arrival Estimation (DOAE accuracy has been carried out. Two contributions are introduced. First, Doppler frequency shift that resulted from the target movement is estimated using the displacement invariance technique (DIT. Second, the effect of Doppler frequency is modeled and incorporated into ESPRIT algorithm in order to increase the estimation accuracy. It is worth mentioning that the subspace approach has been employed into ESPRIT and DIT methods to reduce the computational complexity and the model’s nonlinearity effect. The DOAE accuracy has been verified by closed-form Cramér-Rao bound (CRB. The simulation results of the proposed algorithm are better than those of the previous estimation techniques leading to the estimator performance enhancement.

  12. Introduction: a brief overview of iterative algorithms in X-ray computed tomography.

    Science.gov (United States)

    Soleimani, M; Pengpen, T

    2015-06-13

    This paper presents a brief overview of some basic iterative algorithms, and more sophisticated methods are presented in the research papers in this issue. A range of algebraic iterative algorithms are covered here including ART, SART and OS-SART. A major limitation of the traditional iterative methods is their computational time. The Krylov subspace based methods such as the conjugate gradients (CG) algorithm and its variants can be used to solve linear systems of equations arising from large-scale CT with possible implementation using modern high-performance computing tools. The overall aim of this theme issue is to stimulate international efforts to develop the next generation of X-ray computed tomography (CT) image reconstruction software. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

  13. Kronecker Products on Preconditioning

    KAUST Repository

    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. Dependence of accuracy of ESPRIT estimates on signal eigenvalues: the case of a noisy sum of two real exponentials.

    Science.gov (United States)

    Alexandrov, Theodore; Golyandina, Nina; Timofeyev, Alexey

    2009-02-26

    This paper is devoted to estimation of parameters for a noisy sum of two real exponential functions. Singular Spectrum Analysis is used to extract the signal subspace and then the ESPRIT method exploiting signal subspace features is applied to obtain estimates of the desired exponential rates. Dependence of estimation quality on signal eigenvalues is investigated. The special design to test this relation is elaborated.

  15. Introduction to the spectral distribution method. Application example to the subspaces with a large number of quasi particles

    International Nuclear Information System (INIS)

    Arvieu, R.

    The assumptions and principles of the spectral distribution method are reviewed. The object of the method is to deduce information on the nuclear spectra by constructing a frequency function which has the same first few moments, as the exact frequency function, these moments being then exactly calculated. The method is applied to subspaces containing a large number of quasi particles [fr

  16. Quasistatic Seismic Damage Indicators for RC Structures from Dissipating Energies in Tangential Subspaces

    Directory of Open Access Journals (Sweden)

    Wilfried B. Krätzig

    2014-01-01

    Full Text Available This paper applies recent research on structural damage description to earthquake-resistant design concepts. Based on the primary design aim of life safety, this work adopts the necessity of additional protection aims for property, installation, and equipment. This requires the definition of damage indicators, which are able to quantify the arising structural damage. As in present design, it applies nonlinear quasistatic (pushover concepts due to code provisions as simplified dynamic design tools. Substituting so nonlinear time-history analyses, seismic low-cycle fatigue of RC structures is approximated in similar manner. The treatment will be embedded into a finite element environment, and the tangential stiffness matrix KT in tangential subspaces then is identified as the most general entry for structural damage information. Its spectra of eigenvalues λi or natural frequencies ωi of the structure serve to derive damage indicators Di, applicable to quasistatic evaluation of seismic damage. Because det KT=0 denotes structural failure, such damage indicators range from virgin situation Di=0 to failure Di=1 and thus correspond with Fema proposals on performance-based seismic design. Finally, the developed concept is checked by reanalyses of two experimentally investigated RC frames.

  17. Speech Denoising in White Noise Based on Signal Subspace Low-rank Plus Sparse Decomposition

    Directory of Open Access Journals (Sweden)

    yuan Shuai

    2017-01-01

    Full Text Available In this paper, a new subspace speech enhancement method using low-rank and sparse decomposition is presented. In the proposed method, we firstly structure the corrupted data as a Toeplitz matrix and estimate its effective rank for the underlying human speech signal. Then the low-rank and sparse decomposition is performed with the guidance of speech rank value to remove the noise. Extensive experiments have been carried out in white Gaussian noise condition, and experimental results show the proposed method performs better than conventional speech enhancement methods, in terms of yielding less residual noise and lower speech distortion.

  18. Removing Ocular Movement Artefacts by a Joint Smoothened Subspace Estimator

    Directory of Open Access Journals (Sweden)

    Ronald Phlypo

    2007-01-01

    Full Text Available To cope with the severe masking of background cerebral activity in the electroencephalogram (EEG by ocular movement artefacts, we present a method which combines lower-order, short-term and higher-order, long-term statistics. The joint smoothened subspace estimator (JSSE calculates the joint information in both statistical models, subject to the constraint that the resulting estimated source should be sufficiently smooth in the time domain (i.e., has a large autocorrelation or self predictive power. It is shown that the JSSE is able to estimate a component from simulated data that is superior with respect to methodological artefact suppression to those of FastICA, SOBI, pSVD, or JADE/COM1 algorithms used for blind source separation (BSS. Interference and distortion suppression are of comparable order when compared with the above-mentioned methods. Results on patient data demonstrate that the method is able to suppress blinking and saccade artefacts in a fully automated way.

  19. Parallel Implicit Algorithms for CFD

    Science.gov (United States)

    Keyes, David E.

    1998-01-01

    The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.

  20. Multi-Level iterative methods in computational plasma physics

    International Nuclear Information System (INIS)

    Knoll, D.A.; Barnes, D.C.; Brackbill, J.U.; Chacon, L.; Lapenta, G.

    1999-01-01

    Plasma physics phenomena occur on a wide range of spatial scales and on a wide range of time scales. When attempting to model plasma physics problems numerically the authors are inevitably faced with the need for both fine spatial resolution (fine grids) and implicit time integration methods. Fine grids can tax the efficiency of iterative methods and large time steps can challenge the robustness of iterative methods. To meet these challenges they are developing a hybrid approach where multigrid methods are used as preconditioners to Krylov subspace based iterative methods such as conjugate gradients or GMRES. For nonlinear problems they apply multigrid preconditioning to a matrix-few Newton-GMRES method. Results are presented for application of these multilevel iterative methods to the field solves in implicit moment method PIC, multidimensional nonlinear Fokker-Planck problems, and their initial efforts in particle MHD

  1. Model reduction of parametrized systems

    CERN Document Server

    Ohlberger, Mario; Patera, Anthony; Rozza, Gianluigi; Urban, Karsten

    2017-01-01

    The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters ca...

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

    Energy Technology Data Exchange (ETDEWEB)

    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.

  3. Quantum entanglement analysis of an optically excited coupling of two nuclear spins via a mediator: Combining the quantum concurrence and negativity

    Science.gov (United States)

    Fu, Chenghua; Hu, Zhanning

    2018-03-01

    In this paper, we investigate the characteristics of the nuclear spin entanglement generated by an intermedium with an optically excited triplet. Significantly, the interaction between the two nuclear spins presents to be a direct XY coupling in each of the effective subspace Hamiltonians which are obtained by applying a transformation on the natural Hamiltonian. The quantum concurrence and negativity are discussed to quantitatively describe the quantum entanglement, and a comparison between them can reveal the nature of their relationship. An innovative general equation describing the relationship between the concurrence and negativity is explicitly obtained.

  4. Prewhitening for Rank-Deficient Noise in Subspace Methods for Noise Reduction

    DEFF Research Database (Denmark)

    Hansen, Per Christian; Jensen, Søren Holdt

    2005-01-01

    A fundamental issue in connection with subspace methods for noise reduction is that the covariance matrix for the noise is required to have full rank, in order for the prewhitening step to be defined. However, there are important cases where this requirement is not fulfilled, e.g., when the noise...... has narrow-band characteristics, or in the case of tonal noise. We extend the concept of prewhitening to include the case when the noise covariance matrix is rank deficient, using a weighted pseudoinverse and the quotient SVD, and we show how to formulate a general rank-reduction algorithm that works...... also for rank deficient noise. We also demonstrate how to formulate this algorithm by means of a quotient ULV decomposition, which allows for faster computation and updating. Finally we apply our algorithm to a problem involving a speech signal contaminated by narrow-band noise....

  5. Estimating the number of components and detecting outliers using Angle Distribution of Loading Subspaces (ADLS) in PCA analysis.

    Science.gov (United States)

    Liu, Y J; Tran, T; Postma, G; Buydens, L M C; Jansen, J

    2018-08-22

    Principal Component Analysis (PCA) is widely used in analytical chemistry, to reduce the dimensionality of a multivariate data set in a few Principal Components (PCs) that summarize the predominant patterns in the data. An accurate estimate of the number of PCs is indispensable to provide meaningful interpretations and extract useful information. We show how existing estimates for the number of PCs may fall short for datasets with considerable coherence, noise or outlier presence. We present here how Angle Distribution of the Loading Subspaces (ADLS) can be used to estimate the number of PCs based on the variability of loading subspace across bootstrap resamples. Based on comprehensive comparisons with other well-known methods applied on simulated dataset, we show that ADLS (1) may quantify the stability of a PCA model with several numbers of PCs simultaneously; (2) better estimate the appropriate number of PCs when compared with the cross-validation and scree plot methods, specifically for coherent data, and (3) facilitate integrated outlier detection, which we introduce in this manuscript. We, in addition, demonstrate how the analysis of different types of real-life spectroscopic datasets may benefit from these advantages of ADLS. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

  6. Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

    Science.gov (United States)

    Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

    2018-03-01

    In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

  7. Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-Based Predictive Control

    KAUST Repository

    Siddiqui, Bilal A.; El-Ferik, Sami; Abdelkader, Mohamed

    2016-01-01

    In this work, a cascade structure of a time-scale separated integral sliding mode and model predictive control is proposed as a viable alternative for fault-tolerant control. A multi-variable sliding mode control law is designed as the inner loop of the flight control system. Subspace identification is carried out on the aircraft in closed loop. The identified plant is then used for model predictive controllers in the outer loop. The overall control law demonstrates improved robustness to measurement noise, modeling uncertainties, multiple faults and severe wind turbulence and gusts. In addition, the flight control system employs filters and dead-zone nonlinear elements to reduce chattering and improve handling quality. Simulation results demonstrate the efficiency of the proposed controller using conventional fighter aircraft without control redundancy.

  8. Fault Tolerant Flight Control Using Sliding Modes and Subspace Identification-Based Predictive Control

    KAUST Repository

    Siddiqui, Bilal A.

    2016-07-26

    In this work, a cascade structure of a time-scale separated integral sliding mode and model predictive control is proposed as a viable alternative for fault-tolerant control. A multi-variable sliding mode control law is designed as the inner loop of the flight control system. Subspace identification is carried out on the aircraft in closed loop. The identified plant is then used for model predictive controllers in the outer loop. The overall control law demonstrates improved robustness to measurement noise, modeling uncertainties, multiple faults and severe wind turbulence and gusts. In addition, the flight control system employs filters and dead-zone nonlinear elements to reduce chattering and improve handling quality. Simulation results demonstrate the efficiency of the proposed controller using conventional fighter aircraft without control redundancy.

  9. Subspace identification of Hammer stein models using support vector machines

    International Nuclear Information System (INIS)

    Al-Dhaifallah, Mujahed

    2011-01-01

    System identification is the art of finding mathematical tools and algorithms that build an appropriate mathematical model of a system from measured input and output data. Hammerstein model, consisting of a memoryless nonlinearity followed by a dynamic linear element, is often a good trade-off as it can represent some dynamic nonlinear systems very accurately, but is nonetheless quite simple. Moreover, the extensive knowledge about LTI system representations can be applied to the dynamic linear block. On the other hand, finding an effective representation for the nonlinearity is an active area of research. Recently, support vector machines (SVMs) and least squares support vector machines (LS-SVMs) have demonstrated powerful abilities in approximating linear and nonlinear functions. In contrast with other approximation methods, SVMs do not require a-priori structural information. Furthermore, there are well established methods with guaranteed convergence (ordinary least squares, quadratic programming) for fitting LS-SVMs and SVMs. The general objective of this research is to develop new subspace algorithms for Hammerstein systems based on SVM regression.

  10. Acoustic Source Localization via Subspace Based Method Using Small Aperture MEMS Arrays

    Directory of Open Access Journals (Sweden)

    Xin Zhang

    2014-01-01

    Full Text Available Small aperture microphone arrays provide many advantages for portable devices and hearing aid equipment. In this paper, a subspace based localization method is proposed for acoustic source using small aperture arrays. The effects of array aperture on localization are analyzed by using array response (array manifold. Besides array aperture, the frequency of acoustic source and the variance of signal power are simulated to demonstrate how to optimize localization performance, which is carried out by introducing frequency error with the proposed method. The proposed method for 5 mm array aperture is validated by simulations and experiments with MEMS microphone arrays. Different types of acoustic sources can be localized with the highest precision of 6 degrees even in the presence of wind noise and other noises. Furthermore, the proposed method reduces the computational complexity compared with other methods.

  11. Optimal Design of Large Dimensional Adaptive Subspace Detectors

    KAUST Repository

    Ben Atitallah, Ismail; Kammoun, Abla; Alouini, Mohamed-Slim; Alnaffouri, Tareq Y.

    2016-01-01

    This paper addresses the design of Adaptive Subspace Matched Filter (ASMF) detectors in the presence of a mismatch in the steering vector. These detectors are coined as adaptive in reference to the step of utilizing an estimate of the clutter covariance matrix using training data of signalfree observations. To estimate the clutter covariance matrix, we employ regularized covariance estimators that, by construction, force the eigenvalues of the covariance estimates to be greater than a positive scalar . While this feature is likely to increase the bias of the covariance estimate, it presents the advantage of improving its conditioning, thus making the regularization suitable for handling high dimensional regimes. In this paper, we consider the setting of the regularization parameter and the threshold for ASMF detectors in both Gaussian and Compound Gaussian clutters. In order to allow for a proper selection of these parameters, it is essential to analyze the false alarm and detection probabilities. For tractability, such a task is carried out under the asymptotic regime in which the number of observations and their dimensions grow simultaneously large, thereby allowing us to leverage existing results from random matrix theory. Simulation results are provided in order to illustrate the relevance of the proposed design strategy and to compare the performances of the proposed ASMF detectors versus Adaptive normalized Matched Filter (ANMF) detectors under mismatch scenarios.

  12. Optimal Design of Large Dimensional Adaptive Subspace Detectors

    KAUST Repository

    Ben Atitallah, Ismail

    2016-05-27

    This paper addresses the design of Adaptive Subspace Matched Filter (ASMF) detectors in the presence of a mismatch in the steering vector. These detectors are coined as adaptive in reference to the step of utilizing an estimate of the clutter covariance matrix using training data of signalfree observations. To estimate the clutter covariance matrix, we employ regularized covariance estimators that, by construction, force the eigenvalues of the covariance estimates to be greater than a positive scalar . While this feature is likely to increase the bias of the covariance estimate, it presents the advantage of improving its conditioning, thus making the regularization suitable for handling high dimensional regimes. In this paper, we consider the setting of the regularization parameter and the threshold for ASMF detectors in both Gaussian and Compound Gaussian clutters. In order to allow for a proper selection of these parameters, it is essential to analyze the false alarm and detection probabilities. For tractability, such a task is carried out under the asymptotic regime in which the number of observations and their dimensions grow simultaneously large, thereby allowing us to leverage existing results from random matrix theory. Simulation results are provided in order to illustrate the relevance of the proposed design strategy and to compare the performances of the proposed ASMF detectors versus Adaptive normalized Matched Filter (ANMF) detectors under mismatch scenarios.

