Sun, Xiao-Dong; Ge, Zhong-Hui; Li, Zhen-Chun
2017-09-01
Although conventional reverse time migration can be perfectly applied to structural imaging it lacks the capability of enabling detailed delineation of a lithological reservoir due to irregular illumination. To obtain reliable reflectivity of the subsurface it is necessary to solve the imaging problem using inversion. The least-square reverse time migration (LSRTM) (also known as linearized reflectivity inversion) aims to obtain relatively high-resolution amplitude preserving imaging by including the inverse of the Hessian matrix. In practice, the conjugate gradient algorithm is proven to be an efficient iterative method for enabling use of LSRTM. The velocity gradient can be derived from a cross-correlation between observed data and simulated data, making LSRTM independent of wavelet signature and thus more robust in practice. Tests on synthetic and marine data show that LSRTM has good potential for use in reservoir description and four-dimensional (4D) seismic images compared to traditional RTM and Fourier finite difference (FFD) migration. This paper investigates the first order approximation of LSRTM, which is also known as the linear Born approximation. However, for more complex geological structures a higher order approximation should be considered to improve imaging quality.
An improved conjugate gradient scheme to the solution of least squares SVM.
Chu, Wei; Ong, Chong Jin; Keerthi, S Sathiya
2005-03-01
The least square support vector machines (LS-SVM) formulation corresponds to the solution of a linear system of equations. Several approaches to its numerical solutions have been proposed in the literature. In this letter, we propose an improved method to the numerical solution of LS-SVM and show that the problem can be solved using one reduced system of linear equations. Compared with the existing algorithm for LS-SVM, the approach used in this letter is about twice as efficient. Numerical results using the proposed method are provided for comparisons with other existing algorithms.
A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
Chan, Tony; Szeto, Tedd
1994-03-01
We propose a new and more stable variant of the CGS method [27] for solving nonsymmetric linear systems. The method is based on squaring the Composite Step BCG method, introduced recently by Bank and Chan [1,2], which itself is a stabilized variant of BCG in that it skips over steps for which the BCG iterate is not defined and causes one kind of breakdown in BCG. By doing this, we obtain a method (Composite Step CGS or CSCGS) which not only handles the breakdowns described above, but does so with the advantages of CGS, namely, no multiplications by the transpose matrix and a faster convergence rate than BCG. Our strategy for deciding whether to skip a step does not involve any machine dependent parameters and is designed to skip near breakdowns as well as produce smoother iterates. Numerical experiments show that the new method does produce improved performance over CGS on practical problems.
Block-conjugate-gradient method
International Nuclear Information System (INIS)
McCarthy, J.F.
1989-01-01
It is shown that by using the block-conjugate-gradient method several, say s, columns of the inverse Kogut-Susskind fermion matrix can be found simultaneously, in less time than it would take to run the standard conjugate-gradient algorithm s times. The method improves in efficiency relative to the standard conjugate-gradient algorithm as the fermion mass is decreased and as the value of the coupling is pushed to its limit before the finite-size effects become important. Thus it is potentially useful for measuring propagators in large lattice-gauge-theory calculations of the particle spectrum
Pengpen, T; Soleimani, M
2015-06-13
Cone beam computed tomography (CBCT) is an imaging modality that has been used in image-guided radiation therapy (IGRT). For applications such as lung radiation therapy, CBCT images are greatly affected by the motion artefacts. This is mainly due to low temporal resolution of CBCT. Recently, a dual modality of electrical impedance tomography (EIT) and CBCT has been proposed, in which the high temporal resolution EIT imaging system provides motion data to a motion-compensated algebraic reconstruction technique (ART)-based CBCT reconstruction software. High computational time associated with ART and indeed other variations of ART make it less practical for real applications. This paper develops a motion-compensated conjugate gradient least-squares (CGLS) algorithm for CBCT. A motion-compensated CGLS offers several advantages over ART-based methods, including possibilities for explicit regularization, rapid convergence and parallel computations. This paper for the first time demonstrates motion-compensated CBCT reconstruction using CGLS and reconstruction results are shown in limited data CBCT considering only a quarter of the full dataset. The proposed algorithm is tested using simulated motion data in generic motion-compensated CBCT as well as measured EIT data in dual EIT-CBCT imaging. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Orderings for conjugate gradient preconditionings
Ortega, James M.
1991-01-01
The effect of orderings on the rate of convergence of the conjugate gradient method with SSOR or incomplete Cholesky preconditioning is examined. Some results also are presented that help to explain why red/black ordering gives an inferior rate of convergence.
Preconditioning the modified conjugate gradient method ...
African Journals Online (AJOL)
In this paper, the convergence analysis of the conventional conjugate Gradient method was reviewed. And the convergence analysis of the modified conjugate Gradient method was analysed with our extension on preconditioning the algorithm. Convergence of the algorithm is a function of the condition number of M-1A.
Approximate error conjugation gradient minimization methods
Kallman, Jeffrey S
2013-05-21
In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.
A fast, preconditioned conjugate gradient Toeplitz solver
Pan, Victor; Schrieber, Robert
1989-01-01
A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.
Nonlinear conjugate gradient methods in micromagnetics
Directory of Open Access Journals (Sweden)
J. Fischbacher
2017-04-01
Full Text Available Conjugate gradient methods for energy minimization in micromagnetics are compared. The comparison of analytic results with numerical simulation shows that standard conjugate gradient method may fail to produce correct results. A method that restricts the step length in the line search is introduced, in order to avoid this problem. When the step length in the line search is controlled, conjugate gradient techniques are a fast and reliable way to compute the hysteresis properties of permanent magnets. The method is applied to investigate demagnetizing effects in NdFe12 based permanent magnets. The reduction of the coercive field by demagnetizing effects is μ0ΔH = 1.4 T at 450 K.
Conjugate gradient algorithms using multiple recursions
Energy Technology Data Exchange (ETDEWEB)
Barth, T.; Manteuffel, T.
1996-12-31
Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuffel gave necessary and sufficient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all possible recursions. This became evident when Jagels and Reichel used an algorithm of Gragg for unitary matrices to demonstrate that the class of matrices for which a practical conjugate gradient algorithm exists can be extended to include unitary and shifted unitary matrices. The implementation uses short double recursions for the direction vectors. This motivates the study of multiple recursion algorithms.
Conjugate Gradient Algorithms For Manipulator Simulation
Fijany, Amir; Scheid, Robert E.
1991-01-01
Report discusses applicability of conjugate-gradient algorithms to computation of forward dynamics of robotic manipulators. Rapid computation of forward dynamics essential to teleoperation and other advanced robotic applications. Part of continuing effort to find algorithms meeting requirements for increased computational efficiency and speed. Method used for iterative solution of systems of linear equations.
International Nuclear Information System (INIS)
Chen, G.S.
1997-01-01
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)
Application of Conjugate Gradient methods to tidal simulation
Barragy, E.; Carey, G.F.; Walters, R.A.
1993-01-01
A harmonic decomposition technique is applied to the shallow water equations to yield a complex, nonsymmetric, nonlinear, Helmholtz type problem for the sea surface and an accompanying complex, nonlinear diagonal problem for the velocities. The equation for the sea surface is linearized using successive approximation and then discretized with linear, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparative evaluation includes both standard iterative methods for the real subsystems and complex versions of the well known Bi-Conjugate Gradient and Bi-Conjugate Gradient Squared methods. Several Incomplete LU type preconditioners are discussed, and the effects of node ordering, rejection strategy, domain geometry and Coriolis parameter (affecting asymmetry) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made with a frontal solver. ?? 1993.
MODIFIED ARMIJO RULE ON GRADIENT DESCENT AND CONJUGATE GRADIENT
Directory of Open Access Journals (Sweden)
ZURAIDAH FITRIAH
2017-10-01
Full Text Available Armijo rule is an inexact line search method to determine step size in some descent method to solve unconstrained local optimization. Modified Armijo was introduced to increase the numerical performance of several descent algorithms that applying this method. The basic difference of Armijo and its modified are in existence of a parameter and estimating the parameter that is updated in every iteration. This article is comparing numerical solution and time of computation of gradient descent and conjugate gradient hybrid Gilbert-Nocedal (CGHGN that applying modified Armijo rule. From program implementation in Matlab 6, it's known that gradient descent was applying modified Armijo more effectively than CGHGN from one side: iteration needed to reach some norm of the gradient (input by the user. The amount of iteration was representing how long the step size of each algorithm in each iteration. In another side, time of computation has the same conclusion.
Error Estimation in Preconditioned Conjugate Gradients
Czech Academy of Sciences Publication Activity Database
Strakoš, Zdeněk; Tichý, Petr
2005-01-01
Roč. 45, - (2005), s. 789-817 ISSN 0006-3835 R&D Projects: GA AV ČR 1ET400300415; GA AV ČR KJB1030306 Institutional research plan: CEZ:AV0Z10300504 Keywords : preconditioned conjugate gradient method * error bounds * stopping criteria * evaluation of convergence * numerical stability * finite precision arithmetic * rounding errors Subject RIV: BA - General Mathematics Impact factor: 0.509, year: 2005
Conjugate gradient optimization programs for shuttle reentry
Powers, W. F.; Jacobson, R. A.; Leonard, D. A.
1972-01-01
Two computer programs for shuttle reentry trajectory optimization are listed and described. Both programs use the conjugate gradient method as the optimization procedure. The Phase 1 Program is developed in cartesian coordinates for a rotating spherical earth, and crossrange, downrange, maximum deceleration, total heating, and terminal speed, altitude, and flight path angle are included in the performance index. The programs make extensive use of subroutines so that they may be easily adapted to other atmospheric trajectory optimization problems.
M-step preconditioned conjugate gradient methods
Adams, L.
1983-01-01
Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.
Total variation superiorized conjugate gradient method for image reconstruction
Zibetti, Marcelo V. W.; Lin, Chuan; Herman, Gabor T.
2018-03-01
The conjugate gradient (CG) method is commonly used for the relatively-rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization should be utilized. Total variation (TV) is a useful regularization penalty, frequently utilized in image reconstruction for generating images with sharp edges. When a non-quadratic norm is selected for regularization, as is the case for TV, then it is no longer possible to use CG. Non-linear CG is an alternative, but it does not share the efficiency that CG shows with least squares and methods such as fast iterative shrinkage-thresholding algorithms (FISTA) are preferred for problems with TV norm. A different approach to including prior information is superiorization. In this paper it is shown that the conjugate gradient method can be superiorized. Five different CG variants are proposed, including preconditioned CG. The CG methods superiorized by the total variation norm are presented and their performance in image reconstruction is demonstrated. It is illustrated that some of the proposed variants of the superiorized CG method can produce reconstructions of superior quality to those produced by FISTA and in less computational time, due to the speed of the original CG for least squares problems. In the Appendix we examine the behavior of one of the superiorized CG methods (we call it S-CG); one of its input parameters is a positive number ɛ. It is proved that, for any given ɛ that is greater than the half-squared-residual for the least squares solution, S-CG terminates in a finite number of steps with an output for which the half-squared-residual is less than or equal to ɛ. Importantly, it is also the case that the output will have a lower value of TV than what would be provided by unsuperiorized CG for the same value ɛ of the half-squared residual.
PET regularization by envelope guided conjugate gradients
International Nuclear Information System (INIS)
Kaufman, L.; Neumaier, A.
1996-01-01
The authors propose a new way to iteratively solve large scale ill-posed problems and in particular the image reconstruction problem in positron emission tomography by exploiting the relation between Tikhonov regularization and multiobjective optimization to obtain iteratively approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approximate L-curves allows us to adjust the regularization parameter adaptively during a preconditioned conjugate gradient iteration, so that the desired solution can be reconstructed with a small number of iterations
The multigrid preconditioned conjugate gradient method
Tatebe, Osamu
1993-01-01
A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.
Minimizing inner product data dependencies in conjugate gradient iteration
Vanrosendale, J.
1983-01-01
The amount of concurrency available in conjugate gradient iteration is limited by the summations required in the inner product computations. The inner product of two vectors of length N requires time c log(N), if N or more processors are available. This paper describes an algebraic restructuring of the conjugate gradient algorithm which minimizes data dependencies due to inner product calculations. After an initial start up, the new algorithm can perform a conjugate gradient iteration in time c*log(log(N)).
Dai-Kou type conjugate gradient methods with a line search only using gradient.
Huang, Yuanyuan; Liu, Changhe
2017-01-01
In this paper, the Dai-Kou type conjugate gradient methods are developed to solve the optimality condition of an unconstrained optimization, they only utilize gradient information and have broader application scope. Under suitable conditions, the developed methods are globally convergent. Numerical tests and comparisons with the PRP+ conjugate gradient method only using gradient show that the methods are efficient.
New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems
International Nuclear Information System (INIS)
Al-Bayati, A.; Al-Asadi, N.
1997-01-01
This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab
Conjugate Gradient like methods and their application to fixed source neutron diffusion problems
International Nuclear Information System (INIS)
Suetomi, Eiichi; Sekimoto, Hiroshi
1989-01-01
This paper presents a number of fast iterative methods for solving systems of linear equations appearing in fixed source problems for neutron diffusion. We employed the conjugate gradient and conjugate residual methods. In order to accelerate the conjugate residual method, we proposed the conjugate residual squared method by transforming the residual polynomial of the conjugate residual method. Since the convergence of these methods depends on the spectrum of coefficient matrix, we employed the incomplete Choleski (IC) factorization and the modified IC (MIC) factorization as preconditioners. These methods were applied to some neutron diffusion problems and compared with the successive overrelaxation (SOR) method. The results of these numerical experiments showed superior convergence characteristics of the conjugate gradient like method with MIC factorization to the SOR method, especially for a problem involving void region. The CPU time of the MICCG, MICCR and MICCRS methods showed no great difference. In order to vectorize the conjugate gradient like methods based on (M)IC factorization, the hyperplane method was used and implemented on the vector computers, the HITAC S-820/80 and ETA10-E (one processor mode). Significant decrease of the CPU times was observed on the S-820/80. Since the scaled conjugate gradient (SCG) method can be vectorized with no manipulation, it was also compared with the above methods. It turned out the SCG method was the fastest with respect to the CPU times on the ETA10-E. These results suggest that one should implement suitable algorithm for different vector computers. (author)
New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods
International Nuclear Information System (INIS)
Dai, Y.-H.; Liao, L.-Z.
2001-01-01
Conjugate gradient methods are a class of important methods for unconstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis for the two methods is provided. Our numerical results show that one of the methods is very efficient for the given test problems
Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization
Directory of Open Access Journals (Sweden)
San-Yang Liu
2014-01-01
Full Text Available This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent condition gkTdk≤-1-1/4θkgk2 θk>1/4 and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.
International Nuclear Information System (INIS)
Chen, G.S.; Yang, D.Y.
1998-01-01
We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used: TFQMR (transpose free quasi-minimal residual algorithm) CGS (conjugate gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These subroutines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. The reasons to choose the generalized conjugate gradient methods are that the methods have better residual (equivalent to error) control procedures in the computation and have better convergent rate. The pointwise incomplete LU factorization ILU, modified pointwise incomplete LU factorization MILU, block incomplete factorization BILU and modified blockwise incomplete LU factorization MBILU are the preconditioning techniques used in the several testing problems. In Bi-CGSTAB, CGS, TFQMR and QMRCGSTAB method, we find that either CGS or Bi-CGSTAB method combined with preconditioner MBILU is the most efficient algorithm in these methods in the several testing problems. The numerical solution of flux by preconditioned CGS and Bi-CGSTAB methods has the same result as those from Cray computer, obtained by either the point successive relaxation method or the line successive relaxation method combined with Gaussian elimination
Adaptive Regularization of Neural Networks Using Conjugate Gradient
DEFF Research Database (Denmark)
Goutte, Cyril; Larsen, Jan
1998-01-01
Andersen et al. (1997) and Larsen et al. (1996, 1997) suggested a regularization scheme which iteratively adapts regularization parameters by minimizing validation error using simple gradient descent. In this contribution we present an improved algorithm based on the conjugate gradient technique........ Numerical experiments with feedforward neural networks successfully demonstrate improved generalization ability and lower computational cost...
Modified conjugate gradient method for diagonalizing large matrices.
Jie, Quanlin; Liu, Dunhuan
2003-11-01
We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.
Comparison of genetic algorithms with conjugate gradient methods
Bosworth, J. L.; Foo, N. Y.; Zeigler, B. P.
1972-01-01
Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.
Experiments with conjugate gradient algorithms for homotopy curve tracking
Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.
1991-01-01
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
A feasible DY conjugate gradient method for linear equality constraints
LI, Can
2017-09-01
In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.
A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method
Directory of Open Access Journals (Sweden)
Shengwei Yao
2014-01-01
Full Text Available The conjugate gradient (CG method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001. Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.
A constrained conjugate gradient algorithm for computed tomography
Energy Technology Data Exchange (ETDEWEB)
Azevedo, S.G.; Goodman, D.M. [Lawrence Livermore National Lab., CA (United States)
1994-11-15
Image reconstruction from projections of x-ray, gamma-ray, protons and other penetrating radiation is a well-known problem in a variety of fields, and is commonly referred to as computed tomography (CT). Various analytical and series expansion methods of reconstruction and been used in the past to provide three-dimensional (3D) views of some interior quantity. The difficulties of these approaches lie in the cases where (a) the number of views attainable is limited, (b) the Poisson (or other) uncertainties are significant, (c) quantifiable knowledge of the object is available, but not implementable, or (d) other limitations of the data exist. We have adapted a novel nonlinear optimization procedure developed at LLNL to address limited-data image reconstruction problems. The technique, known as nonlinear least squares with general constraints or constrained conjugate gradients (CCG), has been successfully applied to a number of signal and image processing problems, and is now of great interest to the image reconstruction community. Previous applications of this algorithm to deconvolution problems and x-ray diffraction images for crystallography have shown the great promise.
Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.
Temel, Burcin; Mills, Greg; Metiu, Horia
2008-03-27
We describe and test an implementation, using a basis set of Chebyshev polynomials, of a variational method for solving scattering problems in quantum mechanics. This minimum error method (MEM) determines the wave function Psi by minimizing the least-squares error in the function (H Psi - E Psi), where E is the desired scattering energy. We compare the MEM to an alternative, the Kohn variational principle (KVP), by solving the Secrest-Johnson model of two-dimensional inelastic scattering, which has been studied previously using the KVP and for which other numerical solutions are available. We use a conjugate gradient (CG) method to minimize the error, and by preconditioning the CG search, we are able to greatly reduce the number of iterations necessary; the method is thus faster and more stable than a matrix inversion, as is required in the KVP. Also, we avoid errors due to scattering off of the boundaries, which presents substantial problems for other methods, by matching the wave function in the interaction region to the correct asymptotic states at the specified energy; the use of Chebyshev polynomials allows this boundary condition to be implemented accurately. The use of Chebyshev polynomials allows for a rapid and accurate evaluation of the kinetic energy. This basis set is as efficient as plane waves but does not impose an artificial periodicity on the system. There are problems in surface science and molecular electronics which cannot be solved if periodicity is imposed, and the Chebyshev basis set is a good alternative in such situations.
A Spectral Conjugate Gradient Method for Unconstrained Optimization
International Nuclear Information System (INIS)
Birgin, E. G.; Martinez, J. M.
2001-01-01
A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak-Ribiere and the Fletcher-Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented
Computing several eigenpairs of Hermitian problems by conjugate gradient iterations
International Nuclear Information System (INIS)
Ovtchinnikov, E.E.
2008-01-01
The paper is concerned with algorithms for computing several extreme eigenpairs of Hermitian problems based on the conjugate gradient method. We analyse computational strategies employed by various algorithms of this kind reported in the literature and identify their limitations. Our criticism is illustrated by numerical tests on a set of problems from electronic structure calculations and acoustics
Conjugate-Gradient Algorithms For Dynamics Of Manipulators
Fijany, Amir; Scheid, Robert E.
1993-01-01
Algorithms for serial and parallel computation of forward dynamics of multiple-link robotic manipulators by conjugate-gradient method developed. Parallel algorithms have potential for speedup of computations on multiple linked, specialized processors implemented in very-large-scale integrated circuits. Such processors used to stimulate dynamics, possibly faster than in real time, for purposes of planning and control.
Deflation in preconditioned conjugate gradient methods for Finite Element Problems
Vermolen, F.J.; Vuik, C.; Segal, A.
2002-01-01
We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous
Implementing the conjugate gradient algorithm on multi-core systems
Wiggers, W.A.; Bakker, Vincent; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria; Nurmi, J.; Takala, J.; Vainio, O.
2007-01-01
In linear solvers, like the conjugate gradient algorithm, sparse-matrix vector multiplication is an important kernel. Due to the sparseness of the matrices, the solver runs relatively slow. For digital optical tomography (DOT), a large set of linear equations have to be solved which currently takes
Accurate conjugate gradient methods for families of shifted systems
Eshof, J. van den; Sleijpen, G.L.G.
We present an efficient and accurate variant of the conjugate gradient method for solving families of shifted systems. In particular we are interested in shifted systems that occur in Tikhonov regularization for inverse problems since these problems can be sensitive to roundoff errors. The
Accurate reanalysis of structures by a preconditioned conjugate gradient method
Czech Academy of Sciences Publication Activity Database
Kirsch, U.; Kočvara, Michal; Zowe, J.
2002-01-01
Roč. 55, č. 2 (2002), s. 233-251 ISSN 0029-5981 R&D Projects: GA AV ČR IAA1075005 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : preconditioned conjugate gradient s * structural reanalysis Subject RIV: BA - General Mathematics Impact factor: 1.468, year: 2002
Parallel conjugate gradient algorithms for manipulator dynamic simulation
Fijany, Amir; Scheld, Robert E.
1989-01-01
Parallel conjugate gradient algorithms for the computation of multibody dynamics are developed for the specialized case of a robot manipulator. For an n-dimensional positive-definite linear system, the Classical Conjugate Gradient (CCG) algorithms are guaranteed to converge in n iterations, each with a computation cost of O(n); this leads to a total computational cost of O(n sq) on a serial processor. A conjugate gradient algorithms is presented that provide greater efficiency using a preconditioner, which reduces the number of iterations required, and by exploiting parallelism, which reduces the cost of each iteration. Two Preconditioned Conjugate Gradient (PCG) algorithms are proposed which respectively use a diagonal and a tridiagonal matrix, composed of the diagonal and tridiagonal elements of the mass matrix, as preconditioners. Parallel algorithms are developed to compute the preconditioners and their inversions in O(log sub 2 n) steps using n processors. A parallel algorithm is also presented which, on the same architecture, achieves the computational time of O(log sub 2 n) for each iteration. Simulation results for a seven degree-of-freedom manipulator are presented. Variants of the proposed algorithms are also developed which can be efficiently implemented on the Robot Mathematics Processor (RMP).
The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic
Czech Academy of Sciences Publication Activity Database
Meurant, G.; Strakoš, Zdeněk
2006-01-01
Roč. 15, - (2006), s. 471-542 ISSN 0962-4929 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lanczos method * conjugate gradient method * finite precision arithmetic * numerical stability * iterative methods Subject RIV: BA - General Mathematics
Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.
Yang, Qiang; Vogel, Curtis R; Ellerbroek, Brent L
2006-07-20
By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.
Application of preconditioned conjugate gradient-like methods to reactor kinetics
International Nuclear Information System (INIS)
Yang, D.Y.; Chen, G.S.; Chou, H.P.
1993-01-01
Several conjugate gradient-like (CG-like) methods are applied to solve the nonsymmetric linear systems of equations derived from the time-dependent two-dimensional two-energy-group neutron diffusion equations by a finite difference approximation. The methods are: the generalized conjugate residual method; the generalized conjugate gradient least-square method; the generalized minimal residual method (GMRES); the conjugate gradient square method; and a variant of bi-conjugate gradient method (Bi-CGSTAB). In order to accelerate these methods, six preconditioning techniques are investigated. Two are based on pointwise incomplete factorization: the incomplete LU (ILU) and the modified incomplete LU (MILU) decompositions; two, based on the block tridiagonal structure of the coefficient matrix, are blockwise and modified blockwise incomplete factorizations, BILU and MBILU; two are the alternating-direction implicit and symmetric successive overrelaxation (SSOR) preconditioners, derived from the basic iterative schemes. Comparisons are made by using CG-like methods combined with different preconditioners to solve a sequence of time-step reactor transient problems. Numerical tests indicate that preconditioned BI-CGSTAB with the preconditioner MBILU requires less CPU time and fewer iterations than other methods. The preconditioned CG-like methods are less sensitive to the time-step size used than the Chebyshev semi-iteration method and line SOR method. The indication is that the CGS, Bi-CGSTAB and GMRES methods are, on average, better than the other methods in reactor kinetics computation and that a good preconditioner is more important than the choice of CG-like methods. The MILU decomposition based on the conventional row-sum criterion has difficulty yielding a convergent solution and an improved version is introduced. (author)
Nonnegative least-squares image deblurring: improved gradient projection approaches
Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.
2010-02-01
The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.
Conjugate gradient heat bath for ill-conditioned actions.
Ceriotti, Michele; Bussi, Giovanni; Parrinello, Michele
2007-08-01
We present a method for performing sampling from a Boltzmann distribution of an ill-conditioned quadratic action. This method is based on heat-bath thermalization along a set of conjugate directions, generated via a conjugate-gradient procedure. The resulting scheme outperforms local updates for matrices with very high condition number, since it avoids the slowing down of modes with lower eigenvalue, and has some advantages over the global heat-bath approach, compared to which it is more stable and allows for more freedom in devising case-specific optimizations.
Blockwise conjugate gradient methods for image reconstruction in volumetric CT.
Qiu, W; Titley-Peloquin, D; Soleimani, M
2012-11-01
Cone beam computed tomography (CBCT) enables volumetric image reconstruction from 2D projection data and plays an important role in image guided radiation therapy (IGRT). Filtered back projection is still the most frequently used algorithm in applications. The algorithm discretizes the scanning process (forward projection) into a system of linear equations, which must then be solved to recover images from measured projection data. The conjugate gradients (CG) algorithm and its variants can be used to solve (possibly regularized) linear systems of equations Ax=b and linear least squares problems minx∥b-Ax∥2, especially when the matrix A is very large and sparse. Their applications can be found in a general CT context, but in tomography problems (e.g. CBCT reconstruction) they have not widely been used. Hence, CBCT reconstruction using the CG-type algorithm LSQR was implemented and studied in this paper. In CBCT reconstruction, the main computational challenge is that the matrix A usually is very large, and storing it in full requires an amount of memory well beyond the reach of commodity computers. Because of these memory capacity constraints, only a small fraction of the weighting matrix A is typically used, leading to a poor reconstruction. In this paper, to overcome this difficulty, the matrix A is partitioned and stored blockwise, and blockwise matrix-vector multiplications are implemented within LSQR. This implementation allows us to use the full weighting matrix A for CBCT reconstruction without further enhancing computer standards. Tikhonov regularization can also be implemented in this fashion, and can produce significant improvement in the reconstructed images. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.
Directory of Open Access Journals (Sweden)
Gonglin Yuan
Full Text Available Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1 βk ≥ 0 2 the search direction has the trust region property without the use of any line search method 3 the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.
Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou
2015-01-01
Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.
MILC staggered conjugate gradient performance on Intel KNL
DeTar, Carleton; Doerfler, Douglas; Gottlieb, Steven; Jha, Ashish; Kalamkar, Dhiraj; Li, Ruizi; Toussaint, Doug
2016-01-01
We review our work done to optimize the staggered conjugate gradient (CG) algorithm in the MILC code for use with the Intel Knights Landing (KNL) architecture. KNL is the second gener- ation Intel Xeon Phi processor. It is capable of massive thread parallelism, data parallelism, and high on-board memory bandwidth and is being adopted in supercomputing centers for scientific research. The CG solver consumes the majority of time in production running, so we have spent most of our effort on it. ...
Gadolinium burnable absorber optimization by the method of conjugate gradients
International Nuclear Information System (INIS)
Drumm, C.R.; Lee, J.C.
1987-01-01
The optimal axial distribution of gadolinium burnable poison in a pressurized water reactor is determined to yield an improved power distribution. The optimization scheme is based on Pontryagin's maximum principle, with the objective function accounting for a target power distribution. The conjugate gradients optimization method is used to solve the resulting Euler-Lagrange equations iteratively, efficiently handling the high degree of nonlinearity of the problem
A partitioned conjugate gradient algorithm for lattice Green functions
International Nuclear Information System (INIS)
Bowler, K.C.; Kenway, R.D.; Pawley, G.S.; Wallace, D.J.
1984-01-01
Partitioning reduces by one the dimensionality of the lattice on which a propagator need be calculated using, for example, the conjugate gradient algorithm. Thus the quark propagator in lattice QCD may be determined by a computation on a single spatial hyperplane. For free fermions on a 16 3 x N lattice 2N-bit accuracy in the propagator is required to avoid rounding errors. (orig.)
Moving force identification based on modified preconditioned conjugate gradient method
Chen, Zhen; Chan, Tommy H. T.; Nguyen, Andy
2018-06-01
This paper develops a modified preconditioned conjugate gradient (M-PCG) method for moving force identification (MFI) by improving the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods with a modified Gram-Schmidt algorithm. The method aims to obtain more accurate and more efficient identification results from the responses of bridge deck caused by vehicles passing by, which are known to be sensitive to ill-posed problems that exist in the inverse problem. A simply supported beam model with biaxial time-varying forces is used to generate numerical simulations with various analysis scenarios to assess the effectiveness of the method. Evaluation results show that regularization matrix L and number of iterations j are very important influence factors to identification accuracy and noise immunity of M-PCG. Compared with the conventional counterpart SVD embedded in the time domain method (TDM) and the standard form of CG, the M-PCG with proper regularization matrix has many advantages such as better adaptability and more robust to ill-posed problems. More importantly, it is shown that the average optimal numbers of iterations of M-PCG can be reduced by more than 70% compared with PCG and this apparently makes M-PCG a preferred choice for field MFI applications.
Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization.
Lu, Hanbing; Jesmanowicz, Andrzej; Li, Shi-Jiang; Hyde, James S
2004-01-01
MRI gradient coil design is a type of nonlinear constrained optimization. A practical problem in transverse gradient coil design using the conjugate gradient descent (CGD) method is that wire elements move at different rates along orthogonal directions (r, phi, z), and tend to cross, breaking the constraints. A momentum-weighted conjugate gradient descent (MW-CGD) method is presented to overcome this problem. This method takes advantage of the efficiency of the CGD method combined with momentum weighting, which is also an intrinsic property of the Levenberg-Marquardt algorithm, to adjust step sizes along the three orthogonal directions. A water-cooled, 12.8 cm inner diameter, three axis torque-balanced gradient coil for rat imaging was developed based on this method, with an efficiency of 2.13, 2.08, and 4.12 mT.m(-1).A(-1) along X, Y, and Z, respectively. Experimental data demonstrate that this method can improve efficiency by 40% and field uniformity by 27%. This method has also been applied to the design of a gradient coil for the human brain, employing remote current return paths. The benefits of this design include improved gradient field uniformity and efficiency, with a shorter length than gradient coil designs using coaxial return paths. Copyright 2003 Wiley-Liss, Inc.
T2CG1, a package of preconditioned conjugate gradient solvers for TOUGH2
International Nuclear Information System (INIS)
Moridis, G.; Pruess, K.; Antunez, E.
1994-03-01
Most of the computational work in the numerical simulation of fluid and heat flows in permeable media arises in the solution of large systems of linear equations. The simplest technique for solving such equations is by direct methods. However, because of large storage requirements and accumulation of roundoff errors, the application of direct solution techniques is limited, depending on matrix bandwidth, to systems of a few hundred to at most a few thousand simultaneous equations. T2CG1, a package of preconditioned conjugate gradient solvers, has been added to TOUGH2 to complement its direct solver and significantly increase the size of problems tractable on PCs. T2CG1 includes three different solvers: a Bi-Conjugate Gradient (BCG) solver, a Bi-Conjugate Gradient Squared (BCGS) solver, and a Generalized Minimum Residual (GMRES) solver. Results from six test problems with up to 30,000 equations show that T2CG1 (1) is significantly (and invariably) faster and requires far less memory than the MA28 direct solver, (2) it makes possible the solution of very large three-dimensional problems on PCs, and (3) that the BCGS solver is the fastest of the three in the tested problems. Sample problems are presented related to heat and fluid flow at Yucca Mountain and WIPP, environmental remediation by the Thermal Enhanced Vapor Extraction System, and geothermal resources
Solving large mixed linear models using preconditioned conjugate gradient iteration.
Strandén, I; Lidauer, M
1999-12-01
Continuous evaluation of dairy cattle with a random regression test-day model requires a fast solving method and algorithm. A new computing technique feasible in Jacobi and conjugate gradient based iterative methods using iteration on data is presented. In the new computing technique, the calculations in multiplication of a vector by a matrix were recorded to three steps instead of the commonly used two steps. The three-step method was implemented in a general mixed linear model program that used preconditioned conjugate gradient iteration. Performance of this program in comparison to other general solving programs was assessed via estimation of breeding values using univariate, multivariate, and random regression test-day models. Central processing unit time per iteration with the new three-step technique was, at best, one-third that needed with the old technique. Performance was best with the test-day model, which was the largest and most complex model used. The new program did well in comparison to other general software. Programs keeping the mixed model equations in random access memory required at least 20 and 435% more time to solve the univariate and multivariate animal models, respectively. Computations of the second best iteration on data took approximately three and five times longer for the animal and test-day models, respectively, than did the new program. Good performance was due to fast computing time per iteration and quick convergence to the final solutions. Use of preconditioned conjugate gradient based methods in solving large breeding value problems is supported by our findings.
Program generator for the Incomplete Cholesky Conjugate Gradient (ICCG) method
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Petravic, M.
1978-04-01
The Incomplete Cholesky Conjugate Gradient (ICCG) method has been found very effective for the solution of sparse systems of linear equations. Its implementation on a computer, however, requires a considerable amount of careful coding to achieve good machine efficiency. Furthermore, the resulting code is necessarily inflexible and cannot be easily adapted to different problems. We present in this paper a code generator GENIC which, given a small amount of information concerning the sparsity pattern and size of the system of equations, generates a solver package. This package, called SOLIC, is tailor made for a particular problem and can be easily incorporated into any user program
Conjugate gradient coupled with multigrid for an indefinite problem
Gozani, J.; Nachshon, A.; Turkel, E.
1984-01-01
An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.
Parallel preconditioned conjugate gradient algorithm applied to neutron diffusion problem
International Nuclear Information System (INIS)
Majumdar, A.; Martin, W.R.
1992-01-01
Numerical solution of the neutron diffusion problem requires solving a linear system of equations such as Ax = b, where A is an n x n symmetric positive definite (SPD) matrix; x and b are vectors with n components. The preconditioned conjugate gradient (PCG) algorithm is an efficient iterative method for solving such a linear system of equations. In this paper, the authors describe the implementation of a parallel PCG algorithm on a shared memory machine (BBN TC2000) and on a distributed workstation (IBM RS6000) environment created by the parallel virtual machine parallelization software
Weighted graph based ordering techniques for preconditioned conjugate gradient methods
Clift, Simon S.; Tang, Wei-Pai
1994-01-01
We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.
Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn
2007-01-01
Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.
Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics
Fijany, Amir; Scheid, Robert E.
1989-01-01
The applicability of conjugate gradient algorithms for computation of the manipulator forward dynamics is investigated. The redundancies in the previously proposed conjugate gradient algorithm are analyzed. A new version is developed which, by avoiding these redundancies, achieves a significantly greater efficiency. A preconditioned conjugate gradient algorithm is also presented. A diagonal matrix whose elements are the diagonal elements of the inertia matrix is proposed as the preconditioner. In order to increase the computational efficiency, an algorithm is developed which exploits the synergism between the computation of the diagonal elements of the inertia matrix and that required by the conjugate gradient algorithm.
MILC staggered conjugate gradient performance on Intel KNL
Energy Technology Data Exchange (ETDEWEB)
Li, Ruiz [Indiana Univ., Bloomington, IN (United States). Dept. of Physics; Detar, Carleton [Univ. of Utah, Salt Lake City, UT (United States). Dept. of Physics and Astronomy; Doerfler, Douglas W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Gottlieb, Steven [Indiana Univ., Bloomington, IN (United States). Dept. of Physics; Jha, Asish [Intel Corp., Hillsboro, OR (United States). Sofware and Services Group; Kalamkar, Dhiraj [Intel Labs., Bangalore (India). Parallel Computing Lab.; Toussaint, Doug [Univ. of Arizona, Tucson, AZ (United States). Physics Dept.
2016-11-03
We review our work done to optimize the staggered conjugate gradient (CG) algorithm in the MILC code for use with the Intel Knights Landing (KNL) architecture. KNL is the second gener- ation Intel Xeon Phi processor. It is capable of massive thread parallelism, data parallelism, and high on-board memory bandwidth and is being adopted in supercomputing centers for scientific research. The CG solver consumes the majority of time in production running, so we have spent most of our effort on it. We compare performance of an MPI+OpenMP baseline version of the MILC code with a version incorporating the QPhiX staggered CG solver, for both one-node and multi-node runs.
Improved Conjugate Gradient Bundle Adjustment of Dunhuang Wall Painting Images
Hu, K.; Huang, X.; You, H.
2017-09-01
Bundle adjustment with additional parameters is identified as a critical step for precise orthoimage generation and 3D reconstruction of Dunhuang wall paintings. Due to the introduction of self-calibration parameters and quasi-planar constraints, the structure of coefficient matrix of the reduced normal equation is banded-bordered, making the solving process of bundle adjustment complex. In this paper, Conjugate Gradient Bundle Adjustment (CGBA) method is deduced by calculus of variations. A preconditioning method based on improved incomplete Cholesky factorization is adopt to reduce the condition number of coefficient matrix, as well as to accelerate the iteration rate of CGBA. Both theoretical analysis and experimental results comparison with conventional method indicate that, the proposed method can effectively conquer the ill-conditioned problem of normal equation and improve the calculation efficiency of bundle adjustment with additional parameters considerably, while maintaining the actual accuracy.
IMPROVED CONJUGATE GRADIENT BUNDLE ADJUSTMENT OF DUNHUANG WALL PAINTING IMAGES
Directory of Open Access Journals (Sweden)
K. Hu
2017-09-01
Full Text Available Bundle adjustment with additional parameters is identified as a critical step for precise orthoimage generation and 3D reconstruction of Dunhuang wall paintings. Due to the introduction of self-calibration parameters and quasi-planar constraints, the structure of coefficient matrix of the reduced normal equation is banded-bordered, making the solving process of bundle adjustment complex. In this paper, Conjugate Gradient Bundle Adjustment (CGBA method is deduced by calculus of variations. A preconditioning method based on improved incomplete Cholesky factorization is adopt to reduce the condition number of coefficient matrix, as well as to accelerate the iteration rate of CGBA. Both theoretical analysis and experimental results comparison with conventional method indicate that, the proposed method can effectively conquer the ill-conditioned problem of normal equation and improve the calculation efficiency of bundle adjustment with additional parameters considerably, while maintaining the actual accuracy.
Aerodynamic shape optimization using preconditioned conjugate gradient methods
Burgreen, Greg W.; Baysal, Oktay
1993-01-01
In an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures, a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure. It is demonstrated that preconditioned conjugate gradient-like methodologies dramatically decrease the computational efforts required for such procedures. The design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric (NACA-012) airfoil in inviscid transonic flow and at zero degree angle-of-attack. The complete surface shape is represented using a Bezier-Bernstein polynomial. The present optimization method then automatically obtains supercritical airfoil shapes over a variety of freestream Mach numbers. Furthermore, the best optimization strategy examined resulted in a factor of 8 decrease in computational time as well as a factor of 4 decrease in memory over the most efficient strategies in current use.
Ledoux, L.A.F.; Berkhoff, Arthur P.; Thijssen, J.M.
The Conjugate Gradient Rayleigh method for the calculation of acoustic reflection and transmission at a rough interface between two media was experimentally verified. The method is based on a continuous version of the conjugate gradient technique and plane-wave expansions. We measured the beam
Missing value imputation in DNA microarrays based on conjugate gradient method.
Dorri, Fatemeh; Azmi, Paeiz; Dorri, Faezeh
2012-02-01
Analysis of gene expression profiles needs a complete matrix of gene array values; consequently, imputation methods have been suggested. In this paper, an algorithm that is based on conjugate gradient (CG) method is proposed to estimate missing values. k-nearest neighbors of the missed entry are first selected based on absolute values of their Pearson correlation coefficient. Then a subset of genes among the k-nearest neighbors is labeled as the best similar ones. CG algorithm with this subset as its input is then used to estimate the missing values. Our proposed CG based algorithm (CGimpute) is evaluated on different data sets. The results are compared with sequential local least squares (SLLSimpute), Bayesian principle component analysis (BPCAimpute), local least squares imputation (LLSimpute), iterated local least squares imputation (ILLSimpute) and adaptive k-nearest neighbors imputation (KNNKimpute) methods. The average of normalized root mean squares error (NRMSE) and relative NRMSE in different data sets with various missing rates shows CGimpute outperforms other methods. Copyright © 2011 Elsevier Ltd. All rights reserved.
Pixel-based OPC optimization based on conjugate gradients.
Ma, Xu; Arce, Gonzalo R
2011-01-31
Optical proximity correction (OPC) methods are resolution enhancement techniques (RET) used extensively in the semiconductor industry to improve the resolution and pattern fidelity of optical lithography. In pixel-based OPC (PBOPC), the mask is divided into small pixels, each of which is modified during the optimization process. Two critical issues in PBOPC are the required computational complexity of the optimization process, and the manufacturability of the optimized mask. Most current OPC optimization methods apply the steepest descent (SD) algorithm to improve image fidelity augmented by regularization penalties to reduce the complexity of the mask. Although simple to implement, the SD algorithm converges slowly. The existing regularization penalties, however, fall short in meeting the mask rule check (MRC) requirements often used in semiconductor manufacturing. This paper focuses on developing OPC optimization algorithms based on the conjugate gradient (CG) method which exhibits much faster convergence than the SD algorithm. The imaging formation process is represented by the Fourier series expansion model which approximates the partially coherent system as a sum of coherent systems. In order to obtain more desirable manufacturability properties of the mask pattern, a MRC penalty is proposed to enlarge the linear size of the sub-resolution assistant features (SRAFs), as well as the distances between the SRAFs and the main body of the mask. Finally, a projection method is developed to further reduce the complexity of the optimized mask pattern.
Acceleration of monte Carlo solution by conjugate gradient method
International Nuclear Information System (INIS)
Toshihisa, Yamamoto
2005-01-01
The conjugate gradient method (CG) was applied to accelerate Monte Carlo solutions in fixed source problems. The equilibrium model based formulation enables to use CG scheme as well as initial guess to maximize computational performance. This method is available to arbitrary geometry provided that the neutron source distribution in each subregion can be regarded as flat. Even if it is not the case, the method can still be used as a powerful tool to provide an initial guess very close to the converged solution. The major difference of Monte Carlo CG to deterministic CG is that residual error is estimated using Monte Carlo sampling, thus statistical error exists in the residual. This leads to a flow diagram specific to Monte Carlo-CG. Three pre-conditioners were proposed for CG scheme and the performance was compared with a simple 1-D slab heterogeneous test problem. One of them, Sparse-M option, showed an excellent performance in convergence. The performance per unit cost was improved by four times in the test problem. Although direct estimation of efficiency of the method is impossible mainly because of the strong problem-dependence of the optimized pre-conditioner in CG, the method seems to have efficient potential as a fast solution algorithm for Monte Carlo calculations. (author)
Fully 3D PET image reconstruction using a fourier preconditioned conjugate-gradient algorithm
International Nuclear Information System (INIS)
Fessler, J.A.; Ficaro, E.P.
1996-01-01
Since the data sizes in fully 3D PET imaging are very large, iterative image reconstruction algorithms must converge in very few iterations to be useful. One can improve the convergence rate of the conjugate-gradient (CG) algorithm by incorporating preconditioning operators that approximate the inverse of the Hessian of the objective function. If the 3D cylindrical PET geometry were not truncated at the ends, then the Hessian of the penalized least-squares objective function would be approximately shift-invariant, i.e. G'G would be nearly block-circulant, where G is the system matrix. We propose a Fourier preconditioner based on this shift-invariant approximation to the Hessian. Results show that this preconditioner significantly accelerates the convergence of the CG algorithm with only a small increase in computation
International Nuclear Information System (INIS)
Kowsary, F.; Pooladvand, K.; Pourshaghaghy, A.
2007-01-01
In this paper, an appropriate distribution of the heating elements' strengths in a radiation furnace is estimated using inverse methods so that a pre-specified temperature and heat flux distribution is attained on the design surface. Minimization of the sum of the squares of the error function is performed using the variable metric method (VMM), and the results are compared with those obtained by the conjugate gradient method (CGM) established previously in the literature. It is shown via test cases and a well-founded validation procedure that the VMM, when using a 'regularized' estimator, is more accurate and is able to reach at a higher quality final solution as compared to the CGM. The test cases used in this study were two-dimensional furnaces filled with an absorbing, emitting, and scattering gas
Vogel, Curtis R; Yang, Qiang
2006-08-21
We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.
Preconditioned Conjugate Gradient methods for low speed flow calculations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1993-01-01
An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel
2018-02-12
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost required to solve the corresponding system of equations using a direct LU factorization solver dramatically reduces (up to a factor of 55) Garcia et al. (2017). At the same time, rIGA enriches the IGA spaces, thus improving the best approximation error. In this work, we extend the complexity analysis of rIGA to the case of iterative solvers. We build an iterative solver as follows: we first construct the Schur complements using a direct solver over small subdomains (macro-elements). We then assemble those Schur complements into a global skeleton system. Subsequently, we solve this system iteratively using Conjugate Gradients (CG) with an incomplete LU (ILU) preconditioner. For a 2D Poisson model problem with a structured mesh and a uniform polynomial degree of approximation, rIGA achieves moderate savings with respect to IGA in terms of the number of Floating Point Operations (FLOPs) and computational time (in seconds) required to solve the resulting system of linear equations. For instance, for a mesh with four million elements and polynomial degree p=3, the iterative solver is approximately 2.6 times faster (in time) when applied to the rIGA system than to the IGA one. These savings occur because the skeleton rIGA system contains fewer non-zero entries than the IGA one. The opposite situation occurs for 3D problems, and as a result, 3D rIGA discretizations provide no gains with respect to their IGA counterparts when considering iterative solvers.
Numerical Simulation of Solid Combustion with a Robust Conjugate-Gradient Solution for Pressure
National Research Council Canada - National Science Library
Wang, Yi-Zun
2002-01-01
A Bi-Conjugate Gradient method (Bi-CGSTAB) is studied and tested for solid combustion in which the gas and solid phases are coupled by a set of conditions describing mass, momentum and heat transport across the interface...
Application of the conjugate-gradient method to ground-water models
Manteuffel, T.A.; Grove, D.B.; Konikow, Leonard F.
1984-01-01
The conjugate-gradient method can solve efficiently and accurately finite-difference approximations to the ground-water flow equation. An aquifer-simulation model using the conjugate-gradient method was applied to a problem of ground-water flow in an alluvial aquifer at the Rocky Mountain Arsenal, Denver, Colorado. For this application, the accuracy and efficiency of the conjugate-gradient method compared favorably with other available methods for steady-state flow. However, its efficiency relative to other available methods depends on the nature of the specific problem. The main advantage of the conjugate-gradient method is that it does not require the use of iteration parameters, thereby eliminating this partly subjective procedure. (USGS)
A three-term conjugate gradient method under the strong-Wolfe line search
Khadijah, Wan; Rivaie, Mohd; Mamat, Mustafa
2017-08-01
Recently, numerous studies have been concerned in conjugate gradient methods for solving large-scale unconstrained optimization method. In this paper, a three-term conjugate gradient method is proposed for unconstrained optimization which always satisfies sufficient descent direction and namely as Three-Term Rivaie-Mustafa-Ismail-Leong (TTRMIL). Under standard conditions, TTRMIL method is proved to be globally convergent under strong-Wolfe line search. Finally, numerical results are provided for the purpose of comparison.
Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction.
Fessler, J A; Booth, S D
1999-01-01
Gradient-based iterative methods often converge slowly for tomographic image reconstruction and image restoration problems, but can be accelerated by suitable preconditioners. Diagonal preconditioners offer some improvement in convergence rate, but do not incorporate the structure of the Hessian matrices in imaging problems. Circulant preconditioners can provide remarkable acceleration for inverse problems that are approximately shift-invariant, i.e., for those with approximately block-Toeplitz or block-circulant Hessians. However, in applications with nonuniform noise variance, such as arises from Poisson statistics in emission tomography and in quantum-limited optical imaging, the Hessian of the weighted least-squares objective function is quite shift-variant, and circulant preconditioners perform poorly. Additional shift-variance is caused by edge-preserving regularization methods based on nonquadratic penalty functions. This paper describes new preconditioners that approximate more accurately the Hessian matrices of shift-variant imaging problems. Compared to diagonal or circulant preconditioning, the new preconditioners lead to significantly faster convergence rates for the unconstrained conjugate-gradient (CG) iteration. We also propose a new efficient method for the line-search step required by CG methods. Applications to positron emission tomography (PET) illustrate the method.
Accurate conjugate gradient methods for families of shifted systems
Eshof, J. van den; Sleijpen, G.L.G.
2003-01-01
We consider the solution of the linear system (ATA + σI)xσ = ATb, for various real values of σ. This family of shifted systems arises, for example, in Tikhonov regularization and computations in lattice quantum chromodynamics. For each single shift σ this system can be solved using the conjugate
Application of conjugate gradient method to Commix-1B three-dimensional momentum equation
International Nuclear Information System (INIS)
King, J.B.; Domanus, H.
1987-01-01
Conjugate gradient method which is a special case of the variational method was implemented in the momentum section of the COMMIX-1B thermal hydraulics code. The comparisons between this method and the conventional iterative method of Successive Over Relation (S.O.R.) were made. Using COMMIX-1B, three steady state problems were analyzed. These problems were flow distribution in a scaled model of the Clinch River Fast Breeder Reactor outlet plenum, flow of coolant in the cold leg and downcomer of a PWR and isothermal air flow through a partially blocked pipe. It was found that if the conjugate gradient method is used, the execution time required to solve the resulting COMMIX-1B system of equations can be reduced by a factor of about 2 for the first two problems. For the isothermal air flow problem, the conjugate gradient method did not improve the execution time
Ghani, N. H. A.; Mohamed, N. S.; Zull, N.; Shoid, S.; Rivaie, M.; Mamat, M.
2017-09-01
Conjugate gradient (CG) method is one of iterative techniques prominently used in solving unconstrained optimization problems due to its simplicity, low memory storage, and good convergence analysis. This paper presents a new hybrid conjugate gradient method, named NRM1 method. The method is analyzed under the exact and inexact line searches in given conditions. Theoretically, proofs show that the NRM1 method satisfies the sufficient descent condition with both line searches. The computational result indicates that NRM1 method is capable in solving the standard unconstrained optimization problems used. On the other hand, the NRM1 method performs better under inexact line search compared with exact line search.
Chowdhary, J; Keyes, T
2002-02-01
Instantaneous normal modes (INM's) are calculated during a conjugate-gradient (CG) descent of the potential energy landscape, starting from an equilibrium configuration of a liquid or crystal. A small number (approximately equal to 4) of CG steps removes all the Im-omega modes in the crystal and leaves the liquid with diffusive Im-omega which accurately represent the self-diffusion constant D. Conjugate gradient filtering appears to be a promising method, applicable to any system, of obtaining diffusive modes and facilitating INM theory of D. The relation of the CG-step dependent INM quantities to the landscape and its saddles is discussed.
Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.
2017-10-01
This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution
Conjugate gradient minimisation approach to generating holographic traps for ultracold atoms.
Harte, Tiffany; Bruce, Graham D; Keeling, Jonathan; Cassettari, Donatella
2014-11-03
Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.
PRECONDITIONED BI-CONJUGATE GRADIENT METHOD FOR RADIATIVE TRANSFER IN SPHERICAL MEDIA
International Nuclear Information System (INIS)
Anusha, L. S.; Nagendra, K. N.; Paletou, F.; Leger, L.
2009-01-01
A robust numerical method called the Preconditioned Bi-Conjugate Gradient (Pre-BiCG) method is proposed for the solution of the radiative transfer equation in spherical geometry. A variant of this method called Stabilized Preconditioned Bi-Conjugate Gradient (Pre-BiCG-STAB) is also presented. These are iterative methods based on the construction of a set of bi-orthogonal vectors. The application of the Pre-BiCG method in some benchmark tests shows that the method is quite versatile, and can handle difficult problems that may arise in astrophysical radiative transfer theory.
Necessary and sufficient conditions for the existence of a conjugate gradient method
International Nuclear Information System (INIS)
Faber, V.; Manteuffel, T.
1984-01-01
The authors characterize the class CG(s) of matrices A for which the linear system Ax = b can be solved by an s-term conjugate gradient method. The authors show that, except for a few anomalies, the class CG(s) consists of matrices A for which conjugate gradient methods are already known. These matrices are the Hermitian matrices, A* = A, and the matrices of the form A = e/sup i theta/(dI + B), with B* = -B. 7 references
Directory of Open Access Journals (Sweden)
Jianfei Zhang
2013-01-01
Full Text Available Graphics processing unit (GPU has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture (CUDA. Sliced block ELLPACK (SBELL format is introduced to store sparse matrix arising from finite element discretization of elasticity with fewer padding zeros than traditional ELLPACK-based formats. Polynomial preconditioning methods have been investigated both in convergence and running time. From the overall performance, the least-squares (L-S polynomial method is chosen as a preconditioner in PCG solver to finite element equations derived from elasticity for its best results on different example meshes. In the PCG solver, mixed precision algorithm is used not only to reduce the overall computational, storage requirements and bandwidth but to make full use of the capacity of the GPU devices. With SBELL format and mixed precision algorithm, the GPU-based L-S preconditioned CG can get a speedup of about 7–9 to CPU-implementation.
Acceptable solutions obtained by unfolding noisy data with a conjugate gradient technique
International Nuclear Information System (INIS)
Lang, D.W.
1976-01-01
A linear resolution function in a physical measurement leads to data values and standard deviations at, say, N points. It is noted that the associated resolution functions may require that a number n of particular linear combinations of the data values be each not significantly different from zero. One is left with at most N-n parameters to evaluate. If the resolution functions are reasonably behaved, one can show that one sensible way to describe the underlying spectrum treats it as a linear combination of the given resolution functions and includes all the significant information from the data. An iterative search for the best component available to minimize the chi-square of the next fit to the data leads to a conjugate gradient technique. Programs based on the technique have been successfully used to obtain neutron spectra as a function of energy; in raw data from a pulse height analysis of proton recoils in a proportional counter, and where the raw data are time of flight spectra from a time dependent pulse of known form. It is planned to incorporate these, together with working programs respectively for photonuclear analysis and to explore the impurity concentration profile in a surface, into a single ''work-bench'' type program. A suitably difficult model unfolding problem has been developed and used to show the strengths and weaknesses of a number of other methods that have been used for unfolding
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method
International Nuclear Information System (INIS)
Egido, J.L.; Robledo, L.M.
1995-01-01
The conjugate gradient method is formulated in the Hilbert space for density and non-density dependent Hamiltonians. We apply it to the solution of the Hartree-Fock-Bogoliubov equations with constraints. As a numerical application we show calculations with the finite range density dependent Gogny force. The number of iterations required to reach convergence is reduced by a factor of three to four as compared with the standard gradient method. (orig.)
Two-level preconditioned conjugate gradient methods with applications to bubbly flow problems
Tang, J.M.
2008-01-01
The Preconditioned Conjugate Gradient (PCG) method is one of the most popular iterative methods for solving large linear systems with a symmetric and positive semi-definite coefficient matrix. However, if the preconditioned coefficient matrix is ill-conditioned, the convergence of the PCG method
The influence of deflation vectors at interfaces on the deflated conjugate gradient method
Vermolen, F.J.; Vuik, C.
2001-01-01
We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods. Our set-up is a Laplace problem in two dimensions with continuous or discontinuous coeffcients that vary in several orders of magnitude. In the
Solving large test-day models by iteration on data and preconditioned conjugate gradient.
Lidauer, M; Strandén, I; Mäntysaari, E A; Pösö, J; Kettunen, A
1999-12-01
A preconditioned conjugate gradient method was implemented into an iteration on a program for data estimation of breeding values, and its convergence characteristics were studied. An algorithm was used as a reference in which one fixed effect was solved by Gauss-Seidel method, and other effects were solved by a second-order Jacobi method. Implementation of the preconditioned conjugate gradient required storing four vectors (size equal to number of unknowns in the mixed model equations) in random access memory and reading the data at each round of iteration. The preconditioner comprised diagonal blocks of the coefficient matrix. Comparison of algorithms was based on solutions of mixed model equations obtained by a single-trait animal model and a single-trait, random regression test-day model. Data sets for both models used milk yield records of primiparous Finnish dairy cows. Animal model data comprised 665,629 lactation milk yields and random regression test-day model data of 6,732,765 test-day milk yields. Both models included pedigree information of 1,099,622 animals. The animal model ¿random regression test-day model¿ required 122 ¿305¿ rounds of iteration to converge with the reference algorithm, but only 88 ¿149¿ were required with the preconditioned conjugate gradient. To solve the random regression test-day model with the preconditioned conjugate gradient required 237 megabytes of random access memory and took 14% of the computation time needed by the reference algorithm.
A fast nonlinear conjugate gradient based method for 3D frictional contact problems
Zhao, J.; Vollebregt, E.A.H.; Oosterlee, C.W.
2014-01-01
This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar
An M-step preconditioned conjugate gradient method for parallel computation
Adams, L.
1983-01-01
This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.
A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems
J. Zhao (Jing); E.A.H. Vollebregt (Edwin); C.W. Oosterlee (Cornelis)
2015-01-01
htmlabstractThis paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One
Directory of Open Access Journals (Sweden)
San-Yang Liu
2014-01-01
Full Text Available Two unified frameworks of some sufficient descent conjugate gradient methods are considered. Combined with the hyperplane projection method of Solodov and Svaiter, they are extended to solve convex constrained nonlinear monotone equations. Their global convergence is proven under some mild conditions. Numerical results illustrate that these methods are efficient and can be applied to solve large-scale nonsmooth equations.
Efficient two-level preconditionined conjugate gradient method on the GPU
Gupta, R.; Van Gijzen, M.B.; Vuik, K.
2011-01-01
We present an implementation of Two-Level Preconditioned Conjugate Gradient Method for the GPU. We investigate a Truncated Neumann Series based preconditioner in combination with deflation and compare it with Block Incomplete Cholesky schemes. This combination exhibits fine-grain parallelism and
Analysis and performance estimation of the Conjugate Gradient method on multiple GPUs
Verschoor, M.; Jalba, A.C.
2012-01-01
The Conjugate Gradient (CG) method is a widely-used iterative method for solving linear systems described by a (sparse) matrix. The method requires a large amount of Sparse-Matrix Vector (SpMV) multiplications, vector reductions and other vector operations to be performed. We present a number of
A complete implementation of the conjugate gradient algorithm on a reconfigurable supercomputer
International Nuclear Information System (INIS)
Dubois, David H.; Dubois, Andrew J.; Connor, Carolyn M.; Boorman, Thomas M.; Poole, Stephen W.
2008-01-01
The conjugate gradient is a prominent iterative method for solving systems of sparse linear equations. Large-scale scientific applications often utilize a conjugate gradient solver at their computational core. In this paper we present a field programmable gate array (FPGA) based implementation of a double precision, non-preconditioned, conjugate gradient solver for fmite-element or finite-difference methods. OUf work utilizes the SRC Computers, Inc. MAPStation hardware platform along with the 'Carte' software programming environment to ease the programming workload when working with the hybrid (CPUIFPGA) environment. The implementation is designed to handle large sparse matrices of up to order N x N where N <= 116,394, with up to 7 non-zero, 64-bit elements per sparse row. This implementation utilizes an optimized sparse matrix-vector multiply operation which is critical for obtaining high performance. Direct parallel implementations of loop unrolling and loop fusion are utilized to extract performance from the various vector/matrix operations. Rather than utilize the FPGA devices as function off-load accelerators, our implementation uses the FPGAs to implement the core conjugate gradient algorithm. Measured run-time performance data is presented comparing the FPGA implementation to a software-only version showing that the FPGA can outperform processors running up to 30x the clock rate. In conclusion we take a look at the new SRC-7 system and estimate the performance of this algorithm on that architecture.
Bernal, Javier; Torres-Jimenez, Jose
2015-01-01
SAGRAD (Simulated Annealing GRADient), a Fortran 77 program for computing neural networks for classification using batch learning, is discussed. Neural network training in SAGRAD is based on a combination of simulated annealing and Møller's scaled conjugate gradient algorithm, the latter a variation of the traditional conjugate gradient method, better suited for the nonquadratic nature of neural networks. Different aspects of the implementation of the training process in SAGRAD are discussed, such as the efficient computation of gradients and multiplication of vectors by Hessian matrices that are required by Møller's algorithm; the (re)initialization of weights with simulated annealing required to (re)start Møller's algorithm the first time and each time thereafter that it shows insufficient progress in reaching a possibly local minimum; and the use of simulated annealing when Møller's algorithm, after possibly making considerable progress, becomes stuck at a local minimum or flat area of weight space. Outlines of the scaled conjugate gradient algorithm, the simulated annealing procedure and the training process used in SAGRAD are presented together with results from running SAGRAD on two examples of training data.
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
Freund, Roland
1989-01-01
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on 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.
Strong source heat transfer simulations based on a GalerKin/Gradient - least - squares method
International Nuclear Information System (INIS)
Franca, L.P.; Carmo, E.G.D. do.
1989-05-01
Heat conduction problems with temperature-dependent strong sources are modeled by an equation with a laplacian term, a linear term and a given source distribution term. When the linear-temperature-dependent source term is much larger than the laplacian term, we have a singular perturbation problem. In this case, boundary layers are formed to satisfy the Dirichlet boundary conditions. Although this is an elliptic equation, the standard Galerkin method solution is contaminated by spurious oscillations in the neighborhood of the boundary layers. Herein we employ a Galerkin/Gradient-least-squares method which eliminates all pathological phenomena of the Galerkin method. The method is constructed by adding to the Galerkin method a mesh-dependent term obtained by the least-squares form of the gradient of the Euler-Lagrange equation. Error estimates, numerical simulations in one-and multi-dimensions are given that attest the good stability and accuracy properties of the method [pt
Solving Optimal Control Problem of Monodomain Model Using Hybrid Conjugate Gradient Methods
Directory of Open Access Journals (Sweden)
Kin Wei Ng
2012-01-01
Full Text Available We present the numerical solutions for the PDE-constrained optimization problem arising in cardiac electrophysiology, that is, the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model. The monodomain model consists of a parabolic partial differential equation coupled to a system of nonlinear ordinary differential equations, which has been widely used for simulating cardiac electrical activity. Our control objective is to dampen the excitation wavefront using optimal applied extracellular current. Two hybrid conjugate gradient methods are employed for computing the optimal applied extracellular current, namely, the Hestenes-Stiefel-Dai-Yuan (HS-DY method and the Liu-Storey-Conjugate-Descent (LS-CD method. Our experiment results show that the excitation wavefronts are successfully dampened out when these methods are used. Our experiment results also show that the hybrid conjugate gradient methods are superior to the classical conjugate gradient methods when Armijo line search is used.
Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
Directory of Open Access Journals (Sweden)
Jinkui Liu
2012-01-01
Full Text Available A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition gkTdk<−∥gk∥2. Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995 in contrast to the famous CD method, FR method, and PRP method.
Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics
Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.
2003-09-01
Multiconjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wave-front control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10-2 Hz, i.e., 4-5 orders of magnitude lower than the typical 103 Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.
Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics.
Gilles, Luc; Ellerbroek, Brent L; Vogel, Curtis R
2003-09-10
Multiconjugate adaptive optics (MCAO) systems with 10(4)-10(5) degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of adaptive optics degrees of freedom. We develop scalable open-loop iterative sparse matrix implementations of minimum variance wave-front reconstruction for telescope diameters up to 32 m with more than 10(4) actuators. The basic approach is the preconditioned conjugate gradient method with an efficient preconditioner, whose block structure is defined by the atmospheric turbulent layers very much like the layer-oriented MCAO algorithms of current interest. Two cost-effective preconditioners are investigated: a multigrid solver and a simpler block symmetric Gauss-Seidel (BSGS) sweep. Both options require off-line sparse Cholesky factorizations of the diagonal blocks of the matrix system. The cost to precompute these factors scales approximately as the three-halves power of the number of estimated phase grid points per atmospheric layer, and their average update rate is typically of the order of 10(-2) Hz, i.e., 4-5 orders of magnitude lower than the typical 10(3) Hz temporal sampling rate. All other computations scale almost linearly with the total number of estimated phase grid points. We present numerical simulation results to illustrate algorithm convergence. Convergence rates of both preconditioners are similar, regardless of measurement noise level, indicating that the layer-oriented BSGS sweep is as effective as the more elaborated multiresolution preconditioner.
Tsuruta, S; Misztal, I; Strandén, I
2001-05-01
Utility of the preconditioned conjugate gradient algorithm with a diagonal preconditioner for solving mixed-model equations in animal breeding applications was evaluated with 16 test problems. The problems included single- and multiple-trait analyses, with data on beef, dairy, and swine ranging from small examples to national data sets. Multiple-trait models considered low and high genetic correlations. Convergence was based on relative differences between left- and right-hand sides. The ordering of equations was fixed effects followed by random effects, with no special ordering within random effects. The preconditioned conjugate gradient program implemented with double precision converged for all models. However, when implemented in single precision, the preconditioned conjugate gradient algorithm did not converge for seven large models. The preconditioned conjugate gradient and successive overrelaxation algorithms were subsequently compared for 13 of the test problems. The preconditioned conjugate gradient algorithm was easy to implement with the iteration on data for general models. However, successive overrelaxation requires specific programming for each set of models. On average, the preconditioned conjugate gradient algorithm converged in three times fewer rounds of iteration than successive overrelaxation. With straightforward implementations, programs using the preconditioned conjugate gradient algorithm may be two or more times faster than those using successive overrelaxation. However, programs using the preconditioned conjugate gradient algorithm would use more memory than would comparable implementations using successive overrelaxation. Extensive optimization of either algorithm can influence rankings. The preconditioned conjugate gradient implemented with iteration on data, a diagonal preconditioner, and in double precision may be the algorithm of choice for solving mixed-model equations when sufficient memory is available and ease of implementation is
Ghosh, A
1988-08-01
Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.
Feng, Shuo; Ji, Jim
2014-04-01
Parallel excitation (pTx) techniques with multiple transmit channels have been widely used in high field MRI imaging to shorten the RF pulse duration and/or reduce the specific absorption rate (SAR). However, the efficiency of pulse design still needs substantial improvement for practical real-time applications. In this paper, we present a detailed description of a fast pulse design method with Fourier domain gridding and a conjugate gradient method. Simulation results of the proposed method show that the proposed method can design pTx pulses at an efficiency 10 times higher than that of the conventional conjugate-gradient based method, without reducing the accuracy of the desirable excitation patterns.
Conjugate gradient based projection - A new explicit methodology for frictional contact
Tamma, Kumar K.; Li, Maocheng; Sha, Desong
1993-01-01
With special attention towards the applicability to parallel computation or vectorization, a new and effective explicit approach for linear complementary formulations involving a conjugate gradient based projection methodology is proposed in this study for contact problems with Coulomb friction. The overall objectives are focussed towards providing an explicit methodology of computation for the complete contact problem with friction. In this regard, the primary idea for solving the linear complementary formulations stems from an established search direction which is projected to a feasible region determined by the non-negative constraint condition; this direction is then applied to the Fletcher-Reeves conjugate gradient method resulting in a powerful explicit methodology which possesses high accuracy, excellent convergence characteristics, fast computational speed and is relatively simple to implement for contact problems involving Coulomb friction.
HIRFL-SSC trim coil currents calculation by conjugate gradients method
International Nuclear Information System (INIS)
Liu, W.
2005-01-01
For accelerating different kinds of ions to various energies, the HIRFL-SSC should form the corresponding isochronous magnetic field by its main coil and trim coils. Previously, there were errors in fitting the theoretical isochronous magnetic field in the small radius region, which led to some operation difficulties for ion acceleration in the inject region. After further investigation of the restrictive condition of the maximum current limitation, the trim coil currents for fitting the theoretical isochronous magnetic field were recalculated by the conjugate gradients method. Better results were obtained in the operation of HIRFL-SSC. This article introduces the procedure to calculate the trim coil currents. The calculation method of conjugate gradients is introduced and the fitting error is analysed. (author)
Directory of Open Access Journals (Sweden)
Zhongbo Sun
2014-01-01
Full Text Available Two modified three-term type conjugate gradient algorithms which satisfy both the descent condition and the Dai-Liao type conjugacy condition are presented for unconstrained optimization. The first algorithm is a modification of the Hager and Zhang type algorithm in such a way that the search direction is descent and satisfies Dai-Liao’s type conjugacy condition. The second simple three-term type conjugate gradient method can generate sufficient decent directions at every iteration; moreover, this property is independent of the steplength line search. Also, the algorithms could be considered as a modification of the MBFGS method, but with different zk. Under some mild conditions, the given methods are global convergence, which is independent of the Wolfe line search for general functions. The numerical experiments show that the proposed methods are very robust and efficient.
New generalized conjugate gradient methods for the non-quadratic model in unconstrained optimization
International Nuclear Information System (INIS)
Al-Bayati, A.
2001-01-01
This paper present two new conjugate gradient algorithms which use the non-quadratic model in unconstrained optimization. The first is a new generalized self-scaling variable metric algorithm based on the sloboda generalized conjugate gradient method which is invariant to a nonlinear scaling of a stricity convex quadratic function; the second is an interleaving between the generalized sloboda method and the first algorithm; all these algorithm use exact line searches. Numerical comparisons over twenty test functions show that the interleaving algorithm is best overall and requires only about half the function evaluations of the Sloboda method: interleaving algorithms are likely to be preferred when the dimensionality of the problem is increased. (author). 29 refs., 1 tab
A nonsmooth nonlinear conjugate gradient method for interactive contact force problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....