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

    Czech Academy of Sciences Publication Activity Database

    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

  14. A unified classifier for robust face recognition based on combining multiple subspace algorithms

    Science.gov (United States)

    Ijaz Bajwa, Usama; Ahmad Taj, Imtiaz; Waqas Anwar, Muhammad

    2012-10-01

    Face recognition being the fastest growing biometric technology has expanded manifold in the last few years. Various new algorithms and commercial systems have been proposed and developed. However, none of the proposed or developed algorithm is a complete solution because it may work very well on one set of images with say illumination changes but may not work properly on another set of image variations like expression variations. This study is motivated by the fact that any single classifier cannot claim to show generally better performance against all facial image variations. To overcome this shortcoming and achieve generality, combining several classifiers using various strategies has been studied extensively also incorporating the question of suitability of any classifier for this task. The study is based on the outcome of a comprehensive comparative analysis conducted on a combination of six subspace extraction algorithms and four distance metrics on three facial databases. The analysis leads to the selection of the most suitable classifiers which performs better on one task or the other. These classifiers are then combined together onto an ensemble classifier by two different strategies of weighted sum and re-ranking. The results of the ensemble classifier show that these strategies can be effectively used to construct a single classifier that can successfully handle varying facial image conditions of illumination, aging and facial expressions.

  15. Representation of discrete Steklov-Poincare operator arising in domain decomposition methods in wavelet basis

    Energy Technology Data Exchange (ETDEWEB)

    Jemcov, A.; Matovic, M.D. [Queen`s Univ., Kingston, Ontario (Canada)

    1996-12-31

    This paper examines the sparse representation and preconditioning of a discrete Steklov-Poincare operator which arises in domain decomposition methods. A non-overlapping domain decomposition method is applied to a second order self-adjoint elliptic operator (Poisson equation), with homogeneous boundary conditions, as a model problem. It is shown that the discrete Steklov-Poincare operator allows sparse representation with a bounded condition number in wavelet basis if the transformation is followed by thresholding and resealing. These two steps combined enable the effective use of Krylov subspace methods as an iterative solution procedure for the system of linear equations. Finding the solution of an interface problem in domain decomposition methods, known as a Schur complement problem, has been shown to be equivalent to the discrete form of Steklov-Poincare operator. A common way to obtain Schur complement matrix is by ordering the matrix of discrete differential operator in subdomain node groups then block eliminating interface nodes. The result is a dense matrix which corresponds to the interface problem. This is equivalent to reducing the original problem to several smaller differential problems and one boundary integral equation problem for the subdomain interface.

  16. Model, analysis, and evaluation of the effects of analog VLSI arithmetic on linear subspace-based image recognition.

    Science.gov (United States)

    Carvajal, Gonzalo; Figueroa, Miguel

    2014-07-01

    Typical image recognition systems operate in two stages: feature extraction to reduce the dimensionality of the input space, and classification based on the extracted features. Analog Very Large Scale Integration (VLSI) is an attractive technology to achieve compact and low-power implementations of these computationally intensive tasks for portable embedded devices. However, device mismatch limits the resolution of the circuits fabricated with this technology. Traditional layout techniques to reduce the mismatch aim to increase the resolution at the transistor level, without considering the intended application. Relating mismatch parameters to specific effects in the application level would allow designers to apply focalized mismatch compensation techniques according to predefined performance/cost tradeoffs. This paper models, analyzes, and evaluates the effects of mismatched analog arithmetic in both feature extraction and classification circuits. For the feature extraction, we propose analog adaptive linear combiners with on-chip learning for both Least Mean Square (LMS) and Generalized Hebbian Algorithm (GHA). Using mathematical abstractions of analog circuits, we identify mismatch parameters that are naturally compensated during the learning process, and propose cost-effective guidelines to reduce the effect of the rest. For the classification, we derive analog models for the circuits necessary to implement Nearest Neighbor (NN) approach and Radial Basis Function (RBF) networks, and use them to emulate analog classifiers with standard databases of face and hand-writing digits. Formal analysis and experiments show how we can exploit adaptive structures and properties of the input space to compensate the effects of device mismatch at the application level, thus reducing the design overhead of traditional layout techniques. Results are also directly extensible to multiple application domains using linear subspace methods. Copyright © 2014 Elsevier Ltd. All rights

  17. A "feasible direction" search for Lineal Programming problem solving

    Directory of Open Access Journals (Sweden)

    Jaime U Malpica Angarita

    2003-07-01

    Full Text Available The study presents an approach to solve linear programming problems with no artificial variables. A primal linear minimization problem is standard form and its associated dual linear maximization problem are used. Initially, the dual (or a partial dual program is solved by a "feasible direction" search, where the Karush-Kuhn-Tucker conditions help to verify its optimality and then its feasibility. The "feasible direction" search exploits the characteristics of the convex polyhedron (or prototype formed by the dual program constraints to find a starting point and then follows line segments, whose directions are found in afine subspaces defined by boundary hyperplanes of polyhedral faces, to find next points up to the (an optimal one. Them, the remaining dual constraints not satisfaced at that optimal dual point, if there are any, are handled as nonbasic variables of the primal program, which is to be solved by such "feasible direction" search.

  18. Recovering task fMRI signals from highly under-sampled data with low-rank and temporal subspace constraints.

    Science.gov (United States)

    Chiew, Mark; Graedel, Nadine N; Miller, Karla L

    2018-07-01

    Recent developments in highly accelerated fMRI data acquisition have employed low-rank and/or sparsity constraints for image reconstruction, as an alternative to conventional, time-independent parallel imaging. When under-sampling factors are high or the signals of interest are low-variance, however, functional data recovery can be poor or incomplete. We introduce a method for improving reconstruction fidelity using external constraints, like an experimental design matrix, to partially orient the estimated fMRI temporal subspace. Combining these external constraints with low-rank constraints introduces a new image reconstruction model that is analogous to using a mixture of subspace-decomposition (PCA/ICA) and regression (GLM) models in fMRI analysis. We show that this approach improves fMRI reconstruction quality in simulations and experimental data, focusing on the model problem of detecting subtle 1-s latency shifts between brain regions in a block-design task-fMRI experiment. Successful latency discrimination is shown at acceleration factors up to R = 16 in a radial-Cartesian acquisition. We show that this approach works with approximate, or not perfectly informative constraints, where the derived benefit is commensurate with the information content contained in the constraints. The proposed method extends low-rank approximation methods for under-sampled fMRI data acquisition by leveraging knowledge of expected task-based variance in the data, enabling improvements in the speed and efficiency of fMRI data acquisition without the loss of subtle features. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

  19. Two-level method for unsteady Navier-Stokes equations based on a new projection

    International Nuclear Information System (INIS)

    Hou Yanren; Li Kaitai

    2004-12-01

    A two-level algorithm for the two dimensional unsteady Navier-Stokes equations based on a new projection is proposed and investigated. The approximate solution is solved as a sum of a large eddy component and a small eddy component, which are in the sense of the new projection, constructed in this paper. These two terms advance in time explicitly. Actually, the new algorithm proposed here can be regarded as a sort of postprocessing algorithm for the standard Galerkin method (SGM). The large eddy part is solved by SGM in the usual L 2 -based large eddy subspace while the small eddy part (the correction part) is obtained in its complement subspace in the sense of the new projection. The stability analysis indicates the improvement of the stability comparing with SGM of the same scale, and the L 2 -error estimate shows that the scheme can improve the accuracy of SGM approximation for half order. We also propose a numerical implementation based on Lagrange multiplier for this two-level algorithm. (author)

  20. Supervised orthogonal discriminant subspace projects learning for face recognition.

    Science.gov (United States)

    Chen, Yu; Xu, Xiao-Hong

    2014-02-01

    In this paper, a new linear dimension reduction method called supervised orthogonal discriminant subspace projection (SODSP) is proposed, which addresses high-dimensionality of data and the small sample size problem. More specifically, given a set of data points in the ambient space, a novel weight matrix that describes the relationship between the data points is first built. And in order to model the manifold structure, the class information is incorporated into the weight matrix. Based on the novel weight matrix, the local scatter matrix as well as non-local scatter matrix is defined such that the neighborhood structure can be preserved. In order to enhance the recognition ability, we impose an orthogonal constraint into a graph-based maximum margin analysis, seeking to find a projection that maximizes the difference, rather than the ratio between the non-local scatter and the local scatter. In this way, SODSP naturally avoids the singularity problem. Further, we develop an efficient and stable algorithm for implementing SODSP, especially, on high-dimensional data set. Moreover, the theoretical analysis shows that LPP is a special instance of SODSP by imposing some constraints. Experiments on the ORL, Yale, Extended Yale face database B and FERET face database are performed to test and evaluate the proposed algorithm. The results demonstrate the effectiveness of SODSP. Copyright © 2013 Elsevier Ltd. All rights reserved.

  1. Direct and indirect two-photon processes in semiconductors

    International Nuclear Information System (INIS)

    Hassan, A.R.

    1986-07-01

    The expressions describing direct and indirect two-photon absorption in crystals are given. They are valid both near and far from the energy gap. A perturbative approach through two different band models is adopted. The effects of the non-parabolicity and the degeneracy of the energy bands are considered. The numerical results are compared with the other theories and with a recent experimental data in Zn and AgCl. It is shown that the dominant transition mechanisms are of the allowed-allowed type near and far from the gap for both direct and indirect processes. (author)

  2. Efficient response spectrum analysis of a reactor using Model Order Reduction

    International Nuclear Information System (INIS)

    Oh, Jin Ho; Choi, Jin Bok; Ryu, Jeong Soo

    2012-01-01

    A response spectrum analysis (RSA) has been widely used to evaluate the structural integrity of various structural components in the nuclear industry. However, solving the large and complex structural systems numerically using the RSA requires a considerable amount of computational resources and time. To overcome this problem, this paper proposes the RSA based on the model order reduction (MOR) technique achieved by applying a projection from a higher order to a lower order space using Krylov subspaces generated by the Arnoldi algorithm. The dynamic characteristics of the final reduced system are almost identical with those of the full system by matching the moments of the reduced system with those of the full system up to the required nth order. It is remarkably efficient in terms of computation time and does not require a global system. Numerical examples demonstrate that the proposed method saves computational costs effectively, and provides a reduced system framework that predicts the accurate responses of a global system

  3. The application of projected conjugate gradient solvers on graphical processing units

    International Nuclear Information System (INIS)

    Lin, Youzuo; Renaut, Rosemary

    2011-01-01

    Graphical processing units introduce the capability for large scale computation at the desktop. Presented numerical results verify that efficiencies and accuracies of basic linear algebra subroutines of all levels when implemented in CUDA and Jacket are comparable. But experimental results demonstrate that the basic linear algebra subroutines of level three offer the greatest potential for improving efficiency of basic numerical algorithms. We consider the solution of the multiple right hand side set of linear equations using Krylov subspace-based solvers. Thus, for the multiple right hand side case, it is more efficient to make use of a block implementation of the conjugate gradient algorithm, rather than to solve each system independently. Jacket is used for the implementation. Furthermore, including projection from one system to another improves efficiency. A relevant example, for which simulated results are provided, is the reconstruction of a three dimensional medical image volume acquired from a positron emission tomography scanner. Efficiency of the reconstruction is improved by using projection across nearby slices.

  4. Survey on efficient linear solvers for porous media flow models on recent hardware architectures

    International Nuclear Information System (INIS)

    Anciaux-Sedrakian, Ani; Gratien, Jean-Marc; Guignon, Thomas; Gottschling, Peter

    2014-01-01

    In the past few years, High Performance Computing (HPC) technologies led to General Purpose Processing on Graphics Processing Units (GPGPU) and many-core architectures. These emerging technologies offer massive processing units and are interesting for porous media flow simulators may used for CO 2 geological sequestration or Enhanced Oil Recovery (EOR) simulation. However the crucial point is 'are current algorithms and software able to use these new technologies efficiently?' The resolution of large sparse linear systems, almost ill-conditioned, constitutes the most CPU-consuming part of such simulators. This paper proposes a survey on various solver and pre-conditioner algorithms, analyzes their efficiency and performance regarding these distinct architectures. Furthermore it proposes a novel approach based on a hybrid programming model for both GPU and many-core clusters. The proposed optimization techniques are validated through a Krylov subspace solver; BiCGStab and some pre-conditioners like ILU0 on GPU, multi-core and many-core architectures, on various large real study cases in EOR simulation. (authors)

  5. The application of projected conjugate gradient solvers on graphical processing units

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Youzuo [Los Alamos National Laboratory; Renaut, Rosemary [ARIZONA STATE UNIV.

    2011-01-26

    Graphical processing units introduce the capability for large scale computation at the desktop. Presented numerical results verify that efficiencies and accuracies of basic linear algebra subroutines of all levels when implemented in CUDA and Jacket are comparable. But experimental results demonstrate that the basic linear algebra subroutines of level three offer the greatest potential for improving efficiency of basic numerical algorithms. We consider the solution of the multiple right hand side set of linear equations using Krylov subspace-based solvers. Thus, for the multiple right hand side case, it is more efficient to make use of a block implementation of the conjugate gradient algorithm, rather than to solve each system independently. Jacket is used for the implementation. Furthermore, including projection from one system to another improves efficiency. A relevant example, for which simulated results are provided, is the reconstruction of a three dimensional medical image volume acquired from a positron emission tomography scanner. Efficiency of the reconstruction is improved by using projection across nearby slices.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1994-12-31

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

  7. Thick restarting of the Davidson method: An extension to implicit restarting

    Energy Technology Data Exchange (ETDEWEB)

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

    1996-12-31

    The solution of the large, sparse, eigenvalue problem Ax = {lambda}x, for a few eigenpairs is central to many scientific applications. The Arnoldi method, and its equivalent in the symmetric case the Lanczos method, have been the traditional approach to solving these problems. Preconditioning, through some shift-and-invert technique, is frequently employed, because of the difficulty of these problems. A different approach is followed by the Generalized Davidson (GD) method which is a popular preconditioned variant of the Lanczos iteration. Instead of using a three-term recurrence to build an orthonormal basis for the Krylov subspace, the GD algorithm obtains the next basis vector by explicitly orthogonalizing the preconditioned residual (M - {lambda}I){sup -1} (A - {lambda}I)x against the existing basis. A straightforward extension to the non-symmetric case has also been studied in. The GD method can be regarded as a way of improving convergence and robustness at the expense of a more complicated step.