Conjugate gradient method for phase retrieval based on the Wirtinger derivative.
Wei, Zhun; Chen, Wen; Qiu, Cheng-Wei; Chen, Xudong
2017-05-01
A conjugate gradient Wirtinger flow (CG-WF) algorithm for phase retrieval is proposed in this paper. It is shown that, compared with recently reported Wirtinger flow and its modified methods, the proposed CG-WF algorithm is able to dramatically accelerate the convergence rate while keeping the dominant computational cost of each iteration unchanged. We numerically illustrate the effectiveness of our method in recovering 1D Gaussian signals and 2D natural color images under both Gaussian and coded diffraction pattern models.
Bhaya, Amit; Kaszkurewicz, Eugenius
2004-01-01
It is pointed out that the so called momentum method, much used in the neural network literature as an acceleration of the backpropagation method, is a stationary version of the conjugate gradient method. Connections with the continuous optimization method known as heavy ball with friction are also made. In both cases, adaptive (dynamic) choices of the so called learning rate and momentum parameters are obtained using a control Liapunov function analysis of the system.
A family of conjugate gradient methods for large-scale nonlinear equations
Directory of Open Access Journals (Sweden)
Dexiang Feng
2017-09-01
Full Text Available Abstract In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.
Mariano-Goulart, D; Fourcade, M; Bernon, J L; Rossi, M; Zanca, M
2003-01-01
Thanks to an experimental study based on simulated and physical phantoms, the propagation of the stochastic noise in slices reconstructed using the conjugate gradient algorithm has been analysed versus iterations. After a first increase corresponding to the reconstruction of the signal, the noise stabilises before increasing linearly with iterations. The level of the plateau as well as the slope of the subsequent linear increase depends on the noise in the projection data.
The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.
Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie
2016-01-01
In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).
The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.
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Gonglin Yuan
Full Text Available In this paper, the Hager and Zhang (HZ conjugate gradient (CG method and the modified HZ (MHZ CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables.
A family of conjugate gradient methods for large-scale nonlinear equations.
Feng, Dexiang; Sun, Min; Wang, Xueyong
2017-01-01
In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.
Frequency-domain beamformers using conjugate gradient techniques for speech enhancement.
Zhao, Shengkui; Jones, Douglas L; Khoo, Suiyang; Man, Zhihong
2014-09-01
A multiple-iteration constrained conjugate gradient (MICCG) algorithm and a single-iteration constrained conjugate gradient (SICCG) algorithm are proposed to realize the widely used frequency-domain minimum-variance-distortionless-response (MVDR) beamformers and the resulting algorithms are applied to speech enhancement. The algorithms are derived based on the Lagrange method and the conjugate gradient techniques. The implementations of the algorithms avoid any form of explicit or implicit autocorrelation matrix inversion. Theoretical analysis establishes formal convergence of the algorithms. Specifically, the MICCG algorithm is developed based on a block adaptation approach and it generates a finite sequence of estimates that converge to the MVDR solution. For limited data records, the estimates of the MICCG algorithm are better than the conventional estimators and equivalent to the auxiliary vector algorithms. The SICCG algorithm is developed based on a continuous adaptation approach with a sample-by-sample updating procedure and the estimates asymptotically converge to the MVDR solution. An illustrative example using synthetic data from a uniform linear array is studied and an evaluation on real data recorded by an acoustic vector sensor array is demonstrated. Performance of the MICCG algorithm and the SICCG algorithm are compared with the state-of-the-art approaches.
Use of a preconditioned Bi-conjugate gradient method for hybrid plasma stability analysis
International Nuclear Information System (INIS)
Mikic, Z.; Morse, E.C.
1985-01-01
The numerical stability analysis of compact toroidal plasmas using implicit time differencing requires the solution of a set of coupled, 2-dimensional, elliptic partial differential equations for the field quantities at every timestep. When the equations are spatially finite-differenced and written in matrix form, the resulting matrix is large, sparse, complex, non-Hermitian, and indefinite. The use of the preconditioned bi-conjugate gradient method for solving these equations is discussed. The effect of block-diagonal preconditioning and incomplete block-LU preconditionig on the convergence of the method is investigated. For typical matrices arising in our studies, the eigenvalue spectra of the original and preconditioned matrices are calculated as an illustration of the effectiveness of the preconditioning. We show that the preconditioned bi-conjugate gradient method coverages more rapidly than the conjugate gradient method applied to the normal equations, and that it is an effective iterative method for the class of non-Hermitian, indefinite problems of interest
Problem of unstable pivots in the incomplete LU-conjugate gradient method
International Nuclear Information System (INIS)
Kershaw, D.S.
1978-01-01
Incomplete LU and incomplete-Cholesky conjugate gradient methods are becoming widely used in both laser and magnetic fusion research. In my original presentation of these methods, the problem of what to do if a pivot [L/sub ii/U/sub ii/) becomes very small or zero was raised and only partially answered by the suggestion that it be arbitrarily set to some non-zero value. In what follows it will be shown precisely how small the pivot can become before it must be fixed and precisely what value it should be set to in order to minimize the error in LU. Numerical examples will be given to show that not only does this prescription improve incomplete LU-conjugate gradient methods , but exact LU decomposition carried out with this prescription for handling small pivots and followed by a few linear or conjugate gradient iterations can be much faster than the permutations of rows and columns usually employed to circumvent small pivot problems
A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation
Rieser, Daniel; Mayer-Guerr, Torsten
2014-05-01
The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.
And still, a new beginning: the Galerkin least-squares gradient method
International Nuclear Information System (INIS)
Franca, L.P.; Carmo, E.G.D. do
1988-08-01
A finite element method is proposed to solve a scalar singular diffusion problem. The method is constructed by adding to the standard Galerkin a mesh-dependent term obtained by taking the gradient of the Euler-lagrange equation and multiplying it by its least-squares. For the one-dimensional homogeneous problem the method is designed to develop nodal exact solution. An error estimate shows that the method converges optimaly for any value of the singular parameter. Numerical results demonstrate the good stability and accuracy properties of the method. (author) [pt
Du, Shouqiang; Chen, Miao
2018-01-01
We consider a kind of nonsmooth optimization problems with [Formula: see text]-norm minimization, which has many applications in compressed sensing, signal reconstruction, and the related engineering problems. Using smoothing approximate techniques, this kind of nonsmooth optimization problem can be transformed into a general unconstrained optimization problem, which can be solved by the proposed smoothing modified three-term conjugate gradient method. The smoothing modified three-term conjugate gradient method is based on Polak-Ribière-Polyak conjugate gradient method. For the Polak-Ribière-Polyak conjugate gradient method has good numerical properties, the proposed method possesses the sufficient descent property without any line searches, and it is also proved to be globally convergent. Finally, the numerical experiments show the efficiency of the proposed method.
Directory of Open Access Journals (Sweden)
Zhifeng Dai
2014-01-01
Full Text Available Combining the Rosen gradient projection method with the two-term Polak-Ribière-Polyak (PRP conjugate gradient method, we propose a two-term Polak-Ribière-Polyak (PRP conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses some attractive properties: (1 search direction generated by the proposed method is a feasible descent direction; consequently the generated iterates are feasible points; (2 the sequences of function are decreasing. Under some mild conditions, we show that it is globally convergent with Armijio-type line search. Preliminary numerical results show that the proposed method is promising.
Penalty Algorithm Based on Conjugate Gradient Method for Solving Portfolio Management Problem
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Wang YaLin
2009-01-01
Full Text Available A new approach was proposed to reformulate the biobjectives optimization model of portfolio management into an unconstrained minimization problem, where the objective function is a piecewise quadratic polynomial. We presented some properties of such an objective function. Then, a class of penalty algorithms based on the well-known conjugate gradient methods was developed to find the solution of portfolio management problem. By implementing the proposed algorithm to solve the real problems from the stock market in China, it was shown that this algorithm is promising.
A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics
DEFF Research Database (Denmark)
Engell-Nørregård, Morten; Erleben, Kenny
2009-01-01
Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...
International Nuclear Information System (INIS)
Burkitt, A.N.; Irving, A.C.
1988-01-01
Two of the methods that are widely used in lattice gauge theory calculations requiring inversion of the fermion matrix are the Lanczos and the conjugate gradient algorithms. Those algorithms are already known to be closely related. In fact for matrix inversion, in exact arithmetic, they give identical results at each iteration and are just alternative formulations of a single algorithm. This equivalence survives rounding errors. We give the identities between the coefficients of the two formulations, enabling many of the best features of them to be combined. (orig.)
Inversion of the fermion matrix and the equivalence of the conjugate gradient and Lanczos algorithms
International Nuclear Information System (INIS)
Burkitt, A.N.; Irving, A.C.
1990-01-01
The Lanczos and conjugate gradient algorithms are widely used in lattice QCD calculations. The previously known close relationship between the two methods is explored and two commonly used implementations are shown to give identically the same results at each iteration, in exact arithmetic, for matrix inversion. The identities between the coefficients of the two algorithms are given, and many of the features of the two algorithms can now be combined. The effects of finite arithmetic are investigated and the particular Lanczos formulation is found to be most stable with respect to rounding errors. (orig.)
New hybrid conjugate gradient methods with the generalized Wolfe line search.
Xu, Xiao; Kong, Fan-Yu
2016-01-01
The conjugate gradient method was an efficient technique for solving the unconstrained optimization problem. In this paper, we made a linear combination with parameters β k of the DY method and the HS method, and putted forward the hybrid method of DY and HS. We also proposed the hybrid of FR and PRP by the same mean. Additionally, to present the two hybrid methods, we promoted the Wolfe line search respectively to compute the step size α k of the two hybrid methods. With the new Wolfe line search, the two hybrid methods had descent property and global convergence property of the two hybrid methods that can also be proved.
A fast pulse design for parallel excitation with gridding conjugate gradient.
Feng, Shuo; Ji, Jim
2013-01-01
Parallel excitation (pTx) is recognized as a crucial technique in high field MRI to address the transmit field inhomogeneity problem. However, it can be time consuming to design pTx pulses which is not desirable. In this work, we propose a pulse design with gridding conjugate gradient (CG) based on the small-tip-angle approximation. The two major time consuming matrix-vector multiplications are substituted by two operators which involves with FFT and gridding only. Simulation results have shown that the proposed method is 3 times faster than conventional method and the memory cost is reduced by 1000 times.
Czech Academy of Sciences Publication Activity Database
Strakoš, Zdeněk; Tichý, Petr
2002-01-01
Roč. 13, - (2002), s. 56-80 ISSN 1068-9613 R&D Projects: GA ČR GA201/02/0595 Institutional research plan: AV0Z1030915 Keywords : conjugate gradient method * Gauss kvadrature * evaluation of convergence * error bounds * finite precision arithmetic * rounding errors * loss of orthogonality Subject RIV: BA - General Mathematics Impact factor: 0.565, year: 2002 http://etna.mcs.kent.edu/volumes/2001-2010/vol13/abstract.php?vol=13&pages=56-80
Cao, Xu; Zhang, Bin; Liu, Fei; Wang, Xin; Bai, Jing
2011-12-01
Limited-projection fluorescence molecular tomography (FMT) can greatly reduce the acquisition time, which is suitable for resolving fast biology processes in vivo but suffers from severe ill-posedness because of the reconstruction using only limited projections. To overcome the severe ill-posedness, we report a reconstruction method based on the projected restarted conjugate gradient normal residual. The reconstruction results of two phantom experiments demonstrate that the proposed method is feasible for limited-projection FMT. © 2011 Optical Society of America
A conjugate gradient method with descent properties under strong Wolfe line search
Zull, N.; ‘Aini, N.; Shoid, S.; Ghani, N. H. A.; Mohamed, N. S.; Rivaie, M.; Mamat, M.
2017-09-01
The conjugate gradient (CG) method is one of the optimization methods that are often used in practical applications. The continuous and numerous studies conducted on the CG method have led to vast improvements in its convergence properties and efficiency. In this paper, a new CG method possessing the sufficient descent and global convergence properties is proposed. The efficiency of the new CG algorithm relative to the existing CG methods is evaluated by testing them all on a set of test functions using MATLAB. The tests are measured in terms of iteration numbers and CPU time under strong Wolfe line search. Overall, this new method performs efficiently and comparable to the other famous methods.
Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction.
Gilles, Luc; Vogel, Curtis R; Ellerbroek, Brent L
2002-09-01
We introduce a multigrid preconditioned conjugate-gradient (MGCG) iterative scheme for computing open-loop wave-front reconstructors for extreme adaptive optics systems. We present numerical simulations for a 17-m class telescope with n = 48756 sensor measurement grid points within the aperture, which indicate that our MGCG method has a rapid convergence rate for a wide range of subaperture average slope measurement signal-to-noise ratios. The total computational cost is of order n log n. Hence our scheme provides for fast wave-front simulation and control in large-scale adaptive optics systems.
Frequency domain optical tomography using a conjugate gradient method without line search
International Nuclear Information System (INIS)
Kim, Hyun Keol; Charette, Andre
2007-01-01
A conjugate gradient method without line search (CGMWLS) is presented. This method is used to retrieve the local maps of absorption and scattering coefficients inside the tissue-like test medium, with the synthetic data. The forward problem is solved with a discrete-ordinates finite-difference method based on the frequency domain formulation of radiative transfer equation. The inversion results demonstrate that the CGMWLS can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by reducing cross-talk between absorption and scattering coefficients
Microwave imaging of dielectric cylinder using level set method and conjugate gradient algorithm
International Nuclear Information System (INIS)
Grayaa, K.; Bouzidi, A.; Aguili, T.
2011-01-01
In this paper, we propose a computational method for microwave imaging cylinder and dielectric object, based on combining level set technique and the conjugate gradient algorithm. By measuring the scattered field, we tried to retrieve the shape, localisation and the permittivity of the object. The forward problem is solved by the moment method, while the inverse problem is reformulate in an optimization one and is solved by the proposed scheme. It found that the proposed method is able to give good reconstruction quality in terms of the reconstructed shape and permittivity.
International Nuclear Information System (INIS)
Andrei, Petru; Oniciuc, Liviu; Stancu, Alexandru; Stoleriu, Laurentiu
2007-01-01
An identification technique for the parameters of phenomenological models of hysteresis is presented. The basic idea of our technique is to set up a system of equations for the parameters of the model as a function of known quantities on the major or minor hysteresis loops (e.g. coercive force, susceptibilities at various points, remanence), or other magnetization curves. This system of equations can be either over or underspecified and is solved by using the conjugate gradient method. Numerical results related to the identification of parameters in the Energetic, Jiles-Atherton, and Preisach models are presented
International Nuclear Information System (INIS)
Kari, R.E.; Mezey, P.G.; Csizmadia, I.G.
1975-01-01
Expressions are given for calculating the energy gradient vector in the exponent space of Gaussian basis sets and a technique to optimize orbital exponents using the method of conjugate gradients is described. The method is tested on the (9/sups/5/supp/) Gaussian basis space and optimum exponents are determined for the carbon atom. The analysis of the results shows that the calculated one-electron properties converge more slowly to their optimum values than the total energy converges to its optimum value. In addition, basis sets approximating the optimum total energy very well can still be markedly improved for the prediction of one-electron properties. For smaller basis sets, this improvement does not warrant the necessary expense
International Nuclear Information System (INIS)
Reifman, J.; Vitela, J.E.
1994-01-01
The method of conjugate gradients is used to expedite the learning process of feedforward multilayer artificial neural networks and to systematically update both the learning parameter and the momentum parameter at each training cycle. The mechanism for the occurrence of premature saturation of the network nodes observed with the back propagation algorithm is described, suggestions are made to eliminate this undesirable phenomenon, and the reason by which this phenomenon is precluded in the method of conjugate gradients is presented. The proposed method is compared with the standard back propagation algorithm in the training of neural networks to classify transient events in neural power plants simulated by the Midland Nuclear Power Plant Unit 2 simulator. The comparison results indicate that the rate of convergence of the proposed method is much greater than the standard back propagation, that it reduces both the number of training cycles and the CPU time, and that it is less sensitive to the choice of initial weights. The advantages of the method are more noticeable and important for problems where the network architecture consists of a large number of nodes, the training database is large, and a tight convergence criterion is desired
Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method
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Huan Ma
2015-01-01
Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.
Wanto, Anjar; Zarlis, Muhammad; Sawaluddin; Hartama, Dedy
2017-12-01
Backpropagation is a good artificial neural network algorithm used to predict, one of which is to predict the rate of Consumer Price Index (CPI) based on the foodstuff sector. While conjugate gradient fletcher reeves is a suitable optimization method when juxtaposed with backpropagation method, because this method can shorten iteration without reducing the quality of training and testing result. Consumer Price Index (CPI) data that will be predicted to come from the Central Statistics Agency (BPS) Pematangsiantar. The results of this study will be expected to contribute to the government in making policies to improve economic growth. In this study, the data obtained will be processed by conducting training and testing with artificial neural network backpropagation by using parameter learning rate 0,01 and target error minimum that is 0.001-0,09. The training network is built with binary and bipolar sigmoid activation functions. After the results with backpropagation are obtained, it will then be optimized using the conjugate gradient fletcher reeves method by conducting the same training and testing based on 5 predefined network architectures. The result, the method used can increase the speed and accuracy result.
Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique
International Nuclear Information System (INIS)
Formiconi, A.R.; Pupi, A.; Passeri, A.
1989-01-01
A procedure for determination of the system matrix in single photon emission tomography (SPECT) is described which use a conjugate gradient reconstruction technique to take into account the variable system resolution of a camera equipped with parallel-hole collimators. The procedure involves acquisition of system line spread functions (LSF) in the region occupied by the object studied. Those data are used to generate a set of weighting factors based on the assumption that the LSFs of the collimated camera are of Gaussian shape with full width at half maximum (FWHM) linearly dependent on source depth in the span of image space. Factors are stored on a disc file for subsequent use in reconstruction. Afterwards reconstruction is performed using the conjugate gradient method with the system matrix modified by incorporation of these precalculated factors to take into account variable geometrical system response. The set of weighting factors is regenerated whenever acquisition conditions are changed (collimator, radius of rotation) with an ultra high resolution (UHR) collimator 2000 weighting factors need to be calculated. (author)
A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging.
van Dongen, Koen W A; Wright, William M D
2006-10-01
Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.
Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Ph.D. Thesis
Poole, E. L.
1986-01-01
In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.
Method of T2 spectrum inversion with conjugate gradient algorithm from NMR data
International Nuclear Information System (INIS)
Li Pengju; Shi Shangming; Song Yanjie
2010-01-01
Based on the optimization techniques, the T 2 spectrum inversion method of conjugate gradient that is easy to realize non-negativity constraint of T2 spectrum is proposed. The method transforms the linear mixed-determined problem of T2 spectrum inversion into the typical optimization problem of searching the minimum of objective function by building up the objective function according to the basic idea of geophysics modeling. The optimization problem above is solved with the conjugate gradient algorithm that has quick convergence rate and quadratic termination. The method has been applied to the inversion of noise free echo train generated from artificial spectrum, artificial echo train with signal-to-noise ratio (SNR)=25 and NMR experimental data of drilling core. The comparison between the inversion results of this paper and artificial spectrum or the result of software imported in NMR laboratory shows that the method can correctly invert T 2 spectrum from artificial NMR relaxation data even though SNR=25 and that inversion T 2 spectrum with good continuity and smoothness from core NMR experimental data accords perfectly with that of laboratory software imported, and moreover,the absolute error between the NMR porosity computed from T 2 spectrum and helium (He) porosity in laboratory is 0.65%. (authors)
Energy Technology Data Exchange (ETDEWEB)
Han, Liang; Wang, Meijing; Jia, Xiangmeng; Chen, Wei; Qian, Hujun; He, Feng
2018-02-28
Two-dimensional (2-D) micro- and nano- architectures are attractive because of their unique properties caused by their ultrathin and flat morphologies. However, the formation of 2-D supramolecular highly symmetrical structures with considerable control is still a major challenge. Here, we presented a simple approach for the preparation of regular and homogeneous 2-D fluorescent square noncrystallization micelles with conjugated diblock copolymers PPV12-b-P2VPn through a process of dissolving-cooling-aging. The scale of the formed micelles could be controlled by the ratio of PPV/P2VP blocks and the concentration of the solution. The forming process of the platelet square micelles was analyzed by UV-Vis, DLS and SLS, while the molecular arrangement was characterized by GIXD. The results revealed that the micelles of PPV12-b-P2VPn initially form 1-D structures and then grow into 2-D structures in solution, and the growth is driven by intermolecular π-π interactions with the PPV12 blocks. The formation of 2-D square micelles is induced by herringbone arrangement of the molecules, which is closely related to the presence of the branched alkyl chains attached to conjugated PPV12 cores.
Benediktsson, J. A.; Swain, P. H.; Ersoy, O. K.
1993-01-01
Application of neural networks to classification of remote sensing data is discussed. Conventional two-layer backpropagation is found to give good results in classification of remote sensing data but is not efficient in training. A more efficient variant, based on conjugate-gradient optimization, is used for classification of multisource remote sensing and geographic data and very-high-dimensional data. The conjugate-gradient neural networks give excellent performance in classification of multisource data, but do not compare as well with statistical methods in classification of very-high-dimentional data.
Directory of Open Access Journals (Sweden)
ChunPing Ren
2017-01-01
Full Text Available We propose a novel mathematical algorithm to offer a solution for the inverse random dynamic force identification in practical engineering. Dealing with the random dynamic force identification problem using the proposed algorithm, an improved maximum entropy (IME regularization technique is transformed into an unconstrained optimization problem, and a novel conjugate gradient (NCG method was applied to solve the objective function, which was abbreviated as IME-NCG algorithm. The result of IME-NCG algorithm is compared with that of ME, ME-CG, ME-NCG, and IME-CG algorithm; it is found that IME-NCG algorithm is available for identifying the random dynamic force due to smaller root mean-square-error (RMSE, lower restoration time, and fewer iterative steps. Example of engineering application shows that L-curve method is introduced which is better than Generalized Cross Validation (GCV method and is applied to select regularization parameter; thus the proposed algorithm can be helpful to alleviate the ill-conditioned problem in identification of dynamic force and to acquire an optimal solution of inverse problem in practical engineering.
International Nuclear Information System (INIS)
Rukolaine, Sergey A.
2010-01-01
Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a 'two-dimensional' polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a 'two-dimensional' radiant enclosure.
A conjugate gradient method for solving the non-LTE line radiation transfer problem
Paletou, F.; Anterrieu, E.
2009-12-01
This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and successive over-relaxation (GS/SOR) schemes. Our study is indeed based on applying a preconditioned bi-conjugate gradient method (BiCG-P). Standard tests, in 1D plane parallel geometry and in the frame of the two-level atom model with monochromatic scattering are discussed. Rates of convergence between the previously mentioned iterative schemes are compared, as are their respective timing properties. The smoothing capability of the BiCG-P method is also demonstrated.
A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search
Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd
2017-08-01
A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.
Oliker, Leonid; Heber, Gerd; Biswas, Rupak
2000-01-01
The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. A sparse matrix-vector multiply (SPMV) usually accounts for most of the floating-point operations within a CG iteration. In this paper, we investigate the effects of various ordering and partitioning strategies on the performance of parallel CG and SPMV using different programming paradigms and architectures. Results show that for this class of applications, ordering significantly improves overall performance, that cache reuse may be more important than reducing communication, and that it is possible to achieve message passing performance using shared memory constructs through careful data ordering and distribution. However, a multi-threaded implementation of CG on the Tera MTA does not require special ordering or partitioning to obtain high efficiency and scalability.
International Nuclear Information System (INIS)
Vecharynski, Eugene; Yang, Chao; Pask, John E.
2015-01-01
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer
Shi, Junwei; Zhang, Bin; Liu, Fei; Luo, Jianwen; Bai, Jing
2013-09-15
For the ill-posed fluorescent molecular tomography (FMT) inverse problem, the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise. However, the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory, especially for large-scale problems. An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption. The reconstruction results from phantom experiments demonstrate that the proposed algorithm can obtain high spatial resolution and high signal-to-noise ratio, as well as high localization accuracy for fluorescence targets.
Conjugate-gradient optimization method for orbital-free density functional calculations.
Jiang, Hong; Yang, Weitao
2004-08-01
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. (c) 2004 American Institute of Physics.
He, Xiaowei; Liang, Jimin; Wang, Xiaorui; Yu, Jingjing; Qu, Xiaochao; Wang, Xiaodong; Hou, Yanbin; Chen, Duofang; Liu, Fang; Tian, Jie
2010-11-22
In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.
An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search
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Ahmad Alhawarat
2015-01-01
Full Text Available Conjugate gradient (CG method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.
Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
An efficient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the nonorthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel.
International Nuclear Information System (INIS)
Huang, C.-H.; Wu, H.-H.
2006-01-01
In the present study an inverse hyperbolic heat conduction problem is solved by the conjugate gradient method (CGM) in estimating the unknown boundary heat flux based on the boundary temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where three different heat flux distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the boundary heat flux. Moreover, the drawbacks of the previous study for this similar inverse problem, such as (1) the inverse solution has phase error and (2) the inverse solution is sensitive to measurement error, can be avoided in the present algorithm. Finally, it is concluded that accurate boundary heat flux can be estimated in this study
On computing quadrature-based bounds for the A-norm of the error in conjugate gradients
Czech Academy of Sciences Publication Activity Database
Meurant, G.; Tichý, Petr
2013-01-01
Roč. 62, č. 2 (2013), s. 163-191 ISSN 1017-1398 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : conjugate gradients * norm of the error * bounds for the error norm Subject RIV: BA - General Mathematics Impact factor: 1.005, year: 2013
Directory of Open Access Journals (Sweden)
Qiuyu Wang
2014-01-01
descent method at first finite number of steps and then by conjugate gradient method subsequently. Under some appropriate conditions, we show that the algorithm converges globally. Numerical experiments and comparisons by using some box-constrained problems from CUTEr library are reported. Numerical comparisons illustrate that the proposed method is promising and competitive with the well-known method—L-BFGS-B.
On computing quadrature-based bounds for the A-norm of the error in conjugate gradients
Czech Academy of Sciences Publication Activity Database
Meurant, G.; Tichý, Petr
2013-01-01
Roč. 62, č. 2 (2013), s. 163-191 ISSN 1017-1398 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : conjugate gradient s * norm of the error * bounds for the error norm Subject RIV: BA - General Mathematics Impact factor: 1.005, year: 2013
Madyastha, Raghavendra K.; Aazhang, Behnaam; Henson, Troy F.; Huxhold, Wendy L.
1992-01-01
This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.
The application of projected conjugate gradient solvers on graphical processing units
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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.
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.
Use of the preconditioned conjugate gradient method to accelerate S/sub n/ iterations
International Nuclear Information System (INIS)
Derstine, K.L.; Gelbard, E.M.
1985-01-01
It is well known that specially tailored diffusion difference equations are required in the synthetic method. The tailoring process is not trivial, and for some S/sub n/ schemes (e.g., in hexagonal geometry) tailored diffusion operators are not available. The need for alternative acceleration methods has been noted by Larsen who has, in fact, proposed two alternatives. The proposed methods, however, do not converge to the S/sub n/ solution, and their accuracy is still largely unknown. Los Alamos acceleration methods are required to converge for any mesh, no matter how coarse. Since negative flux-fix ups (normally involved when mesh widths are large) may impede convergence, it is not clear that such a strict condition is really practical. Here a lesser objective is chosen. The authors wish to develop an acceleration method useful for a wide (though finite) range of mesh widths, but to avoid the use of special diffusion difference equations. It is shown that the conjugate gradient (CG) method, with the standard box-centered (BC) diffusion equation as a preconditioner, yields an algorithm that, for fixed-source problems with isotropic scattering, is mechanically very similar to the synthetic method; but, in two-dimensional test problems in various geometries, the CG method is substantially more stable
Generalized conjugate-gradient methods for the Navier-Stokes equations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1991-01-01
A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.
Tripathi, Ashish; McNulty, Ian; Shpyrko, Oleg G
2014-01-27
Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.
A modified three-term PRP conjugate gradient algorithm for optimization models.
Wu, Yanlin
2017-01-01
The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.
A new modified conjugate gradient coefficient for solving system of linear equations
Hajar, N.; ‘Aini, N.; Shapiee, N.; Abidin, Z. Z.; Khadijah, W.; Rivaie, M.; Mamat, M.
2017-09-01
Conjugate gradient (CG) method is an evolution of computational method in solving unconstrained optimization problems. This approach is easy to implement due to its simplicity and has been proven to be effective in solving real-life application. Although this field has received copious amount of attentions in recent years, some of the new approaches of CG algorithm cannot surpass the efficiency of the previous versions. Therefore, in this paper, a new CG coefficient which retains the sufficient descent and global convergence properties of the original CG methods is proposed. This new CG is tested on a set of test functions under exact line search. Its performance is then compared to that of some of the well-known previous CG methods based on number of iterations and CPU time. The results show that the new CG algorithm has the best efficiency amongst all the methods tested. This paper also includes an application of the new CG algorithm for solving large system of linear equations
International Nuclear Information System (INIS)
King, J.B.; Anghaie, S.; Domanus, H.M.
1987-01-01
Finite difference approximations to the continuity, momentum, and energy equations in thermal hydraulics codes result in a system of N by N equations for a problem having N field points. In a three dimensional problem, N increases as the problem becomes larger or more complex, and more rapidly as the computational mesh size is reduced. As a consequence, the execution time required to solve the problem increases, which may lead to placing limits on the problem resolution or accuracy. A conventinal method of solution of these systems of equations is the Successive Over Relaxation (SOR) technique. However, for a wide range of problems the execution time may be reduced by using a more efficient linear equation solver. One such method is the conjugate gradient method which was implemented in COMMIX-1B thermal hydraulics code. It was found that the execution time required to solve the resulting system of equations was reduced by a factor of about 2 for some problems. This paper summarizes the characteristics of these iterative solution procedures and compares their performance in modeling of a variety of reactor thermal hydraulic problems, using the COMMIX-1B computer code
International Nuclear Information System (INIS)
Perez, L; Autrique, L; Gillet, M
2008-01-01
The aim of this paper is to investigate the thermal diffusivity identification of a multilayered material dedicated to fire protection. In a military framework, fire protection needs to meet specific requirements, and operational protective systems must be constantly improved in order to keep up with the development of new weapons. In the specific domain of passive fire protections, intumescent coatings can be an effective solution on the battlefield. Intumescent materials have the ability to swell up when they are heated, building a thick multi-layered coating which provides efficient thermal insulation to the underlying material. Due to the heat aggressions (fire or explosion) leading to the intumescent phenomena, high temperatures are considered and prevent from linearization of the mathematical model describing the system state evolution. Previous sensitivity analysis has shown that the thermal diffusivity of the multilayered intumescent coating is a key parameter in order to validate the predictive numerical tool and therefore for thermal protection optimisation. A conjugate gradient method is implemented in order to minimise the quadratic cost function related to the error between predicted temperature and measured temperature. This regularisation algorithm is well adapted for a large number of unknown parameters.
Shi, Junwei; Liu, Fei; Zhang, Guanglei; Luo, Jianwen; Bai, Jing
2014-04-01
Owing to the high degree of scattering of light through tissues, the ill-posedness of fluorescence molecular tomography (FMT) inverse problem causes relatively low spatial resolution in the reconstruction results. Unlike L2 regularization, L1 regularization can preserve the details and reduce the noise effectively. Reconstruction is obtained through a restarted L1 regularization-based nonlinear conjugate gradient (re-L1-NCG) algorithm, which has been proven to be able to increase the computational speed with low memory consumption. The algorithm consists of inner and outer iterations. In the inner iteration, L1-NCG is used to obtain the L1-regularized results. In the outer iteration, the restarted strategy is used to increase the convergence speed of L1-NCG. To demonstrate the performance of re-L1-NCG in terms of spatial resolution, simulation and physical phantom studies with fluorescent targets located with different edge-to-edge distances were carried out. The reconstruction results show that the re-L1-NCG algorithm has the ability to resolve targets with an edge-to-edge distance of 0.1 cm at a depth of 1.5 cm, which is a significant improvement for FMT.
Adjustment technique without explicit formation of normal equations /conjugate gradient method/
Saxena, N. K.
1974-01-01
For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).
A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT).
Wang, Qi; Wang, Huaxiang
2011-04-01
During the past few decades, computerized tomography (CT) was widely used for non-destructive testing (NDT) and non-destructive examination (NDE) in the industrial area because of its characteristics of non-invasiveness and visibility. Recently, CT technology has been applied to multi-phase flow measurement. Using the principle of radiation attenuation measurements along different directions through the investigated object with a special reconstruction algorithm, cross-sectional information of the scanned object can be worked out. It is a typical inverse problem and has always been a challenge for its nonlinearity and ill-conditions. The Tikhonov regulation method is widely used for similar ill-posed problems. However, the conventional Tikhonov method does not provide reconstructions with qualities good enough, the relative errors between the reconstructed images and the real distribution should be further reduced. In this paper, a modified conjugate gradient (CG) method is applied to a Tikhonov system (MCGT method) for reconstructing CT images. The computational load is dominated by the number of independent measurements m, and a preconditioner is imported to lower the condition number of the Tikhonov system. Both simulation and experiment results indicate that the proposed method can reduce the computational time and improve the quality of image reconstruction. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.
Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure
Hill, Mary C.
1990-01-01
The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.
Kaporin, I. E.
2012-02-01
In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.
3D DC Resistivity Inversion with Topography Based on Regularized Conjugate Gradient Method
Directory of Open Access Journals (Sweden)
Jian-ke Qiang
2013-01-01
Full Text Available During the past decades, we observed a strong interest in 3D DC resistivity inversion and imaging with complex topography. In this paper, we implemented 3D DC resistivity inversion based on regularized conjugate gradient method with FEM. The Fréchet derivative is assembled with the electric potential in order to speed up the inversion process based on the reciprocity theorem. In this study, we also analyzed the sensitivity of the electric potential on the earth’s surface to the conductivity in each cell underground and introduced an optimized weighting function to produce new sensitivity matrix. The synthetic model study shows that this optimized weighting function is helpful to improve the resolution of deep anomaly. By incorporating topography into inversion, the artificial anomaly which is actually caused by topography can be eliminated. As a result, this algorithm potentially can be applied to process the DC resistivity data collected in mountain area. Our synthetic model study also shows that the convergence and computation speed are very stable and fast.
Optimization of gadolinium burnable poison loading by the conjugate gradients method
International Nuclear Information System (INIS)
Drumm, C.R.
1984-01-01
Improved use of burnable poison is suggested for pressurized water reactors (PWR's) to insure a sufficiently negative moderator temperature coefficient of reactivity for extended burnup cycles and low leakage refueling patterns. The use of gadolinium as a burnable poison can lead to large axial fluctuations in the power distribution through the cycle. The goal of this work is to determine the optimal axial distribution of gadolinium burnable poison in a PWR to overcome the axial fluctuations, yielding an improved power distribution. The conjugate gradients optimization method is used in this work because of the high degree of nonlinearity of the problem. The neutron diffusion and depletion equations are solved for a one-dimensional one-group core model. The state variables are the flux, the critical soluble boron concentration, and the burnup. The control variables are the number of gadolinium pins per assembly and the beginning-of-cycle gadolinium concentration, which determine the gadolinium cross section. Two separate objectives are considered: 1) to minimize the power peaking factor, which will minimize the capital cost of the plant; and 2) to maximize the cycle length, which will minimize the fuel cost for the plant. It is shown in this work that optimizing the gadolinium distribution can yield an improved power distribution
Embedding SAS approach into conjugate gradient algorithms for asymmetric 3D elasticity problems
Energy Technology Data Exchange (ETDEWEB)
Chen, Hsin-Chu; Warsi, N.A. [Clark Atlanta Univ., GA (United States); Sameh, A. [Univ. of Minnesota, Minneapolis, MN (United States)
1996-12-31
In this paper, we present two strategies to embed the SAS (symmetric-and-antisymmetric) scheme into conjugate gradient (CG) algorithms to make solving 3D elasticity problems, with or without global reflexive symmetry, more efficient. The SAS approach is physically a domain decomposition scheme that takes advantage of reflexive symmetry of discretized physical problems, and algebraically a matrix transformation method that exploits special reflexivity properties of the matrix resulting from discretization. In addition to offering large-grain parallelism, which is valuable in a multiprocessing environment, the SAS scheme also has the potential for reducing arithmetic operations in the numerical solution of a reasonably wide class of scientific and engineering problems. This approach can be applied directly to problems that have global reflexive symmetry, yielding smaller and independent subproblems to solve, or indirectly to problems with partial symmetry, resulting in loosely coupled subproblems. The decomposition is achieved by separating the reflexive subspace from the antireflexive one, possessed by a special class of matrices A, A {element_of} C{sup n x n} that satisfy the relation A = PAP where P is a reflection matrix (symmetric signed permutation matrix).
Hill, Mary C.
1990-01-01
This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.
Freund, Roland
1988-01-01
Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.
Czech Academy of Sciences Publication Activity Database
Gutknecht, M. H.; Rozložník, Miroslav
2002-01-01
Roč. 41, - (2002), s. 7-22 ISSN 0168-9274 R&D Projects: GA AV ČR IAA1030103; GA ČR GA101/00/1035 Institutional research plan: AV0Z1030915 Keywords : sparse linear systems * Krylov space method * orthogonal residual method * minimal residual method * conjugate gradient method * residual smoothing * CG * CGNE * CGNR * CR * FOM * GMRES * PRES Subject RIV: BA - General Mathematics Impact factor: 0.504, year: 2002
A new family of Polak-Ribiere-Polyak conjugate gradient method with the strong-Wolfe line search
Ghani, Nur Hamizah Abdul; Mamat, Mustafa; Rivaie, Mohd
2017-08-01
Conjugate gradient (CG) method is an important technique in unconstrained optimization, due to its effectiveness and low memory requirements. The focus of this paper is to introduce a new CG method for solving large scale unconstrained optimization. Theoretical proofs show that the new method fulfills sufficient descent condition if strong Wolfe-Powell inexact line search is used. Besides, computational results show that our proposed method outperforms to other existing CG methods.
Preconditioned conjugate-gradient methods for low-speed flow calculations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1993-01-01
An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.
Experience with the Incomplete Cholesky Conjugate Gradient method in a diffusion code
International Nuclear Information System (INIS)
Hoebel, W.
1985-01-01
For the numerical solution of sparse systems of linear equations arising from finite difference approximation of the multidimensional neutron diffusion equation fast methods are needed. Effective algorithms for scalar computers may not be likewise suitable on vector computers. In the improved version DIXY2 of the Karlsruhe two-dimensional neutron diffusion code for rectangular geometries an Incomplete Cholesky Conjugate Gradient (ICCG) algorithm has been combined with the originally implemented Cyclically Reduced 4-Lines SOR (CR4LSOR) inner iteration method. The combined procedure is automatically activated for slowly converging applications, thus leading to a drastic reduction of iterations as well as CPU-times on a scalar computer. In a follow-up benchmark study necessary modifications to ICCG and CR4LSOR for their use on a vector computer were investigated. It was found that a modified preconditioning for the ICCG algorithm restricted to the block diagonal matrix is an effective method both on scalar and vector computers. With a splitting of the 9-band-matrix in two triangular Cholesky matrices necessary inversions are performed on a scalar machine by recursive forward and backward substitutions. On vector computers an additional factorization of the triangular matrices into four bidiagonal matrices enables Buneman reduction and the recursive inversion is restricted to a small system. A similar strategy can be realized with CR4LSOR if the unvectorizable Gauss-Seidel iteration is replaced by Double Jacobi and Buneman technique for a vector computer. Compared to single line blocking over the original mesh the cyclical 4-lines reduction of the DIXY inner iteration scheme reduces numbers of iterations and CPU-times considerably
A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics
Kurdila, Andrew J.
1990-01-01
While excellent progress has been made in deriving algorithms that are efficient for certain combinations of system topologies and concurrent multiprocessing hardware, several issues must be resolved to incorporate transient simulation in the control design process for large space structures. Specifically, strategies must be developed that are applicable to systems with numerous degrees of freedom. In addition, the algorithms must have a growth potential in that they must also be amenable to implementation on forthcoming parallel system architectures. For mechanical system simulation, this fact implies that algorithms are required that induce parallelism on a fine scale, suitable for the emerging class of highly parallel processors; and transient simulation methods must be automatically load balancing for a wider collection of system topologies and hardware configurations. These problems are addressed by employing a combination range space/preconditioned conjugate gradient formulation of multi-degree-of-freedom dynamics. The method described has several advantages. In a sequential computing environment, the method has the features that: by employing regular ordering of the system connectivity graph, an extremely efficient preconditioner can be derived from the 'range space metric', as opposed to the system coefficient matrix; because of the effectiveness of the preconditioner, preliminary studies indicate that the method can achieve performance rates that depend linearly upon the number of substructures, hence the title 'Order N'; and the method is non-assembling. Furthermore, the approach is promising as a potential parallel processing algorithm in that the method exhibits a fine parallel granularity suitable for a wide collection of combinations of physical system topologies/computer architectures; and the method is easily load balanced among processors, and does not rely upon system topology to induce parallelism.
Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M; El Fakhri, Georges
2013-10-01
Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach. Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach. At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG. The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.
Experience with the incomplete Cholesky conjugate gradient method in a diffusion code
International Nuclear Information System (INIS)
Hoebel, W.
1986-01-01
For the numerical solution of sparse systems of linear equations arising from the finite difference approximation of the multidimensional neutron diffusion equation, fast methods are needed. Effective algorithms for scalar computers may not be likewise suitable on vector computers. In the improved version (DIXY2) of the Karlsruhe two-dimensional neutron diffusion code for rectangular geometries, an incomplete Cholesky conjugate gradient (ICCG) algorithm has been combined with the originally implemented cyclically reduced four-line successive overrelaxation (CR4LSOR) inner iteration method. The combined procedure is automatically activated for slowly converging applications, thus leading to a drastic reduction of iterations as well as CPU times on a scalar computer. In a follow-up benchmark study, necessary modifications to ICCG and CR4LSOR for use on a vector computer were investigated. It was found that a modified preconditioning for the ICCG algorithm restricted to the block diagonal matrix is an effective method both on scalar and vector computers. With a splitting of the nine-band matrix in two triangular Cholesky matrices, necessary inversions are performed on a scalar machine by recursive forward and backward substitutions. On vector computers an additional factorization of the triangular matrices into four bidiagonal matrices enables Buneman reduction, and the recursive inversion is restricted to a small system. A similar strategy can be realized with CR4LSOR if the unvectorizable Gauss-eidel iteration is replaced by Double Jacobi and Buneman techniques for a vector computer. Compared to single-line blocking over the original mesh, the cyclical four-line reduction of the DIXY inner iteration scheme reduces numbers of iterations and CPU times considerably
Least squares inversion of Stokes profiles in the presence of velocity gradients
International Nuclear Information System (INIS)
Skumanich, A.; Rees, D.E.; Lites, B.W.; Sacramento Peak Observatory, Sunspot, NM)
1985-01-01
The Auer, Heasley and House Stokes inversion procedure in use at High Altitude Observatory is based on the analytic solution of the equation of transfer for polarized light where the representation of the thermodynamic and magnetic structure of the atmosphere is assumed to have a high degree of invariance, namely, a Milne-Eddington (ME) structure with a constant magnetic field. In the presence of invariance breaking gradients the resultant Stokes profiles are represented only approximately, if at all, by analytic forms. The accuracy of the inversion parameters and their significance as measures of actual structure are explored for the ME and the Landman-Finn sunspot models under the effects of velocity gradients. The resulting field parameters are good to a few percent and prove to be insensitive to the errors committed by the use of a ME-representation, but the resulting ME parameters yield a less precise measure of thermal structure
Antoine, Xavier; Levitt, Antoine; Tang, Qinglin
2017-08-01
We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoint, leading to numerically solve a dissipative equation. Based on this IMT equation, we analyze the forward Euler (FE), Crank-Nicolson (CN) and the classical backward Euler (BE) schemes for linear problems and recognize classical power iterations, allowing us to derive convergence rates. By considering the alternative point of view of minimization problems, we propose the preconditioned steepest descent (PSD) and conjugate gradient (PCG) methods for the GS computation of the GPE. We investigate the choice of the preconditioner, which plays a key role in the acceleration of the convergence process. The performance of the new algorithms is tested in 1D, 2D and 3D. We conclude that the PCG method outperforms all the previous methods, most particularly for 2D and 3D fast rotating BECs, while being simple to implement.
Pan, Fan; Yang, Wende; Li, Wei; Yang, Xiao-Yan; Liu, Shuhao; Li, Xin; Zhao, Xiaoxu; Ding, Hui; Qin, Li; Pan, Yunlong
2017-07-01
Several studies have revealed the potential of normalizing tumor vessels in anti-angiogenic treatment. Recombinant human endostatin is an anti-angiogenic agent which has been applied in clinical tumor treatment. Our previous research indicated that gold nanoparticles could be a nanoparticle carrier for recombinant human endostatin delivery. The recombinant human endostatin-gold nanoparticle conjugates normalized vessels, which improved chemotherapy. However, the mechanism of recombinant human endostatin-gold nanoparticle-induced vascular normalization has not been explored. Anterior gradient 2 has been reported to be over-expressed in many malignant tumors and involved in tumor angiogenesis. To date, the precise efficacy of recombinant human endostatin-gold nanoparticles on anterior gradient 2-mediated angiogenesis or anterior gradient 2-related signaling cohort remained unknown. In this study, we aimed to explore whether recombinant human endostatin-gold nanoparticles could normalize vessels in metastatic colorectal cancer xenografts, and we further elucidated whether recombinant human endostatin-gold nanoparticles could interrupt anterior gradient 2-induced angiogenesis. In vivo, it was indicated that recombinant human endostatin-gold nanoparticles increased pericyte expression while inhibit vascular endothelial growth factor receptor 2 and anterior gradient 2 expression in metastatic colorectal cancer xenografts. In vitro, we uncovered that recombinant human endostatin-gold nanoparticles reduced cell migration and tube formation induced by anterior gradient 2 in human umbilical vein endothelial cells. Treatment with recombinant human endostatin-gold nanoparticles attenuated anterior gradient 2-mediated activation of MMP2, cMyc, VE-cadherin, phosphorylation of p38, and extracellular signal-regulated protein kinases 1 and 2 (ERK1/2) in human umbilical vein endothelial cells. Our findings demonstrated recombinant human endostatin-gold nanoparticles might normalize
Burrows, R. R.
1972-01-01
A particular type of three-impulse transfer between two circular orbits is analyzed. The possibility of three plane changes is recognized, and the problem is to optimally distribute these plane changes to minimize the sum of the individual impulses. Numerical difficulties and their solution are discussed. Numerical results obtained from a conjugate gradient technique are presented for both the case where the individual plane changes are unconstrained and for the case where they are constrained. Possibly not unexpectedly, multiple minima are found. The techniques presented could be extended to the finite burn case, but primarily the contents are addressed to preliminary mission design and vehicle sizing.
Wei, Yongjie; Ge, Baozhen; Wei, Yaolin
2009-03-20
In general, model-independent algorithms are sensitive to noise during laser particle size measurement. An improved conjugate gradient algorithm (ICGA) that can be used to invert particle size distribution (PSD) from diffraction data is presented. By use of the ICGA to invert simulated data with multiplicative or additive noise, we determined that additive noise is the main factor that induces distorted results. Thus the ICGA is amended by introduction of an iteration step-adjusting parameter and is used experimentally on simulated data and some samples. The experimental results show that the sensitivity of the ICGA to noise is reduced and the inverted results are in accord with the real PSD.
Kim, Hwi; Min, Sung-Wook; Lee, Byoungho
2008-12-01
Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.
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Xiangrong Li
Full Text Available It is generally acknowledged that the conjugate gradient (CG method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.
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Shoubin Wang
2017-01-01
Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.
Li, Xiangrong; Zhao, Xupei; Duan, Xiabin; Wang, Xiaoliang
2015-01-01
It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence--with at most a linear convergence rate--because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.
International Nuclear Information System (INIS)
Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem
2008-01-01
In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by aids of an adjoint problem and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2012-04-01
Full Text Available It is well known that the numerical algorithms of the steepest descent method (SDM, and the conjugate gradient method (CGM are effective for solving well-posed linear systems. However, they are vulnerable to noisy disturbance for solving ill-posed linear systems. We propose the modifications of SDM and CGM, namely the modified steepest descent method (MSDM, and the modified conjugate gradient method (MCGM. The starting point is an invariant manifold defined in terms of a minimum functional and a fictitious time-like variable; however, in the final stage we can derive a purely iterative algorithm including an acceleration parameter. Through the Hopf bifurcation, this parameter indeed plays a major role to switch the situation of slow convergence to a new situation that the functional is stepwisely decreased very fast. Several numerical examples are examined and compared with exact solutions, revealing that the new algorithms of MSDM and MCGM have good computational efficiency and accuracy, even for the highly ill-conditioned linear equations system with a large noise being imposed on the given data.
International Nuclear Information System (INIS)
Biffle, J.H.
1991-01-01
1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory
International Nuclear Information System (INIS)
Bull, James N.; Fitchett, Christopher M.; Tennant, W. Craighead
2010-01-01
This paper reports the determination of the electric-field-gradient and mean-squared-displacement tensors in 57 Fe symmetry-related sites of 1-bar Laue class in monoclinic FeCl 2 .4H 2 O at room temperature by single-crystal Mössbauer spectroscopy. Contrary to all previous work, the mean-squared-displacement matrix (tensor), , is not constrained to be isotropic resulting in the determination of physically meaningful estimates of microscopic (local) electric-field gradient (efg) and tensors. As a consequence of anisotropy in the tensor the absorber recoilless fractions are also anisotropic. As expected of a low-symmetry site, Laue class 1-bar in this case, no two principal axes of the efg and tensors are coaxial, within the combined errors in the two. Further, no principal direction of the efg tensor seems related to bond directions in the unit cell. Within error, and in agreement with an earlier study of sodium nitroprusside, it appears that the tensor principal directions lie close to the crystallographic axes suggesting that they are determined by long wavelength (phonon) vibrations in the crystal rather than by approximate local symmetry about the 57 Fe nucleus. Concurrent with the Mössbauer measurements, we determined as part of a new X-ray structural determination, precise atomic displacement parameters (ADPs) leading to an alternative determination of the matrix (tensor). The average of the eigenvalues of the Mössbauer-determined exceeds that of the average of the X-ray-determined eigenvalues by a factor of around 2.2. Assuming isotropic absorber recoilless fractions leads to substantially the same (macroscopic) efg tensor as had been determined in earlier work. Taking 1/3 x the trace of the anisotropic absorber recoilless fractions leads to an isotropic value of 0.304 in good agreement with earlier single crystal studies where isotropy was assumed.
Iterative methods for weighted least-squares
Energy Technology Data Exchange (ETDEWEB)
Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.
Chen, Weitian; Sica, Christopher T; Meyer, Craig H
2008-11-01
Off-resonance effects can cause image blurring in spiral scanning and various forms of image degradation in other MRI methods. Off-resonance effects can be caused by both B0 inhomogeneity and concomitant gradient fields. Previously developed off-resonance correction methods focus on the correction of a single source of off-resonance. This work introduces a computationally efficient method of correcting for B0 inhomogeneity and concomitant gradients simultaneously. The method is a fast alternative to conjugate phase reconstruction, with the off-resonance phase term approximated by Chebyshev polynomials. The proposed algorithm is well suited for semiautomatic off-resonance correction, which works well even with an inaccurate or low-resolution field map. The proposed algorithm is demonstrated using phantom and in vivo data sets acquired by spiral scanning. Semiautomatic off-resonance correction alone is shown to provide a moderate amount of correction for concomitant gradient field effects, in addition to B0 imhomogeneity effects. However, better correction is provided by the proposed combined method. The best results were produced using the semiautomatic version of the proposed combined method.
Liu, Guhuan; Hu, Jinming; Zhang, Guoying; Liu, Shiyong
2015-07-15
Spatiotemporal switching of respective phototherapy modes at the cellular level with minimum side effects and high therapeutic efficacy is a major challenge for cancer phototherapy. Herein we demonstrate how to address this issue by employing photosensitizer-conjugated pH-responsive block copolymers in combination with intracellular endocytic pH gradients. At neutral pH corresponding to extracellular and cytosol milieu, the copolymers self-assemble into micelles with prominently quenched fluorescence emission and low (1)O2 generation capability, favoring a highly efficient photothermal module. Under mildly acidic pH associated with endolysosomes, protonation-triggered micelle-to-unimer transition results in recovered emission and enhanced photodynamic (1)O2 efficiency, which synergistically actuates release of encapsulated drugs, endosomal escape, and photochemical internalization processes.
Bowman, D; Harte, T L; Chardonnet, V; De Groot, C; Denny, S J; Le Goc, G; Anderson, M; Ireland, P; Cassettari, D; Bruce, G D
2017-05-15
We demonstrate simultaneous control of both the phase and amplitude of light using a conjugate gradient minimisation-based hologram calculation technique and a single phase-only spatial light modulator (SLM). A cost function, which incorporates the inner product of the light field with a chosen target field within a defined measure region, is efficiently minimised to create high fidelity patterns in the Fourier plane of the SLM. A fidelity of F = 0.999997 is achieved for a pattern resembling an LG10 mode with a calculated light-usage efficiency of 41.5%. Possible applications of our method in optical trapping and ultracold atoms are presented and we show uncorrected experimental realisation of our patterns with F = 0.97 and 7.8% light efficiency.
International Nuclear Information System (INIS)
Wang Hua; Liu Feng; Crozier, Stuart; Xia Ling
2008-01-01
This paper presents a stabilized Bi-conjugate gradient algorithm (BiCGstab) that can significantly improve the performance of the impedance method, which has been widely applied to model low-frequency field induction phenomena in voxel phantoms. The improved impedance method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional, successive over-relaxation (SOR)-based algorithm. The scheme has been validated against other numerical/analytical solutions on a lossy, multilayered sphere phantom excited by an ideal coil loop. To demonstrate the computational performance and application capability of the developed algorithm, the induced fields inside a human phantom due to a low-frequency hyperthermia device is evaluated. The simulation results show the numerical accuracy and superior performance of the method.
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Bakhtawar Baluch
2017-01-01
Full Text Available A new modified three-term conjugate gradient (CG method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.
Wang, Hua; Liu, Feng; Xia, Ling; Crozier, Stuart
2008-11-21
This paper presents a stabilized Bi-conjugate gradient algorithm (BiCGstab) that can significantly improve the performance of the impedance method, which has been widely applied to model low-frequency field induction phenomena in voxel phantoms. The improved impedance method offers remarkable computational advantages in terms of convergence performance and memory consumption over the conventional, successive over-relaxation (SOR)-based algorithm. The scheme has been validated against other numerical/analytical solutions on a lossy, multilayered sphere phantom excited by an ideal coil loop. To demonstrate the computational performance and application capability of the developed algorithm, the induced fields inside a human phantom due to a low-frequency hyperthermia device is evaluated. The simulation results show the numerical accuracy and superior performance of the method.
On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method
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Min Sun
2014-01-01
Full Text Available Recently, Zhang et al. proposed a sufficient descent Polak-Ribière-Polyak (SDPRP conjugate gradient method for large-scale unconstrained optimization problems and proved its global convergence in the sense that lim infk→∞∥∇f(xk∥=0 when an Armijo-type line search is used. In this paper, motivated by the line searches proposed by Shi et al. and Zhang et al., we propose two new Armijo-type line searches and show that the SDPRP method has strong convergence in the sense that limk→∞∥∇f(xk∥=0 under the two new line searches. Numerical results are reported to show the efficiency of the SDPRP with the new Armijo-type line searches in practical computation.
International Nuclear Information System (INIS)
Wang, J.J.H.; Dubberley, J.R.
1989-01-01
Electromagnetic (EM) fields in a three-dimensional, arbitrarily shaped heterogeneous dielectric or biological body illuminated by a plane wave are computed by an iterative conjugate gradient method. The method is a generalized method of moments applied to the volume integral equation. Because no matrix is explicitly involved or stored, the present iterative method is capable of computing EM fields in objects an order of magnitude larger than those that can be handled by the conventional method of moments. Excellent numerical convergence is achieved. Perfect convergence to the result of the conventional moment method using the same basis and weighted with delta functions is consistently achieved in all the cases computed, indicating that these two algorithms (direct and interactive) are equivalent
International Nuclear Information System (INIS)
Krishnamoorthy, Gautham
2017-01-01
Highlights: • The P_1 radiation model was interfaced with high performance linear solvers. • Pre-conditioned conjugate gradient (PC CG) method improved convergence by 50% • PC CG was more than 30 times faster than classical iterative methods. • The time to solution scaled linearly with increase in problem size employing PC CG. • Employing WSGGM with P_1 model compared reasonably well against benchmark data. - Abstract: The iterative convergence of the P_1 radiation model can be slow in optically thin scenarios when employing classical iterative methods. In order to remedy this shortcoming, an in-house P_1 radiation model was interfaced with high performance, scalable, linear solver libraries. Next, the accuracies of P_1 radiation model calculations was assessed by comparing its predictions against discrete ordinates (DO) model calculations for prototypical problems representative of modern combustion systems. Corresponding benchmark results were also included for comparison. Utilizing Pre-Conditioners (PC) to the Conjugate Gradients (CG) method, the convergence time of the P_1 radiation model reduced by a factor of 30 for modest problem sizes and a factor of 70 for larger sized problems when compared against classical Gauss Seidel sweeps. Further, PC provided 50% computational savings compared to employing CG in a standalone mode. The P_1 model calculation times were about 25–30% of the DO model calculation time. The time to solution also scaled linearly with an increase in problem size. The weighted sum of gray gases model employed in this study in conjunction with the P_1 model provided good agreement against benchmark data with L_2 error norms (defined relative to corresponding DO calculations) improving when isotropic intensities were prevalent.
International Nuclear Information System (INIS)
Kim, Hyun Keol; Charette, Andre
2007-01-01
The Sensitivity Function-based Conjugate Gradient Method (SFCGM) is described. This method is used to solve the inverse problems of function estimation, such as the local maps of absorption and scattering coefficients, as applied to optical tomography for biomedical imaging. A highly scattering, absorbing, non-reflecting, non-emitting medium is considered here and simultaneous reconstructions of absorption and scattering coefficients inside the test medium are achieved with the proposed optimization technique, by using the exit intensity measured at boundary surfaces. The forward problem is solved with a discrete-ordinates finite-difference method on the framework of the frequency-domain full equation of radiative transfer. The modulation frequency is set to 600 MHz and the frequency data, obtained with the source modulation, is used as the input data. The inversion results demonstrate that the SFCGM can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by significantly reducing a cross-talk between inter-parameters. It is also observed that the closer-to-detector objects are better retrieved
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Shuang Rong
2015-12-01
Full Text Available Aiming to relieve the large amount of wind power curtailment during the heating period in the North China region, a thermal-electric decoupling (TED approach is proposed to both bring down the constraint of forced power output of combined heat and power plants and increase the electric load level during valley load times that assist the power grid in consuming more wind power. The operating principles of the thermal-electric decoupling approach is described, the mathematical model of its profits is developed, the constraint conditions of its operation are listed, also, an improved parallel conjugate gradient is utilized to bypass the saddle problem and accelerate the optimal speed. Numerical simulations are implemented and reveal an optimal allocation of TED which with a rated power of 280 MW and 185 MWh heat storage capacity are possible. This allocation of TED could bring approximately 16.9 billion Yuan of economic profit and consume more than 80% of the surplus wind energy which would be curtailed without the participation of TED. The results in this article verify the effectiveness of this method that could provide a referential guidance for thermal-electric decoupling system allocation in practice.
Jung, Youngkyoo; Samsonov, Alexey A; Bydder, Mark; Block, Walter F
2011-04-01
To remove phase inconsistencies between multiple echoes, an algorithm using a radial acquisition to provide inherent phase and magnitude information for self correction was developed. The information also allows simultaneous support for parallel imaging for multiple coil acquisitions. Without a separate field map acquisition, a phase estimate from each echo in multiple echo train was generated. When using a multiple channel coil, magnitude and phase estimates from each echo provide in vivo coil sensitivities. An algorithm based on the conjugate gradient method uses these estimates to simultaneously remove phase inconsistencies between echoes, and in the case of multiple coil acquisition, simultaneously provides parallel imaging benefits. The algorithm is demonstrated on single channel, multiple channel, and undersampled data. Substantial image quality improvements were demonstrated. Signal dropouts were completely removed and undersampling artifacts were well suppressed. The suggested algorithm is able to remove phase cancellation and undersampling artifacts simultaneously and to improve image quality of multiecho radial imaging, the important technique for fast three-dimensional MRI data acquisition. Copyright © 2011 Wiley-Liss, Inc.
Woodward, Richard B; Spanias, John A; Hargrove, Levi J
2016-08-01
Powered lower limb prostheses have the ability to provide greater mobility for amputee patients. Such prostheses often have pre-programmed modes which can allow activities such as climbing stairs and descending ramps, something which many amputees struggle with when using non-powered limbs. Previous literature has shown how pattern classification can allow seamless transitions between modes with a high accuracy and without any user interaction. Although accurate, training and testing each subject with their own dependent data is time consuming. By using subject independent datasets, whereby a unique subject is tested against a pooled dataset of other subjects, we believe subject training time can be reduced while still achieving an accurate classification. We present here an intent recognition system using an artificial neural network (ANN) with a scaled conjugate gradient learning algorithm to classify gait intention with user-dependent and independent datasets for six unilateral lower limb amputees. We compare these results against a linear discriminant analysis (LDA) classifier. The ANN was found to have significantly lower classification error (P<;0.05) than LDA with all user-dependent step-types, as well as transitional steps for user-independent datasets. Both types of classifiers are capable of making fast decisions; 1.29 and 2.83 ms for the LDA and ANN respectively. These results suggest that ANNs can provide suitable and accurate offline classification in prosthesis gait prediction.
Barkeshli, Kasra; Volakis, John L.
1991-01-01
The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.
Tavakoli, Behnoosh; Zhu, Quing
2013-01-01
Ultrasound-guided diffuse optical tomography (DOT) is a promising method for characterizing malignant and benign lesions in the female breast. We introduce a new two-step algorithm for DOT inversion in which the optical parameters are estimated with the global optimization method, genetic algorithm. The estimation result is applied as an initial guess to the conjugate gradient (CG) optimization method to obtain the absorption and scattering distributions simultaneously. Simulations and phantom experiments have shown that the maximum absorption and reduced scattering coefficients are reconstructed with less than 10% and 25% errors, respectively. This is in contrast with the CG method alone, which generates about 20% error for the absorption coefficient and does not accurately recover the scattering distribution. A new measure of scattering contrast has been introduced to characterize benign and malignant breast lesions. The results of 16 clinical cases reconstructed with the two-step method demonstrates that, on average, the absorption coefficient and scattering contrast of malignant lesions are about 1.8 and 3.32 times higher than the benign cases, respectively.
Partial update least-square adaptive filtering
Xie, Bei
2014-01-01
Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity (O(N)) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster a
Gilles, Luc; Massioni, Paolo; Kulcsár, Caroline; Raynaud, Henri-François; Ellerbroek, Brent
2013-05-01
This paper discusses the performance and cost of two computationally efficient Fourier-based tomographic wavefront reconstruction algorithms for wide-field laser guide star (LGS) adaptive optics (AO). The first algorithm is the iterative Fourier domain preconditioned conjugate gradient (FDPCG) algorithm developed by Yang et al. [Appl. Opt.45, 5281 (2006)], combined with pseudo-open-loop control (POLC). FDPCG's computational cost is proportional to N log(N), where N denotes the dimensionality of the tomography problem. The second algorithm is the distributed Kalman filter (DKF) developed by Massioni et al. [J. Opt. Soc. Am. A28, 2298 (2011)], which is a noniterative spatially invariant controller. When implemented in the Fourier domain, DKF's cost is also proportional to N log(N). Both algorithms are capable of estimating spatial frequency components of the residual phase beyond the wavefront sensor (WFS) cutoff frequency thanks to regularization, thereby reducing WFS spatial aliasing at the expense of more computations. We present performance and cost analyses for the LGS multiconjugate AO system under design for the Thirty Meter Telescope, as well as DKF's sensitivity to uncertainties in wind profile prior information. We found that, provided the wind profile is known to better than 10% wind speed accuracy and 20 deg wind direction accuracy, DKF, despite its spatial invariance assumptions, delivers a significantly reduced wavefront error compared to the static FDPCG minimum variance estimator combined with POLC. Due to its nonsequential nature and high degree of parallelism, DKF is particularly well suited for real-time implementation on inexpensive off-the-shelf graphics processing units.
Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.
1998-01-01
This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves
Ge, Lan; Kino, Aya; Lee, Daniel; Dharmakumar, Rohan; Carr, James C; Li, Debiao
2010-01-01
First-pass perfusion magnetic resonance imaging (MRI) is a promising technique for detecting ischemic heart disease. However, the diagnostic value of the method is limited by the low spatial coverage, resolution, signal-to-noise ratio (SNR), and cardiac motion-related image artifacts. A combination of sliding window and conjugate-gradient HighlY constrained back-PRojection reconstruction (SW-CG-HYPR) method has been proposed in healthy volunteer studies to reduce the acquisition window for each slice while maintaining the temporal resolution of 1 frame per heartbeat in myocardial perfusion MRI. This method allows for improved spatial coverage, resolution, and SNR. In this study, we use a controlled animal model to test whether the myocardial territory supplied by a stenotic coronary artery can be detected accurately by SW-CG-HYPR perfusion method under pharmacological stress. Results from 6 mongrel dogs (15-25 kg) studies demonstrate the feasibility of SW-CG-HYPR to detect regional perfusion defects. Using this method, the acquisition time per cardiac cycle was reduced by a factor of 4, and the spatial coverage was increased from 2 to 3 slices to 6 slices as compared with the conventional techniques including both turbo-Fast Low Angle Short (FLASH) and echoplanar imaging (EPI). The SNR of the healthy myocardium at peak enhancement with SW-CG-HYPR (12.68 ± 2.46) is significantly higher (P < 0.01) than the turbo-FLASH (8.65 ± 1.93) and EPI (5.48 ± 1.24). The spatial resolution of SW-CG-HYPR images is 1.2 × 1.2 × 8.0 mm, which is better than the turbo-FLASH (1.8 × 1.8 × 8.0 mm) and EPI (2.0 × 1.8 × 8.0 mm). Sliding-window CG-HYPR is a promising technique for myocardial perfusion MRI. This technique provides higher image quality with respect to significantly improved SNR and spatial resolution of the myocardial perfusion images, which might improve myocardial perfusion imaging in a clinical setting.
Aviat, Félix; Lagardère, Louis; Piquemal, Jean-Philip
2017-10-01
In a recent paper [F. Aviat et al., J. Chem. Theory Comput. 13, 180-190 (2017)], we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in truncating the conjugate gradient algorithm at a fixed predetermined order leading to a fixed computational cost and can thus be considered "non-iterative." This gives the possibility to derive analytical forces avoiding the usual energy conservation (i.e., drifts) issues occurring with iterative approaches. A key point concerns the evaluation of the analytical gradients, which is more complex than that with a usual solver. In this paper, after reviewing the present state of the art of polarization solvers, we detail a viable strategy for the efficient implementation of the TCG calculation. The complete cost of the approach is then measured as it is tested using a multi-time step scheme and compared to timings using usual iterative approaches. We show that the TCG methods are more efficient than traditional techniques, making it a method of choice for future long molecular dynamics simulations using polarizable force fields where energy conservation matters. We detail the various steps required for the implementation of the complete method by software developers.
International Nuclear Information System (INIS)
Kalkreuter, T.; Simma, H.
1995-07-01
The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalizations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional SU(2) gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes 4 4 - 16 4 an acceleration of the pure CG method by a factor of 4 - 8 is found. (orig.)
Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.
1998-01-01
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
International Nuclear Information System (INIS)
Aruchunan, E.
2015-01-01
In this paper, we have examined the effectiveness of the quarter-sweep iteration concept on conjugate gradient normal residual (CGNR) iterative method by using composite Simpson's (CS) and finite difference (FD) discretization schemes in solving Fredholm integro-differential equations. For comparison purposes, Gauss- Seidel (GS) and the standard or full- and half-sweep CGNR methods namely FSCGNR and HSCGNR are also presented. To validate the efficacy of the proposed method, several analyses were carried out such as computational complexity and percentage reduction on the proposed and existing methods. (author)
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.
Directory of Open Access Journals (Sweden)
J. De Keyser
2007-05-01
Full Text Available This paper describes a general-purpose algorithm for computing the gradients in space and time of a scalar field, a vector field, or a divergence-free vector field, from in situ measurements by one or more spacecraft. The algorithm provides total error estimates on the computed gradient, including the effects of measurement errors, the errors due to a lack of spatio-temporal homogeneity, and errors due to small-scale fluctuations. It also has the ability to diagnose the conditioning of the problem. Optimal use is made of the data, in terms of exploiting the maximum amount of information relative to the uncertainty on the data, by solving the problem in a weighted least-squares sense. The method is illustrated using Cluster magnetic field and electron density data to compute various gradients during a traversal of the inner magnetosphere. In particular, Cluster is shown to cross azimuthal density structure, and the existence of field-aligned currents in the plasmasphere is demonstrated.
Güntürkün, Rüştü
2010-08-01
In this study, Elman recurrent neural networks have been defined by using conjugate gradient algorithm in order to determine the depth of anesthesia in the continuation stage of the anesthesia and to estimate the amount of medicine to be applied at that moment. The feed forward neural networks are also used for comparison. The conjugate gradient algorithm is compared with back propagation (BP) for training of the neural Networks. The applied artificial neural network is composed of three layers, namely the input layer, the hidden layer and the output layer. The nonlinear activation function sigmoid (sigmoid function) has been used in the hidden layer and the output layer. EEG data has been recorded with Nihon Kohden 9200 brand 22-channel EEG device. The international 8-channel bipolar 10-20 montage system (8 TB-b system) has been used in assembling the recording electrodes. EEG data have been recorded by being sampled once in every 2 milliseconds. The artificial neural network has been designed so as to have 60 neurons in the input layer, 30 neurons in the hidden layer and 1 neuron in the output layer. The values of the power spectral density (PSD) of 10-second EEG segments which correspond to the 1-50 Hz frequency range; the ratio of the total power of PSD values of the EEG segment at that moment in the same range to the total of PSD values of EEG segment taken prior to the anesthesia.