  8. Output-only cyclo-stationary linear-parameter time-varying stochastic subspace identification method for rotating machinery and spinning structures

    Science.gov (United States)

    Velazquez, Antonio; Swartz, R. Andrew

    2015-02-01

    Economical maintenance and operation are critical issues for rotating machinery and spinning structures containing blade elements, especially large slender dynamic beams (e.g., wind turbines). Structural health monitoring systems represent promising instruments to assure reliability and good performance from the dynamics of the mechanical systems. However, such devices have not been completely perfected for spinning structures. These sensing technologies are typically informed by both mechanistic models coupled with data-driven identification techniques in the time and/or frequency domain. Frequency response functions are popular but are difficult to realize autonomously for structures of higher order, especially when overlapping frequency content is present. Instead, time-domain techniques have shown to possess powerful advantages from a practical point of view (i.e. low-order computational effort suitable for real-time or embedded algorithms) and also are more suitable to differentiate closely-related modes. Customarily, time-varying effects are often neglected or dismissed to simplify this analysis, but such cannot be the case for sinusoidally loaded structures containing spinning multi-bodies. A more complex scenario is constituted when dealing with both periodic mechanisms responsible for the vibration shaft of the rotor-blade system and the interaction of the supporting substructure. Transformations of the cyclic effects on the vibrational data can be applied to isolate inertial quantities that are different from rotation-generated forces that are typically non-stationary in nature. After applying these transformations, structural identification can be carried out by stationary techniques via data-correlated eigensystem realizations. In this paper, an exploration of a periodic stationary or cyclo-stationary subspace identification technique is presented here for spinning multi-blade systems by means of a modified Eigensystem Realization Algorithm (ERA) via

  9. A Variational Approach to Video Registration with Subspace Constraints.

    Science.gov (United States)

    Garg, Ravi; Roussos, Anastasios; Agapito, Lourdes

    2013-01-01

    This paper addresses the problem of non-rigid video registration, or the computation of optical flow from a reference frame to each of the subsequent images in a sequence, when the camera views deformable objects. We exploit the high correlation between 2D trajectories of different points on the same non-rigid surface by assuming that the displacement of any point throughout the sequence can be expressed in a compact way as a linear combination of a low-rank motion basis. This subspace constraint effectively acts as a trajectory regularization term leading to temporally consistent optical flow. We formulate it as a robust soft constraint within a variational framework by penalizing flow fields that lie outside the low-rank manifold. The resulting energy functional can be decoupled into the optimization of the brightness constancy and spatial regularization terms, leading to an efficient optimization scheme. Additionally, we propose a novel optimization scheme for the case of vector valued images, based on the dualization of the data term. This allows us to extend our approach to deal with colour images which results in significant improvements on the registration results. Finally, we provide a new benchmark dataset, based on motion capture data of a flag waving in the wind, with dense ground truth optical flow for evaluation of multi-frame optical flow algorithms for non-rigid surfaces. Our experiments show that our proposed approach outperforms state of the art optical flow and dense non-rigid registration algorithms.

  10. Synergistic Instance-Level Subspace Alignment for Fine-Grained Sketch-Based Image Retrieval.

    Science.gov (United States)

    Li, Ke; Pang, Kaiyue; Song, Yi-Zhe; Hospedales, Timothy M; Xiang, Tao; Zhang, Honggang

    2017-08-25

    We study the problem of fine-grained sketch-based image retrieval. By performing instance-level (rather than category-level) retrieval, it embodies a timely and practical application, particularly with the ubiquitous availability of touchscreens. Three factors contribute to the challenging nature of the problem: (i) free-hand sketches are inherently abstract and iconic, making visual comparisons with photos difficult, (ii) sketches and photos are in two different visual domains, i.e. black and white lines vs. color pixels, and (iii) fine-grained distinctions are especially challenging when executed across domain and abstraction-level. To address these challenges, we propose to bridge the image-sketch gap both at the high-level via parts and attributes, as well as at the low-level, via introducing a new domain alignment method. More specifically, (i) we contribute a dataset with 304 photos and 912 sketches, where each sketch and image is annotated with its semantic parts and associated part-level attributes. With the help of this dataset, we investigate (ii) how strongly-supervised deformable part-based models can be learned that subsequently enable automatic detection of part-level attributes, and provide pose-aligned sketch-image comparisons. To reduce the sketch-image gap when comparing low-level features, we also (iii) propose a novel method for instance-level domain-alignment, that exploits both subspace and instance-level cues to better align the domains. Finally (iv) these are combined in a matching framework integrating aligned low-level features, mid-level geometric structure and high-level semantic attributes. Extensive experiments conducted on our new dataset demonstrate effectiveness of the proposed method.

  11. A constrained optimization algorithm for total energy minimization in electronic structure calculations

    International Nuclear Information System (INIS)

    Yang Chao; Meza, Juan C.; Wang Linwang

    2006-01-01

    A new direct constrained optimization algorithm for minimizing the Kohn-Sham (KS) total energy functional is presented in this paper. The key ingredients of this algorithm involve projecting the total energy functional into a sequence of subspaces of small dimensions and seeking the minimizer of total energy functional within each subspace. The minimizer of a subspace energy functional not only provides a search direction along which the KS total energy functional decreases but also gives an optimal 'step-length' to move along this search direction. Numerical examples are provided to demonstrate that this new direct constrained optimization algorithm can be more efficient than the self-consistent field (SCF) iteration

  12. DOA Estimation Based on Real-Valued Cross Correlation Matrix of Coprime Arrays.

    Science.gov (United States)

    Li, Jianfeng; Wang, Feng; Jiang, Defu

    2017-03-20

    A fast direction of arrival (DOA) estimation method using a real-valued cross-correlation matrix (CCM) of coprime subarrays is proposed. Firstly, real-valued CCM with extended aperture is constructed to obtain the signal subspaces corresponding to the two subarrays. By analysing the relationship between the two subspaces, DOA estimations from the two subarrays are simultaneously obtained with automatic pairing. Finally, unique DOA is determined based on the common results from the two subarrays. Compared to partial spectral search (PSS) method and estimation of signal parameter via rotational invariance (ESPRIT) based method for coprime arrays, the proposed algorithm has lower complexity but achieves better DOA estimation performance and handles more sources. Simulation results verify the effectiveness of the approach.

  13. A description of the location and structure of the essential spectrum of a model operator in a subspace of a Fock space

    Energy Technology Data Exchange (ETDEWEB)

    Yodgorov, G R [Navoi State Pedagogical Institute, Navoi (Uzbekistan); Ismail, F [Universiti Putra Malaysia, Selangor (Malaysia); Muminov, Z I [Malaysia – Japan International Institute of Technology, Kuala Lumpur (Malaysia)

    2014-12-31

    We consider a certain model operator acting in a subspace of a fermionic Fock space. We obtain an analogue of Faddeev's equation. We describe the location of the essential spectrum of the operator under consideration and show that the essential spectrum consists of the union of at most four segments. Bibliography: 19 titles.

  14. A fully implicit Newton-Krylov-Schwarz method for tokamak magnetohydrodynamics: Jacobian construction and preconditioner formulation

    KAUST Repository

    Reynolds, Daniel R.

    2012-01-01

    Single-fluid resistive magnetohydrodynamics (MHD) is a fluid description of fusion plasmas which is often used to investigate macroscopic instabilities in tokamaks. In MHD modeling of tokamaks, it is often desirable to compute MHD phenomena to resistive time scales or a combination of resistive-Alfvén time scales, which can render explicit time stepping schemes computationally expensive. We present recent advancements in the development of preconditioners for fully nonlinearly implicit simulations of single-fluid resistive tokamak MHD. Our work focuses on simulations using a structured mesh mapped into a toroidal geometry with a shaped poloidal cross-section, and a finite-volume spatial discretization of the partial differential equation model. We discretize the temporal dimension using a fully implicit or the backwards differentiation formula method, and solve the resulting nonlinear algebraic system using a standard inexact Newton-Krylov approach, provided by the sundials library. The focus of this paper is on the construction and performance of various preconditioning approaches for accelerating the convergence of the iterative solver algorithms. Effective preconditioners require information about the Jacobian entries; however, analytical formulae for these Jacobian entries may be prohibitive to derive/implement without error. We therefore compute these entries using automatic differentiation with OpenAD. We then investigate a variety of preconditioning formulations inspired by standard solution approaches in modern MHD codes, in order to investigate their utility in a preconditioning context. We first describe the code modifications necessary for the use of the OpenAD tool and sundials solver library. We conclude with numerical results for each of our preconditioning approaches in the context of pellet-injection fueling of tokamak plasmas. Of these, our optimal approach results in a speedup of a factor of 3 compared with non-preconditioned implicit tests, with

  15. Study of I11-conditioning of Linac stereotactic irradiation subspaces using singular values decomposition analysis

    International Nuclear Information System (INIS)

    Platoni, K.; Lefkopoulos, D.; Grandjean, P.; Schlienger, M.

    1999-01-01

    A Linac sterotactic irradiation space is characterized by different angular separations of beams because of the geometry of the stereotactic irradiation. The regions of the stereotactic space characterized by low angular separations are one of the causes of ill-conditioning of the stereotactic irradiation inverse problem. The singular value decomposition (SVD) is a powerful mathematical analysis that permits the measurement of the ill-conditioning of the stereotactic irradiation problem. This study examines the ill-conditioning of the stereotactic irradiation space, provoked by the different angular separations of beams, using the SVD analysis. We subdivided the maximum irradiation space (MIS: (AA) AP x (AA) RL =180 x 180 ) into irradiation subspaces (ISSs), each characterized by its own angular separation. We studied the influence of ISSs on the SVD analysis and the evolution of the reconstruction quality of well defined three-dimensional dose matrices in each configuration. The more the ISS is characterized by low angular separation the more the condition number and the reconstruction inaccuracy are increased. Based on the above results we created two reduced irradiation spaces (RIS: (AA) AP x (AA) RL =180 x 140 and (AA) AP x (AA) RL =180 x 120 ) and compared the reconstruction quality of the RISs with respect to the MIS. The more an irradiation space is free of low angular separations the more the irradiation space contains useful singular components. (orig.)

  16. Structural damage detection based on stochastic subspace identification and statistical pattern recognition: I. Theory

    Science.gov (United States)

    Ren, W. X.; Lin, Y. Q.; Fang, S. E.

    2011-11-01

    One of the key issues in vibration-based structural health monitoring is to extract the damage-sensitive but environment-insensitive features from sampled dynamic response measurements and to carry out the statistical analysis of these features for structural damage detection. A new damage feature is proposed in this paper by using the system matrices of the forward innovation model based on the covariance-driven stochastic subspace identification of a vibrating system. To overcome the variations of the system matrices, a non-singularity transposition matrix is introduced so that the system matrices are normalized to their standard forms. For reducing the effects of modeling errors, noise and environmental variations on measured structural responses, a statistical pattern recognition paradigm is incorporated into the proposed method. The Mahalanobis and Euclidean distance decision functions of the damage feature vector are adopted by defining a statistics-based damage index. The proposed structural damage detection method is verified against one numerical signal and two numerical beams. It is demonstrated that the proposed statistics-based damage index is sensitive to damage and shows some robustness to the noise and false estimation of the system ranks. The method is capable of locating damage of the beam structures under different types of excitations. The robustness of the proposed damage detection method to the variations in environmental temperature is further validated in a companion paper by a reinforced concrete beam tested in the laboratory and a full-scale arch bridge tested in the field.

  17. Two-Stage Regularized Linear Discriminant Analysis for 2-D Data.

    Science.gov (United States)

    Zhao, Jianhua; Shi, Lei; Zhu, Ji

    2015-08-01

    Fisher linear discriminant analysis (LDA) involves within-class and between-class covariance matrices. For 2-D data such as images, regularized LDA (RLDA) can improve LDA due to the regularized eigenvalues of the estimated within-class matrix. However, it fails to consider the eigenvectors and the estimated between-class matrix. To improve these two matrices simultaneously, we propose in this paper a new two-stage method for 2-D data, namely a bidirectional LDA (BLDA) in the first stage and the RLDA in the second stage, where both BLDA and RLDA are based on the Fisher criterion that tackles correlation. BLDA performs the LDA under special separable covariance constraints that incorporate the row and column correlations inherent in 2-D data. The main novelty is that we propose a simple but effective statistical test to determine the subspace dimensionality in the first stage. As a result, the first stage reduces the dimensionality substantially while keeping the significant discriminant information in the data. This enables the second stage to perform RLDA in a much lower dimensional subspace, and thus improves the two estimated matrices simultaneously. Experiments on a number of 2-D synthetic and real-world data sets show that BLDA+RLDA outperforms several closely related competitors.

  18. Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

    International Nuclear Information System (INIS)

    Godoy, William F.; Liu Xu

    2012-01-01

    The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.

  19. Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis

    International Nuclear Information System (INIS)

    Abdel-Khalik, Hany S.; Bang, Youngsuk; Wang, Congjian

    2013-01-01

    Highlights: ► We overview the state-of-the-art in uncertainty quantification and sensitivity analysis. ► We overview new developments in above areas using hybrid methods. ► We give a tutorial introduction to above areas and the new developments. ► Hybrid methods address the explosion in dimensionality in nonlinear models. ► Representative numerical experiments are given. -- Abstract: The role of modeling and simulation has been heavily promoted in recent years to improve understanding of complex engineering systems. To realize the benefits of modeling and simulation, concerted efforts in the areas of uncertainty quantification and sensitivity analysis are required. The manuscript intends to serve as a pedagogical presentation of the material to young researchers and practitioners with little background on the subjects. We believe this is important as the role of these subjects is expected to be integral to the design, safety, and operation of existing as well as next generation reactors. In addition to covering the basics, an overview of the current state-of-the-art will be given with particular emphasis on the challenges pertaining to nuclear reactor modeling. The second objective will focus on presenting our own development of hybrid subspace methods intended to address the explosion in the computational overhead required when handling real-world complex engineering systems.

  20. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    International Nuclear Information System (INIS)

    Kılıç, Emre; Eibert, Thomas F.

    2015-01-01

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

  1. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    Energy Technology Data Exchange (ETDEWEB)

    Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

    2015-05-01

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

  2. A Robust Real Time Direction-of-Arrival Estimation Method for Sequential Movement Events of Vehicles.

    Science.gov (United States)

    Liu, Huawei; Li, Baoqing; Yuan, Xiaobing; Zhou, Qianwei; Huang, Jingchang

    2018-03-27

    Parameters estimation of sequential movement events of vehicles is facing the challenges of noise interferences and the demands of portable implementation. In this paper, we propose a robust direction-of-arrival (DOA) estimation method for the sequential movement events of vehicles based on a small Micro-Electro-Mechanical System (MEMS) microphone array system. Inspired by the incoherent signal-subspace method (ISM), the method that is proposed in this work employs multiple sub-bands, which are selected from the wideband signals with high magnitude-squared coherence to track moving vehicles in the presence of wind noise. The field test results demonstrate that the proposed method has a better performance in emulating the DOA of a moving vehicle even in the case of severe wind interference than the narrowband multiple signal classification (MUSIC) method, the sub-band DOA estimation method, and the classical two-sided correlation transformation (TCT) method.

  3. Directional detection of dark matter with two-dimensional targets

    Science.gov (United States)

    Hochberg, Yonit; Kahn, Yonatan; Lisanti, Mariangela; Tully, Christopher G.; Zurek, Kathryn M.

    2017-09-01

    We propose two-dimensional materials as targets for direct detection of dark matter. Using graphene as an example, we focus on the case where dark matter scattering deposits sufficient energy on a valence-band electron to eject it from the target. We show that the sensitivity of graphene to dark matter of MeV to GeV mass can be comparable, for similar exposure and background levels, to that of semiconductor targets such as silicon and germanium. Moreover, a two-dimensional target is an excellent directional detector, as the ejected electron retains information about the angular dependence of the incident dark matter particle. This proposal can be implemented by the PTOLEMY experiment, presenting for the first time an opportunity for directional detection of sub-GeV dark matter.