Aviat, Félix; Levitt, Antoine; Stamm, Benjamin; Maday, Yvon; Ren, Pengyu; Ponder, Jay W; Lagardère, Louis; Piquemal, Jean-Philip
2017-01-10
We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration ("peek"), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production
Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming
1990-01-01
A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.
International Nuclear Information System (INIS)
Yoon, Jong Seon; Choi, Hyoung Gwon; Jeon, Byoung Jin; Jung, Hye Dong
2016-01-01
A parallel algorithm of bi-conjugate gradient method was developed based on CUDA for parallel computation of the incompressible Navier-Stokes equations. The governing equations were discretized using splitting P2P1 finite element method. Asymmetric stenotic flow problem was solved to validate the proposed algorithm, and then the parallel performance of the GPU was examined by measuring the elapsed times. Further, the GPU performance for sparse matrix-vector multiplication was also investigated with a matrix of fluid-structure interaction problem. A kernel was generated to simultaneously compute the inner product of each row of sparse matrix and a vector. In addition, the kernel was optimized to improve the performance by using both parallel reduction and memory coalescing. In the kernel construction, the effect of warp on the parallel performance of the present CUDA was also examined. The present GPU computation was more than 7 times faster than the single CPU by double precision.
International Nuclear Information System (INIS)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere
Energy Technology Data Exchange (ETDEWEB)
Yoon, Jong Seon; Choi, Hyoung Gwon [Seoul Nat’l Univ. of Science and Technology, Seoul (Korea, Republic of); Jeon, Byoung Jin [Yonsei Univ., Seoul (Korea, Republic of); Jung, Hye Dong [Korea Electronics Technology Institute, Seongnam (Korea, Republic of)
2016-09-15
A parallel algorithm of bi-conjugate gradient method was developed based on CUDA for parallel computation of the incompressible Navier-Stokes equations. The governing equations were discretized using splitting P2P1 finite element method. Asymmetric stenotic flow problem was solved to validate the proposed algorithm, and then the parallel performance of the GPU was examined by measuring the elapsed times. Further, the GPU performance for sparse matrix-vector multiplication was also investigated with a matrix of fluid-structure interaction problem. A kernel was generated to simultaneously compute the inner product of each row of sparse matrix and a vector. In addition, the kernel was optimized to improve the performance by using both parallel reduction and memory coalescing. In the kernel construction, the effect of warp on the parallel performance of the present CUDA was also examined. The present GPU computation was more than 7 times faster than the single CPU by double precision.
International Nuclear Information System (INIS)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.
Directory of Open Access Journals (Sweden)
Lanfa Liu
2017-12-01
Full Text Available Soil spectroscopy has experienced a tremendous increase in soil property characterisation, and can be used not only in the laboratory but also from the space (imaging spectroscopy. Partial least squares (PLS regression is one of the most common approaches for the calibration of soil properties using soil spectra. Besides functioning as a calibration method, PLS can also be used as a dimension reduction tool, which has scarcely been studied in soil spectroscopy. PLS components retained from high-dimensional spectral data can further be explored with the gradient-boosted decision tree (GBDT method. Three soil sample categories were extracted from the Land Use/Land Cover Area Frame Survey (LUCAS soil library according to the type of land cover (woodland, grassland, and cropland. First, PLS regression and GBDT were separately applied to build the spectroscopic models for soil organic carbon (OC, total nitrogen content (N, and clay for each soil category. Then, PLS-derived components were used as input variables for the GBDT model. The results demonstrate that the combined PLS-GBDT approach has better performance than PLS or GBDT alone. The relative important variables for soil property estimation revealed by the proposed method demonstrated that the PLS method is a useful dimension reduction tool for soil spectra to retain target-related information.
International Nuclear Information System (INIS)
Yang, Xiaoli; Hofmann, Ralf; Dapp, Robin; Van de Kamp, Thomas; Rolo, Tomy dos Santos; Xiao, Xianghui; Moosmann, Julian; Kashef, Jubin; Stotzka, Rainer
2015-01-01
High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration o fin vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation
International Nuclear Information System (INIS)
Gelebart, Lionel; Mondon-Cancel, Romain
2013-01-01
FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted to periodic boundary conditions, which is of a great interest in the context of numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously to use Conjugate Gradient based solvers in order to improve the convergence properties (when compared to the basic scheme, proposed initially in 1994). The purpose of the paper is to extend this idea to the case of non-linear behaviors. The proposed method is based on a Newton-Raphson algorithm and can be applied to various kinds of behaviors (time dependant or independent, with or without internal variables) through a conventional integration procedure as used in finite element codes. It must be pointed out that this approach is fundamentally different from the traditional FFT-based approaches which rely on a fixed-point algorithm (e.g. basic scheme, Eyre and Milton accelerated scheme, Augmented Lagrangian scheme, etc.). The method is compared to the basic scheme on the basis of a simple application (a linear elastic spherical inclusion within a non-linear elastic matrix): a low sensitivity to the reference material and an improved efficiency, for a soft or a stiff inclusion, are observed. At first proposed for a prescribed macroscopic strain, the method is then extended to mixed loadings. (authors)
Yang, Xiaoli; Hofmann, Ralf; Dapp, Robin; van de Kamp, Thomas; dos Santos Rolo, Tomy; Xiao, Xianghui; Moosmann, Julian; Kashef, Jubin; Stotzka, Rainer
2015-03-09
High-resolution, three-dimensional (3D) imaging of soft tissues requires the solution of two inverse problems: phase retrieval and the reconstruction of the 3D image from a tomographic stack of two-dimensional (2D) projections. The number of projections per stack should be small to accommodate fast tomography of rapid processes and to constrain X-ray radiation dose to optimal levels to either increase the duration of in vivo time-lapse series at a given goal for spatial resolution and/or the conservation of structure under X-ray irradiation. In pursuing the 3D reconstruction problem in the sense of compressive sampling theory, we propose to reduce the number of projections by applying an advanced algebraic technique subject to the minimisation of the total variation (TV) in the reconstructed slice. This problem is formulated in a Lagrangian multiplier fashion with the parameter value determined by appealing to a discrete L-curve in conjunction with a conjugate gradient method. The usefulness of this reconstruction modality is demonstrated for simulated and in vivo data, the latter acquired in parallel-beam imaging experiments using synchrotron radiation.
Ma, Heng; Yang, Jun; Liu, Jing; Ge, Lan; An, Jing; Tang, Qing; Li, Han; Zhang, Yu; Chen, David; Wang, Yong; Liu, Jiabin; Liang, Zhigang; Lin, Kai; Jin, Lixin; Bi, Xiaoming; Li, Kuncheng; Li, Debiao
2012-04-15
Myocardial perfusion magnetic resonance imaging (MRI) with sliding-window conjugate-gradient highly constrained back-projection reconstruction (SW-CG-HYPR) allows whole left ventricular coverage, improved temporal and spatial resolution and signal/noise ratio, and reduced cardiac motion-related image artifacts. The accuracy of this technique for detecting coronary artery disease (CAD) has not been determined in a large number of patients. We prospectively evaluated the diagnostic performance of myocardial perfusion MRI with SW-CG-HYPR in patients with suspected CAD. A total of 50 consecutive patients who were scheduled for coronary angiography with suspected CAD underwent myocardial perfusion MRI with SW-CG-HYPR at 3.0 T. The perfusion defects were interpreted qualitatively by 2 blinded observers and were correlated with x-ray angiographic stenoses ≥50%. The prevalence of CAD was 56%. In the per-patient analysis, the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy of SW-CG-HYPR was 96% (95% confidence interval 82% to 100%), 82% (95% confidence interval 60% to 95%), 87% (95% confidence interval 70% to 96%), 95% (95% confidence interval 74% to100%), and 90% (95% confidence interval 82% to 98%), respectively. In the per-vessel analysis, the corresponding values were 98% (95% confidence interval 91% to 100%), 89% (95% confidence interval 80% to 94%), 86% (95% confidence interval 76% to 93%), 99% (95% confidence interval 93% to 100%), and 93% (95% confidence interval 89% to 97%), respectively. In conclusion, myocardial perfusion MRI using SW-CG-HYPR allows whole left ventricular coverage and high resolution and has high diagnostic accuracy in patients with suspected CAD. Copyright © 2012 Elsevier Inc. All rights reserved.
Liu, Youshan; Teng, Jiwen; Xu, Tao; Badal, José; Liu, Qinya; Zhou, Bing
2017-05-01
We carry out full waveform inversion (FWI) in time domain based on an alternative frequency-band selection strategy that allows us to implement the method with success. This strategy aims at decomposing the seismic data within partially overlapped frequency intervals by carrying out a concatenated treatment of the wavelet to largely avoid redundant frequency information to adapt to wavelength or wavenumber coverage. A pertinent numerical test proves the effectiveness of this strategy. Based on this strategy, we comparatively analyze the effects of update parameters for the nonlinear conjugate gradient (CG) method and step-length formulas on the multiscale FWI through several numerical tests. The investigations of up to eight versions of the nonlinear CG method with and without Gaussian white noise make clear that the HS (Hestenes and Stiefel in J Res Natl Bur Stand Sect 5:409-436, 1952), CD (Fletcher in Practical methods of optimization vol. 1: unconstrained optimization, Wiley, New York, 1987), and PRP (Polak and Ribière in Revue Francaise Informat Recherche Opertionelle, 3e Année 16:35-43, 1969; Polyak in USSR Comput Math Math Phys 9:94-112, 1969) versions are more efficient among the eight versions, while the DY (Dai and Yuan in SIAM J Optim 10:177-182, 1999) version always yields inaccurate result, because it overestimates the deeper parts of the model. The application of FWI algorithms using distinct step-length formulas, such as the direct method ( Direct), the parabolic search method ( Search), and the two-point quadratic interpolation method ( Interp), proves that the Interp is more efficient for noise-free data, while the Direct is more efficient for Gaussian white noise data. In contrast, the Search is less efficient because of its slow convergence. In general, the three step-length formulas are robust or partly insensitive to Gaussian white noise and the complexity of the model. When the initial velocity model deviates far from the real model or the
He, Qiaolin; Glowinski, Roland; Wang, Xiao Ping
2011-01-01
element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
DEFF Research Database (Denmark)
Forchhammer, Søren; Kim, Chul E
1988-01-01
Digital squares are defined and their geometric properties characterized. A linear time algorithm is presented that considers a convex digital region and determines whether or not it is a digital square. The algorithm also determines the range of the values of the parameter set of its preimages....... The analysis involves transforming the boundary of a digital region into parameter space of slope and y-intercept...
Indian Academy of Sciences (India)
Admin
2012-09-07
Sep 7, 2012 ... must first talk of permutations and Latin squares. A permutation of a finite set of objects is a linear arrange- ment of ... with a special element 1 ... Of course, this has .... tion method to disprove Euler's conjecture for infinitely.
Lyon, Betty Clayton
1990-01-01
One method of making magic squares using a prolongated square is illustrated. Discussed are third-order magic squares, fractional magic squares, fifth-order magic squares, decimal magic squares, and even magic squares. (CW)
DEFF Research Database (Denmark)
Rose, Jeremy; Sæbø, Øystein
2005-01-01
On-line political communities, such as the Norwegian site Demokratitorget (Democracy Square), are often designed according to a set of un-reflected assumptions about the political interests of their potential members. In political science, democracy is not taken as given in this way, but can...... be represented by different models which characterize different relationships between politicians and the citizens they represent. This paper uses quantitative and qualitative content analysis to analyze the communication mediated by the Democracy Square discussion forum in the first ten months of its life......-Republican model. In the qualitative analysis the discourse is analysed as repeating genres – patterns in the communication form which also reflect the conflict of interest between citizens and politicians. Though the analysis gives insight into the nature of the discourse the site supports, little is known about...
Directory of Open Access Journals (Sweden)
H. Luce
2017-03-01
Full Text Available New comparisons between the square of the generalized potential refractive index gradient M2, estimated from the very high-frequency (VHF Middle and Upper Atmosphere (MU Radar, located at Shigaraki, Japan, and unmanned aerial vehicle (UAV measurements are presented. These comparisons were performed at unprecedented temporal and range resolutions (1–4 min and ∼ 20 m, respectively in the altitude range ∼ 1.27–4.5 km from simultaneous and nearly collocated measurements made during the ShUREX (Shigaraki UAV-Radar Experiment 2015 campaign. Seven consecutive UAV flights made during daytime on 7 June 2015 were used for this purpose. The MU Radar was operated in range imaging mode for improving the range resolution at vertical incidence (typically a few tens of meters. The proportionality of the radar echo power to M2 is reported for the first time at such high time and range resolutions for stratified conditions for which Fresnel scatter or a reflection mechanism is expected. In more complex features obtained for a range of turbulent layers generated by shear instabilities or associated with convective cloud cells, M2 estimated from UAV data does not reproduce observed radar echo power profiles. Proposed interpretations of this discrepancy are presented.
Double diffusive conjugate heat transfer: Part I
Azeem, Soudagar, Manzoor Elahi M.
2018-05-01
The present work is undertaken to investigate the effect of solid wall being placed at left of square cavity filled with porous medium. The presence of a solid wall in the porous medium turns the situation into a conjugate heat transfer problem. The boundary conditions are such that the left vertical surface is maintained at highest temperature and concentration whereas right vertical surface at lowest temperature and concentration in the medium. The top and bottom surfaces are adiabatic. The additional conduction equation along with the regular momentum and energy equations of porous medium are solved in an iterative manner with the help of finite element method. It is seen that the heat and mass transfer rate is lesser due to smaller thermal and concentration gradients.
1972-01-01
With the existing Systems for using the accelerated protons, it is possible to supply only one slow ejected beam (feeding the East Hall) and, at the same time, to have only a small percentage of the beam on an internal target (feeding the South Hall). The arrangement will be replaced by a new System called SQUARE (Semi- QUAdrupole Resonant Extraction) which will give greater flexibility in supplying the three areas.
Comparing implementations of penalized weighted least-squares sinogram restoration
International Nuclear Information System (INIS)
Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick
2010-01-01
Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix
Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems
Directory of Open Access Journals (Sweden)
Oskar Cahueñas
2013-05-01
Full Text Available We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new preconditioning strategies are embedded into simple and well-known iterative schemes that avoid the use of the, usually ill-conditioned, normal equations. We analyze a scheme to approximate the pseudoinverse, based on Schulz iterative method, and also different iterative schemes, based on extensions of Richardson's method, and the conjugate gradient method, that are suitable for preconditioning strategies. We present preliminary numerical results to illustrate the advantages of the proposed schemes.
Conjugate descent formulation of backpropagation error in ...
African Journals Online (AJOL)
nique of backpropagation was popularized in a paper by Rumelhart, et al. ... the training of a multilayer neural network using a gradient descent approach applied to a .... superior convergence of the conjugate descent method over a standard ...
Skeletonized Least Squares Wave Equation Migration
Zhan, Ge
2010-10-17
The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).
Masuda, Y; Misztal, I; Legarra, A; Tsuruta, S; Lourenco, D A L; Fragomeni, B O; Aguilar, I
2017-01-01
This paper evaluates an efficient implementation to multiply the inverse of a numerator relationship matrix for genotyped animals () by a vector (). The computation is required for solving mixed model equations in single-step genomic BLUP (ssGBLUP) with the preconditioned conjugate gradient (PCG). The inverse can be decomposed into sparse matrices that are blocks of the sparse inverse of a numerator relationship matrix () including genotyped animals and their ancestors. The elements of were rapidly calculated with the Henderson's rule and stored as sparse matrices in memory. Implementation of was by a series of sparse matrix-vector multiplications. Diagonal elements of , which were required as preconditioners in PCG, were approximated with a Monte Carlo method using 1,000 samples. The efficient implementation of was compared with explicit inversion of with 3 data sets including about 15,000, 81,000, and 570,000 genotyped animals selected from populations with 213,000, 8.2 million, and 10.7 million pedigree animals, respectively. The explicit inversion required 1.8 GB, 49 GB, and 2,415 GB (estimated) of memory, respectively, and 42 s, 56 min, and 13.5 d (estimated), respectively, for the computations. The efficient implementation required <1 MB, 2.9 GB, and 2.3 GB of memory, respectively, and <1 sec, 3 min, and 5 min, respectively, for setting up. Only <1 sec was required for the multiplication in each PCG iteration for any data sets. When the equations in ssGBLUP are solved with the PCG algorithm, is no longer a limiting factor in the computations.
preconditioning the modified conjugate gradient method
African Journals Online (AJOL)
Admin
steepest descent method, the number of matrix-vector products per iteration .... modified CGM algorithm is used for large class of problems that is not ..... New Trends in the Mathematical and Computer Sciences with Applications to Real World.
Optimising a parallel conjugate gradient solver
Energy Technology Data Exchange (ETDEWEB)
Field, M.R. [O`Reilly Institute, Dublin (Ireland)
1996-12-31
This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2003-01-01
We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation
Quaternion Gradient and Hessian
Xu, Dongpo; Mandic, Danilo P.
2014-01-01
The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel gen...
Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics
Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.
2003-02-01
Multi-conjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of AO degrees of freedom. In this paper, we develop an iterative sparse matrix implementation of minimum variance wavefront reconstruction for telescope diameters up to 32m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method, using a multigrid preconditioner incorporating a layer-oriented (block) symmetric Gauss-Seidel iterative smoothing operator. We present open-loop numerical simulation results to illustrate algorithm convergence.
He, Qiaolin
2011-06-01
In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
Watson, Gale A.
2003-01-01
Demonstrates the transformations that are possible to construct a variety of magic squares, including modifications to challenge students from elementary grades through algebra. Presents an example of using magic squares with students who have special needs. (YDS)
Multisource least-squares reverse-time migration with structure-oriented filtering
Fan, Jing-Wen; Li, Zhen-Chun; Zhang, Kai; Zhang, Min; Liu, Xue-Tong
2016-09-01
The technology of simultaneous-source acquisition of seismic data excited by several sources can significantly improve the data collection efficiency. However, direct imaging of simultaneous-source data or blended data may introduce crosstalk noise and affect the imaging quality. To address this problem, we introduce a structure-oriented filtering operator as preconditioner into the multisource least-squares reverse-time migration (LSRTM). The structure-oriented filtering operator is a nonstationary filter along structural trends that suppresses crosstalk noise while maintaining structural information. The proposed method uses the conjugate-gradient method to minimize the mismatch between predicted and observed data, while effectively attenuating the interference noise caused by exciting several sources simultaneously. Numerical experiments using synthetic data suggest that the proposed method can suppress the crosstalk noise and produce highly accurate images.
Least-squares finite-element method for shallow-water equations with source terms
Institute of Scientific and Technical Information of China (English)
Shin-Jye Liang; Tai-Wen Hsu
2009-01-01
Numerical solution of shallow-water equations (SWE) has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include: the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.
A systematic approach to robust preconditioning for gradient-based inverse scattering algorithms
International Nuclear Information System (INIS)
Nordebo, Sven; Fhager, Andreas; Persson, Mikael; Gustafsson, Mats
2008-01-01
This paper presents a systematic approach to robust preconditioning for gradient-based nonlinear inverse scattering algorithms. In particular, one- and two-dimensional inverse problems are considered where the permittivity and conductivity profiles are unknown and the input data consist of the scattered field over a certain bandwidth. A time-domain least-squares formulation is employed and the inversion algorithm is based on a conjugate gradient or quasi-Newton algorithm together with an FDTD-electromagnetic solver. A Fisher information analysis is used to estimate the Hessian of the error functional. A robust preconditioner is then obtained by incorporating a parameter scaling such that the scaled Fisher information has a unit diagonal. By improving the conditioning of the Hessian, the convergence rate of the conjugate gradient or quasi-Newton methods are improved. The preconditioner is robust in the sense that the scaling, i.e. the diagonal Fisher information, is virtually invariant to the numerical resolution and the discretization model that is employed. Numerical examples of image reconstruction are included to illustrate the efficiency of the proposed technique
Misiurewicz, Michal
2013-01-01
If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?
Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method
Sun, Yong; Meng, Zhaohai; Li, Fengting
2018-03-01
Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.
International Nuclear Information System (INIS)
Akita, Junji; Honma, Toei.
1975-01-01
Object: To provide a square through tube involving thermal movement in pipelines such as water supply pump driving turbine exhaust pipe (square-shaped), which is wide in freedom with respect to shape and dimension thereof for efficient installation at site. Structure: In a through tube to be airtightly retained for purpose of decontamination in an atomic power plant, comprising a seal rubber plate, a band and a bolt and a nut for securing said plate, the seal rubber plate being worked into the desired shape so that it may be placed in intimate contact with the concrete floor surface by utilization of elasticity of rubber, thereby providing airtightness at a corner portion of the square tube. (Kamimura, M.)
Fisher, Robert A
1983-01-01
This book appears at a time of intense activity in optical phase conjugation. We chose not to await the maturation of the field, but instead to provide this material in time to be useful in its development. We have tried very hard to elucidate and interrelate the various nonlinear phenomena which can be used for optical phase conjugation.
International Nuclear Information System (INIS)
Ward, G.J.; Heckbert, P.S.; Technische Hogeschool Delft
1992-04-01
A new method for improving the accuracy of a diffuse interreflection calculation is introduced in a ray tracing context. The information from a hemispherical sampling of the luminous environment is interpreted in a new way to predict the change in irradiance as a function of position and surface orientation. The additional computation involved is modest and the benefit is substantial. An improved interpolation of irradiance resulting from the gradient calculation produces smoother, more accurate renderings. This result is achieved through better utilization of ray samples rather than additional samples or alternate sampling strategies. Thus, the technique is applicable to a variety of global illumination algorithms that use hemicubes or Monte Carlo sampling techniques
Conjugate descent formulation of backpropagation error in ...
African Journals Online (AJOL)
The feedforward neural network architecture uses backpropagation learning to determine optimal weights between dierent interconnected layers. This learning procedure uses a gradient descent technique applied to a sum-of-squares error function for the given input-output pattern. It employs an iterative procedure to ...
Conjugate descent formulation of backpropagation error in feedforward neural networks
Directory of Open Access Journals (Sweden)
NK Sharma
2009-06-01
Full Text Available The feedforward neural network architecture uses backpropagation learning to determine optimal weights between different interconnected layers. This learning procedure uses a gradient descent technique applied to a sum-of-squares error function for the given input-output pattern. It employs an iterative procedure to minimise the error function for a given set of patterns, by adjusting the weights of the network. The first derivates of the error with respect to the weights identify the local error surface in the descent direction. Hence the network exhibits a different local error surface for every different pattern presented to it, and weights are iteratively modified in order to minimise the current local error. The determination of an optimal weight vector is possible only when the total minimum error (mean of the minimum local errors for all patterns from the training set may be minimised. In this paper, we present a general mathematical formulation for the second derivative of the error function with respect to the weights (which represents a conjugate descent for arbitrary feedforward neural network topologies, and we use this derivative information to obtain the optimal weight vector. The local error is backpropagated among the units of hidden layers via the second order derivative of the error with respect to the weights of the hidden and output layers independently and also in combination. The new total minimum error point may be evaluated with the help of the current total minimum error and the current minimised local error. The weight modification processes is performed twice: once with respect to the present local error and once more with respect to the current total or mean error. We present some numerical evidence that our proposed method yields better network weights than those determined via a conventional gradient descent approach.
Penyelesaian Persamaan Poisson 2D dengan Menggunakan Metode Gauss-Seidel dan Conjugate Gradien
Mahmudah, Dewi Erla; Naf'an, Muhammad Zidny
2017-01-01
In this paper we focus on solution of 2D Poisson equation numerically. 2D Poisson equation is a partial differential equation of second order elliptical type. This equation is a particular form or non-homogeneous form of the Laplace equation. The solution of 2D Poisson equation is performed numerically using Gauss Seidel method and Conjugate Gradient method. The result is the value using Gauss Seidel method and Conjugate Gradient method is same. But, consider the iteration process, the conver...
Particle-in-a-box model of exciton absorption and electroabsorption in conjugated polymers
Pedersen, Thomas G.
2000-12-01
The recently proposed particle-in-a-box model of one-dimensional excitons in conjugated polymers is applied in calculations of optical absorption and electroabsorption spectra. It is demonstrated that for polymers of long conjugation length a superposition of single exciton resonances produces a line shape characterized by a square-root singularity in agreement with experimental spectra near the absorption edge. The effects of finite conjugation length on both absorption and electroabsorption spectra are analyzed.
International Nuclear Information System (INIS)
Dory, R.A.; Uckan, N.A.; Ard, W.B.
1986-10-01
The ELMO Bumpy Square (EBS) concept consists of four straight magnetic mirror arrays linked by four high-field corner coils. Extensive calculations show that this configuration offers major improvements over the ELMO Bumpy Torus (EBT) in particle confinement, heating, transport, ring production, and stability. The components of the EBT device at Oak Ridge National Laboratory can be reconfigured into a square arrangement having straight sides composed of EBT coils, with new microwave cavities and high-field corners designed and built for this application. The elimination of neoclassical convection, identified as the dominant mechanism for the limited confinement in EBT, will give the EBS device substantially improved confinement and the flexibility to explore the concepts that produce this improvement. The primary goals of the EBS program are twofold: first, to improve the physics of confinement in toroidal systems by developing the concepts of plasma stabilization using the effects of energetic electrons and confinement optimization using magnetic field shaping and electrostatic potential control to limit particle drift, and second, to develop bumpy toroid devices as attractive candidates for fusion reactors. This report presents a brief review of the physics analyses that support the EBS concept, discussions of the design and expected performance of the EBS device, a description of the EBS experimental program, and a review of the reactor potential of bumpy toroid configurations. Detailed information is presented in the appendices
Qualidade conjugal: mapeando conceitos
Directory of Open Access Journals (Sweden)
Clarisse Mosmann
2006-12-01
Full Text Available Apesar da ampla utilização do conceito de qualidade conjugal, identifica-se falta de clareza conceitual acerca das variáveis que o compõem. Esse artigo apresenta revisão da literatura na área com o objetivo de mapear o conceito de qualidade conjugal. Foram analisadas sete principais teorias sobre o tema: Troca Social, Comportamental, Apego, Teoria da Crise, Interacionismo Simbólico. Pelos postulados propostos nas diferentes teorias, podem-se identificar três grupos de variáveis fundamentais na definição da qualidade conjugal: recursos pessoais dos cônjuges, contexto de inserção do casal e processos adaptativos. Neste sentido, a qualidade conjugal é resultado do processo dinâmico e interativo do casal, razão deste caráter multidimensional.
... version Home Brain, Spinal Cord, and Nerve Disorders Cranial Nerve Disorders Conjugate Gaze Palsies Horizontal gaze palsy Vertical ... Version. DOCTORS: Click here for the Professional Version Cranial Nerve Disorders Overview of the Cranial Nerves Internuclear Ophthalmoplegia ...
Conjugated Polymer Solar Cells
National Research Council Canada - National Science Library
Paraschuk, Dmitry Y
2006-01-01
This report results from a contract tasking Moscow State University as follows: Conjugated polymers are promising materials for many photonics applications, in particular, for photovoltaic and solar cell devices...
Polymers for Protein Conjugation
Directory of Open Access Journals (Sweden)
Gianfranco Pasut
2014-01-01
Full Text Available Polyethylene glycol (PEG at the moment is considered the leading polymer for protein conjugation in view of its unique properties, as well as to its low toxicity in humans, qualities which have been confirmed by its extensive use in clinical practice. Other polymers that are safe, biodegradable and custom-designed have, nevertheless, also been investigated as potential candidates for protein conjugation. This review will focus on natural polymers and synthetic linear polymers that have been used for protein delivery and the results associated with their use. Genetic fusion approaches for the preparation of protein-polypeptide conjugates will be also reviewed and compared with the best known chemical conjugation ones.
Williams, Horace E.
1974-01-01
A method for generating 3x3 magic squares is developed. A series of questions relating to these magic squares is posed. An invesitgation using matrix methods is suggested with some questions for consideration. (LS)
Refined isogeometric analysis for a preconditioned conjugate gradient solver
Garcia, Daniel; Pardo, D.; Dalcin, Lisandro; Calo, Victor M.
2018-01-01
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces C0 hyperplanes that act as separators for the direct LU factorization solver. As a result, the total computational cost
A Projected Conjugate Gradient Method for Sparse Minimax Problems
DEFF Research Database (Denmark)
Madsen, Kaj; Jonasson, Kristjan
1993-01-01
A new method for nonlinear minimax problems is presented. The method is of the trust region type and based on sequential linear programming. It is a first order method that only uses first derivatives and does not approximate Hessians. The new method is well suited for large sparse problems...... as it only requires that software for sparse linear programming and a sparse symmetric positive definite equation solver are available. On each iteration a special linear/quadratic model of the function is minimized, but contrary to the usual practice in trust region methods the quadratic model is only...... with the method are presented. In fact, we find that the number of iterations required is comparable to that of state-of-the-art quasi-Newton codes....
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
Czech Academy of Sciences Publication Activity Database
Benzi, M.; Cullum, J. K.; Tůma, Miroslav
2000-01-01
Roč. 22, č. 4 (2000), s. 1318-1332 ISSN 1064-8275 R&D Projects: GA AV ČR IAA2030706; GA AV ČR IAA2030801 Institutional research plan: AV0Z1030915 Subject RIV: BA - General Mathematics Impact factor: 1.421, year: 2000
Preconditioned conjugate gradient methods for the Navier-Stokes equations
Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing
1994-01-01
A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.
A conjugate gradient method for the spectral partitioning of graphs
Kruyt, Nicolaas P.
1997-01-01
The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and
Using Conjugate Gradient Network to Classify Stress Level of Patients.
Directory of Open Access Journals (Sweden)
Er. S. Pawar
2013-02-01
Full Text Available Diagnosis of stress is important because it can cause many diseases e.g., heart disease, headache, migraine, sleep problems, irritability etc. Diagnosis of stress in patients often involves acquisition of biological signals for example heart rate, electrocardiogram (ECG, electromyography signals (EMG etc. Stress diagnosis using biomedical signals is difficult and since the biomedical signals are too complex to generate any rule an experienced person or expert is needed to determine stress levels. Also, it is not feasible to use all the features that are available or possible to extract from the signal. So, relevant features should be chosen from the extracted features that are capable to diagnose stress. Electronics devices are increasingly being seen in the field of medicine for diagnosis, therapy, checking of stress levels etc. The research and development work of medical electronics engineers leads to the manufacturing of sophisticated diagnostic medical equipment needed to ensure good health care. Biomedical engineering combines the design and problem solving skills of engineering with medical and biological sciences to improve health care diagnosis and treatment.
The Deflated Preconditioned Conjugate Gradient Method Applied to Composite Materials
Jönsthövel, T.B.
2012-01-01
Simulations with composite materials often involve large jumps in the coefficients of the underlying stiffness matrix. These jumps can introduce unfavorable eigenvalues in the spectrum of the stiffness matrix. We show that the rigid body modes; the translations and rotations, of the disjunct rigid
Mapping the Conjugate Gradient Algorithm onto High Performance Heterogeneous Computers
2014-05-01
Solution of sparse indefinite systems of linear equations. Society for Industrial and Applied Mathematis 12(4), 617 –629. Parker, M. ( 2009 ). Taking advantage...44 vii 11 LIST OF SYMBOLS, ABBREVIATIONS, AND NOMENCLATURE API Application Programming Interface ASIC Application Specific Integrated Circuit...FPGA designer, 1 16 2 thus, final implementations were nearly always performed using fixed-point or integer arithmetic (Parker 2009 ). With the recent
Gradient-type methods in inverse parabolic problems
International Nuclear Information System (INIS)
Kabanikhin, Sergey; Penenko, Aleksey
2008-01-01
This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.
Chen, Y.-M.; Koniges, A. E.; Anderson, D. V.
1989-10-01
The biconjugate gradient method (BCG) provides an attractive alternative to the usual conjugate gradient algorithms for the solution of sparse systems of linear equations with nonsymmetric and indefinite matrix operators. A preconditioned algorithm is given, whose form resembles the incomplete L-U conjugate gradient scheme (ILUCG2) previously presented. Although the BCG scheme requires the storage of two additional vectors, it converges in a significantly lesser number of iterations (often half), while the number of calculations per iteration remains essentially the same.
DEFF Research Database (Denmark)
Hansen, Paul Robert
2015-01-01
To produce antibodies against synthetic peptides it is necessary to couple them to a protein carrier. This chapter provides a nonspecialist overview of peptide-carrier conjugation. Furthermore, a protocol for coupling cysteine-containing peptides to bovine serum albumin is outlined....
Photoluminescence in conjugated polymers
International Nuclear Information System (INIS)
Furst, J.E.; Laugesen, R.; Dastoor, P.; McNeill, C.
2002-01-01
Full text: Conjugated polymers combine the electronic and optical properties of semiconductors with the processability of polymers. They contain a sequence of alternate single and double carbon bonds so that the overlap of unhybridised p z orbitals creates a delocalised ρ system which gives semiconducting properties with p-bonding (valence) and p* -antibonding (conduction) bands. Photoluminesence (PL) in conjugated polymers results from the radiative decay of singlet excitons confined to a single chain. The present work is the first in a series of studies in our laboratory that will characterize the optical properties of conjugated polymers. The experiment involves the illumination of thin films of conjugated polymer with UV light (I=360 nm) and observing the subsequent fluorescence using a custom-built, fluorescence spectrometer. Photoluminesence spectra provide basic information about the structure of the polymer film. A typical spectrum is shown in the accompanying figure. The position of the first peak is related to the polymer chain length and resolved multiple vibronic peaks are an indication of film structure and morphology. We will also present results related to the optical degradation of these materials when exposed to air and UV light
Hsiao, Shih-Chia; Francis, Matthew B.; Bertozzi, Carolyn; Mathies, Richard; Chandra, Ravi; Douglas, Erik; Twite, Amy; Toriello, Nicholas; Onoe, Hiroaki
2018-05-15
The present invention provides conjugates of DNA and cells by linking the DNA to a native functional group on the cell surface. The cells can be without cell walls or can have cell walls. The modified cells can be linked to a substrate surface and used in assay or bioreactors.
Hsiao, Shih-Chia; Francis, Matthew B.; Bertozzi, Carolyn; Mathies, Richard; Chandra, Ravi; Douglas, Erik; Twite, Amy; Toriello, Nicholas; Onoe, Hiroaki
2016-05-03
The present invention provides conjugates of DNA and cells by linking the DNA to a native functional group on the cell surface. The cells can be without cell walls or can have cell walls. The modified cells can be linked to a substrate surface and used in assay or bioreactors.
From Square Dance to Mathematics
Bremer, Zoe
2010-01-01
In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…
International Nuclear Information System (INIS)
Pontaza, J.P.; Reddy, J.N.
2004-01-01
We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least-squares
Scintillation Reduction using Conjugate-Plane Imaging (Abstract)
Vander Haagen, G. A.
2017-12-01
(Abstract only) All observatories are plagued by atmospheric turbulence exhibited as star scintillation or "twinkle" whether a high altitude adaptive optics research or a 30-cm amateur telescope. It is well known that these disturbances are caused by wind and temperature-driven refractive gradients in the atmosphere and limit the ultimate photometric resolution of land-based facilities. One approach identified by Fuchs (1998) for scintillation noise reduction was to create a conjugate image space at the telescope and focus on the dominant conjugate turbulent layer within that space. When focused on the turbulent layer little or no scintillation exists. This technique is described whereby noise reductions of 6 to 11/1 have been experienced with mathematical and optical bench simulations. Discussed is a proof-of-principle conjugate optical train design for an 80-mm, f7 telescope.
Sparse least-squares reverse time migration using seislets
Dutta, Gaurav
2015-08-19
We propose sparse least-squares reverse time migration (LSRTM) using seislets as a basis for the reflectivity distribution. This basis is used along with a dip-constrained preconditioner that emphasizes image updates only along prominent dips during the iterations. These dips can be estimated from the standard migration image or from the gradient using plane-wave destruction filters or structural tensors. Numerical tests on synthetic datasets demonstrate the benefits of this method for mitigation of aliasing artifacts and crosstalk noise in multisource least-squares migration.
Full Gradient Solution to Adaptive Hybrid Control
Bean, Jacob; Schiller, Noah H.; Fuller, Chris
2017-01-01
This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.
Counting Triangles to Sum Squares
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
Antibody-radioisotope conjugates for tumor localization and treatment
International Nuclear Information System (INIS)
Larson, S.M.; Carrasquillo, J.A.
1985-01-01
In principle, anti-tumor antibodies can be used to carry radioactivity to tumors for in-vivo diagnosis and treatment of cancer. First, for diagnostic purposes, an antibody that targets a specific antigen (for example, the p97 antigen of human melanoma tumor), is labeled with a tracer amount of radioactivity. When this antibody-radioisotope conjugate is injected into the blood stream, the antibody carries the radioactivity throughout the body and in time, percolates through all the tissues of the body. Because the tumor has specific antigens to which the antibody can bind, the antibody conjugate progressively accumulates in the tumor. Using conventional nuclear medicine imaging equipment, the body of the patient is scanned for radioactivity content, and a map of the distribution of the radioactivity is displayed on photographic film. The tumor shows up as a dense area of radio-activity. These same antibody-radioisotope conjugates may be used for therapy of tumors, except that in this case large amounts of radioactivity are loaded on the antibody. After localization of the conjugate there is sufficient radiation deposited in the tumor of radiotherapy. The success of this approach in the clinic is determined in large measure by the concentration gradient that can be achieved between tissue antibody conjugate in tumor versus normal tissue
A Weighted Least Squares Approach To Robustify Least Squares Estimates.
Lin, Chowhong; Davenport, Ernest C., Jr.
This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…
Moreno, Carlos J
2005-01-01
Introduction Prerequisites Outline of Chapters 2 - 8 Elementary Methods Introduction Some Lemmas Two Fundamental Identities Euler's Recurrence for Sigma(n)More Identities Sums of Two Squares Sums of Four Squares Still More Identities Sums of Three Squares An Alternate Method Sums of Polygonal Numbers Exercises Bernoulli Numbers Overview Definition of the Bernoulli Numbers The Euler-MacLaurin Sum Formula The Riemann Zeta Function Signs of Bernoulli Numbers Alternate The von Staudt-Clausen Theorem Congruences of Voronoi and Kummer Irregular Primes Fractional Parts of Bernoulli Numbers Exercises Examples of Modular Forms Introduction An Example of Jacobi and Smith An Example of Ramanujan and Mordell An Example of Wilton: t (n) Modulo 23 An Example of Hamburger Exercises Hecke's Theory of Modular FormsIntroduction Modular Group ? and its Subgroup ? 0 (N) Fundamental Domains For ? and ? 0 (N) Integral Modular Forms Modular Forms of Type Mk(? 0(N);chi) and Euler-Poincare series Hecke Operators Dirichlet Series and ...
Organometallic B12-DNA conjugate
DEFF Research Database (Denmark)
Hunger, Miriam; Mutti, Elena; Rieder, Alexander
2014-01-01
Design, synthesis, and structural characterization of a B12-octadecanucleotide are presented herein, a new organometallic B12-DNA conjugate. In such covalent conjugates, the natural B12 moiety may be a versatile vector for controlled in vivo delivery of oligonucleotides to cellular targets in hum...
Graphs whose complement and square are isomorphic
DEFF Research Database (Denmark)
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Quantitative clinical uptake measurements using conjugate counting
International Nuclear Information System (INIS)
Lathrop, K.A.; Bartlett, R.D.; Chen, C.T.; Chou, J.S.; Faulhaber, P.F.; Harper, P.V.; Stark, V.J.
1986-01-01
While the use of conjugate counting for determination of organ uptake in human subjects has been extensively described, in the present study the determination of the organ uptake of ortho-iodohippurate presented several opportunities for validation of the in vivo counting data. Ortho-iodohippurate is distributed in the extracellular space, is largely extracted on each pass through the kidneys, and is not significantly deiodinated in vivo. Thus, the kidney uptake rate should be proportional to the blood level, the appearance rate of activity in the bladder is equal to the disappearance rate from the kidneys, and direct measurement of activity in the urine after voiding provides an internal standard for imaging measurements of bladder activity. Since the activity levels in the kidneys, bladder, and remainder of the body changed fairly rapidly, especially in the first 20 to 30 minutes following injection, posterior images of the trunk including kidneys and bladder were obtained continuously using a gamma camera fitted with a diverging collimator for 30 minutes and then at intervals for several hours. Simultaneous conjugate counting determinations were made using a whole body scanning system previously described at these meetings. Imaging data corrected for decay and adjacent background were fitted by least squares methods to curves representing a sum of exponentials, and the curves were normalized to the conjugate uptake measurements. The uptake curves of the kidneys and bladder matched well with the direct measurements of the urinary excretion. Data were collected in 16 normal subjects, and the estimated absorbed dose was calculated for the kidneys, the bladder and the remainder of the body for seven radioisotopes of iodine. 4 references, 6 figures, 2 tables
Agglomerative clustering of growing squares
Castermans, Thom; Speckmann, Bettina; Staals, Frank; Verbeek, Kevin; Bender, M.A.; Farach-Colton, M.; Mosteiro, M.A.
2018-01-01
We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish
Conjugation in Escherichia coli
Boyer, Herbert
1966-01-01
Boyer, Herbert (Yale University, New Haven, Conn.). Conjugation in Escherichia coli. J. Bacteriol. 91:1767–1772. 1966.—The sex factor of Escherichia coli K-12 was introduced into an E. coli B/r strain by circumventing the host-controlled modification and restriction incompatibilities known to exist between these closely related strains. The sexual properties of the constructed F+ B strain and its Hfr derivatives were examined. These studies showed that the E. coli strain B/r F+ and Hfr derivatives are similar to the E. coli strain K-12 F+ and Hfr derivatives. However, the site of sex factor integration was found to be dependent on the host genome. PMID:5327905
Electrochromic in conjugated polymers
International Nuclear Information System (INIS)
Picado Valenzuela, Alfredo
2007-01-01
This revision considered object the description of one of the materials with the greatest potential in the field of electrochromic (mainly in the visible region): the conjugated polymers (CP), area of enormous potential both now and in a short time ahead. The CP are insulating materials and organic semiconductors in a state not doped. They can be doped positively or negatively being observed a significant increase in the conductivity and being generated a color change in these materials. The understanding of how optical properties vary based on the chemical structure of the polymer or its mixtures and more precisely of the alternatives that can be entered into the conjugated system or π system to obtain a material that besides to be flexible, environmentally stable, presents the colored states. The revision was centred chiefly in the polypyrrole (Ppy), the polythiophene (PTh) and their derivatives such as poly (3.4-ethylenedioxythiophene) (PEDOT). The advantage of using monomers with variable structure, to adjust the composition of the copolymer, or to blend with the PC, allows to obtain a variety of colored states that can be modulated through the visible spectrum and even with applications to wavelengths outside of this region. Because the PC presented at least two different colored states can be varied continuously as a function of the voltage applied. In some cases, they may submit multicoloured statements, which offers a range of possibilities for their application in flexible electronic devices type screens and windows. Applications include smart windows, camouflage clothing and data screens. This type of material is emerging as one of the substitutes of the traditional inorganic semiconductor, with the advantage of its low cost, high flexibility and the possibility to generate multiple colors through the handling of the monomers in the structure and control of energy of his band gap. (author) [es
Ono, Shunsuke
2017-04-01
Minimizing L 0 gradient, the number of the non-zero gradients of an image, together with a quadratic data-fidelity to an input image has been recognized as a powerful edge-preserving filtering method. However, the L 0 gradient minimization has an inherent difficulty: a user-given parameter controlling the degree of flatness does not have a physical meaning since the parameter just balances the relative importance of the L 0 gradient term to the quadratic data-fidelity term. As a result, the setting of the parameter is a troublesome work in the L 0 gradient minimization. To circumvent the difficulty, we propose a new edge-preserving filtering method with a novel use of the L 0 gradient. Our method is formulated as the minimization of the quadratic data-fidelity subject to the hard constraint that the L 0 gradient is less than a user-given parameter α . This strategy is much more intuitive than the L 0 gradient minimization because the parameter α has a clear meaning: the L 0 gradient value of the output image itself, so that one can directly impose a desired degree of flatness by α . We also provide an efficient algorithm based on the so-called alternating direction method of multipliers for computing an approximate solution of the nonconvex problem, where we decompose it into two subproblems and derive closed-form solutions to them. The advantages of our method are demonstrated through extensive experiments.
Gradient pattern analysis applied to galaxy morphology
Rosa, R. R.; de Carvalho, R. R.; Sautter, R. A.; Barchi, P. H.; Stalder, D. H.; Moura, T. C.; Rembold, S. B.; Morell, D. R. F.; Ferreira, N. C.
2018-06-01
Gradient pattern analysis (GPA) is a well-established technique for measuring gradient bilateral asymmetries of a square numerical lattice. This paper introduces an improved version of GPA designed for galaxy morphometry. We show the performance of the new method on a selected sample of 54 896 objects from the SDSS-DR7 in common with Galaxy Zoo 1 catalogue. The results suggest that the second gradient moment, G2, has the potential to dramatically improve over more conventional morphometric parameters. It separates early- from late-type galaxies better (˜ 90 per cent) than the CAS system (C˜ 79 per cent, A˜ 50 per cent, S˜ 43 per cent) and a benchmark test shows that it is applicable to hundreds of thousands of galaxies using typical processing systems.
Energy Transfer Using Gradient Index Metamaterial
Directory of Open Access Journals (Sweden)
Boopalan Ganapathy
2018-01-01
Full Text Available The gradient refractive index structure in this paper is used to increase the quantum of energy transfer. This is done by improving the directive gain of the pyramidal horn antenna at a frequency of 10 GHz. A three-dimensional array of closed square rings is placed in front of the horn antenna aperture to form a gradient refractive index structure. This structure increases the directive gain by 1.6 dB as compared to that of the conventional horn antenna. The structure nearly doubles the wireless power transfer quantum between the transmitter and the receiver when placed at both ends. The increase in the directivity is achieved by converting the spherical wave emanating from the horn to a plane wave once it passes through the structure. This transformation is realized by the gradient refractive index structure being placed perpendicular to the direction of propagation. The gradient refractive index is constructed by changing the dimensions of a closed square ring placed in the unit cell of the array. The change in the refractive index gives rise to an improvement of the half power beam width and side lobe level compared to that of the normal horn. The design and simulation were done using CST Studio software.
Solar multi-conjugate adaptive optics performance improvement
Zhang, Zhicheng; Zhang, Xiaofang; Song, Jie
2015-08-01
In order to overcome the effect of the atmospheric anisoplanatism, Multi-Conjugate Adaptive Optics (MCAO), which was developed based on turbulence correction by means of several deformable mirrors (DMs) conjugated to different altitude and by which the limit of a small corrected FOV that is achievable with AO is overcome and a wider FOV is able to be corrected, has been widely used to widen the field-of-view (FOV) of a solar telescope. With the assistance of the multi-threaded Adaptive Optics Simulator (MAOS), we can make a 3D reconstruction of the distorted wavefront. The correction is applied by one or more DMs. This technique benefits from information about atmospheric turbulence at different layers, which can be used to reconstruct the wavefront extremely well. In MAOS, the sensors are either simulated as idealized wavefront gradient sensors, tip-tilt sensors based on the best Zernike fit, or a WFS using physical optics and incorporating user specified pixel characteristics and a matched filter pixel processing algorithm. Only considering the atmospheric anisoplanatism, we focus on how the performance of a solar MCAO system is related to the numbers of DMs and their conjugate heights. We theoretically quantify the performance of the tomographic solar MCAO system. The results indicate that the tomographic AO system can improve the average Strehl ratio of a solar telescope by only employing one or two DMs conjugated to the optimum altitude. And the S.R. has a significant increase when more deformable mirrors are used. Furthermore, we discuss the effects of DM conjugate altitude on the correction achievable by the MCAO system, and present the optimum DM conjugate altitudes.
NIF optics phase gradient specfication
International Nuclear Information System (INIS)
Williams, W.; Auerbach, J.; Hunt, J.; Lawson, L.; Manes, K.; Orth, C.; Sacks, R.; Trenholme, J.; Wegner, P.
1997-01-01
A root-mean-square (rms) phase gradient specification seems to allow a good connection between the NIP optics quality and focal spot requirements. Measurements on Beamlet optics individually, and as a chain, indicate they meet the assumptions necessary to use this specification, and that they have a typical rms phase gradient of ∼80 angstrom/cm. This may be sufficient for NIP to meet the proposed Stockpile Stewardship Management Program (SSMP) requirements of 80% of a high- power beam within a 200-250 micron diameter spot. Uncertainties include, especially, the scale length of the optics phase noise, the ability of the adaptive optic to correct against pump-induced distortions and optics noise, and the possibility of finding mitigation techniques against whole-beam self-focusing (e.g. a pre- correction optic). Further work is needed in these areas to better determine the NIF specifications. This memo is a written summary of a presentation on this topic given by W. Williams 24 April 1997 to NIP and LS ampersand T personnel
Entanglements in Conjugated Polymers
Xie, Renxuan; Lee, Youngmin; Aplan, Melissa; Caggiano, Nick; Gomez, Enrique; Colby, Ralph
Conjugated polymers, such as poly(3-hexylthiophene-2,5-diyl) (P3HT) and poly-((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-bis(thiophen-5-yl)-2,1,3-benzothiadiazole]-2',2''-diyl) (PFTBT), are widely used as hole and electron transport materials in a variety of electronic devices. However, fundamental knowledge regarding chain entanglements and nematic-to-isotropic transition is still lacking and are crucial to maximize charge transport properties. A systematic melt rheology study on P3HT with various molecular weights and regio regularities was performed. We find that the entanglement molecular weight Me is 5.0 kg/mol for regiorandom P3HT, but the apparent Me for regioregular P3HT is significantly higher. The difference is postulated to arise from the presence of a nematic phase only in regioregular P3HT. Analogously, PFTBT shows a clear rheological signature of the nematic-to-isotropic transition as a reversible sharp transition at 278 C. Shearing of this nematic phase leads to anisotropic crystalline order in PFTBT. We postulate that aligning the microstructure will impact charge transport and thereby advance the field of conducting polymers. National Science Foundation.
Regularized image denoising based on spectral gradient optimization
International Nuclear Information System (INIS)
Lukić, Tibor; Lindblad, Joakim; Sladoje, Nataša
2011-01-01
Image restoration methods, such as denoising, deblurring, inpainting, etc, are often based on the minimization of an appropriately defined energy function. We consider energy functions for image denoising which combine a quadratic data-fidelity term and a regularization term, where the properties of the latter are determined by a used potential function. Many potential functions are suggested for different purposes in the literature. We compare the denoising performance achieved by ten different potential functions. Several methods for efficient minimization of regularized energy functions exist. Most are only applicable to particular choices of potential functions, however. To enable a comparison of all the observed potential functions, we propose to minimize the objective function using a spectral gradient approach; spectral gradient methods put very weak restrictions on the used potential function. We present and evaluate the performance of one spectral conjugate gradient and one cyclic spectral gradient algorithm, and conclude from experiments that both are well suited for the task. We compare the performance with three total variation-based state-of-the-art methods for image denoising. From the empirical evaluation, we conclude that denoising using the Huber potential (for images degraded by higher levels of noise; signal-to-noise ratio below 10 dB) and the Geman and McClure potential (for less noisy images), in combination with the spectral conjugate gradient minimization algorithm, shows the overall best performance
Purification Efficacy of Synthetic Cannabinoid Conjugates Using High-Pressure Liquid Chromatography
conducted using high-pressure liquid chromatography and gradient screens to determine the most effective means of purifying the SC:dark quencher conjugates...to obtain the highest yields and purity. The purity was verified using liquid chromatographycoupled mass spectroscopy and nuclear magnetic resonance.
Protein carriers of conjugate vaccines
Pichichero, Michael E
2013-01-01
The immunogenicity of polysaccharides as human vaccines was enhanced by coupling to protein carriers. Conjugation transformed the T cell-independent polysaccharide vaccines of the past to T cell-dependent antigenic vaccines that were much more immunogenic and launched a renaissance in vaccinology. This review discusses the conjugate vaccines for prevention of infections caused by Hemophilus influenzae type b, Streptococcus pneumoniae, and Neisseria meningitidis. Specifically, the characteristics of the proteins used in the construction of the vaccines including CRM, tetanus toxoid, diphtheria toxoid, Neisseria meningitidis outer membrane complex, and Hemophilus influenzae protein D are discussed. The studies that established differences among and key features of conjugate vaccines including immunologic memory induction, reduction of nasopharyngeal colonization and herd immunity, and antibody avidity and avidity maturation are presented. Studies of dose, schedule, response to boosters, of single protein carriers with single and multiple polysaccharides, of multiple protein carriers with multiple polysaccharides and conjugate vaccines administered concurrently with other vaccines are discussed along with undesirable consequences of conjugate vaccines. The clear benefits of conjugate vaccines in improving the protective responses of the immature immune systems of young infants and the senescent immune systems of the elderly have been made clear and opened the way to development of additional vaccines using this technology for future vaccine products. PMID:23955057
Fullwood, James; Wang, Dongxu
2018-01-01
We introduce a class of F-theory vacua whose smooth elliptic fibers admit a vanishing $j$-invariant, and construct a weak coupling limit associated with such vacua which we view as the `square' of the Sen limit. We find that while Sen's limit is naturally viewed as an orientifold theory, the universal tadpole relation which equates the D3 charge between the associated F-theory compactification and the limit we construct suggests that perhaps the limiting theory is in fact an oriented theory c...
Renaming Zagreb Streets and Squares
Directory of Open Access Journals (Sweden)
Jelena Stanić
2009-06-01
Full Text Available The paper deals with changes in street names in the city of Zagreb. Taking the Lower Town (Donji grad city area as an example, the first part of the paper analyses diachronic street name changes commencing from the systematic naming of streets in 1878. Analysis of official changes in street names throughout Zagreb’s history resulted in categorisation of five periods of ideologically motivated naming/name-changing: 1. the Croatia modernisation period, when the first official naming was put into effect, with a marked tendency towards politicisation and nationalisation of the urban landscape; 2. the period of the Kingdom of the Serbs, Croatians and Slovenians/Yugoslavia, when symbols of the new monarchy, the idea of the fellowship of the Southern Slavs, Slavenophilism and the pro-Slavic geopolitical orientation were incorporated into the street names, and when the national idea was highly evident and remained so in that process; 3. the period of the NDH, the Independent State of Croatia, with decanonisation of the tokens of the Yugoslavian monarchy and the Southern Slavic orientation, and reference to the Ustashi and the German Nazi and Italian Fascist movement; 4. the period of Socialism, embedding the ideals and heroes of the workers’ movement and the War of National Liberation into the canonical system; and, 5. the period following the democratic changes in 1990, when almost all the signs of Socialism and the Communist/Antifascist struggle were erased, with the prominent presence of a process of installing new references to early national culture and historical tradition. The closing part of the paper deals with public discussions connected with the selection of a location for a square to bear the name of the first president of independent Croatia, Franjo Tuđman. Analysis of these public polemics shows two opposing discourses: the right-wing political option, which supports a central position for the square and considers the chosen area to
Latin squares and their applications
Keedwell, A Donald
2015-01-01
Latin Squares and Their Applications Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader 'from the beginnings of the subject to the frontiers of research'. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the
Wavelet methods in multi-conjugate adaptive optics
International Nuclear Information System (INIS)
Helin, T; Yudytskiy, M
2013-01-01
The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem, a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domains. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate-gradient-based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory. (paper)
Conjugated Fatty Acid Synthesis
Rawat, Richa; Yu, Xiao-Hong; Sweet, Marie; Shanklin, John
2012-01-01
Conjugated linolenic acids (CLNs), 18:3 Δ9,11,13, lack the methylene groups found between the double bonds of linolenic acid (18:3 Δ9,12,15). CLNs are produced by conjugase enzymes that are homologs of the oleate desaturases FAD2. The goal of this study was to map the domain(s) within the Momordica charantia conjugase (FADX) responsible for CLN formation. To achieve this, a series of Momordica FADX-Arabidopsis FAD2 chimeras were expressed in the Arabidopsis fad3fae1 mutant, and the transformed seeds were analyzed for the accumulation of CLN. These experiments identified helix 2 and the first histidine box as a determinant of conjugase product partitioning into punicic acid (18:3 Δ9cis,11trans,13cis) or α-eleostearic acid (18:3 Δ9cis,11trans,13trans). This was confirmed by analysis of a FADX mutant containing six substitutions in which the sequence of helix 2 and first histidine box was converted to that of FAD2. Each of the six FAD2 substitutions was individually converted back to the FADX equivalent identifying residues 111 and 115, adjacent to the first histidine box, as key determinants of conjugase product partitioning. Additionally, expression of FADX G111V and FADX G111V/D115E resulted in an approximate doubling of eleostearic acid accumulation to 20.4% and 21.2%, respectively, compared with 9.9% upon expression of the native Momordica FADX. Like the Momordica conjugase, FADX G111V and FADX D115E produced predominantly α-eleostearic acid and little punicic acid, but the FADX G111V/D115E double mutant produced approximately equal amounts of α-eleostearic acid and its isomer, punicic acid, implicating an interactive effect of residues 111 and 115 in punicic acid formation. PMID:22451660
Quantum dot conjugates in a sub-micrometer fluidic channel
Stavis, Samuel M.; Edel, Joshua B.; Samiee, Kevan T.; Craighead, Harold G.
2010-04-13
A nanofluidic channel fabricated in fused silica with an approximately 500 nm square cross section was used to isolate, detect and identify individual quantum dot conjugates. The channel enables the rapid detection of every fluorescent entity in solution. A laser of selected wavelength was used to excite multiple species of quantum dots and organic molecules, and the emission spectra were resolved without significant signal rejection. Quantum dots were then conjugated with organic molecules and detected to demonstrate efficient multicolor detection. PCH was used to analyze coincident detection and to characterize the degree of binding. The use of a small fluidic channel to detect quantum dots as fluorescent labels was shown to be an efficient technique for multiplexed single molecule studies. Detection of single molecule binding events has a variety of applications including high throughput immunoassays.
Quantum dot conjugates in a sub-micrometer fluidic channel
Stavis, Samuel M [Ithaca, NY; Edel, Joshua B [Brookline, MA; Samiee, Kevan T [Ithaca, NY; Craighead, Harold G [Ithaca, NY
2008-07-29
A nanofluidic channel fabricated in fused silica with an approximately 500 nm square cross section was used to isolate, detect and identify individual quantum dot conjugates. The channel enables the rapid detection of every fluorescent entity in solution. A laser of selected wavelength was used to excite multiple species of quantum dots and organic molecules, and the emission spectra were resolved without significant signal rejection. Quantum dots were then conjugated with organic molecules and detected to demonstrate efficient multicolor detection. PCH was used to analyze coincident detection and to characterize the degree of binding. The use of a small fluidic channel to detect quantum dots as fluorescent labels was shown to be an efficient technique for multiplexed single molecule studies. Detection of single molecule binding events has a variety of applications including high throughput immunoassays.
Research study of conjugate materials; Conjugate material no chosa kenkyu
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-03-01
The paper reported an introductory research on possibilities of new glass `conjugate materials.` The report took up the structure and synthetic process of conjugate materials to be researched/developed, classified them according to structural elements on molecular, nanometer and cluster levels, and introduced the structures and functions. Further, as glasses with new functions to be proposed, the paper introduced transparent and high-strength glass used for houses and vehicles, light modulation glass which realizes energy saving and optical data processing, and environmentally functional glass which realizes environmental cleaning or high performance biosensor. An initial survey was also conducted on rights of intellectual property to be taken notice of in Japan and abroad in the present situation. Reports were summed up and introduced of Osaka National Research Institute, Electrotechnical Laboratory, and National Industrial Research Institute of Nagoya which are all carrying out leading studies of conjugate materials. 235 refs., 135 figs., 6 tabs.
Travelling gradient thermocouple calibration
International Nuclear Information System (INIS)
Broomfield, G.H.
1975-01-01
A short discussion of the origins of the thermocouple EMF is used to re-introduce the idea that the Peltier and Thompson effects are indistinguishable from one another. Thermocouples may be viewed as devices which generate an EMF at junctions or as integrators of EMF's developed in thermal gradients. The thermal gradient view is considered the more appropriate, because of its better accord with theory and behaviour, the correct approach to calibration, and investigation of service effects is immediately obvious. Inhomogeneities arise in thermocouples during manufacture and in service. The results of travelling gradient measurements are used to show that such effects are revealed with a resolution which depends on the length of the gradient although they may be masked during simple immersion calibration. Proposed tests on thermocouples irradiated in a nuclear reactor are discussed
Conjugated polymer nanoparticles, methods of using, and methods of making
Habuchi, Satoshi
2017-03-16
Embodiments of the present disclosure provide for conjugated polymer nanoparticle, method of making conjugated polymer nanoparticles, method of using conjugated polymer nanoparticle, polymers, and the like.
Conjugated polymer nanoparticles, methods of using, and methods of making
Habuchi, Satoshi; Piwonski, Hubert Marek; Michinobu, Tsuyoshi
2017-01-01
Embodiments of the present disclosure provide for conjugated polymer nanoparticle, method of making conjugated polymer nanoparticles, method of using conjugated polymer nanoparticle, polymers, and the like.
Conjugated polymer zwitterions and solar cells comprising conjugated polymer zwitterions
Emrick, Todd; Russell, Thomas; Page, Zachariah; Liu, Yao
2018-06-05
A conjugated polymer zwitterion includes repeating units having structure (I), (II), or a combination thereof ##STR00001## wherein Ar is independently at each occurrence a divalent substituted or unsubstituted C3-30 arylene or heteroarylene group; L is independently at each occurrence a divalent C1-16 alkylene group, C6-30arylene or heteroarylene group, or alkylene oxide group; and R1 is independently at each occurrence a zwitterion. A polymer solar cell including the conjugated polymer zwitterion is also disclosed.
Squares of Random Linear Codes
DEFF Research Database (Denmark)
Cascudo Pueyo, Ignacio; Cramer, Ronald; Mirandola, Diego
2015-01-01
a positive answer, for codes of dimension $k$ and length roughly $\\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$. The proof uses random coding and combinatorial arguments, together with algebraic tools involving the precise......Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code ``typically'' fill the whole space? We give...
Gradient Alloy for Optical Packaging
National Aeronautics and Space Administration — Advances in additive manufacturing, such as Laser Engineered Net Shaping (LENS), enables the fabrication of compositionally gradient microstructures, i.e. gradient...
Square-root measurement for pure states
International Nuclear Information System (INIS)
Huang Siendong
2005-01-01
Square-root measurement is a very useful suboptimal measurement in many applications. It was shown that the square-root measurement minimizes the squared error for pure states. In this paper, the least squared error problem is reformulated and a new proof is provided. It is found that the least squared error depends only on the average density operator of the input states. The properties of the least squared error are then discussed, and it is shown that if the input pure states are uniformly distributed, the average probability of error has an upper bound depending on the least squared error, the rank of the average density operator, and the number of the input states. The aforementioned properties help explain why the square-root measurement can be effective in decoding processes
36 CFR 910.67 - Square guidelines.
2010-07-01
... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Square guidelines. 910.67... GUIDELINES AND UNIFORM STANDARDS FOR URBAN PLANNING AND DESIGN OF DEVELOPMENT WITHIN THE PENNSYLVANIA AVENUE DEVELOPMENT AREA Glossary of Terms § 910.67 Square guidelines. Square Guidelines establish the Corporation's...
High Gradient Accelerator Research
International Nuclear Information System (INIS)
Temkin, Richard
2016-01-01
The goal of the MIT program of research on high gradient acceleration is the development of advanced acceleration concepts that lead to a practical and affordable next generation linear collider at the TeV energy level. Other applications, which are more near-term, include accelerators for materials processing; medicine; defense; mining; security; and inspection. The specific goals of the MIT program are: • Pioneering theoretical research on advanced structures for high gradient acceleration, including photonic structures and metamaterial structures; evaluation of the wakefields in these advanced structures • Experimental research to demonstrate the properties of advanced structures both in low-power microwave cold test and high-power, high-gradient test at megawatt power levels • Experimental research on microwave breakdown at high gradient including studies of breakdown phenomena induced by RF electric fields and RF magnetic fields; development of new diagnostics of the breakdown process • Theoretical research on the physics and engineering features of RF vacuum breakdown • Maintaining and improving the Haimson / MIT 17 GHz accelerator, the highest frequency operational accelerator in the world, a unique facility for accelerator research • Providing the Haimson / MIT 17 GHz accelerator facility as a facility for outside users • Active participation in the US DOE program of High Gradient Collaboration, including joint work with SLAC and with Los Alamos National Laboratory; participation of MIT students in research at the national laboratories • Training the next generation of Ph. D. students in the field of accelerator physics.
Spectrum of resistivity gradient driven turbulence
International Nuclear Information System (INIS)
Terry, P.W.; Diamond, P.H.; Shaing, K.C.; Garcia, L.; Carreras, B.A.
1986-01-01
The resistivity fluctuation correlation function and electrostatic potential spectrum of resistivity gradient driven turbulence are calculated analytically and compared to the results of three dimensional numerical calculations. Resistivity gradient driven turbulence is characterized by effective Reynolds' numbers of order unity. Steady-state solution of the renormalized spectrum equations yields an electrostatic potential spectrum (circumflex phi 2 )/sub ktheta/ approx. k/sub theta//sup -3.25/. Agreement of the analytically calculated potential spectrum and mean-square radial velocity with the results of multiple helicity numerical calculations is excellent. This comparison constitutes a quantitative test of the analytical turbulence theory used. The spectrum of magnetic fluctuations is also calculated, and agrees well with that obtained from the numerical computations. 13 refs., 8 figs
Conjugal Pairing in Escherichia Coli
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 8. Conjugal Pairing in Escherichia Coli. Joshua Lederberg. Classics Volume 13 Issue 8 August 2008 pp 793-794. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/013/08/0793-0794 ...
Persistence Mechanisms of Conjugative Plasmids
DEFF Research Database (Denmark)
Bahl, Martin Iain; Hansen, Lars H.; Sørensen, Søren Johannes
2009-01-01
Are plasmids selfish parasitic DNA molecules or an integrated part of the bacterial genome? This chapter reviews the current understanding of the persistence mechanisms of conjugative plasmids harbored by bacterial cells and populations. The diversity and intricacy of mechanisms affecting the suc...
Bacteriophytochromes control conjugation in Agrobacterium fabrum.
Bai, Yingnan; Rottwinkel, Gregor; Feng, Juan; Liu, Yiyao; Lamparter, Tilman
2016-08-01
Bacterial conjugation, the transfer of single stranded plasmid DNA from donor to recipient cell, is mediated through the type IV secretion system. We performed conjugation assays using a transmissible artificial plasmid as reporter. With this assay, conjugation in Agrobacterium fabrum was modulated by the phytochromes Agp1 and Agp2, photoreceptors that are most sensitive in the red region of visible light. In conjugation studies with wild-type donor cells carrying a pBIN-GUSINT plasmid as reporter that lacked the Ti (tumor inducing) plasmid, no conjugation was observed. When either agp1(-) or agp2(-) knockout donor strains were used, plasmid DNA was delivered to the recipient, indicating that both phytochromes suppress conjugation in the wild type donor. In the recipient strains, the loss of Agp1 or Agp2 led to diminished conjugation. When wild type cells with Ti plasmid and pBIN-GUS reporter plasmid were used as donor, a high rate of conjugation was observed. The DNA transfer was down regulated by red or far-red light by a factor of 3.5. With agp1(-) or agp2(-) knockout donor cells, conjugation in the dark was about 10 times lower than with the wild type donor, and with the double knockout donor no conjugation was observed. These results imply that the phytochrome system has evolved to inhibit conjugation in the light. The decrease of conjugation under different temperature correlated with the decrease of phytochrome autophosphorylation. Copyright © 2015 Elsevier B.V. All rights reserved.
REVIEW ARTICLE Conjugated Hyperbilirubinaemia in Early Infancy ...
African Journals Online (AJOL)
REVIEW ARTICLE Conjugated Hyperbilirubinaemia in Early Infancy. AOK Johnson. Abstract. Conjugated hyperbilirubinaemia exists when the conjugated serum bilirubin level is more than 2 mg/dl or more than 20 per cent of the total serum bilirubin. It is always pathological in early infancy. The causes are many and diverse ...
Purification of SUMO conjugating enzymes and kinetic analysis of substrate conjugation
Yunus, Ali A.; Lima, Christopher D.
2009-01-01
SUMO conjugation to protein substrates requires the concerted action of a dedicated E2 ubiquitin conjugation enzyme (Ubc9) and associated E3 ligases. Although Ubc9 can directly recognize and modify substrate lysine residues that occur within a consensus site for SUMO modification, E3 ligases can redirect specificity and enhance conjugation rates during SUMO conjugation in vitro and in vivo. In this chapter, we will describe methods utilized to purify SUMO conjugating enzymes and model substrates which can be used for analysis of SUMO conjugation in vitro. We will also describe methods to extract kinetic parameters during E3-dependent or E3-independent substrate conjugation. PMID:19107417
Giovannini, Massimo
2015-01-01
Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
High gradient superconducting quadrupoles
International Nuclear Information System (INIS)
Lundy, R.A.; Brown, B.C.; Carson, J.A.; Fisk, H.E.; Hanft, R.H.; Mantsch, P.M.; McInturff, A.D.; Remsbottom, R.H.