  4. Predictor-Year Subspace Clustering Based Ensemble Prediction of Indian Summer Monsoon

    Directory of Open Access Journals (Sweden)

    Moumita Saha

    2016-01-01

    Full Text Available Forecasting the Indian summer monsoon is a challenging task due to its complex and nonlinear behavior. A large number of global climatic variables with varying interaction patterns over years influence monsoon. Various statistical and neural prediction models have been proposed for forecasting monsoon, but many of them fail to capture variability over years. The skill of predictor variables of monsoon also evolves over time. In this article, we propose a joint-clustering of monsoon years and predictors for understanding and predicting the monsoon. This is achieved by subspace clustering algorithm. It groups the years based on prevailing global climatic condition using statistical clustering technique and subsequently for each such group it identifies significant climatic predictor variables which assist in better prediction. Prediction model is designed to frame individual cluster using random forest of regression tree. Prediction of aggregate and regional monsoon is attempted. Mean absolute error of 5.2% is obtained for forecasting aggregate Indian summer monsoon. Errors in predicting the regional monsoons are also comparable in comparison to the high variation of regional precipitation. Proposed joint-clustering based ensemble model is observed to be superior to existing monsoon prediction models and it also surpasses general nonclustering based prediction models.

  5. Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

    Science.gov (United States)

    Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

    2016-11-01

    A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates

  6. Concept of a collective subspace associated with the invariance principle of the Schroedinger equation

    International Nuclear Information System (INIS)

    Marumori, Toshio; Hayashi, Akihisa; Tomoda, Toshiaki; Kuriyama, Atsushi; Maskawa, Toshihide

    1980-01-01

    The aim of this series of papers is to propose a microscopic theory to go beyond the situations where collective motions are described by the random phase approximation, i.e., by small amplitude harmonic oscillations about equilibrium. The theory is thus appropriate for the microscopic description of the large amplitude collective motion of soft nuclei. The essential idea is to develop a method to determine the collective subspace (or submanifold) in the many-particle Hilbert space in an optimal way, on the basis of a fundamental principle called the invariance principle of the Schroedinger equation. By using the principle within the framework of the Hartree-Fock theory, it is shown that the theory can clarify the structure of the so-called ''phonon-bands'' by self-consistently deriving the collective Hamiltonian where the number of the ''physical phonon'' is conserved. The purpose of this paper is not to go into detailed quantitative discussion, but rather to develop the basic idea. (author)

  7. Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

    Science.gov (United States)

    Georgievskii, D. V.

    2017-07-01

    The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke's law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.

  8. DOA Estimation Based on Real-Valued Cross Correlation Matrix of Coprime Arrays

    Directory of Open Access Journals (Sweden)

    Jianfeng Li

    2017-03-01

    Full Text Available A fast direction of arrival (DOA estimation method using a real-valued cross-correlation matrix (CCM of coprime subarrays is proposed. Firstly, real-valued CCM with extended aperture is constructed to obtain the signal subspaces corresponding to the two subarrays. By analysing the relationship between the two subspaces, DOA estimations from the two subarrays are simultaneously obtained with automatic pairing. Finally, unique DOA is determined based on the common results from the two subarrays. Compared to partial spectral search (PSS method and estimation of signal parameter via rotational invariance (ESPRIT based method for coprime arrays, the proposed algorithm has lower complexity but achieves better DOA estimation performance and handles more sources. Simulation results verify the effectiveness of the approach.

  9. Towards an exhaustive sampling of the configurational spaces of the two forms of the peptide hormone guanylin

    NARCIS (Netherlands)

    de Groot, B.L.; Amadei, A; van Aalten, D.M.F.; Berendsen, H.J.C.

    The recently introduced Essential Dynamics sampling method is extended such that an exhaustive sampling of the available (backbone) configurational space can be achieved. From an initial Molecular Dynamics simulation an approximated definition of the essential subspace is obtained. This subspace is

  10. Dissatisfaction of Compact Picard Condition (CPC) with GRACE satellite data and its treatment by Generalized Tikhonov in Sobolev subspace

    Science.gov (United States)

    AllahTavakoli, Y.; Bagheri, H.; Safari, A.; Sharifi, M.

    2012-04-01

    This paper is mainly aiming to prove that the stripy noises in the map of earth's surface mass-density changes derived from GRACE Satellites gravimetry, is due to a dissatisfaction of Compact Picard Condition (CPC) with the GRACE data in the inversion of the Newton Integral Equation over the thin layer of earth; and hence the paper proposes the regularization strategies as efficient tools to treat the Ill-posedness and consequently to de-strip the data. First of all, we preferred to slightly modify the mathematical model of earth's surface mass-density changes developed creatively first by J. Wahr and et.al (1998), according to the all their previous assumptions plus taking into consideration the effect of the earth topography. By the modification we expect that some uncertainties in the prior model have been reduced to some extent. Then we analyzed the CPC on the model and we demonstrated how to perform Generalized Tikhonov regularization in Sobolev subspace for overcoming the instability of the problem. Then we applied the strategy in some simulations and case studies to validate our ideas. The simulations confirm that the stripy noises in the GRACE-derived map of the mass-density changes are due to the CPC dissatisfaction and furthermore the case studies show that Generalized Tikhonov regularization in Sobolev subspace is an influential filtering tool to de-strip the noisy data. Also, the case studies interestingly show that the effect of the topography is comparable to the effect of the load Love numbers on the Wahr's model; hence it may be taken into consideration when the load Love numbers have been taken into account.

  11. MODAL TRACKING of A Structural Device: A Subspace Identification Approach

    Energy Technology Data Exchange (ETDEWEB)

    Candy, J. V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Franco, S. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Ruggiero, E. L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Emmons, M. C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Lopez, I. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Stoops, L. M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2017-03-20

    Mechanical devices operating in an environment contaminated by noise, uncertainties, and extraneous disturbances lead to low signal-to-noise-ratios creating an extremely challenging processing problem. To detect/classify a device subsystem from noisy data, it is necessary to identify unique signatures or particular features. An obvious feature would be resonant (modal) frequencies emitted during its normal operation. In this report, we discuss a model-based approach to incorporate these physical features into a dynamic structure that can be used for such an identification. The approach we take after pre-processing the raw vibration data and removing any extraneous disturbances is to obtain a representation of the structurally unknown device along with its subsystems that capture these salient features. One approach is to recognize that unique modal frequencies (sinusoidal lines) appear in the estimated power spectrum that are solely characteristic of the device under investigation. Therefore, the objective of this effort is based on constructing a black box model of the device that captures these physical features that can be exploited to “diagnose” whether or not the particular device subsystem (track/detect/classify) is operating normally from noisy vibrational data. Here we discuss the application of a modern system identification approach based on stochastic subspace realization techniques capable of both (1) identifying the underlying black-box structure thereby enabling the extraction of structural modes that can be used for analysis and modal tracking as well as (2) indicators of condition and possible changes from normal operation.

  12. BRST quantization of Polyakov's two-dimensional gravity

    International Nuclear Information System (INIS)

    Itoh, Katsumi

    1990-01-01

    Two-dimensional gravity coupled to minimal models is quantized in the chiral gauge by the BRST method. By using the Wakimoto construction for the gravity sector, we show how the quartet mechanism of Kugo and Ojima works and solve the physical state condition. As a result the positive semi-definiteness of the physical subspace is shown. The formula of Knizhnik et al. for gravitational scaling dimensions is rederived from the physical state condition. We also observe a relation between the chiral gauge and the conformal gauge. (orig.)

  13. Dynamic access control for two-direction shared traffic lanes

    NARCIS (Netherlands)

    Ebben, Mark; van der Zee, D.J.; van der Heijden, Matthijs C.

    2001-01-01

    In specific traffic situations, a single lane is available for traffic from two directions. Examples are traffic accidents or road maintenance reducing the number of available lanes on a road or, as we faced in a project on underground freight transportation, construction of a single lane for two

  14. Dynamic access control for two-direction shared traffic lanes

    NARCIS (Netherlands)

    Ebben, M.J.R.; van der Zee, D.J.; van der Heijden, M.C.

    2000-01-01

    In specilic traflic situations, a single lane is available for traiffic from two directions. Examples are traffic accidents or road maintenance reducing thc number of available lanes on a road or, as we faced in a project on underground freight transportation, construction of a slnglc lane for two

  15. Special geometry on the moduli space for the two-moduli non-Fermat Calabi–Yau

    Directory of Open Access Journals (Sweden)

    Konstantin Aleshkin

    2018-01-01

    Full Text Available We clarify the recently proposed method for computing a special Kähler metric on a Calabi–Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.

  16. Special geometry on the moduli space for the two-moduli non-Fermat Calabi-Yau

    Science.gov (United States)

    Aleshkin, Konstantin; Belavin, Alexander

    2018-01-01

    We clarify the recently proposed method for computing a special Kähler metric on a Calabi-Yau complex structure moduli space using the fact that the moduli space is a subspace of a particular Frobenius manifold. We use this method to compute a previously unknown special Kähler metric in a two-moduli non-Fermat model.

  17. Two-component multistep direct reactions: A microscopic approach

    International Nuclear Information System (INIS)

    Koning, A.J.; Chadwick, M.B.

    1998-03-01

    The authors present two principal advances in multistep direct theory: (1) A two-component formulation of multistep direct reactions, where neutron and proton excitations are explicitly accounted for in the evolution of the reaction, for all orders of scattering. While this may at first seem to be a formidable task, especially for multistep processes where the many possible reaction pathways becomes large in a two-component formalism, the authors show that this is not so -- a rather simple generalization of the FKK convolution expression 1 automatically generates these pathways. Such considerations are particularly relevant when simultaneously analyzing both neutron and proton emission spectra, which is always important since these processes represent competing decay channels. (2) A new, and fully microscopic, method for calculating MSD cross sections which does not make use of particle-hole state densities but instead directly calculates cross sections for all possible particle-hole excitations (again including an exact book-keeping of the neutron/proton type of the particle and hole at all stages of the reaction) determined from a simple non-interacting shell model. This is in contrast to all previous numerical approaches which sample only a small number of such states to estimate the DWBA strength, and utilize simple analytical formulae for the partial state density, based on the equidistant spacing model. The new approach has been applied, along with theories for multistep compound, compound, and collective reactions, to analyze experimental emission spectra for a range of targets and energies. The authors show that the theory correctly accounts for double-differential nucleon spectra

  18. Generation of arbitrary two-point correlated directed networks with given modularity

    International Nuclear Information System (INIS)

    Zhou Jie; Xiao Gaoxi; Wong, Limsoon; Fu Xiuju; Ma, Stefan; Cheng, Tee Hiang

    2010-01-01

    In this Letter, we introduce measures of correlation in directed networks and develop an efficient algorithm for generating directed networks with arbitrary two-point correlation. Furthermore, a method is proposed for adjusting community structure in directed networks without changing the correlation. Effectiveness of both methods is verified by numerical results.

  19. Measurements of the vacuum-plasma response in EXTRAP T2R using generic closed-loop subspace system identification

    Energy Technology Data Exchange (ETDEWEB)

    Olofsson, K. Erik J., E-mail: erik.olofsson@ee.kth.se [School of Electrical Engineering (EES), Royal Institute of Technology (KTH), Stockholm (Sweden); Brunsell, Per R.; Drake, James R. [School of Electrical Engineering (EES), Royal Institute of Technology (KTH), Stockholm (Sweden)

    2012-12-15

    Highlights: Black-Right-Pointing-Pointer Unstable plasma response safely measured using special signal processing techniques. Black-Right-Pointing-Pointer Prediction-capable MIMO models obtained. Black-Right-Pointing-Pointer Computational statistics employed to show physical content of these models. Black-Right-Pointing-Pointer Multifold cross-validation applied for the supervised learning problem. - Abstract: A multibatch formulation of a multi-input multi-output closed-loop subspace system identification method is employed for the purpose of obtaining control-relevant models of the vacuum-plasma response in the magnetic confinement fusion experiment EXTRAP T2R. The accuracy of the estimate of the plant dynamics is estimated by computing bootstrap replication statistics of the dataset. It is seen that the thus identified models exhibit both predictive capabilities and physical spectral properties.

  20. Semiclassical analysis of the weak-coupling limit of SU(2) lattice gauge theory: The subspace of constant fields

    International Nuclear Information System (INIS)

    Bartels, J.; Wu, T.T.

    1988-01-01

    This paper contains the first part of a systematic semiclassical analysis of the weak-coupling limit of lattice gauge theories, using the Hamiltonian formulation. The model consists of an N 3 cubic lattice of pure SU(2) Yang-Mills theory, and in this first part we limit ourselves to the subspace of constant field configurations. We investigate the flow of classical trajectories, with a particular emphasis on the existence and location of caustics. There the ground-state wave function is expected to peak. It is found that regions densely filled with caustics are very close to the origin, i.e., in the domain of weak field configurations. This strongly supports the expectation that caustics are essential for quantities of physical interest

  1. Improved neutron-gamma discrimination for a 3He neutron detector using subspace learning methods

    Science.gov (United States)

    Wang, C. L.; Funk, L. L.; Riedel, R. A.; Berry, K. D.

    2017-05-01

    3He gas based neutron Linear-Position-Sensitive Detectors (LPSDs) have been used for many neutron scattering instruments. Traditional Pulse-height Analysis (PHA) for Neutron-Gamma Discrimination (NGD) resulted in the neutron-gamma efficiency ratio (NGD ratio) on the order of 105-106. The NGD ratios of 3He detectors need to be improved for even better scientific results from neutron scattering. Digital Signal Processing (DSP) analyses of waveforms were proposed for obtaining better NGD ratios, based on features extracted from rise-time, pulse amplitude, charge integration, a simplified Wiener filter, and the cross-correlation between individual and template waveforms of neutron and gamma events. Fisher Linear Discriminant Analysis (FLDA) and three Multivariate Analyses (MVAs) of the features were performed. The NGD ratios are improved by about 102-103 times compared with the traditional PHA method. Our results indicate the NGD capabilities of 3He tube detectors can be significantly improved with subspace-learning based methods, which may result in a reduced data-collection time and better data quality for further data reduction.

  2. Fault Diagnosis for Hydraulic Servo System Using Compressed Random Subspace Based ReliefF

    Directory of Open Access Journals (Sweden)

    Yu Ding

    2018-01-01

    Full Text Available Playing an important role in electromechanical systems, hydraulic servo system is crucial to mechanical systems like engineering machinery, metallurgical machinery, ships, and other equipment. Fault diagnosis based on monitoring and sensory signals plays an important role in avoiding catastrophic accidents and enormous economic losses. This study presents a fault diagnosis scheme for hydraulic servo system using compressed random subspace based ReliefF (CRSR method. From the point of view of feature selection, the scheme utilizes CRSR method to determine the most stable feature combination that contains the most adequate information simultaneously. Based on the feature selection structure of ReliefF, CRSR employs feature integration rules in the compressed domain. Meanwhile, CRSR substitutes information entropy and fuzzy membership for traditional distance measurement index. The proposed CRSR method is able to enhance the robustness of the feature information against interference while selecting the feature combination with balanced information expressing ability. To demonstrate the effectiveness of the proposed CRSR method, a hydraulic servo system joint simulation model is constructed by HyPneu and Simulink, and three fault modes are injected to generate the validation data.