1987-07-01
Prototype superconducting quadrupoles with a 5 cm aperture and gradient of 16 kG/cm have been built and tested as candidate magnets for the final focus at SLC. The magnets are made from NbTi Tevatron style cable with 10 inner and 14 outer turns per quadrant. Quench performance and multipole data are presented. Design and data for a low current, high gradient quadrupole, similar in cross section but wound with a cable consisting of five insulated conductors are also discussed
Conjugated heat transfer in laminar flow between parallel-plates channel
International Nuclear Information System (INIS)
Guedes, R.O.C.; Cotta, R.M.; Brum, N.C.L.
1989-01-01
An analysis is made of conjugated convective-conductive heat transfer in laminar flow of a newtonian fluid between parallel-plates channel, taking into account the longitudinal conduction along the duct walls only, by neglecting the transversal temperature gradients in the solid. This extended Graetz-type problem is then analytically handled through the generalized integral transform technique, providing accurate numerical results for quantities of practical interest sucyh as bulk and wall temperatures, and Nusselt numbers. The effects of a conjugation parameter and Biot number on heat transfer behavior are then investigated. (author)
Superconducting gravity gradiometer and a test of inverse square law
International Nuclear Information System (INIS)
Moody, M.V.; Paik, H.J.
1989-01-01
The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth
Gaze, Eric C.
2005-01-01
We introduce a cooperative learning, group lab for a Calculus III course to facilitate comprehension of the gradient vector and directional derivative concepts. The lab is a hands-on experience allowing students to manipulate a tangent plane and empirically measure the effect of partial derivatives on the direction of optimal ascent. (Contains 7…
Square pulse linear transformer driver
Directory of Open Access Journals (Sweden)
A. A. Kim
2012-04-01
Full Text Available The linear transformer driver (LTD technological approach can result in relatively compact devices that can deliver fast, high current, and high-voltage pulses straight out of the LTD cavity without any complicated pulse forming and pulse compression network. Through multistage inductively insulated voltage adders, the output pulse, increased in voltage amplitude, can be applied directly to the load. The usual LTD architecture [A. A. Kim, M. G. Mazarakis, V. A. Sinebryukhov, B. M. Kovalchuk, V. A. Vizir, S. N Volkov, F. Bayol, A. N. Bastrikov, V. G. Durakov, S. V. Frolov, V. M. Alexeenko, D. H. McDaniel, W. E. Fowler, K. LeCheen, C. Olson, W. A. Stygar, K. W. Struve, J. Porter, and R. M. Gilgenbach, Phys. Rev. ST Accel. Beams 12, 050402 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050402; M. G. Mazarakis, W. E. Fowler, A. A. Kim, V. A. Sinebryukhov, S. T. Rogowski, R. A. Sharpe, D. H. McDaniel, C. L. Olson, J. L. Porter, K. W. Struve, W. A. Stygar, and J. R. Woodworth, Phys. Rev. ST Accel. Beams 12, 050401 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050401] provides sine shaped output pulses that may not be well suited for some applications like z-pinch drivers, flash radiography, high power microwaves, etc. A more suitable power pulse would have a flat or trapezoidal (rising or falling top. In this paper, we present the design and first test results of an LTD cavity that generates such a type of output pulse by including within its circular array a number of third harmonic bricks in addition to the main bricks. A voltage adder made out of a square pulse cavity linear array will produce the same shape output pulses provided that the timing of each cavity is synchronized with the propagation of the electromagnetic pulse.
Weighted conditional least-squares estimation
International Nuclear Information System (INIS)
Booth, J.G.
1987-01-01
A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered
Sets of Mutually Orthogonal Sudoku Latin Squares
Vis, Timothy; Petersen, Ryan M.
2009-01-01
A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…
The Square Light Clock and Special Relativity
Galli, J. Ronald; Amiri, Farhang
2012-01-01
A thought experiment that includes a square light clock is similar to the traditional vertical light beam and mirror clock, except it is made up of four mirrors placed at a 45[degree] angle at each corner of a square of length L[subscript 0], shown in Fig. 1. Here we have shown the events as measured in the rest frame of the square light clock. By…
Bigravity from gradient expansion
International Nuclear Information System (INIS)
Yamashita, Yasuho; Tanaka, Takahiro
2016-01-01
We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.
2010-03-31
nonimaging design capabilities to incorporate 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 12-04-2011 13. SUPPLEMENTARY NOTES The views, opinions...Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Imaging Optics, Nonimaging Optics, Gradient Index Optics, Camera, Concentrator...imaging and nonimaging design capabilities to incorporate manufacturable GRIN lenses can provide imaging lens systems that are compact and
Conjugate heat transfer effects on wall bubble nucleation in subcooled flashing flows
International Nuclear Information System (INIS)
Peterson, P.F.; Hijikata, K.
1990-01-01
A variety of models have been proposed to explain observations that large liquid superheat is required to initiate nucleation in flashing flows of subcooled liquids in nozzles, cracks and pipes. In such flows an abrupt change in the fluid temperature occurs downstream of the nucleating cavities. This paper examines the subcooling of the nucleating cavities due to conjugate heat transfer to the cold downstream fluid. This examination suggests a mechanism limiting the maximum active cavity size. Simple analysis shows that, of the total superheat required to initiate flashing, a substantial portion results from conjugate wall subcooling, which decreases the cavity vapor pressure. The specific case of flashing critical nozzle flow is examined in detail. Here boundary-layer laminarization due to the strong favorable pressure gradient aids the analysis of conjugate heat transfer
Distribution of squares modulo a composite number
Aryan, Farzad
2015-01-01
In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.
Some Theoretical Essences of Lithuania Squares Formation
Directory of Open Access Journals (Sweden)
Gintautas Tiškus
2016-04-01
Full Text Available In the Lithuanian acts of law and in the scientific literature there are no clear criteria and notions to define a square. The unbuilt city space places or the gaps between buildings are often defined as the squares, which do not have clear limits or destination. The mandatory attributes of the place which is called the square are indicated in the article, the notion of square is defined. The article deals with Lithuanian squares theme, analyses the differences between representation and representativeness. The article aims to indicate an influence of city environmental context and monument in the square on its function. The square is an independent element of city plan structure, but it is not an independent element of city spatial structure. The space and environment of the square are related to each other not only by physical, aesthetical relations, but as well as by causalities, which may be named as the essences of squares’ formation. The interdisciplinary discourse analysis method is applied in the article.
Entrywise Squared Transforms for GAMP Supplementary Material
DEFF Research Database (Denmark)
2016-01-01
Supplementary material for a study on Entrywise Squared Transforms for Generalized Approximate Message Passing (GAMP). See the README file for the details.......Supplementary material for a study on Entrywise Squared Transforms for Generalized Approximate Message Passing (GAMP). See the README file for the details....
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
Didar, Tohid Fatanat; Tabrizian, Maryam
2012-11-07
Here we present a microfluidic platform to generate multiplex gradients of biomolecules within parallel microfluidic channels, in which a range of multiplex concentration gradients with different profile shapes are simultaneously produced. Nonlinear polynomial gradients were also generated using this device. The gradient generation principle is based on implementing parrallel channels with each providing a different hydrodynamic resistance. The generated biomolecule gradients were then covalently functionalized onto the microchannel surfaces. Surface gradients along the channel width were a result of covalent attachments of biomolecules to the surface, which remained functional under high shear stresses (50 dyn/cm(2)). An IgG antibody conjugated to three different fluorescence dyes (FITC, Cy5 and Cy3) was used to demonstrate the resulting multiplex concentration gradients of biomolecules. The device enabled generation of gradients with up to three different biomolecules in each channel with varying concentration profiles. We were also able to produce 2-dimensional gradients in which biomolecules were distributed along the length and width of the channel. To demonstrate the applicability of the developed design, three different multiplex concentration gradients of REDV and KRSR peptides were patterned along the width of three parallel channels and adhesion of primary human umbilical vein endothelial cell (HUVEC) in each channel was subsequently investigated using a single chip.
BIOMECHANICS. Why the seahorse tail is square.
Porter, Michael M; Adriaens, Dominique; Hatton, Ross L; Meyers, Marc A; McKittrick, Joanna
2015-07-03
Whereas the predominant shapes of most animal tails are cylindrical, seahorse tails are square prisms. Seahorses use their tails as flexible grasping appendages, in spite of a rigid bony armor that fully encases their bodies. We explore the mechanics of two three-dimensional-printed models that mimic either the natural (square prism) or hypothetical (cylindrical) architecture of a seahorse tail to uncover whether or not the square geometry provides any functional advantages. Our results show that the square prism is more resilient when crushed and provides a mechanism for preserving articulatory organization upon extensive bending and twisting, as compared with its cylindrical counterpart. Thus, the square architecture is better than the circular one in the context of two integrated functions: grasping ability and crushing resistance. Copyright © 2015, American Association for the Advancement of Science.
Structure Property Relationships in Organic Conjugated Systems
O'Neill, Luke
2008-01-01
A series of pi(п) conjugated oligomers containing 1 to 6 monomer units were studied by absorption and photoluminescence spectroscopies. The results are discussed and examined with regard to the variation of the optical properties with the increase of effective conjugation length. It was found that there was a linear relationship between the positioning of the absorption and photoluminescence maxima plotted against inverse conjugation length. The relationships are in good agreement with the si...
Conjugated Polymers for Energy Production
DEFF Research Database (Denmark)
Livi, Francesco
This dissertation is aimed at developing materials for flexible, large area, ITO-free polymer solar cells (PSCs) fully printed under ambient conditions. A large screening of conjugated polymers, both novel and well-known materials, has been carried out in order to find suitable candidates...... polymerization method for industrial production of polymers. Several DArP protocols have been employed for the synthesis of PPDTBT leading to polymers with high structural regularity and photovoltaic performances comparable with the same materials synthesized via Stille cross-coupling polymerization...
Novel ?-cyclodextrin?eosin conjugates
Benkovics, G?bor; Afonso, Damien; Darcsi, Andr?s; B?ni, Szabolcs; Conoci, Sabrina; Fenyvesi, ?va; Szente, Lajos; Malanga, Milo; Sortino, Salvatore
2017-01-01
Eosin B (EoB) and eosin Y (EoY), two xanthene dye derivatives with photosensitizing ability were prepared in high purity through an improved synthetic route. The dyes were grafted to a 6-monoamino-β-cyclodextrin scaffold under mild reaction conditions through a stable amide linkage using the coupling agent 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholinium chloride. The molecular conjugates, well soluble in aqueous medium, were extensively characterized by 1D and 2D NMR spectroscopy an...
Test of charge conjugation invariance
International Nuclear Information System (INIS)
Nefkens, B.M.K.; Prakhov, S.; Gaardestig, A.; Clajus, M.; Marusic, A.; McDonald, S.; Phaisangittisakul, N.; Price, J.W.; Starostin, A.; Tippens, W.B.; Allgower, C.E.; Spinka, H.; Bekrenev, V.; Koulbardis, A.; Kozlenko, N.; Kruglov, S.; Lopatin, I.; Briscoe, W.J.; Shafi, A.; Comfort, J.R.
2005-01-01
We report on the first determination of upper limits on the branching ratio (BR) of η decay to π 0 π 0 γ and to π 0 π 0 π 0 γ. Both decay modes are strictly forbidden by charge conjugation (C) invariance. Using the Crystal Ball multiphoton detector, we obtained BR(η→π 0 π 0 γ) -4 at the 90% confidence level, in support of C invariance of isoscalar electromagnetic interactions of the light quarks. We have also measured BR(η→π 0 π 0 π 0 γ) -5 at the 90% confidence level, in support of C invariance of isovector electromagnetic interactions
Wetting of flat gradient surfaces.
Bormashenko, Edward
2018-04-01
Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces is treated within the variational approach, under which the contact line is free to move along the substrate. Transversality conditions of the variational problem give rise to the generalized Young equation valid for gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet, placed on a gradient surface depends on the radius of the contact line and the values of derivatives of interfacial tensions. The linear approximation of the problem is considered. It is demonstrated that the contact angle hysteresis is inevitable on gradient surfaces. Electrowetting of gradient surfaces is discussed. Copyright © 2018 Elsevier Inc. All rights reserved.
Around and Beyond the Square of Opposition
Béziau, Jean-Yves
2012-01-01
aiThe theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, psychology. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original theory of oppositions of Aristotle. The square of opposition is a very attractive theme which has been going through centuries without evaporating. Since 10 years there is a new growing interest for
Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Sarmin, Nor Haniza
2014-07-01
The nonabelian tensor product was originated in homotopy theory as well as in algebraic K-theory. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action are taken to be conjugation. In this paper, the computation of nonabelian tensor square of a Bieberbach group, which is a torsion free crystallographic group, of dimension five with dihedral point group of order eight is determined. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results.
Study of the convergence behavior of the complex kernel least mean square algorithm.
Paul, Thomas K; Ogunfunmi, Tokunbo
2013-09-01
The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.
Weighted least-squares criteria for electrical impedance tomography
International Nuclear Information System (INIS)
Kallman, J.S.; Berryman, J.G.
1992-01-01
Methods are developed for design of electrical impedance tomographic reconstruction algorithms with specified properties. Assuming a starting model with constant conductivity or some other specified background distribution, an algorithm with the following properties is found: (1) the optimum constant for the starting model is determined automatically; (2) the weighted least-squares error between the predicted and measured power dissipation data is as small as possible; (3) the variance of the reconstructed conductivity from the starting model is minimized; (4) potential distributions with the largest volume integral of gradient squared have the least influence on the reconstructed conductivity, and therefore distributions most likely to be corrupted by contact impedance effects are deemphasized; (5) cells that dissipate the most power during the current injection tests tend to deviate least from the background value. The resulting algorithm maps the reconstruction problem into a vector space where the contribution to the inversion from the background conductivity remains invariant, while the optimum contributions in orthogonal directions are found. For a starting model with nonconstant conductivity, the reconstruction algorithm has analogous properties
Elmo bumpy square plasma confinement device
Owen, L.W.
1985-01-01
The invention is an Elmo bumpy type plasma confinement device having a polygonal configuration of closed magnet field lines for improved plasma confinement. In the preferred embodiment, the device is of a square configuration which is referred to as an Elmo bumpy square (EBS). The EBS is formed by four linear magnetic mirror sections each comprising a plurality of axisymmetric assemblies connected in series and linked by 90/sup 0/ sections of a high magnetic field toroidal solenoid type field generating coils. These coils provide corner confinement with a minimum of radial dispersion of the confined plasma to minimize the detrimental effects of the toroidal curvature of the magnetic field. Each corner is formed by a plurality of circular or elliptical coils aligned about the corner radius to provide maximum continuity in the closing of the magnetic field lines about the square configuration confining the plasma within a vacuum vessel located within the various coils forming the square configuration confinement geometry.
Quantized kernel least mean square algorithm.
Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C
2012-01-01
In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.
Anomalous structural transition of confined hard squares.
Gurin, Péter; Varga, Szabolcs; Odriozola, Gerardo
2016-11-01
Structural transitions are examined in quasi-one-dimensional systems of freely rotating hard squares, which are confined between two parallel walls. We find two competing phases: one is a fluid where the squares have two sides parallel to the walls, while the second one is a solidlike structure with a zigzag arrangement of the squares. Using transfer matrix method we show that the configuration space consists of subspaces of fluidlike and solidlike phases, which are connected with low probability microstates of mixed structures. The existence of these connecting states makes the thermodynamic quantities continuous and precludes the possibility of a true phase transition. However, thermodynamic functions indicate strong tendency for the phase transition and our replica exchange Monte Carlo simulation study detects several important markers of the first order phase transition. The distinction of a phase transition from a structural change is practically impossible with simulations and experiments in such systems like the confined hard squares.
The inverse square law of gravitation
International Nuclear Information System (INIS)
Cook, A.H.
1987-01-01
The inverse square law of gravitation is very well established over the distances of celestial mechanics, while in electrostatics the law has been shown to be followed to very high precision. However, it is only within the last century that any laboratory experiments have been made to test the inverse square law for gravitation, and all but one has been carried out in the last ten years. At the same time, there has been considerable interest in the possibility of deviations from the inverse square law, either because of a possible bearing on unified theories of forces, including gravitation or, most recently, because of a possible additional fifth force of nature. In this article the various lines of evidence for the inverse square law are summarized, with emphasis upon the recent laboratory experiments. (author)
Conjugated polymers developed from alkynes
Institute of Scientific and Technical Information of China (English)
Yajing Liu; Jacky W.Y.Lam; Ben Zhong Tang
2015-01-01
The numerous merits of conjugated polymers(CPs) have encouraged scientists to develop a variety of synthetic routes to CPs with diverse structures and functionalities. Among the large scope of substrates,alkyne plays an important role in constructing polymers with conjugated backbones. In addition to some well-developed reactions including Glaser–Hay and Sonogashira coupling, azide/thiol-yne click reaction and cyclotrimerization, some novel alkyne-based reactions have also been explored such as oxidative polycoupling, decarbonylative polycoupling and multicomponent tandem polymerizations. his review focuses on the recent progress on the synthetic methodology of CPs in the last ive years using monomers with two or more triple bonds and some of their high-technological applications. Selected examples of materials properties of these CPs are given in this review, such as luorescence response to chemical or physical stimuli, magnetism, white light emission, cell imaging and bioprobing. Finally, a short perspective is raised in regard to the outlook of the preparation methodologies, functionalities as well as potential applications of CPs in the future.
Subgap Absorption in Conjugated Polymers
Sinclair, M.; Seager, C. H.; McBranch, D.; Heeger, A. J; Baker, G. L.
1991-01-01
Along with X{sup (3)}, the magnitude of the optical absorption in the transparent window below the principal absorption edge is an important parameter which will ultimately determine the utility of conjugated polymers in active integrated optical devices. With an absorptance sensitivity of materials. We have used PDS to measure the optical absorption spectra of the conjugated polymers poly(1,4-phenylene-vinylene) (and derivitives) and polydiacetylene-4BCMU in the spectral region from 0.55 eV to 3 eV. Our spectra show that the shape of the absorption edge varies considerably from polymer to polymer, with polydiacetylene-4BCMU having the steepest absorption edge. The minimum absorption coefficients measured varied somewhat with sample age and quality, but were typically in the range 1 cm{sup {minus}1} to 10 cm{sup {minus}1}. In the region below 1 eV, overtones of C-H stretching modes were observed, indicating that further improvements in transparency in this spectral region might be achieved via deuteration of fluorination.
Subgap absorption in conjugated polymers
Energy Technology Data Exchange (ETDEWEB)
Sinclair, M.; Seager, C.H. (Sandia National Labs., Albuquerque, NM (USA)); McBranch, D.; Heeger, A.J. (California Univ., Santa Barbara, CA (USA)); Baker, G.L. (Bell Communications Research, Inc., Red Bank, NJ (USA))
1991-01-01
Along with X{sup (3)}, the magnitude of the optical absorption in the transparent window below the principal absorption edge is an important parameter which will ultimately determine the utility of conjugated polymers in active integrated optical devices. With an absorptance sensitivity of < 10{sup {minus}5}, Photothermal Deflection Spectroscopy (PDS) is ideal for determining the absorption coefficients of thin films of transparent'' materials. We have used PDS to measure the optical absorption spectra of the conjugated polymers poly(1,4-phenylene-vinylene) (and derivitives) and polydiacetylene-4BCMU in the spectral region from 0.55 eV to 3 eV. Our spectra show that the shape of the absorption edge varies considerably from polymer to polymer, with polydiacetylene-4BCMU having the steepest absorption edge. The minimum absorption coefficients measured varied somewhat with sample age and quality, but were typically in the range 1 cm{sup {minus}1} to 10 cm{sup {minus}1}. In the region below 1 eV, overtones of C-H stretching modes were observed, indicating that further improvements in transparency in this spectral region might be achieved via deuteration of fluorination. 11 refs., 4 figs.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
Power Efficient Division and Square Root Unit
DEFF Research Database (Denmark)
Liu, Wei; Nannarelli, Alberto
2012-01-01
Although division and square root are not frequent operations, most processors implement them in hardware to not compromise the overall performance. Two classes of algorithms implement division or square root: digit-recurrence and multiplicative (e.g., Newton-Raphson) algorithms. Previous work....... The proposed unit is compared to similar solutions based on the digit-recurrence algorithm and it is compared to a unit based on the multiplicative Newton-Raphson algorithm....
DENDRIMER CONJUGATES FOR SELECTIVE OF PROTEIN AGGREGATES
DEFF Research Database (Denmark)
2004-01-01
Dendrimer conjugates are presented, which are formed between a dendrimer and a protein solubilising substance. Such dendrimer conjugates are effective in the treatment of protein aggregate-related diseases (e.g. prion-related diseases). The protein solubilising substance and the dendrimer together...
Tetrafullerene conjugates for all-organic photovoltaics
Fernández, G.; Sánchez, L.; Veldman, D.; Wienk, M.M.; Atienza, C.M.; Guldi, D.M.; Janssen, R.A.J.; Martin, N.
2008-01-01
The synthesis of two new tetrafullerene nanoconjugates in which four C60 units are covalently connected through different -conjugated oligomers (oligo(p-phenylene ethynylene) and oligo(p-phenylene vinylene)) is described. The photovoltaic (PV) response of these C60-based conjugates was evaluated by
CONJUGATED BLOCK-COPOLYMERS FOR ELECTROLUMINESCENT DIODES
Hilberer, A; Gill, R.E; Herrema, J.K; Malliaras, G.G; Wildeman, J.; Hadziioannou, G
In this article we review results obtained in our laboratory on the design and study of new light-emitting polymers. We are interested in the synthesis and characterisation of block copolymers with regularly alternating conjugated and non conjugated sequences. The blocks giving rise to luminescence
The Conjugate Acid-Base Chart.
Treptow, Richard S.
1986-01-01
Discusses the difficulties that beginning chemistry students have in understanding acid-base chemistry. Describes the use of conjugate acid-base charts in helping students visualize the conjugate relationship. Addresses chart construction, metal ions, buffers and pH titrations, and the organic functional groups and nonaqueous solvents. (TW)
Bio-Conjugates for Nanoscale Applications
DEFF Research Database (Denmark)
Villadsen, Klaus
Bio-conjugates for Nanoscale Applications is the title of this thesis, which covers three different projects in chemical bio-conjugation research, namely synthesis and applications of: Lipidated fluorescent peptides, carbohydrate oxime-azide linkers and N-aryl O-R2 oxyamine derivatives. Lipidated...
Class, Kinship Density, and Conjugal Role Segregation.
Hill, Malcolm D.
1988-01-01
Studied conjugal role segregation in 150 married women from intact families in working-class community. Found that, although involvement in dense kinship networks was associated with conjugal role segregation, respondents' attitudes toward marital roles and phase of family cycle when young children were present were more powerful predictors of…
Least squares shadowing sensitivity analysis of a modified Kuramoto–Sivashinsky equation
International Nuclear Information System (INIS)
Blonigan, Patrick J.; Wang, Qiqi
2014-01-01
Highlights: •Modifying the Kuramoto–Sivashinsky equation and changing its boundary conditions make it an ergodic dynamical system. •The modified Kuramoto–Sivashinsky equation exhibits distinct dynamics for three different ranges of system parameters. •Least squares shadowing sensitivity analysis computes accurate gradients for a wide range of system parameters. - Abstract: Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto–Sivashinsky (K–S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K–S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters
Misonidazole-glutathione conjugates in CHO cells
International Nuclear Information System (INIS)
Varghese, A.J.; Whitmore, G.F.
1984-01-01
Misonidazole, after reduction to the hydroxylamine derivative, reacts with glutathione (GSH) under physiological conditions. The reaction product has been identified as a mixture of two isomeric conjugates. When water soluble extracts of CHO cells exposed to misonidazole under hypoxic conditions are subjected to HPLC analysis, misonidazole derivatives, having the same chromatographic properties as the GSH-MISO conjugates, were detected. When CHO cells were incubated with misonidazole in the presence of added GSH, a substantial increase in the amount of the conjugate was detected. When extracts of CHO cells exposed to misonidazole under hypoxia were subsequently exposed to GSH, an increased formation of the conjugate was observed. A rearrangement product of the hydroxylamine derivative of misonidazole is postulated as the reactive intermediate responsible for the formation of the conjugate
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Test of Newton's inverse-square law in the Greenland ice cap
International Nuclear Information System (INIS)
Ander, M.E.; Zumberge, M.A.; Lautzenhiser, T.
1989-01-01
An Airy-type geophysical experiment was conducted in a 2-km-deep hole in the Greenland ice cap at depths between 213 and 1673 m to test for possible violations of Newton's inverse-square law. An anomalous gravity gradient was observed. We cannot unambiguously attribute it to a breakdown of Newtonian gravity because we have shown that it might be due to unexpected geological features in the rock below the ice
Error analysis of stochastic gradient descent ranking.
Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan
2013-06-01
Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.
Gradient Boosting Machines, A Tutorial
Directory of Open Access Journals (Sweden)
Alexey eNatekin
2013-12-01
Full Text Available Gradient boosting machines are a family of powerful machine-learning techniques that have shown considerable success in a wide range of practical applications. They are highly customizable to the particular needs of the application, like being learned with respect to different loss functions. This article gives a tutorial introduction into the methodology of gradient boosting methods. A theoretical information is complemented with many descriptive examples and illustrations which cover all the stages of the gradient boosting model design. Considerations on handling the model complexity are discussed. A set of practical examples of gradient boosting applications are presented and comprehensively analyzed.
International Nuclear Information System (INIS)
Kim, Kyung Min; Yun, Nam Geon; Jeon, Yun Heung; Lee, Dong Hyun; Cho, Yung Hee
2010-01-01
Prediction of temperature distributions on hot components is important in development of a gas turbine combustion liner. The present study investigated conjugated heat transfer to obtain temperature distributions in a combustion liner with six combustion nozzles. 3D numerical simulations using FVM commercial codes, Fluent and CFX were performed to calculate combustion and heat transfer distributions. The temperature distributions in the combustor liner were calculated by conjugation of conduction and convection (heat transfer coefficients) obtained by combustion and cooling flow analysis. The wall temperature was the highest on the attachment points of the combustion gas from combustion nozzles, but the temperature gradient was high at the after shell section with low wall temperature
Gradient waveform synthesis for magnetic propulsion using MRI gradient coils
International Nuclear Information System (INIS)
Han, B H; Lee, S Y; Park, S
2008-01-01
Navigating an untethered micro device in a living subject is of great interest for both diagnostic and therapeutic applications. Magnetic propulsion of an untethered device carrying a magnetic core in it is one of the promising methods to navigate the device. MRI gradients coils are thought to be suitable for navigating the device since they are capable of magnetic propulsion in any direction while providing magnetic resonance images. For precise navigation of the device, especially in the peripheral region of the gradient coils, the concomitant gradient fields, as well as the linear gradient fields in the main magnetic field direction, should be considered in driving the gradient coils. For simple gradient coil configurations, the Maxwell coil in the z-direction and the Golay coil in the x- and y-directions, we have calculated the magnetic force fields, which are not necessarily the same as the conventional linear gradient fields of MRI. Using the calculated magnetic force fields, we have synthesized gradient waveforms to navigate the device along a desired path
Non-spill control squared cascade
International Nuclear Information System (INIS)
Kai, Tsunetoshi; Inoue, Yoshiya; Oya, Akio; Suemori, Nobuo.
1974-01-01
Object: To reduce a mixed loss thus enhancing separating efficiency by the provision of a simple arrangement wherein a reflux portion in a conventional spill control squared cascade is replaced by a special stage including centrifugal separators. Structure: Steps in the form of a square cascade, in which a plurality of centrifugal separators are connected by pipe lines, are accumulated in multistage fashion to form a squared cascade. Between the adjoining steps is disposed a special stage including a centrifugal separator which receives both lean flow from the upper step and rich flow from the lower step. The centrifugal separator in the special stage has its rich side connected to the upper step and its lean side connected to the lower step. Special stages are each disposed at the upper side of the uppermost step and at the lower side of the lowermost step. (Kamimura, M.)
Least Squares Data Fitting with Applications
DEFF Research Database (Denmark)
Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data....... In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis...
Denaturing gradient gel electrophoresis
International Nuclear Information System (INIS)
Kocherginskaya, S.A.; Cann, I.K.O.; Mackie, R.I.
2005-01-01
It is worthwhile considering that only some 30 species make up the bulk of the bacterial population in human faeces at any one time based on the classical cultivation-based approach. The situation in the rumen is similar. Thus, it is practical to focus on specific groups of interest within the complex community. These may be the predominant or the most active species, specific physiological groups or readily identifiable (genetic) clusters of phylogenetically related organisms. Several 16S rDNA fingerprinting techniques can be invaluable for selecting and monitoring sequences or phylogenetic groups of interest and are described below. Over the past few decades, considerable attention was focussed on the identification of pure cultures of microbes on the basis of genetic polymorphisms of DNA encoding rRNA such as ribotyping, amplified fragment length polymorphism and randomly amplified polymorphic DNA. However, many of these methods require prior cultivation and are less suitable for use in analysis of complex mixed populations although important in describing cultivated microbial diversity in molecular terms. Much less attention was given to molecular characterization of complex communities. In particular, research into diversity and community structure over time has been revolutionized by the advent of molecular fingerprinting techniques for complex communities. Denaturing or temperature gradient gel electrophoresis (DGGE/TGGE) methods have been successfully applied to the analysis of human, pig, cattle, dog and rodent intestinal populations
Ion temperature gradient instability
International Nuclear Information System (INIS)
1989-01-01
Anomalous ion thermal conductivity remains an open physics issue for the present generation of high temperature Tokamaks. It is generally believed to be due to Ion Temperature Gradient Instability (η i mode). However, it has been difficult, if not impossible to identify this instability and study the anomalous transport due to it, directly. Therefore the production and identification of the mode is pursued in the simpler and experimentally convenient configuration of the Columbia Linear Machine (CLM). CLM is a steady state machine which already has all the appropriate parameters, except η i . This parameter is being increased to the appropriate value of the order of 1 by 'feathering' a tungsten screen located between the plasma source and the experimental cell to flatten the density profile and appropriate redesign of heating antennas to steepen the ion temperature profile. Once the instability is produced and identified, a thorough study of the characteristics of the mode can be done via a wide range of variation of all the critical parameters: η i , parallel wavelength, etc
Good Filtrations and the Steinberg Square
DEFF Research Database (Denmark)
Kildetoft, Tobias
that tensoring the Steinberg module with a simple module of restricted highest weight gives a module with a good filtration. This result was first proved by Andersen when the characteristic is large enough. In this dissertation, generalizations of those results, which are joint work with Daniel Nakano......, the socle completely determines how a Steinberg square decomposes. The dissertation also investigates the socle of the Steinberg square for a finite group of Lie type, again providing formulas which describe how to find the multiplicity of a simple module in the socle, given information about...
Characterization of gradient control systems
Cortés, Jorge; van der Schaft, Arjan; Crouch, Peter E.
2005-01-01
Given a general nonlinear affine control system with outputs and a torsion-free affine connection defined on its state space, we investigate the gradient realization problem: we give necessary and sufficient conditions under which the control system can be written as a gradient control system
Characterization of Gradient Control Systems
Cortés, Jorge; Schaft, Arjan van der; Crouch, Peter E.
2005-01-01
Given a general nonlinear affine control system with outputs and a torsion-free affine connection defined on its state space, we investigate the gradient realization problem: we give necessary and sufficient conditions under which the control system can be written as a gradient control system
Sobolev gradients and differential equations
Neuberger, J W
2010-01-01
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...
Electric field gradients in metals
International Nuclear Information System (INIS)
Schatz, G.
1979-01-01
A review of the recent works on electric field gradient in metals is given. The main emphasis is put on the temperature dependence of the electric field gradient in nonmagnetic metals. Some methods of investigation of this effect using nuclear probes are described. One of them is nuclear accoustic resonance method. (S.B.)
Novel Aflatoxin Derivatives and Protein Conjugates
Directory of Open Access Journals (Sweden)
Reinhard Niessner
2007-03-01
Full Text Available Aflatoxins, a group of structurally related mycotoxins, are well known for their toxic and carcinogenic effects in humans and animals. Aflatoxin derivatives and protein conjugates are needed for diverse analytical applications. This work describes a reliable and fast synthesis of novel aflatoxin derivatives, purification by preparative HPLC and characterisation by ESI-MS and one- and two-dimensional NMR. Novel aflatoxin bovine serum albumin conjugates were prepared and characterised by UV absorption and MALDI-MS. These aflatoxin protein conjugates are potentially interesting as immunogens for the generation of aflatoxin selective antibodies with novel specificities.
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...
Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients
Directory of Open Access Journals (Sweden)
Nauman Raza
2016-01-01
Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.
Self-diffusion of particles interacting through a square-well or square-shoulder potential
Wilbertz, H.; Michels, J.; Beijeren, H. van; Leegwater, J.A.
1988-01-01
The diffusion coefficient and velocity autocorrelation function for a fluid of particles interacting through a square-well or square-shoulder potential are calculated from a kinetic theory similar to the Davis-Rice-Sengers theory and the results are compared to those of computer simulations. At low
Multiples least-squares reverse time migration
Zhang, Dongliang; Zhan, Ge; Dai, Wei; Schuster, Gerard T.
2013-01-01
To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated
Least-squares variance component estimation
Teunissen, P.J.G.; Amiri-Simkooei, A.R.
2007-01-01
Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight
Square root approximation to the poisson channel
Tsiatmas, A.; Willems, F.M.J.; Baggen, C.P.M.J.
2013-01-01
Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding
Latin square three dimensional gage master
Jones, Lynn L.
1982-01-01
A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.
Time Scale in Least Square Method
Directory of Open Access Journals (Sweden)
Özgür Yeniay
2014-01-01
Full Text Available Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.
Group-wise partial least square regression
Camacho, José; Saccenti, Edoardo
2018-01-01
This paper introduces the group-wise partial least squares (GPLS) regression. GPLS is a new sparse PLS technique where the sparsity structure is defined in terms of groups of correlated variables, similarly to what is done in the related group-wise principal component analysis. These groups are
Clar sextets in square graphene antidot lattices
DEFF Research Database (Denmark)
Petersen, Rene; Pedersen, Thomas Garm; Jauho, Antti-Pekka
2011-01-01
A periodic array of holes transforms graphene from a semimetal into a semiconductor with a band gap tuneable by varying the parameters of the lattice. In earlier work only hexagonal lattices have been treated. Using atomistic models we here investigate the size of the band gap of a square lattice...
Deformation analysis with Total Least Squares
Directory of Open Access Journals (Sweden)
M. Acar
2006-01-01
Full Text Available Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS and the Total Least Squares (TLS, respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.
Optimistic semi-supervised least squares classification
DEFF Research Database (Denmark)
Krijthe, Jesse H.; Loog, Marco
2017-01-01
The goal of semi-supervised learning is to improve supervised classifiers by using additional unlabeled training examples. In this work we study a simple self-learning approach to semi-supervised learning applied to the least squares classifier. We show that a soft-label and a hard-label variant ...
Least-squares model-based halftoning
Pappas, Thrasyvoulos N.; Neuhoff, David L.
1992-08-01
A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach
International Nuclear Information System (INIS)
Hadley, S.W.; Wilbur, D.S.