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

    International Nuclear Information System (INIS)

    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.

  4. Less is More

    DEFF Research Database (Denmark)

    Assent, Ira; Müller, Emmanuel; Günnemann, Stephan

    2010-01-01

    Clustering is an important data mining task for grouping similar objects. In high dimensional data, however, eects attributed to the \\curse of dimensionality", render clustering in high dimensional data meaningless. Due to this, recent years have seen research on subspace clustering which searches...... subspace clusters which reduce the result set to a manageable size. We discuss techniques for evaluating, visualizing and exploring subspace clusterings, and propose some directions for future work....

  5. Reachable Distance Space: Efficient Sampling-Based Planning for Spatially Constrained Systems

    KAUST Repository

    Xinyu Tang,; Thomas, S.; Coleman, P.; Amato, N. M.

    2010-01-01

    reachable distance space (RD-space), in which all configurations lie in the set of constraint-satisfying subspaces. This enables us to directly sample the constrained subspaces with complexity linear in the number of the robot's degrees of freedom

  6. Spatio-temporal evolution of the 2011 Prague, Oklahoma aftershock sequence revealed using subspace detection and relocation

    Science.gov (United States)

    McMahon, Nicole D; Aster, Richard C.; Yeck, William; McNamara, Daniel E.; Benz, Harley M.

    2017-01-01

    The 6 November 2011 Mw 5.7 earthquake near Prague, Oklahoma is the second largest earthquake ever recorded in the state. A Mw 4.8 foreshock and the Mw 5.7 mainshock triggered a prolific aftershock sequence. Utilizing a subspace detection method, we increase by fivefold the number of precisely located events between 4 November and 5 December 2011. We find that while most aftershock energy is released in the crystalline basement, a significant number of the events occur in the overlying Arbuckle Group, indicating that active Meeker-Prague faulting extends into the sedimentary zone of wastewater disposal. Although the number of aftershocks in the Arbuckle Group is large, comprising ~40% of the aftershock catalog, the moment contribution of Arbuckle Group earthquakes is much less than 1% of the total aftershock moment budget. Aftershock locations are sparse in patches that experienced large slip during the mainshock.

  7. Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Ping; Song, Heda; Wang, Hong; Chai, Tianyou

    2017-09-01

    Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improve modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.

  8. Two applications of direct digital down converters in beam diagnostics

    International Nuclear Information System (INIS)

    Powers, Tom; Flood, Roger; Hovater, Curt; Musson, John

    2000-01-01

    The technologies of direct digital down converters, digital frequency synthesis, and digital signal processing are being used in many commercial applications. Because of this commercialization, the component costs are being reduced to the point where they are economically viable for large scale accelerator applications. This paper will discuss two applications of these technologies to beam diagnostics. In the first application the combination of direct digital frequency synthesis and direct digital down converters are coupled with digital signal processor technology in order to maintain the stable gain environment required for a multi-electrode beam position monitoring system. This is done by injecting a CW reference signal into the electronics as part of the front-end circuitry. In the second application direct digital down converters are used to provide a novel approach to the measurement of beam intensity using cavity current monitors. In this system a pair of reference signals are injected into the cavity through an auxiliary port. The beam current is then calculated as the ratio of the beam signal divided by the average of the magnitude of the two reference signals

  9. Planning with Reachable Distances

    KAUST Repository

    Tang, Xinyu; Thomas, Shawna; Amato, Nancy M.

    2009-01-01

    reachable distance space (RD-space), in which all configurations lie in the set of constraint-satisfying subspaces. This enables us to directly sample the constrained subspaces with complexity linear in the robot's number of degrees of freedom. In addition

  10. Eigenvector Weighting Function in Face Recognition

    Directory of Open Access Journals (Sweden)

    Pang Ying Han

    2011-01-01

    Full Text Available Graph-based subspace learning is a class of dimensionality reduction technique in face recognition. The technique reveals the local manifold structure of face data that hidden in the image space via a linear projection. However, the real world face data may be too complex to measure due to both external imaging noises and the intra-class variations of the face images. Hence, features which are extracted by the graph-based technique could be noisy. An appropriate weight should be imposed to the data features for better data discrimination. In this paper, a piecewise weighting function, known as Eigenvector Weighting Function (EWF, is proposed and implemented in two graph based subspace learning techniques, namely Locality Preserving Projection and Neighbourhood Preserving Embedding. Specifically, the computed projection subspace of the learning approach is decomposed into three partitions: a subspace due to intra-class variations, an intrinsic face subspace, and a subspace which is attributed to imaging noises. Projected data features are weighted differently in these subspaces to emphasize the intrinsic face subspace while penalizing the other two subspaces. Experiments on FERET and FRGC databases are conducted to show the promising performance of the proposed technique.

  11. Gauge equivalence between two-boson KP hierarchies

    International Nuclear Information System (INIS)

    Aratyn, H.

    1994-01-01

    In this paper it is explained the status of the two-boson KP hierarchy, which appears in this setting as an invariant subspace of the coadjoint orbit within the KP l=1 hierarchy. We will work with two main cases of two-boson KP hierarchies, one defined within KP l=1 hierarchy will be called Faa di Bruno KP hierarchy, while the second defined within KP hierarchy for a quadratic two-boson KP hierarchy. It will be established for them the gauge invariance playing the role of generalized Miura transformations. It is emphasized the symplectic character of equivalence of KP l=1 and KP. It is also made a point that the gauge equivalence established for two-boson systems is valid for an arbitrary n-th Poisson bracket structure and not only the first Poisson bracket structure. (author). 7 refs

  12. Two-photon direct frequency comb spectroscopy of alkali atoms

    Science.gov (United States)

    Palm, Christopher; Pradhananga, Trinity; Nguyen, Khoa; Montcrieffe, Caitlin; Kimball, Derek

    2012-11-01

    We have studied transition frequencies and excited state hyperfine structure in rubidium using 2-photon transitions excited directly with the frequency-doubled output of a erbium fiber optical frequency comb. The frequency comb output is directed in two counterpropagating directions through a vapor cell containing the rubidium vapor. A pair of optical filters is used to select teeth of the comb in order to identify the transition wavelengths. A photomultiplier tube (PMT) measures fluorescence from a decay channel wavelength selected with another optical filter. Using different combinations of filters enables a wide range of transitions to be investigated. By scanning the repetition rate, a Doppler-free spectrum can be obtained enabling kHz-resolution spectral measurements. An interesting dependence of the 2-photon spectrum on the energy of the intermediate state of the 2-photon transition is discussed. Our investigations are laying the groundwork for a long-term research program to use direct frequency comb spectroscopy to understand the complex spectra of rare-earth atoms.

  13. A Comparison of Sequential and GPU Implementations of Iterative Methods to Compute Reachability Probabilities

    Directory of Open Access Journals (Sweden)

    Elise Cormie-Bowins

    2012-10-01

    Full Text Available We consider the problem of computing reachability probabilities: given a Markov chain, an initial state of the Markov chain, and a set of goal states of the Markov chain, what is the probability of reaching any of the goal states from the initial state? This problem can be reduced to solving a linear equation Ax = b for x, where A is a matrix and b is a vector. We consider two iterative methods to solve the linear equation: the Jacobi method and the biconjugate gradient stabilized (BiCGStab method. For both methods, a sequential and a parallel version have been implemented. The parallel versions have been implemented on the compute unified device architecture (CUDA so that they can be run on a NVIDIA graphics processing unit (GPU. From our experiments we conclude that as the size of the matrix increases, the CUDA implementations outperform the sequential implementations. Furthermore, the BiCGStab method performs better than the Jacobi method for dense matrices, whereas the Jacobi method does better for sparse ones. Since the reachability probabilities problem plays a key role in probabilistic model checking, we also compared the implementations for matrices obtained from a probabilistic model checker. Our experiments support the conjecture by Bosnacki et al. that the Jacobi method is superior to Krylov subspace methods, a class to which the BiCGStab method belongs, for probabilistic model checking.

  14. A high-order integral solver for scalar problems of diffraction by screens and apertures in three-dimensional space

    Energy Technology Data Exchange (ETDEWEB)

    Bruno, Oscar P., E-mail: obruno@caltech.edu; Lintner, Stéphane K.

    2013-11-01

    We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three-dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules. The new integral formulations involve weighted versions of the classical integral operators related to the thin-screen Dirichlet and Neumann problems as well as a generalization to the open-surface problem of the classical Calderón formulae. The high-order quadrature rules we introduce for these operators, in turn, resolve the multiple Green function and edge singularities (which occur at arbitrarily close distances from each other, and which include weakly singular as well as hypersingular kernels) and thus give rise to super-algebraically fast convergence as the discretization sizes are increased. When used in conjunction with Krylov-subspace linear algebra solvers such as GMRES, the resulting solvers produce results of high accuracy in small numbers of iterations for low and high frequencies alike. We demonstrate our methodology with a variety of numerical results for screen and aperture problems at high frequencies—including simulation of classical experiments such as the diffraction by a circular disc (featuring in particular the famous Poisson spot), evaluation of interference fringes resulting from diffraction across two nearby circular apertures, as well as solution of problems of scattering by more complex geometries consisting of multiple scatterers and cavities.

  15. MASTER-2.0: Multi-purpose analyzer for static and transient effects of reactors

    Energy Technology Data Exchange (ETDEWEB)

    Cho, Byung Oh; Song, Jae Seung; Joo, Han Gyu [Korea Atomic Energy Research Institute, Taejon (Korea)

    1999-01-01

    MASTER-2.0 (Multi-purpose Analyzer for Static and Transient Effects of Reactors) is a nuclear design code based on the two group diffusion theory to calculate the steady-state and transient pressurized water reactor core in a 3-dimensional Cartesian or hexagonal geometry. Its neutronics model solves the space-time dependent neutron diffusion equations with NIM(Nodal Integration Method), NEM (Nodal Expansion Method), AFEN (Analytic Function Expansion Nodal Method)/NEM Hybrid Method, NNEM (Non-linear Nodal Expansion Method) or NANM (Non-linear Analytic Nodal Method) for a Cartesian geometry and with AFEN/NEM Hybrid Method or NLFM (Non-linear Local Fine-Mesh Method) for a hexagonal one. Coarse mesh rebalancing, Krylov Subspace method and asymptotic extrapolation method are implemented to accelerate the convergence of iteration process. Master-2.0 performs microscopic depletion calculations using microscopic cross sections provided by CASMO-3 or HELIOS and also has the reconstruction capability of pin information by use of MSS-IAS (Method of Successive Smoothing with Improved Analytic Solution). For the thermal-hydraulic calculation, fuel temperature table or COBRA3-C/P model can be used selectively. In addition, MASTER-2.0 is designed to cover various PWRs including SMART as well as WH-and CE-type reactors, providing all data required in their design procedures. (author). 39 refs., 12 figs., 4 tabs.

  16. A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

    Science.gov (United States)

    Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

    2018-04-01

    In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

  17. Propagators for the time-dependent Kohn-Sham equations

    International Nuclear Information System (INIS)

    Castro, Alberto; Marques, Miguel A. L.; Rubio, Angel

    2004-01-01

    In this paper we address the problem of the numerical integration of the time-dependent Schroedinger equation i∂ t φ=Hφ. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximate exp(A), where A is a time-independent operator [e.g., A=-iΔtH(τ) for some given time τ]. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. (ii) We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations

  18. Energy Landscape of Pentapeptides in a Higher-Order (ϕ,ψ Conformational Subspace

    Directory of Open Access Journals (Sweden)

    Karim M. ElSawy

    2016-01-01

    Full Text Available The potential energy landscape of pentapeptides was mapped in a collective coordinate principal conformational subspace derived from principal component analysis of a nonredundant representative set of protein structures from the PDB. Three pentapeptide sequences that are known to be distinct in terms of their secondary structure characteristics, (Ala5, (Gly5, and Val.Asn.Thr.Phe.Val, were considered. Partitioning the landscapes into different energy valleys allowed for calculation of the relative propensities of the peptide secondary structures in a statistical mechanical framework. The distribution of the observed conformations of pentapeptide data showed good correspondence to the topology of the energy landscape of the (Ala5 sequence where, in accord with reported trends, the α-helix showed a predominant propensity at 298 K. The topography of the landscapes indicates that the stabilization of the α-helix in the (Ala5 sequence is enthalpic in nature while entropic factors are important for stabilization of the β-sheet in the Val.Asn.Thr.Phe.Val sequence. The results indicate that local interactions within small pentapeptide segments can lead to conformational preference of one secondary structure over the other where account of conformational entropy is important in order to reveal such preference. The method, therefore, can provide critical structural information for ab initio protein folding methods.

  19. Properties of Griffin-Hill-Wheeler spaces - 2. one-parameters and two-conjugate parameter families of generator states

    International Nuclear Information System (INIS)

    Passos, E.J.V. de; Toledo Piza, A.F.R. de.

    The properties of the subspaces of the many-body Hilbert space which are associated with the use of the Generator Coordinate Method (GCM) in connection with one parameter, and with two-conjugate parameter families of generator states are examined in detail. It is shown that natural orthonormal base vectors in each case are immediately related to Peierls-Voccoz and Peierls-Thouless projections respectively. Through the formal consideration of a canonical transformation to collective, P and Q, and intrinsic degrees of freedom, the properties of the GCM subspaces with respect to the kinematical separation of these degrees of freedom are discussed in detail. An application is made, using the ideas developed in this paper, a) to translation; b) to illustrate the qualitative understanting of the content of existing GCM calculations of giant ressonances in light nuclei and c) to the definition of appropriate asymptotic states in current GCM descriptions of scattering [pt

  20. Geometric phases and quantum correlations of superconducting two-qubit system with dissipative effect

    International Nuclear Information System (INIS)

    Xue, Liyuan; Yu, Yanxia; Cai, Xiaoya; Pan, Hui; Wang, Zisheng

    2016-01-01

    Highlights: • We find that the Pancharatnam phases include the information of quantum correlations. • We show that the sudden died and alive phenomena of quantum entanglement is original in the transition of Pancharatnam phase. • We find that the faster the Pancharatnam phases change, the slower the quantum correlations decay. • We find that a subspace of quantum entanglement can exist in the Y-state. • Our results provide a useful approach experimentally to implement the time-dependent geometric quantum computation. - Abstract: We investigate time-dependent Pancharatnam phases and the relations between such geometric phases and quantum correlations, i.e., quantum discord and concurrence, of superconducting two-qubit coupling system in dissipative environment with the mixture effects of four different eigenstates of density matrix. We find that the time-dependent Pancharatnam phases not only keep the motion memory of such a two-qubit system, but also include the information of quantum correlations. We show that the sudden died and alive phenomena of quantum entanglement are intrinsic in the transition of Pancharatnam phase in the X-state and the complex oscillations of Pancharatnam phase in the Y-state. The faster the Pancharatnam phases change, the slower the quantum correlations decay. In particular, we find that a subspace of quantum entanglement can exist in the Y-state by choosing suitable coupling parameters between two-qubit system and its environment, or initial conditions.

  1. Direct Position Determination of Multiple Non-Circular Sources with a Moving Coprime Array

    Directory of Open Access Journals (Sweden)

    Yankui Zhang

    2018-05-01

    Full Text Available Direct position determination (DPD is currently a hot topic in wireless localization research as it is more accurate than traditional two-step positioning. However, current DPD algorithms are all based on uniform arrays, which have an insufficient degree of freedom and limited estimation accuracy. To improve the DPD accuracy, this paper introduces a coprime array to the position model of multiple non-circular sources with a moving array. To maximize the advantages of this coprime array, we reconstruct the covariance matrix by vectorization, apply a spatial smoothing technique, and converge the subspace data from each measuring position to establish the cost function. Finally, we obtain the position coordinates of the multiple non-circular sources. The complexity of the proposed method is computed and compared with that of other methods, and the Cramer–Rao lower bound of DPD for multiple sources with a moving coprime array, is derived. Theoretical analysis and simulation results show that the proposed algorithm is not only applicable to circular sources, but can also improve the positioning accuracy of non-circular sources. Compared with existing two-step positioning algorithms and DPD algorithms based on uniform linear arrays, the proposed technique offers a significant improvement in positioning accuracy with a slight increase in complexity.

  2. Direct Position Determination of Multiple Non-Circular Sources with a Moving Coprime Array.

    Science.gov (United States)

    Zhang, Yankui; Ba, Bin; Wang, Daming; Geng, Wei; Xu, Haiyun

    2018-05-08

    Direct position determination (DPD) is currently a hot topic in wireless localization research as it is more accurate than traditional two-step positioning. However, current DPD algorithms are all based on uniform arrays, which have an insufficient degree of freedom and limited estimation accuracy. To improve the DPD accuracy, this paper introduces a coprime array to the position model of multiple non-circular sources with a moving array. To maximize the advantages of this coprime array, we reconstruct the covariance matrix by vectorization, apply a spatial smoothing technique, and converge the subspace data from each measuring position to establish the cost function. Finally, we obtain the position coordinates of the multiple non-circular sources. The complexity of the proposed method is computed and compared with that of other methods, and the Cramer⁻Rao lower bound of DPD for multiple sources with a moving coprime array, is derived. Theoretical analysis and simulation results show that the proposed algorithm is not only applicable to circular sources, but can also improve the positioning accuracy of non-circular sources. Compared with existing two-step positioning algorithms and DPD algorithms based on uniform linear arrays, the proposed technique offers a significant improvement in positioning accuracy with a slight increase in complexity.

  3. Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow

    International Nuclear Information System (INIS)

    Knoll, D.A.

    1998-01-01

    The authors study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. They use Newton's method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. They investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, mesh sequencing, and a pseudotransient continuation technique is used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with incomplete lower-upper (ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a mesh sequencing implementation provides significant CPU savings for fine grid calculations. Performance comparisons of modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented

  4. Enhanced nonlinear iterative techniques applied to a non-equilibrium plasma flow

    Energy Technology Data Exchange (ETDEWEB)

    Knoll, D.A.; McHugh, P.R. [Idaho National Engineering Lab., Idaho Falls, ID (United States)

    1996-12-31

    We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially-ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales, and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton`s method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, one-way multigrid and a pseudo-transient continuation technique are used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with Incomplete Lower-Upper(ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a one-way multigrid implementation provides significant CPU savings for fine grid calculations. Performance comparisons of the modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented.

  5. Feedforward inhibition and synaptic scaling--two sides of the same coin?

    Science.gov (United States)

    Keck, Christian; Savin, Cristina; Lücke, Jörg

    2012-01-01

    Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing.

  6. Feedforward inhibition and synaptic scaling--two sides of the same coin?

    Directory of Open Access Journals (Sweden)

    Christian Keck

    Full Text Available Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing.

  7. Mass spectrum of the two dimensional lambdaphi4-1/4phi2-μphi quantum field model

    International Nuclear Information System (INIS)

    Imbrie, J.Z.

    1980-01-01

    It is shown that r-particle irreducible kernels in the two-dimensional lambdaphi 4 -1/4phi 2 -μphi quantum field theory have (r+1)-particle decay for vertical stroke μ vertical stroke 2 << 1. As a consequence there is an upper mass gap and, in the subspace of two-particle states, a bound state. The proof extends Spencer's expansion to handle fluctuations between the two wells of the classical potential. A new method for resumming the low temperature cluster expansion is introduced. (orig.)

  8. A computational methodology for a micro launcher engine test bench using a combined linear static and dynamic in frequency response analysis

    Directory of Open Access Journals (Sweden)

    Ion DIMA

    2017-03-01

    Full Text Available This article aims to provide a quick methodology to determine the critical values of the forces, displacements and stress function of frequency, under a combined linear static (101 Solution - Linear Static and dynamic load in frequency response (108 Solution - Frequency Response, Direct Method, applied to a micro launcher engine test bench, using NASTRAN 400 Solution - Implicit Nonlinear. NASTRAN/PATRAN software is used. Practically in PATRAN the preprocessor has to define a linear or nonlinear static load at step 1 and a dynamic in frequency response load (time dependent at step 2. In Analyze the following options are chosen: for Solution Type Implicit Nonlinear Solution (SOL 400 is selected, for Subcases Static Load and Transient Dynamic is chosen and for Subcase Select the two cases static and dynamic will be selected. NASTRAN solver will overlap results from static analysis with the dynamic analysis. The running time will be reduced three times if using Krylov solver. NASTRAN SYSTEM (387 = -1 instruction is used in order to activate Krylov option. Also, in Analysis the OP2 Output Format shall be selected, meaning that in bdf NASTRAN input file the PARAM POST 1 instruction shall be written. The structural damping can be defined in two different ways: either at the material card or using the PARAM, G, 0.05 instruction (in this example a damping coefficient by 5% was used. The SDAMPING instruction in pair with TABDMP1 work only for dynamic in frequency response, modal method, or in direct method with viscoelastic material, not for dynamic in frequency response, direct method (DFREQ, with linear elastic material. The Direct method – DFREQ used in this example is more accurate. A set in translation of boundary conditions was used and defined at the base of the test bench.

  9. Two-step quantum direct communication protocol using the Einstein- Podolsky-Rosen pair block

    CERN Document Server

    Fu Guo Deng; Xiao Shu Liu; 10.1103/PhysRevA.68.042317

    2003-01-01

    A protocol for quantum secure direct communication using blocks of Einstein-Podolsky-Rosen (EPR) pairs is proposed. A set of ordered N EPR pairs is used as a data block for sending secret message directly. The ordered N EPR set is divided into two particle sequences, a checking sequence and a message-coding sequence. After transmitting the checking sequence, the two parties of communication check eavesdropping by measuring a fraction of particles randomly chosen, with random choice of two sets of measuring bases. After insuring the security of the quantum channel, the sender Alice encodes the secret message directly on the message-coding sequence and sends them to Bob. By combining the checking and message-coding sequences together, Bob is able to read out the encoded messages directly. The scheme is secure because an eavesdropper cannot get both sequences simultaneously. We also discuss issues in a noisy channel. (30 refs).

  10. Multigrid for Staggered Lattice Fermions

    Energy Technology Data Exchange (ETDEWEB)

    Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.

    2018-01-23

    Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

  11. Feedforward Inhibition and Synaptic Scaling – Two Sides of the Same Coin?

    Science.gov (United States)

    Lücke, Jörg

    2012-01-01

    Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing. PMID:22457610

  12. Engineering two-photon high-dimensional states through quantum interference

    CSIR Research Space (South Africa)

    Zhang, YI

    2016-02-01

    Full Text Available . ngled photon pairs (see p a nonlinear crystal to ersion (SPDC). At the tate (6) ℓ¼1 stat th , w from ℓ = 0. The subscripts A and B la R E S EARCH ART I C L E o n February 28, 2016 http://advances.sciencem ag.org/ D ow nloaded from stitute of Photonics... contribution from the ℓ = 1, 2, and 3 subspaces in this six-dimensional state (36 × 36 matrix). (B) The state after the filter, which in principle is given byd01jY � 1 〉 þ d 0 3jY � 3 〉; the contribution from the ℓ = 2 subspace is 3.8 ± 0.2% of its original...

  13. Remarks on non compact sigma models

    International Nuclear Information System (INIS)

    Brunini, S.A.; Gomes, M.; Silva, A.J. da.

    1988-01-01

    O(N,1) noncompact sigma models quantized in an indefinite metric space. In two dimensions, by a direct computation the existence of a positive metric subspace where the S matrix is unitary. Is proved the properties of the model as function of the temperature are investigated in various space time dimensions. (author) [pt

  14. Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling

    Energy Technology Data Exchange (ETDEWEB)

    Vrugt, Jasper A [Los Alamos National Laboratory; Hyman, James M [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory; Higdon, Dave [Los Alamos National Laboratory; Ter Braak, Cajo J F [NETHERLANDS; Diks, Cees G H [UNIV OF AMSTERDAM

    2008-01-01

    Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.

  15. Biquaternion beamspace with its application to vector-sensor array direction findings and polarization estimations

    Science.gov (United States)

    Li, Dan; Xu, Feng; Jiang, Jing Fei; Zhang, Jian Qiu

    2017-12-01

    In this paper, a biquaternion beamspace, constructed by projecting the original data of an electromagnetic vector-sensor array into a subspace of a lower dimension via a quaternion transformation matrix, is first proposed. To estimate the direction and polarization angles of sources, biquaternion beamspace multiple signal classification (BB-MUSIC) estimators are then formulated. The analytical results show that the biquaternion beamspaces offer us some additional degrees of freedom to simultaneously achieve three goals. One is to save the memory spaces for storing the data covariance matrix and reduce the computation efforts of the eigen-decomposition. Another is to decouple the estimations of the sources' polarization parameters from those of their direction angles. The other is to blindly whiten the coherent noise of the six constituent antennas in each vector-sensor. It is also shown that the existing biquaternion multiple signal classification (BQ-MUSIC) estimator is a specific case of our BB-MUSIC ones. The simulation results verify the correctness and effectiveness of the analytical ones.

  16. Principles of computational fluid dynamics

    International Nuclear Information System (INIS)

    Wesseling, P.

    2001-01-01

    The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state- of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and how to overcome it by means of slope-limited schemes is discussed. An introduction is given to efficient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers are given to recent literature, to help the reader to quickly reach the current research frontier. (orig.)

  17. A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

    Science.gov (United States)

    Heinkenschloss, Matthias

    2005-01-01

    We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

  18. Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems

    Science.gov (United States)

    Meyer, Gregory; Machado, Francisco; Yao, Norman

    2017-04-01

    Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.

  19. A fast sparse reconstruction algorithm for electrical tomography

    International Nuclear Information System (INIS)

    Zhao, Jia; Xu, Yanbin; Tan, Chao; Dong, Feng

    2014-01-01

    Electrical tomography (ET) has been widely investigated due to its advantages of being non-radiative, low-cost and high-speed. However, the image reconstruction of ET is a nonlinear and ill-posed inverse problem and the imaging results are easily affected by measurement noise. A sparse reconstruction algorithm based on L 1 regularization is robust to noise and consequently provides a high quality of reconstructed images. In this paper, a sparse reconstruction by separable approximation algorithm (SpaRSA) is extended to solve the ET inverse problem. The algorithm is competitive with the fastest state-of-the-art algorithms in solving the standard L 2 −L 1 problem. However, it is computationally expensive when the dimension of the matrix is large. To further improve the calculation speed of solving inverse problems, a projection method based on the Krylov subspace is employed and combined with the SpaRSA algorithm. The proposed algorithm is tested with image reconstruction of electrical resistance tomography (ERT). Both simulation and experimental results demonstrate that the proposed method can reduce the computational time and improve the noise robustness for the image reconstruction. (paper)

  20. Fast solution of elliptic partial differential equations using linear combinations of plane waves.

    Science.gov (United States)

    Pérez-Jordá, José M

    2016-02-01

    Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

  1. Two-Tactor Vibrotactile Navigation Information for the Blind: Directional Resolution and Intuitive Interpretation.

    Science.gov (United States)

    Kessler, Roman; Bach, Michael; Heinrich, Sven P

    2017-03-01

    Lacking vision, blind people have to exploit other senses for navigation. Using the tactile rather than the auditory sense avoids masking important environmental information. Directional information is particularly important and traditionally conveyed through an array of tactors, each coding one direction. Here, we present a different approach to represent arbitrary directions with only two tactors. We tested intuitiveness, plasticity, and variability of direction perception in a behavioral experiment in 33 seeing participants.

  2. Fast Estimation Method of Space-Time Two-Dimensional Positioning Parameters Based on Hadamard Product

    Directory of Open Access Journals (Sweden)

    Haiwen Li

    2018-01-01

    Full Text Available The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA and direction of arrival (DOA parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM system, and the Cramer-Rao bound (CRB is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT algorithm and 2D matrix pencil (MP algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.

  3. Isolation and characterization of monoclonal antibodies directed against two subunits of rabbit poxvirus-associated, DNA-directed RNA polymerase.

    OpenAIRE

    Morrison, D K; Carter, J K; Moyer, R W

    1985-01-01

    A library of monoclonal antibodies directed against individual proteins of the rabbit poxvirus (RPV) virion within a complex immunogenic mixture has been generated through the use of in vivo and in vitro immunization regimens. The relative efficacies of the two procedures were compared. Based on immunoblot analysis, the in vitro immunization regimen led both to a wider variety of monoclonal antibodies to different proteins and to a larger number of antibodies directed against proteins of high...

  4. Construction of a Direct Water-Injected Two-Stroke Engine for Phased Direct Fuel Injection-High Pressure Charging Investigations

    Science.gov (United States)

    Somsel, James P.

    1998-01-01

    The development of a water injected Orbital Combustion Process (OCP) engine was conducted to assess the viability of using the powerplant for high altitude NASA aircraft and General Aviation (GA) applications. An OCP direct fuel injected, 1.2 liter, three cylinder, two-stroke engine has been enhanced to independently inject water directly into the combustion chamber. The engine currently demonstrates low brake specific fuel consumption capability and an excellent power to weight ratio. With direct water injection, significant improvements can be made to engine power, to knock limits/ignition advance timing, and to engine NO(x) emissions. The principal aim of the testing was to validate a cyclic model developed by the Systems Analysis Branch at NASA Ames Research Center. The work is a continuation of Ames' investigations into a Phased Direct Fuel Injection Engine with High Pressure Charging (PDFI-ITPC).

  5. An extended L-curve method for choosing a regularization parameter in electrical resistance tomography

    International Nuclear Information System (INIS)

    Xu, Yanbin; Pei, Yang; Dong, Feng

    2016-01-01

    The L-curve method is a popular regularization parameter choice method for the ill-posed inverse problem of electrical resistance tomography (ERT). However the method cannot always determine a proper parameter for all situations. An investigation into those situations where the L-curve method failed show that a new corner point appears on the L-curve and the parameter corresponding to the new corner point can obtain a satisfactory reconstructed solution. Thus an extended L-curve method, which determines the regularization parameter associated with either global corner or the new corner, is proposed. Furthermore, two strategies are provided to determine the new corner–one is based on the second-order differential of L-curve, and the other is based on the curvature of L-curve. The proposed method is examined by both numerical simulations and experimental tests. And the results indicate that the extended method can handle the parameter choice problem even in the case where the typical L-curve method fails. Finally, in order to reduce the running time of the method, the extended method is combined with a projection method based on the Krylov subspace, which was able to boost the extended L-curve method. The results verify that the speed of the extended L-curve method is distinctly improved. The proposed method extends the application of the L-curve in the field of choosing regularization parameter with an acceptable running time and can also be used in other kinds of tomography. (paper)

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

    Science.gov (United States)

    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.

  7. Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

    Directory of Open Access Journals (Sweden)

    Han Guo

    2012-01-01

    Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

  8. Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

    KAUST Repository

    Loizou, Nicolas

    2017-12-27

    In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

  9. Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

    KAUST Repository

    Loizou, Nicolas; Richtarik, Peter

    2017-01-01

    In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these methods are studied. We choose to perform our analysis in a setting in which all of the above methods are equivalent. We prove global nonassymptotic linear convergence rates for all methods and various measures of success, including primal function values, primal iterates (in L2 sense), and dual function values. We also show that the primal iterates converge at an accelerated linear rate in the L1 sense. This is the first time a linear rate is shown for the stochastic heavy ball method (i.e., stochastic gradient descent method with momentum). Under somewhat weaker conditions, we establish a sublinear convergence rate for Cesaro averages of primal iterates. Moreover, we propose a novel concept, which we call stochastic momentum, aimed at decreasing the cost of performing the momentum step. We prove linear convergence of several stochastic methods with stochastic momentum, and show that in some sparse data regimes and for sufficiently small momentum parameters, these methods enjoy better overall complexity than methods with deterministic momentum. Finally, we perform extensive numerical testing on artificial and real datasets, including data coming from average consensus problems.

  10. A conservative local discontinuous Galerkin method for the solution of nonlinear Schr(o)dinger equation in two dimensions

    Institute of Scientific and Technical Information of China (English)

    ZHANG RongPei; YU XiJun; LI MingJun; LI XiangGui

    2017-01-01

    In this study,we present a conservative local discontinuous Galerkin (LDG) method for numerically solving the two-dimensional nonlinear Schr(o)dinger (NLS) equation.The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux.The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central,alternative and upwind-based flux.We will propose two kinds of time discretization methods for the semi-discrete formulation.One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation.The other one is Krylov implicit integration factor (ⅡF) method which demands much less computational effort.Various numerical experiments are presented to demonstrate the conservation law of mass and energy,the optimal rates of convergence,and the blow-up phenomenon.

  11. Two-directional synthesis as a tool for diversity-oriented synthesis: Synthesis of alkaloid scaffolds

    Directory of Open Access Journals (Sweden)

    Kieron M. G. O’Connell

    2012-06-01

    Full Text Available Two-directional synthesis represents an ideal strategy for the rapid elaboration of simple starting materials and their subsequent transformation into complex molecular architectures. As such, it is becoming recognised as an enabling technology for diversity-oriented synthesis. Herein, we provide a thorough account of our work combining two-directional synthesis with diversity-oriented synthesis, with particular reference to the synthesis of polycyclic alkaloid scaffolds.

  12. Diversity in random subspacing ensembles

    NARCIS (Netherlands)

    Tsymbal, A.; Pechenizkiy, M.; Cunningham, P.; Kambayashi, Y.; Mohania, M.K.; Wöß, W.

    2004-01-01

    Ensembles of learnt models constitute one of the main current directions in machine learning and data mining. It was shown experimentally and theoretically that in order for an ensemble to be effective, it should consist of classifiers having diversity in their predictions. A number of ways are

  13. Scalable Newton-Krylov solver for very large power flow problems

    NARCIS (Netherlands)

    Idema, R.; Lahaye, D.J.P.; Vuik, C.; Van der Sluis, L.

    2010-01-01

    The power flow problem is generally solved by the Newton-Raphson method with a sparse direct solver for the linear system of equations in each iteration. While this works fine for small power flow problems, we will show that for very large problems the direct solver is very slow and we present

  14. Automated invariant alignment to improve canonical variates in image fusion of satellite and weather radar data

    DEFF Research Database (Denmark)

    Vestergaard, Jacob Schack; Nielsen, Allan Aasbjerg

    2013-01-01

    Canonical correlation analysis (CCA) maximizes correlation between two sets of multivariate data. We applied CCA to multivariate satellite data and univariate radar data in order to produce a subspace descriptive of heavily precipitating clouds. A misalignment, inherent to the nature of the two...... data sets, was observed, corrupting the subspace. A method for aligning the two data sets is proposed, in order to overcome this issue and render a useful subspace projection. The observed corruption of the subspace gives rise to the hypothesis that the optimal correspondence, between a heavily...... precipitating cloud in the radar data and the associated cloud top registered in the satellite data, is found by a scale, rotation and translation invariant transformation together with a temporal displacement. The method starts by determining a conformal transformation of the radar data at the time of maximum...

  15. A two-step quantum secure direct communication protocol with hyperentanglement

    International Nuclear Information System (INIS)

    Gu Bin; Zhang Cheng-Yi; Huang Yu-Gai; Fang Xia

    2011-01-01

    We propose a two-step quantum secure direct communication (QSDC) protocol with hyperentanglement in both the spatial-mode and the polarization degrees of freedom of photon pairs which can in principle be produced with a beta barium borate crystal. The secret message can be encoded on the photon pairs with unitary operations in these two degrees of freedom independently. This QSDC protocol has a higher capacity than the original two-step QSDC protocol as each photon pair can carry 4 bits of information. Compared with the QSDC protocol based on hyperdense coding, this QSDC protocol has the immunity to Trojan horse attack strategies with the process for determining the number of the photons in each quantum signal as it is a one-way quantum communication protocol. (general)

  16. Blind Reduced-Rank MMSE Detector for DS-CDMA Systems

    Directory of Open Access Journals (Sweden)

    Xiaodong Cai

    2003-01-01

    Full Text Available We first develop a reduced-rank minimum mean squared error (MMSE detector for direct-sequence (DS code division multiple access (CDMA by forcing the linear MMSE detector to lie in a signal subspace of a reduced dimension. While a reduced-rank MMSE detector has lower complexity, it cannot outperform the full-rank MMSE detector. We then concentrate on the blind reduced-rank MMSE detector which is obtained from an estimated covariance matrix. Our analysis and simulation results show that when the desired user′s signal is in a low-dimensional subspace, there exists an optimal subspace so that the blind reduced-rank MMSE detector lying in this subspace has the best performance. By properly choosing a subsspace, we guarantee that the optimal blind reduced-rank MMSE detector is obtained. An adaptive blind reduced-rank MMSE detector, based on a subspace tracking algorithm, is developed. The adaptive blind reduced-rank MMSE detector exhibits superior steady-state performance and fast convergence speed.

  17. Dynamics of the two-dimensional directed Ising model in the paramagnetic phase

    Science.gov (United States)

    Godrèche, C.; Pleimling, M.

    2014-05-01

    We consider the nonconserved dynamics of the Ising model on the two-dimensional square lattice, where each spin is influenced preferentially by its east and north neighbours. The single-spin flip rates are such that the stationary state is Gibbsian with respect to the usual ferromagnetic Ising Hamiltonian. We show the existence, in the paramagnetic phase, of a dynamical transition between two regimes of violation of the fluctuation-dissipation theorem in the nonequilibrium stationary state: a regime of weak violation where the stationary fluctuation-dissipation ratio is finite, when the asymmetry parameter is less than a threshold value, and a regime of strong violation where this ratio vanishes asymptotically above the threshold. This study suggests that this novel kind of dynamical transition in nonequilibrium stationary states, already found for the directed Ising chain and the spherical model with asymmetric dynamics, might be quite general. In contrast with the latter models, the equal-time correlation function for the two-dimensional directed Ising model depends on the asymmetry.

  18. Evaluation and enhancement of COBRA-TF efficiency for LWR calculations

    International Nuclear Information System (INIS)

    Cuervo, Diana; Avramova, Maria; Ivanov, Kostadin; Miro, Rafael

    2006-01-01

    Detailed representations of the reactor core generate computational meshes with a high number of cells where the fluid dynamics equations must be solved. An exhaustive analysis of the CPU times needed by the thermal-hydraulic subchannel code COBRA-TF for different stages in the solution process has revealed that the solution of the linear system of pressure equations is the most time consuming process. To improve code efficiency two optimized matrix solvers, Super LU library and Krylov non-stationary iterative methods have been implemented in the code and their performance has been tested using a suite of five test cases. The results of performed comparative analyses have demonstrated that for large cases, the implementation of the Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) Krylov method combined with the incomplete LU factorization with dual truncation strategy (ILUT) pre-conditioner reduced the time used by the code for the solution of the pressure matrix by a factor of 20. Both new solvers converge smoothly regardless of the nature of simulated cases and the mesh structures and improve the stability and accuracy of results compared to the classic Gauss-Seidel iterative method. The obtained results indicate that the direct inversion method is the best option for small cases

  19. A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes

    International Nuclear Information System (INIS)

    Bravyi, Sergey; Terhal, Barbara

    2009-01-01

    We study properties of stabilizer codes that permit a local description on a regular D-dimensional lattice. Specifically, we assume that the stabilizer group of a code (the gauge group for subsystem codes) can be generated by local Pauli operators such that the support of any generator is bounded by a hypercube of size O(1). Our first result concerns the optimal scaling of the distance d with the linear size of the lattice L. We prove an upper bound d=O(L D-1 ) which is tight for D=1, 2. This bound applies to both subspace and subsystem stabilizer codes. Secondly, we analyze the suitability of stabilizer codes for building a self-correcting quantum memory. Any stabilizer code with geometrically local generators can be naturally transformed to a local Hamiltonian penalizing states that violate the stabilizer condition. A degenerate ground state of this Hamiltonian corresponds to the logical subspace of the code. We prove that for D=1, 2, different logical states can be mapped into each other by a sequence of single-qubit Pauli errors such that the energy of all intermediate states is upper bounded by a constant independent of the lattice size L. The same result holds if there are unused logical qubits that are treated as 'gauge qubits'. It demonstrates that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D=1, 2. This result is in sharp contrast with the existence of a classical self-correcting memory in the form of a two-dimensional (2D) ferromagnet. Our results leave open the possibility for a self-correcting quantum memory based on 2D subsystem codes or on 3D subspace or subsystem codes.

  20. Direct Power Control for Three-Phase Two-Level Voltage-Source Rectifiers Based on Extended-State Observation

    DEFF Research Database (Denmark)

    Song, Zhanfeng; Tian, Yanjun; Yan, Zhuo

    2016-01-01

    This paper proposed a direct power control strategy for three-phase two-level voltage-source rectifiers based on extended-state observation. Active and reactive powers are directly regulated in the stationary reference frame. Similar to the family of predictive controllers whose inherent characte......This paper proposed a direct power control strategy for three-phase two-level voltage-source rectifiers based on extended-state observation. Active and reactive powers are directly regulated in the stationary reference frame. Similar to the family of predictive controllers whose inherent...

  1. Polymorphism in the two-locus Levene model with nonepistatic directional selection.

    Science.gov (United States)

    Bürger, Reinhard

    2009-11-01

    For the Levene model with soft selection in two demes, the maintenance of polymorphism at two diallelic loci is studied. Selection is nonepistatic and dominance is intermediate. Thus, there is directional selection in every deme and at every locus. We assume that selection is in opposite directions in the two demes because otherwise no polymorphism is possible. If at one locus there is no dominance, then a complete analysis of the dynamical and equilibrium properties is performed. In particular, a simple necessary and sufficient condition for the existence of an internal equilibrium and sufficient conditions for global asymptotic stability are obtained. These results are extended to deme-independent degree of dominance at one locus. A perturbation analysis establishes structural stability within the full parameter space. In the absence of genotype-environment interaction, which requires deme-independent dominance at both loci, nongeneric equilibrium behavior occurs, and the introduction of arbitrarily small genotype-environment interaction changes the equilibrium structure and may destroy stable polymorphism. The volume of the parameter space for which a (stable) two-locus polymorphism is maintained is computed numerically. It is investigated how this volume depends on the strength of selection and on the dominance relations. If the favorable allele is (partially) dominant in its deme, more than 20% of all parameter combinations lead to a globally asymptotically stable, fully polymorphic equilibrium.

  2. Binding Direction-Based Two-Dimensional Flattened Contact Area Computing Algorithm for Protein-Protein Interactions.

    Science.gov (United States)

    Kang, Beom Sik; Pugalendhi, GaneshKumar; Kim, Ku-Jin

    2017-10-13

    Interactions between protein molecules are essential for the assembly, function, and regulation of proteins. The contact region between two protein molecules in a protein complex is usually complementary in shape for both molecules and the area of the contact region can be used to estimate the binding strength between two molecules. Although the area is a value calculated from the three-dimensional surface, it cannot represent the three-dimensional shape of the surface. Therefore, we propose an original concept of two-dimensional contact area which provides further information such as the ruggedness of the contact region. We present a novel algorithm for calculating the binding direction between two molecules in a protein complex, and then suggest a method to compute the two-dimensional flattened area of the contact region between two molecules based on the binding direction.

  3. Binding Direction-Based Two-Dimensional Flattened Contact Area Computing Algorithm for Protein–Protein Interactions

    Directory of Open Access Journals (Sweden)

    Beom Sik Kang

    2017-10-01

    Full Text Available Interactions between protein molecules are essential for the assembly, function, and regulation of proteins. The contact region between two protein molecules in a protein complex is usually complementary in shape for both molecules and the area of the contact region can be used to estimate the binding strength between two molecules. Although the area is a value calculated from the three-dimensional surface, it cannot represent the three-dimensional shape of the surface. Therefore, we propose an original concept of two-dimensional contact area which provides further information such as the ruggedness of the contact region. We present a novel algorithm for calculating the binding direction between two molecules in a protein complex, and then suggest a method to compute the two-dimensional flattened area of the contact region between two molecules based on the binding direction.

  4. Genome-wide association data classification and SNPs selection using two-stage quality-based Random Forests.

    Science.gov (United States)

    Nguyen, Thanh-Tung; Huang, Joshua; Wu, Qingyao; Nguyen, Thuy; Li, Mark

    2015-01-01

    Single-nucleotide polymorphisms (SNPs) selection and identification are the most important tasks in Genome-wide association data analysis. The problem is difficult because genome-wide association data is very high dimensional and a large portion of SNPs in the data is irrelevant to the disease. Advanced machine learning methods have been successfully used in Genome-wide association studies (GWAS) for identification of genetic variants that have relatively big effects in some common, complex diseases. Among them, the most successful one is Random Forests (RF). Despite of performing well in terms of prediction accuracy in some data sets with moderate size, RF still suffers from working in GWAS for selecting informative SNPs and building accurate prediction models. In this paper, we propose to use a new two-stage quality-based sampling method in random forests, named ts-RF, for SNP subspace selection for GWAS. The method first applies p-value assessment to find a cut-off point that separates informative and irrelevant SNPs in two groups. The informative SNPs group is further divided into two sub-groups: highly informative and weak informative SNPs. When sampling the SNP subspace for building trees for the forest, only those SNPs from the two sub-groups are taken into account. The feature subspaces always contain highly informative SNPs when used to split a node at a tree. This approach enables one to generate more accurate trees with a lower prediction error, meanwhile possibly avoiding overfitting. It allows one to detect interactions of multiple SNPs with the diseases, and to reduce the dimensionality and the amount of Genome-wide association data needed for learning the RF model. Extensive experiments on two genome-wide SNP data sets (Parkinson case-control data comprised of 408,803 SNPs and Alzheimer case-control data comprised of 380,157 SNPs) and 10 gene data sets have demonstrated that the proposed model significantly reduced prediction errors and outperformed

  5. Projection preconditioning for Lanczos-type methods

    Energy Technology Data Exchange (ETDEWEB)

    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.

  6. Randomized controlled split-mouth clinical trial of direct laminate veneers with two micro-hybrid resin composites

    NARCIS (Netherlands)

    Gresnigt, Marco M. M.; Kalk, Warner; Ozcan, M.; Ozcan, Mutlu

    Objectives: This randomized, split-mouth clinical study evaluated the survival rate of direct laminate veneers made of two resin-composite materials. Methods: A total of 23 patients (mean age: 52.4 years old) received 96 direct composite laminate veneers using two micro-hybrid composites in

  7. Efficient stabilization and acceleration of numerical simulation of fluid flows by residual recombination

    Science.gov (United States)

    Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.

    2017-09-01

    The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite

  8. Repeated sprint ability in young basketball players: one vs. two changes of direction (Part 2).

    Science.gov (United States)

    Attene, Giuseppe; Laffaye, Guillaume; Chaouachi, Anis; Pizzolato, Fabio; Migliaccio, Gian Mario; Padulo, Johnny

    2015-01-01

    The aim of this study was to compare the training effects based on repeated sprint ability (RSA) (with one change of direction) with an intensive repeated sprint ability (IRSA) (with two changes of direction) on jump performance and aerobic fitness. Eighteen male basketball players were assigned to repeated sprint ability and intensive repeated sprint ability training groups (RSAG and IRSAG). RSA, IRSA, squat jump (SJ), countermovement jump (CMJ) and Yo-Yo intermittent recovery level 1 test were assessed before and after four training weeks. The RSA and IRSA trainings consisted of three sets of six sprints (first two weeks) and eight sprints (second two weeks) with 4-min sets recovery and 20-s of sprints recovery. Four weeks of training led to an overall improvement in most of the measures of RSA, but little evidence of any differences between the two training modes. Jump performance was enhanced: CMJ of 7.5% (P training with one/two changes of direction promotes improvements in both RSA and IRSA respectively but the better increase on jump performance shown a few changes on sprint and endurance performances.

  9. Utilization Of Second Harmonisa Fluxgate For Two Dimension Direct Magnetic Field

    International Nuclear Information System (INIS)

    Limansyah, Ivan; Djamal, Mitra

    2003-01-01

    Fluxgate magnetic field sensor is a cheap, accurate and simple solution to measure DC external weak magnetic field. With adding some modification, this sensor can be used to measure amplitude and direction of the external magnetic field. By adding another pick up coils that orthogonal with ordinary pick up coils, two dimensions fluxgate magnetic field sensor can be build

  10. Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods

    International Nuclear Information System (INIS)

    Men, H.; Nguyen, N.C.; Freund, R.M.; Parrilo, P.A.; Peraire, J.

    2010-01-01

    In this paper, we consider the optimal design of photonic crystal structures for two-dimensional square lattices. The mathematical formulation of the bandgap optimization problem leads to an infinite-dimensional Hermitian eigenvalue optimization problem parametrized by the dielectric material and the wave vector. To make the problem tractable, the original eigenvalue problem is discretized using the finite element method into a series of finite-dimensional eigenvalue problems for multiple values of the wave vector parameter. The resulting optimization problem is large-scale and non-convex, with low regularity and non-differentiable objective. By restricting to appropriate eigenspaces, we reduce the large-scale non-convex optimization problem via reparametrization to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP solvers can be efficiently applied. Numerical results are presented for both transverse magnetic (TM) and transverse electric (TE) polarizations at several frequency bands. The optimized structures exhibit patterns which go far beyond typical physical intuition on periodic media design.

  11. Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

    Science.gov (United States)

    Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

    2018-04-01

    A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

  12. A Channelization-Based DOA Estimation Method for Wideband Signals

    Directory of Open Access Journals (Sweden)

    Rui Guo

    2016-07-01

    Full Text Available In this paper, we propose a novel direction of arrival (DOA estimation method for wideband signals with sensor arrays. The proposed method splits the wideband array output into multiple frequency sub-channels and estimates the signal parameters using a digital channelization receiver. Based on the output sub-channels, a channelization-based incoherent signal subspace method (Channelization-ISM and a channelization-based test of orthogonality of projected subspaces method (Channelization-TOPS are proposed. Channelization-ISM applies narrowband signal subspace methods on each sub-channel independently. Then the arithmetic mean or geometric mean of the estimated DOAs from each sub-channel gives the final result. Channelization-TOPS measures the orthogonality between the signal and the noise subspaces of the output sub-channels to estimate DOAs. The proposed channelization-based method isolates signals in different bandwidths reasonably and improves the output SNR. It outperforms the conventional ISM and TOPS methods on estimation accuracy and dynamic range, especially in real environments. Besides, the parallel processing architecture makes it easy to implement on hardware. A wideband digital array radar (DAR using direct wideband radio frequency (RF digitization is presented. Experiments carried out in a microwave anechoic chamber with the wideband DAR are presented to demonstrate the performance. The results verify the effectiveness of the proposed method.

  13. Bacterial foraging-optimized PID control of a two-wheeled machine with a two-directional handling mechanism.

    Science.gov (United States)

    Goher, K M; Fadlallah, S O

    2017-01-01

    This paper presents the performance of utilizing a bacterial foraging optimization algorithm on a PID control scheme for controlling a five DOF two-wheeled robotic machine with two-directional handling mechanism. The system under investigation provides solutions for industrial robotic applications that require a limited-space working environment. The system nonlinear mathematical model, derived using Lagrangian modeling approach, is simulated in MATLAB/Simulink ® environment. Bacterial foraging-optimized PID control with decoupled nature is designed and implemented. Various working scenarios with multiple initial conditions are used to test the robustness and the system performance. Simulation results revealed the effectiveness of the bacterial foraging-optimized PID control method in improving the system performance compared to the PID control scheme.

  14. Use of upscaled elevation and surface roughness data in two-dimensional surface water models

    Science.gov (United States)

    Hughes, J.D.; Decker, J.D.; Langevin, C.D.

    2011-01-01

    In this paper, we present an approach that uses a combination of cell-block- and cell-face-averaging of high-resolution cell elevation and roughness data to upscale hydraulic parameters and accurately simulate surface water flow in relatively low-resolution numerical models. The method developed allows channelized features that preferentially connect large-scale grid cells at cell interfaces to be represented in models where these features are significantly smaller than the selected grid size. The developed upscaling approach has been implemented in a two-dimensional finite difference model that solves a diffusive wave approximation of the depth-integrated shallow surface water equations using preconditioned Newton–Krylov methods. Computational results are presented to show the effectiveness of the mixed cell-block and cell-face averaging upscaling approach in maintaining model accuracy, reducing model run-times, and how decreased grid resolution affects errors. Application examples demonstrate that sub-grid roughness coefficient variations have a larger effect on simulated error than sub-grid elevation variations.

  15. Passive directional discrimination in laser-Doppler anemometry by the two-wavelength quadrature homodyne technique.

    Science.gov (United States)

    Büttner, Lars; Czarske, Jürgen

    2003-07-01

    We report a method for passive optical directional discrimination in laser-Doppler anemometers. For this purpose frequency-shift elements such as acousto-optic modulators, which are bulky and difficult to align during assembly, have traditionally been employed. We propose to use a quadrature homodyne technique to achieve directional discrimination of the fluid flow without any frequency-shift elements. It is based on the employment of two laser wavelengths, which generate two interference fringe systems with a phase shift of a quarter of the common fringe spacing. Measurement signal pairs with a direction-dependent phase shift of +/- pi/2 are generated. As a robust signal-processing technique, the cross-correlation technique is used. The principles of quadrature homodyne laser-Doppler anemometry are investigated. A setup that provides a constant phase shift of pi/2 throughout the entire measurement volume was achieved with both single-mode and multimode radiation. The directional discrimination was successfully verified with wind tunnel measurements. The complete passive technique offers the potential of building miniaturized measurement heads that can be integrated, e.g., into wind tunnel models.

  16. Development of the next generation reactor analysis code system, MARBLE

    International Nuclear Information System (INIS)

    Yokoyama, Kenji; Hazama, Taira; Nagaya, Yasunobu; Chiba, Go; Kugo, Teruhiko; Ishikawa, Makoto; Tatsumi, Masahiro; Hirai, Yasushi; Hyoudou, Hideaki; Numata, Kazuyuki; Iwai, Takehiko; Jin, Tomoyuki

    2011-03-01

    A next generation reactor analysis code system, MARBLE, has been developed. MARBLE is a successor of the fast reactor neutronics analysis code systems, JOINT-FR and SAGEP-FR (conventional systems), which were developed for so-called JUPITER standard analysis methods. MARBLE has the equivalent analysis capability to the conventional system because MARBLE can utilize sub-codes included in the conventional system without any change. On the other hand, burnup analysis functionality for power reactors is improved compared with the conventional system by introducing models on fuel exchange treatment and control rod operation and so on. In addition, MARBLE has newly developed solvers and some new features of burnup calculation by the Krylov sub-space method and nuclear design accuracy evaluation by the extended bias factor method. In the development of MARBLE, the object oriented technology was adopted from the view-point of improvement of the software quality such as flexibility, expansibility, facilitation of the verification by the modularization and assistance of co-development. And, software structure called the two-layer system consisting of scripting language and system development language was applied. As a result, MARBLE is not an independent analysis code system which simply receives input and returns output, but an assembly of components for building an analysis code system (i.e. framework). Furthermore, MARBLE provides some pre-built analysis code systems such as the fast reactor neutronics analysis code system. SCHEME, which corresponds to the conventional code and the fast reactor burnup analysis code system, ORPHEUS. (author)

  17. The directional propagation characteristics of elastic wave in two-dimensional thin plate phononic crystals

    International Nuclear Information System (INIS)

    Wen Jihong; Yu, Dianlong; Wang Gang; Zhao Honggang; Liu Yaozong; Wen Xisen

    2007-01-01

    The directional propagation characteristics of elastic wave during pass bands in two-dimensional thin plate phononic crystals are analyzed by using the lumped-mass method to yield the phase constant surface. The directions and regions of wave propagation in phononic crystals for certain frequencies during pass bands are predicted with the iso-frequency contour lines of the phase constant surface, which are then validated with the harmonic responses of a finite two-dimensional thin plate phononic crystals with 16x16 unit cells. These results are useful for controlling the wave propagation in the pass bands of phononic crystals

  18. Uni-directional trail sharing by two species of ants a Monte Carlo study

    International Nuclear Information System (INIS)

    Kunduraci, T; Kayacan, O

    2015-01-01

    We study insect traffic, specifically ant traffic on a uni-directional trail which is shared by two species of ants, one of which is ‘good’ at smelling and the other ‘poor’. The two distinct species of ants are placed mixed on the same trail and individuals of both are permitted to make a U-turn when they encounter another ant in front of them. The theoretical scheme for the ant traffic is based on an asymmetric simple exclusion model. The ant traffic on the uni-directional trail is studied as a function of the number of ‘good-smelling’ ants and the evaporation probability of pheromones by keeping the number of ‘poor-smelling ants’ constant during Monte Carlo simulations. (paper)

  19. Two dimentional lattice vibrations from direct product representations of symmetry groups

    Directory of Open Access Journals (Sweden)

    J. N. Boyd

    1983-01-01

    two dimensional crystals. First, the Born cyclic condition is applied to a double chain composed of coupled linear lattices to obtain a cylindrical arrangement. Then the quadratic Lagrangian function for the system is written in matrix notation. The Lagrangian is diagonalized to yield the natural frequencies of the system. The transformation to achieve the diagonalization was obtained from group theorectic considerations. Next, the techniques developed for the double chain are applied to a square lattice. The square lattice is transformed into the toroidal Ising model. The direct product nature of the symmetry group of the torus reveals the transformation to diagonalize the Lagrangian for the Ising model, and the natural frequencies for the principal directions in the model are obtained in closed form.

  20. Contractions without non-trivial invariant subspaces satisfying a positivity condition

    Directory of Open Access Journals (Sweden)

    Bhaggy Duggal

    2016-04-01

    Full Text Available Abstract An operator A ∈ B ( H $A\\in B(\\mathcal{H}$ , the algebra of bounded linear transformations on a complex infinite dimensional Hilbert space H $\\mathcal{H}$ , belongs to class A ( n $\\mathcal{A}(n$ (resp., A ( ∗ − n $\\mathcal{A}(*-n$ if | A | 2 ≤ | A n + 1 | 2 n + 1 $\\vert A\\vert^{2}\\leq\\vert A^{n+1}\\vert^{\\frac{2}{n+1}}$ (resp., | A ∗ | 2 ≤ | A n + 1 | 2 n + 1 $\\vert A^{*}\\vert^{2}\\leq \\vert A^{n+1}\\vert^{\\frac{2}{n+1}}$ for some integer n ≥ 1 $n\\geq1$ , and an operator A ∈ B ( H $A\\in B(\\mathcal{H}$ is called n-paranormal, denoted A ∈ P ( n $A\\in \\mathcal{P}(n$ (resp., ∗ − n $*-n$ -paranormal, denoted A ∈ P ( ∗ − n $A\\in \\mathcal{P}(*-n$ if ∥ A x ∥ n + 1 ≤ ∥ A n + 1 x ∥ ∥ x ∥ n $\\Vert Ax\\Vert ^{n+1}\\leq \\Vert A^{n+1}x\\Vert \\Vert x\\Vert ^{n}$ (resp., ∥ A ∗ x ∥ n + 1 ≤ ∥ A n + 1 x ∥ ∥ x ∥ n $\\Vert A^{*}x\\Vert ^{n+1}\\leq \\Vert A^{n+1}x\\Vert \\Vert x\\Vert ^{n}$ for some integer n ≥ 1 $n\\geq 1$ and all x ∈ H $x \\in\\mathcal{H}$ . In this paper, we prove that if A ∈ { A ( n ∪ P ( n } $A\\in\\{\\mathcal{A}(n\\cup \\mathcal{P}(n\\}$ (resp., A ∈ { A ( ∗ − n ∪ P ( ∗ − n } $A\\in\\{\\mathcal{A}(*-n\\cup \\mathcal{P}(*-n\\}$ is a contraction without a non-trivial invariant subspace, then A, | A n + 1 | 2 n + 1 − | A | 2 $\\vert A^{n+1}\\vert^{\\frac{2}{n+1}}-\\vert A\\vert^{2}$ and | A n + 1 | 2 − n + 1 n | A | 2 + 1 $\\vert A^{n+1}\\vert^{2}- {\\frac{n+1}{n}}\\vert A\\vert^{2}+ 1$ (resp., A, | A n + 1 | 2 n + 1 − | A ∗ | 2 $\\vert A^{n+1}\\vert^{\\frac{2}{n+1}}-\\vert A^{*}\\vert^{2}$ and | A n + 2 | 2 − n + 1 n | A | 2 + 1 ≥ 0 $\\vert A^{n+2}\\vert^{2}- {\\frac{n+1}{n}}\\vert A\\vert^{2}+ 1\\geq0$ are proper contractions.