1990-01-01
The preparations and conjugations of 2,3,5,6-tetrafluorophenyl 5-[125I/131I]iodo-4-pentenoate (7a) and 2,3,5,6-tetrafluorophenyl 3,3-dimethyl-5-[125I/131I]iodo-4-pentenoate (7b) to monoclonal antibodies are reported. Reagents 7a and 7b were prepared in high radiochemical yield by iododestannylation of their corresponding 5-tri-n-butylstannyl precursors. Radioiodinated antibody conjugates were prepared by reaction of 7a or 7b with the protein at basic pH. Evaluation of these conjugates by several in vitro procedures demonstrated that the radiolabel was attached to the antibody in a stable manner and that the conjugates maintained immunoreactivity. Comparative dual-isotope biodistribution studies of a monoclonal antibody Fab fragment conjugate of 7a and 7b with the same Fab fragment labeled with N-succinimidyl p-[131I]iodobenzoate (PIB, p-iodobenzoate, 2) or directly radioiodinated have been carried out in tumor-bearing nude mice. Coinjection of the Fab conjugate of 7a with the Fab conjugate of 2 demonstrated that the biodistributions were similar in most organs, except the neck tissue (thyroid-containing) and the stomach, which contained substantially increased levels of the 7a label. Coinjection of the Fab conjugate of 7a with the Fab fragment radioiodinated by using the chloramine-T method demonstrated that the biodistributions were remarkably similar, suggesting roughly equivalent in vivo deiodination of these labeled antibody fragments. Coinjection of the Fab conjugate of 7a with the Fab conjugate of 7b indicated that there was ∼ a 2-fold reduction in the amount of in vivo deiodination of the 7b conjugate as compared to the 7a conjugate
Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.
Xu, Dongpo; Xia, Yili; Mandic, Danilo P
2016-02-01
The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion variables are essentially nonanalytic, which are prohibitive to the development of quaternion-valued learning systems. To address this issue, we propose new definitions of quaternion gradient and Hessian, based on the novel generalized Hamilton-real (GHR) calculus, thus making a possible efficient derivation of general optimization algorithms directly in the quaternion field, rather than using the isomorphism with the real domain, as is current practice. In addition, unlike the existing quaternion gradients, the GHR calculus allows for the product and chain rule, and for a one-to-one correspondence of the novel quaternion gradient and Hessian with their real counterparts. Properties of the quaternion gradient and Hessian relevant to numerical applications are also introduced, opening a new avenue of research in quaternion optimization and greatly simplified the derivations of learning algorithms. The proposed GHR calculus is shown to yield the same generic algorithm forms as the corresponding real- and complex-valued algorithms. Advantages of the proposed framework are illuminated over illustrative simulations in quaternion signal processing and neural networks.
Investigation of Ionospheric Spatial Gradients for Gagan Error Correction
Chandra, K. Ravi
In India, Indian Space Research Organization (ISRO) has established with an objective to develop space technology and its application to various national tasks. The national tasks include, establishment of major space systems such as Indian National Satellites (INSAT) for communication, television broadcasting and meteorological services, Indian Remote Sensing Satellites (IRS), etc. Apart from these, to cater to the needs of civil aviation applications, GPS Aided Geo Augmented Navigation (GAGAN) system is being jointly implemented along with Airports Authority of India (AAI) over the Indian region. The most predominant parameter affecting the navigation accuracy of GAGAN is ionospheric delay which is a function of total number of electrons present in one square meter cylindrical cross-sectional area in the line of site direction between the satellite and the user on the earth, i.e. Total Electron Content (TEC). In the equatorial and low latitude regions such as India, TEC is often quite high with large spatial gradients. Carrier phase data from the GAGAN network of Indian TEC Stations is used for estimating and identifying ionospheric spatial gradients inmultiple viewing directions. In this paper amongst the satellite signals arriving in multipledirections,Vertical ionospheric gradients (σVIG) are calculated, inturn spatial ionospheric gradients are identified. In addition, estimated temporal gradients, i.e. rate of TEC Index is also compared. These aspects which contribute to errors can be treated for improved GAGAN system performance.
Differential calculus for Dirichlet forms: The measure-valued gradient preserved by image
Bouleau, Nicolas
2005-01-01
In order to develop a differential calculus for error propagation we study local Dirichlet forms on probability spaces with square field operator $\\Gamma$ -- i.e. error structures -- and we are looking for an object related to $\\Gamma$ which is linear and with a good behaviour by images. For this we introduce a new notion called the measure valued gradient which is a randomized square root of $\\Gamma$. The exposition begins with inspecting some natural notions candidate to solve the problem b...
Deep Restricted Kernel Machines Using Conjugate Feature Duality.
Suykens, Johan A K
2017-08-01
The aim of this letter is to propose a theory of deep restricted kernel machines offering new foundations for deep learning with kernel machines. From the viewpoint of deep learning, it is partially related to restricted Boltzmann machines, which are characterized by visible and hidden units in a bipartite graph without hidden-to-hidden connections and deep learning extensions as deep belief networks and deep Boltzmann machines. From the viewpoint of kernel machines, it includes least squares support vector machines for classification and regression, kernel principal component analysis (PCA), matrix singular value decomposition, and Parzen-type models. A key element is to first characterize these kernel machines in terms of so-called conjugate feature duality, yielding a representation with visible and hidden units. It is shown how this is related to the energy form in restricted Boltzmann machines, with continuous variables in a nonprobabilistic setting. In this new framework of so-called restricted kernel machine (RKM) representations, the dual variables correspond to hidden features. Deep RKM are obtained by coupling the RKMs. The method is illustrated for deep RKM, consisting of three levels with a least squares support vector machine regression level and two kernel PCA levels. In its primal form also deep feedforward neural networks can be trained within this framework.
Yan, Yan
2015-01-01
We study a new optimization scheme that generates smooth and robust solutions for Dirichlet velocity boundary control (DVBC) of conjugate heat transfer (CHT) processes. The solutions to the DVBC of the incompressible Navier-Stokes equations are typically nonsmooth, due to the regularity degradation of the boundary stress in the adjoint Navier-Stokes equations. This nonsmoothness is inherited by the solutions to the DVBC of CHT processes, since the CHT process couples the Navier-Stokes equations of fluid motion with the convection-diffusion equations of fluid-solid thermal interaction. Our objective in the CHT boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control.Our strategy to resolve the nonsmoothness of the boundary control solution is based on two features, namely, the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels, and the optimization scheme with either explicit or implicit smoothing effects, such as the smoothed Steepest Descent and the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) methods. Our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function. In the section of numerical studies, we present two suites of experiments. In the first one, we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a Poiseuille flow. In the second one, we illustrate the robustness of our optimization schemes via solving more challenging DVBC problems for both the channel flow and the flow past a square cylinder, which use initial
Soluble polymer conjugates for drug delivery.
Minko, Tamara
2005-01-01
The use of water-soluble polymeric conjugates as drug carriers offers several possible advantages. These advantages include: (1) improved drug pharmacokinetics; (2) decreased toxicity to healthy organs; (3) possible facilitation of accumulation and preferential uptake by targeted cells; (4) programmed profile of drug release. In this review, we will consider the main types of useful polymeric conjugates and their role and effectiveness as carriers in drug delivery systems.: © 2005 Elsevier Ltd . All rights reserved.
Structure Property Relationships in Organic Conjugated Systems
O'Neill, Luke; Lynch, Patrick; McNamara, Mary
2005-01-01
A series of π conjugated oligomers were studied by absorption and photoluminescence spectroscopy. A linear relationship between the positioning of the absorption and photoluminescence maxima plotted against inverse conjugation length is observed. The relationships are in good agreement with the simple particle in a box method, one of the earliest descriptions of the properties of one-dimensional organic molecules. In addition to the electronic transition energies, it was observed that the Sto...
Diffeomorphisms Holder conjugate to Anosov diffeomorphisms
Gogolev, Andrey
2008-01-01
We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large.
Rapid modification of retroviruses using lipid conjugates
International Nuclear Information System (INIS)
Mukherjee, Nimisha G; Le Doux, Joseph M; Andrew Lyon, L
2009-01-01
Methods are needed to manipulate natural nanoparticles. Viruses are particularly interesting because they can act as therapeutic cellular delivery agents. Here we examine a new method for rapidly modifying retroviruses that uses lipid conjugates composed of a lipid anchor (1,2-distearoyl-sn-glycero-3-phosphoethanolamine), a polyethylene glycol chain, and biotin. The conjugates rapidly and stably modified retroviruses and enabled them to bind streptavidin. The implication of this work for modifying viruses for gene therapy and vaccination protocols is discussed.
Mathematical Construction of Magic Squares Utilizing Base-N Arithmetic
O'Brien, Thomas D.
2006-01-01
Magic squares have been of interest as a source of recreation for over 4,500 years. A magic square consists of a square array of n[squared] positive and distinct integers arranged so that the sum of any column, row, or main diagonal is the same. In particular, an array of consecutive integers from 1 to n[squared] forming an nxn magic square is…
Combining Step Gradients and Linear Gradients in Density.
Kumar, Ashok A; Walz, Jenna A; Gonidec, Mathieu; Mace, Charles R; Whitesides, George M
2015-06-16
Combining aqueous multiphase systems (AMPS) and magnetic levitation (MagLev) provides a method to produce hybrid gradients in apparent density. AMPS—solutions of different polymers, salts, or surfactants that spontaneously separate into immiscible but predominantly aqueous phases—offer thermodynamically stable steps in density that can be tuned by the concentration of solutes. MagLev—the levitation of diamagnetic objects in a paramagnetic fluid within a magnetic field gradient—can be arranged to provide a near-linear gradient in effective density where the height of a levitating object above the surface of the magnet corresponds to its density; the strength of the gradient in effective density can be tuned by the choice of paramagnetic salt and its concentrations and by the strength and gradient in the magnetic field. Including paramagnetic salts (e.g., MnSO4 or MnCl2) in AMPS, and placing them in a magnetic field gradient, enables their use as media for MagLev. The potential to create large steps in density with AMPS allows separations of objects across a range of densities. The gradients produced by MagLev provide resolution over a continuous range of densities. By combining these approaches, mixtures of objects with large differences in density can be separated and analyzed simultaneously. Using MagLev to add an effective gradient in density also enables tuning the range of densities captured at an interface of an AMPS by simply changing the position of the container in the magnetic field. Further, by creating AMPS in which phases have different concentrations of paramagnetic ions, the phases can provide different resolutions in density. These results suggest that combining steps in density with gradients in density can enable new classes of separations based on density.
Gradient-based methods for production optimization of oil reservoirs
Energy Technology Data Exchange (ETDEWEB)
Suwartadi, Eka
2012-07-01
Production optimization for water flooding in the secondary phase of oil recovery is the main topic in this thesis. The emphasis has been on numerical optimization algorithms, tested on case examples using simple hypothetical oil reservoirs. Gradientbased optimization, which utilizes adjoint-based gradient computation, is used to solve the optimization problems. The first contribution of this thesis is to address output constraint problems. These kinds of constraints are natural in production optimization. Limiting total water production and water cut at producer wells are examples of such constraints. To maintain the feasibility of an optimization solution, a Lagrangian barrier method is proposed to handle the output constraints. This method incorporates the output constraints into the objective function, thus avoiding additional computations for the constraints gradient (Jacobian) which may be detrimental to the efficiency of the adjoint method. The second contribution is the study of the use of second-order adjoint-gradient information for production optimization. In order to speedup convergence rate in the optimization, one usually uses quasi-Newton approaches such as BFGS and SR1 methods. These methods compute an approximation of the inverse of the Hessian matrix given the first-order gradient from the adjoint method. The methods may not give significant speedup if the Hessian is ill-conditioned. We have developed and implemented the Hessian matrix computation using the adjoint method. Due to high computational cost of the Newton method itself, we instead compute the Hessian-timesvector product which is used in a conjugate gradient algorithm. Finally, the last contribution of this thesis is on surrogate optimization for water flooding in the presence of the output constraints. Two kinds of model order reduction techniques are applied to build surrogate models. These are proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM
Finding A Minimally Informative Dirichlet Prior Using Least Squares
International Nuclear Information System (INIS)
Kelly, Dana
2011-01-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson λ, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Finding a minimally informative Dirichlet prior distribution using least squares
International Nuclear Information System (INIS)
Kelly, Dana; Atwood, Corwin
2011-01-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson λ, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Finding a Minimally Informative Dirichlet Prior Distribution Using Least Squares
International Nuclear Information System (INIS)
Kelly, Dana; Atwood, Corwin
2011-01-01
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straight-forward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in closed form, and so an approximate beta distribution is used in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial aleatory model for common-cause failure, must be estimated from data that is often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method
International Nuclear Information System (INIS)
Chaumet, Patrick C; Belkebir, Kamal
2009-01-01
The aim of the present work is to validate a full vectorial electromagnetic inverse scattering algorithm against experimental data. Data were provided courtesy of Institut Fresnel, Marseille, France. These data were carried out in an anechoic chamber and correspond to different canonical targets as well as one mysterious object which is known only by experimentalists who measured the associated scattered field. The inverse algorithm was first developed in the optical domain and is adapted herein to the microwave domain. It is an iterative approach where the parameter of interest, namely the relative permittivity distribution, is updated gradually by minimizing a cost function describing the discrepancy between data and those that would be obtained via a forward solver for the best available estimate of the relative permittivity. The forward solver is based on the coupled dipole method which was introduced in the seventies to study the scattering of light by non-spherical dielectric grains. The forward and inverse schemes are briefly described and various examples are presented that demonstrate the efficiency of the inverse algorithm
An Introduction to the Conjugate Gradient Method that Even an Idiot Can Understand
1994-03-07
to Omar Ghattas, who taught me much of what I know about numerical methods, and provided me with extensive comments on the first draft of this article...Dongarra, Victor Eijkhout, Roldan Pozo, Charles Romine, and Henk van der Vorst, Templates for the solution of linear systems: Building blocks for iterative
Hoekstra, A.G.; Sloot, P.M.A.; Haan, M.J.; Hertzberger, L.O.; van Leeuwen, J.
1991-01-01
New developments in Computer Science, both hardware and software, offer researchers, such as physicists, unprecedented possibilities to solve their computational intensive problems.However, full exploitation of e.g. new massively parallel computers, parallel languages or runtime environments
Myocardial perfusion MRI with sliding-window conjugate-gradient HYPR.
Ge, Lan; Kino, Aya; Griswold, Mark; Mistretta, Charles; Carr, James C; Li, Debiao
2009-10-01
First-pass perfusion MRI is a promising technique for detecting ischemic heart disease. However, the diagnostic value of the method is limited by the low spatial coverage, resolution, signal-to-noise ratio (SNR), and cardiac motion-related image artifacts. In this study we investigated the feasibility of using a method that combines sliding window and CG-HYPR methods (SW-CG-HYPR) to reduce the acquisition window for each slice while maintaining the temporal resolution of one frame per heartbeat in myocardial perfusion MRI. This method allows an increased number of slices, reduced motion artifacts, and preserves the relatively high SNR and spatial resolution of the "composite images." Results from eight volunteers demonstrate the feasibility of SW-CG-HYPR for accelerated myocardial perfusion imaging with accurate signal intensity changes of left ventricle blood pool and myocardium. Using this method the acquisition time per cardiac cycle was reduced by a factor of 4 and the number of slices was increased from 3 to 8 as compared to the conventional technique. The SNR of the myocardium at peak enhancement with SW-CG-HYPR (13.83 +/- 2.60) was significantly higher (P < 0.05) than the conventional turbo-FLASH protocol (8.40 +/- 1.62). Also, the spatial resolution of the myocardial perfection images was significantly improved. SW-CG-HYPR is a promising technique for myocardial perfusion MRI. (c) 2009 Wiley-Liss, Inc.
On the use of rigid body modes in the deflated preconditioned conjugate gradient method
Jönsthövel, T.B.; Van Gijzen, M.B.; Vuik, C.; Scarpas, A.
2013-01-01
Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the
COVARIANCE ESTIMATION USING CONJUGATE GRADIENT FOR 3D CLASSIFICATION IN CRYO-EM.
Andén, Joakim; Katsevich, Eugene; Singer, Amit
2015-04-01
Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.
On the use of rigid body modes in the deflated preconditioned conjugate gradient method
Jönsthövel, T.B.; Van Gijzen, M.B.; Vuik, C.; Scarpas, A.
2011-01-01
Large discontinuities in material properties, such as encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the Preconditioned
Free terminal time optimal control problem of an HIV model based on a conjugate gradient method.
Jang, Taesoo; Kwon, Hee-Dae; Lee, Jeehyun
2011-10-01
The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a "healthy" steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.
Jönsthövel, T.B.; Van Gijzen, M.B.; MacLachlan, S.; Vuik, C.; Scarpas, A.
2012-01-01
Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with
Jönsthövel, T.B.; Van Gijzen, M.B.; MacLachlan, S.; Vuik, C.; Scarpas, A.
2011-01-01
The demand for large FE meshes increases as parallel computing becomes the standard in FE simulations. Direct and iterative solution methods are used to solve the resulting linear systems. Many applications concern composite materials, which are characterized by large discontinuities in the material
Regularization by truncated total least squares
DEFF Research Database (Denmark)
Hansen, Per Christian; Fierro, R.D; Golub, G.H
1997-01-01
The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use...... schemes for relativistic hydrodynamical equations. Such an approximate Riemann solver is presented in this paper which treats all waves emanating from an initial discontinuity as themselves discontinuous. Therefore, jump conditions for shocks are approximately used for rarefaction waves. The solver...... is easy to implement in a Godunov scheme and converges rapidly for relativistic hydrodynamics. The fast convergence of the solver indicates the potential of a higher performance of a Godunov scheme in which the solver is used....
Total least squares for anomalous change detection
Theiler, James; Matsekh, Anna M.
2010-04-01
A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.
Constrained least squares regularization in PET
International Nuclear Information System (INIS)
Choudhury, K.R.; O'Sullivan, F.O.
1996-01-01
Standard reconstruction methods used in tomography produce images with undesirable negative artifacts in background and in areas of high local contrast. While sophisticated statistical reconstruction methods can be devised to correct for these artifacts, their computational implementation is excessive for routine operational use. This work describes a technique for rapid computation of approximate constrained least squares regularization estimates. The unique feature of the approach is that it involves no iterative projection or backprojection steps. This contrasts with the familiar computationally intensive algorithms based on algebraic reconstruction (ART) or expectation-maximization (EM) methods. Experimentation with the new approach for deconvolution and mixture analysis shows that the root mean square error quality of estimators based on the proposed algorithm matches and usually dominates that of more elaborate maximum likelihood, at a fraction of the computational effort
Classical square-plus-triangle well fluid
International Nuclear Information System (INIS)
Boghdadi, M.
1984-01-01
A simplified model for the intermolecular-potential function which consists of a hard core and a square-plus-triangle well is proposed. The square width is taken to be lambda 1 -1 and the triangle width is lambda 2 -lambda 1 , where the diameter of the molecules is assumed to be epsilon. Under the restriction that the area under the potential well should be equal to 0.5epsilon, which has its own reason, it is shown that the appropriate choice of lambda 1 and lambda 2 that best mimics the Lennard-Jones (LJ) cut-off results is 1.15 and 1.85 respectively. With this choice for lambda 1 and lambda 2 , the proposed model is effective and satisfactory
Dancoff Correction in Square and Hexagonal Lattices
Energy Technology Data Exchange (ETDEWEB)
Carlvik, I
1966-11-15
This report presents the results of a series of calculations of Dancoff corrections for square and hexagonal rod lattices. The tables cover a wide range of volume ratios and moderator cross sections. The results were utilized for checking the approximative formula of Sauer and also the modification of Bonalumi to Sauer's formula. The modified formula calculates the Dancoff correction with an accuracy of 0.01 - 0.02 in cases of practical interest. Calculations have also been performed on square lattices with an empty gap surrounding the rods. The results demonstrate the error involved in treating this kind of geometry by means of homogenizing the gap and the moderator. The calculations were made on the Ferranti Mercury computer of AB Atomenergi before it was closed down. Since then FORTRAN routines for Dancoff corrections have been written, and a subroutine DASQHE is included in the report.
Spatial gradient tuning in metamaterials
Driscoll, Tom; Goldflam, Michael; Jokerst, Nan; Basov, Dimitri; Smith, David
2011-03-01
Gradient Index (GRIN) metamaterials have been used to create devices inspired by, but often surpassing the potential of, conventional GRIN optics. The unit-cell nature of metamaterials presents the opportunity to exert much greater control over spatial gradients than is possible in natural materials. This is true not only during the design phase but also offers the potential for real-time reconfiguration of the metamaterial gradient. This ability fits nicely into the picture of transformation-optics, in which spatial gradients can enable an impressive suite of innovative devices. We discuss methods to exert control over metamaterial response, focusing on our recent demonstrations using Vanadium Dioxide. We give special attention to role of memristance and mem-capacitance observed in Vanadium Dioxide, which simplify the demands of stimuli and addressing, as well as intersecting metamaterials with the field of memory-materials.
Elastic least-squares reverse time migration
Feng, Zongcai; Schuster, Gerard T.
2016-01-01
Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.
Elastic least-squares reverse time migration
Feng, Zongcai
2016-09-06
Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.
Natural convective heat transfer from square cylinder
Energy Technology Data Exchange (ETDEWEB)
Novomestský, Marcel, E-mail: marcel.novomestsky@fstroj.uniza.sk; Smatanová, Helena, E-mail: helena.smatanova@fstroj.uniza.sk; Kapjor, Andrej, E-mail: andrej.kapjor@fstroj.uniza.sk [University of Žilina, Faculty of Mechanical Engineering, Department of Power Engineering, Univerzitná 1, 010 26 Žilina (Slovakia)
2016-06-30
This article is concerned with natural convective heat transfer from square cylinder mounted on a plane adiabatic base, the cylinders having an exposed cylinder surface according to different horizontal angle. The cylinder receives heat from a radiating heater which results in a buoyant flow. There are many industrial applications, including refrigeration, ventilation and the cooling of electrical components, for which the present study may be applicable.
Least Squares Problems with Absolute Quadratic Constraints
Directory of Open Access Journals (Sweden)
R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
Two-Step Proximal Gradient Algorithm for Low-Rank Matrix Completion
Directory of Open Access Journals (Sweden)
Qiuyu Wang
2016-06-01
Full Text Available In this paper, we propose a two-step proximal gradient algorithm to solve nuclear norm regularized least squares for the purpose of recovering low-rank data matrix from sampling of its entries. Each iteration generated by the proposed algorithm is a combination of the latest three points, namely, the previous point, the current iterate, and its proximal gradient point. This algorithm preserves the computational simplicity of classical proximal gradient algorithm where a singular value decomposition in proximal operator is involved. Global convergence is followed directly in the literature. Numerical results are reported to show the efficiency of the algorithm.
Clavel, Marie-Annick; Magne, Julien; Pibarot, Philippe
2016-09-07
An important proportion of patients with aortic stenosis (AS) have a 'low-gradient' AS, i.e. a small aortic valve area (AVA gradient (gradient discrepancy raises uncertainty about the actual stenosis severity and thus about the indication for aortic valve replacement (AVR) if the patient has symptoms and/or left ventricular (LV) systolic dysfunction. The most frequent cause of low-gradient (LG) AS is the presence of a low LV outflow state, which may occur with reduced left ventricular ejection fraction (LVEF), i.e. classical low-flow, low-gradient (LF-LG), or preserved LVEF, i.e. paradoxical LF-LG. Furthermore, a substantial proportion of patients with AS may have a normal-flow, low-gradient (NF-LG) AS: i.e. a small AVA-low-gradient combination but with a normal flow. One of the most important clinical challenges in these three categories of patients with LG AS (classical LF-LG, paradoxical LF-LG, and NF-LG) is to differentiate a true-severe AS that generally benefits from AVR vs. a pseudo-severe AS that should be managed conservatively. A low-dose dobutamine stress echocardiography may be used for this purpose in patients with classical LF-LG AS, whereas aortic valve calcium scoring by multi-detector computed tomography is the preferred modality in those with paradoxical LF-LG or NF-LG AS. Although patients with LF-LG severe AS have worse outcomes than those with high-gradient AS following AVR, they nonetheless display an important survival benefit with this intervention. Some studies suggest that transcatheter AVR may be superior to surgical AVR in patients with LF-LG AS. Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2016. For permissions please email: journals.permissions@oup.com.
A least-squares computational ''tool kit''
International Nuclear Information System (INIS)
Smith, D.L.
1993-04-01
The information assembled in this report is intended to offer a useful computational ''tool kit'' to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications
Advancing Astrophysics with the Square Kilometre Array
Fender, Rob; Govoni, Federica; Green, Jimi; Hoare, Melvin; Jarvis, Matt; Johnston-Hollitt, Melanie; Keane, Evan; Koopmans, Leon; Kramer, Michael; Maartens, Roy; Macquart, Jean-Pierre; Mellema, Garrelt; Oosterloo, Tom; Prandoni, Isabella; Pritchard, Jonathan; Santos, Mario; Seymour, Nick; Stappers, Ben; Staveley-Smith, Lister; Tian, Wen Wu; Umana, Grazia; Wagg, Jeff; Bourke, Tyler L; AASKA14
2015-01-01
In 2014 it was 10 years since the publication of the comprehensive ‘Science with the Square Kilometre Array’ book and 15 years since the first such volume appeared in 1999. In that time numerous and unexpected advances have been made in the fields of astronomy and physics relevant to the capabilities of the Square Kilometre Array (SKA). The SKA itself progressed from an idea to a developing reality with a baselined Phase 1 design (SKA1) and construction planned from 2017. To facilitate the publication of a new, updated science book, which will be relevant to the current astrophysical context, the meeting "Advancing Astrophysics with the Square Kilometre Array" was held in Giardina Naxos, Sicily. Articles were solicited from the community for that meeting to document the scientific advances enabled by the first phase of the SKA and those pertaining to future SKA deployments, with expected gains of 5 times the Phase 1 sensitivity below 350 MHz, about 10 times the Phase 1 sensitivity above 350 MHz and with f...
Graded/Gradient Porous Biomaterials
Directory of Open Access Journals (Sweden)
Xigeng Miao
2009-12-01
Full Text Available Biomaterials include bioceramics, biometals, biopolymers and biocomposites and they play important roles in the replacement and regeneration of human tissues. However, dense bioceramics and dense biometals pose the problem of stress shielding due to their high Young’s moduli compared to those of bones. On the other hand, porous biomaterials exhibit the potential of bone ingrowth, which will depend on porous parameters such as pore size, pore interconnectivity, and porosity. Unfortunately, a highly porous biomaterial results in poor mechanical properties. To optimise the mechanical and the biological properties, porous biomaterials with graded/gradient porosity, pores size, and/or composition have been developed. Graded/gradient porous biomaterials have many advantages over graded/gradient dense biomaterials and uniform or homogenous porous biomaterials. The internal pore surfaces of graded/gradient porous biomaterials can be modified with organic, inorganic, or biological coatings and the internal pores themselves can also be filled with biocompatible and biodegradable materials or living cells. However, graded/gradient porous biomaterials are generally more difficult to fabricate than uniform or homogenous porous biomaterials. With the development of cost-effective processing techniques, graded/gradient porous biomaterials can find wide applications in bone defect filling, implant fixation, bone replacement, drug delivery, and tissue engineering.
Dose gradient curve: A new tool for evaluating dose gradient.
Sung, KiHoon; Choi, Young Eun
2018-01-01
Stereotactic radiotherapy, which delivers an ablative high radiation dose to a target volume for maximum local tumor control, requires a rapid dose fall-off outside the target volume to prevent extensive damage to nearby normal tissue. Currently, there is no tool to comprehensively evaluate the dose gradient near the target volume. We propose the dose gradient curve (DGC) as a new tool to evaluate the quality of a treatment plan with respect to the dose fall-off characteristics. The average distance between two isodose surfaces was represented by the dose gradient index (DGI) estimated by a simple equation using the volume and surface area of isodose levels. The surface area was calculated by mesh generation and surface triangulation. The DGC was defined as a plot of the DGI of each dose interval as a function of the dose. Two types of DGCs, differential and cumulative, were generated. The performance of the DGC was evaluated using stereotactic radiosurgery plans for virtual targets. Over the range of dose distributions, the dose gradient of each dose interval was well-characterized by the DGC in an easily understandable graph format. Significant changes in the DGC were observed reflecting the differences in planning situations and various prescription doses. The DGC is a rational method for visualizing the dose gradient as the average distance between two isodose surfaces; the shorter the distance, the steeper the dose gradient. By combining the DGC with the dose-volume histogram (DVH) in a single plot, the DGC can be utilized to evaluate not only the dose gradient but also the target coverage in routine clinical practice.
Gradient metasurface for four-direction anomalous reflection in terahertz
Wang, Jiao; Jiang, Yannan
2018-06-01
In this paper, a four-direction anomalous reflection metasurface is proposed. The basic cells comprise of squares and circles, which are designed at various sizes and arranged in a super cell at regular spacing. Then, properly combining super cells molds a square phase gradient metasurface (PGM). It is mounted on an optical thickness gold mirror, which inhibits all light transmission. Markedly different from previously reported metasurfaces, the square PGM is characterized by four-direction reflection beams. It takes into consideration the normal incidence and the oblique incidence. For the normal incidence, that the degrees of the four reflection angles are identical is due to the x, - x, y and - y directional discontinuous phase gradients, and lies on the symmetric structure in the xoy plane, which is then revealed by the surface current distribution. Incident angles varying from -20° to 20°, the reflection angles are demonstrated in the oblique incidence. Moreover, the PGM is polarization-independent. The performance is attributed to the symmetry of structure, which is verified by Radar cross section. Simulated results prove that our method offers a simple and effective strategy for metasurface design in terahertz. The proposed PGM can aid in focused beams, steering beams, and shaped beams.
International Nuclear Information System (INIS)
Favre, F.; Colomer, G.; Lehmkuhl, O.; Oliva, A.
2016-01-01
Dynamic and thermal interaction problems involving fluids and solids were studied through a finite volume-based Navier-Stokes solver, combined with immersed-boundary techniques and the net radiation method. Source terms were included in the momentum and energy equations to enforce the non-slip condition and the conjugate boundary condition including the radiative heat exchange. Code validation was performed through the simulation of two cases from the literature: conjugate natural convection in a square cavity with a conducting side wall; and a cubical cavity with conducting walls and a heat source. The accuracy of the methodology and the validation of the inclusion of moving bodies into the simulation was performed via a theoretical case (paper)
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
Lax-pair operators for squared-sum and squared-difference eigenfunctions
International Nuclear Information System (INIS)
Ichikawa, Yoshihiko; Iino, Kazuhiro.
1984-10-01
Inter-relationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of Lax-pair operators of the sine-Gordon equation and the modified Korteweg-de Vries equation. In particular, it is shown explicitly that there exists Lax-pair operators for the squared-sum and squared-difference eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation. (author)
Bouchard, M
2001-01-01
In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.
Polyhedral meshing in numerical analysis of conjugate heat transfer
Sosnowski, Marcin; Krzywanski, Jaroslaw; Grabowska, Karolina; Gnatowska, Renata
2018-06-01
Computational methods have been widely applied in conjugate heat transfer analysis. The very first and crucial step in such research is the meshing process which consists in dividing the analysed geometry into numerous small control volumes (cells). In Computational Fluid Dynamics (CFD) applications it is desirable to use the hexahedral cells as the resulting mesh is characterized by low numerical diffusion. Unfortunately generating such mesh can be a very time-consuming task and in case of complicated geometry - it may not be possible to generate cells of good quality. Therefore tetrahedral cells have been implemented into commercial pre-processors. Their advantage is the ease of its generation even in case of very complex geometry. On the other hand tetrahedrons cannot be stretched excessively without decreasing the mesh quality factor, so significantly larger number of cells has to be used in comparison to hexahedral mesh in order to achieve a reasonable accuracy. Moreover the numerical diffusion of tetrahedral elements is significantly higher. Therefore the polyhedral cells are proposed within the paper in order to combine the advantages of hexahedrons (low numerical diffusion resulting in accurate solution) and tetrahedrons (rapid semi-automatic generation) as well as to overcome the disadvantages of both the above mentioned mesh types. The major benefit of polyhedral mesh is that each individual cell has many neighbours, so gradients can be well approximated. Polyhedrons are also less sensitive to stretching than tetrahedrons which results in better mesh quality leading to improved numerical stability of the model. In addition, numerical diffusion is reduced due to mass exchange over numerous faces. This leads to a more accurate solution achieved with a lower cell count. Therefore detailed comparison of numerical modelling results concerning conjugate heat transfer using tetrahedral and polyhedral meshes is presented in the paper.
Luminance gradient at object borders communicates object location to the human oculomotor system.
Kilpeläinen, Markku; Georgeson, Mark A
2018-01-25
The locations of objects in our environment constitute arguably the most important piece of information our visual system must convey to facilitate successful visually guided behaviour. However, the relevant objects are usually not point-like and do not have one unique location attribute. Relatively little is known about how the visual system represents the location of such large objects as visual processing is, both on neural and perceptual level, highly edge dominated. In this study, human observers made saccades to the centres of luminance defined squares (width 4 deg), which appeared at random locations (8 deg eccentricity). The phase structure of the square was manipulated such that the points of maximum luminance gradient at the square's edges shifted from trial to trial. The average saccade endpoints of all subjects followed those shifts in remarkable quantitative agreement. Further experiments showed that the shifts were caused by the edge manipulations, not by changes in luminance structure near the centre of the square or outside the square. We conclude that the human visual system programs saccades to large luminance defined square objects based on edge locations derived from the points of maximum luminance gradients at the square's edges.
Leonardo Pisano (Fibonacci) the book of squares
Sigler, L E
1987-01-01
The Book of Squares by Fibonacci is a gem in the mathematical literature and one of the most important mathematical treatises written in the Middle Ages. It is a collection of theorems on indeterminate analysis and equations of second degree which yield, among other results, a solution to a problem proposed by Master John of Palermo to Leonardo at the Court of Frederick II. The book was dedicated and presented to the Emperor at Pisa in 1225. Dating back to the 13th century the book exhibits the early and continued fascination of men with our number system and the relationship among numbers
Least Squares Methods for Equidistant Tree Reconstruction
Fahey, Conor; Hosten, Serkan; Krieger, Nathan; Timpe, Leslie
2008-01-01
UPGMA is a heuristic method identifying the least squares equidistant phylogenetic tree given empirical distance data among $n$ taxa. We study this classic algorithm using the geometry of the space of all equidistant trees with $n$ leaves, also known as the Bergman complex of the graphical matroid for the complete graph $K_n$. We show that UPGMA performs an orthogonal projection of the data onto a maximal cell of the Bergman complex. We also show that the equidistant tree with the least (Eucl...
Magnetics calculations for an ELMO Bumpy square
International Nuclear Information System (INIS)
Santoro, R.T.; Uckan, N.A.; Schmidt, R.J.
1985-01-01
Advanced ELMO Bumpy Torus (EBT) concepts have been studied in an effort to determine the potential for new and different concepts as confinement experiments or as reactors. Several magnetic configurations based on the EBT confinement concept were developed including the ELMO Bumpy Square (EBS). The EBS was selected as a possible candidate for near-term study because of its potential for resolving critical EBT issues, for its desirability as a reactor, and for anticipated contributions to the physics and technology of fusion. This paper summarizes magnetics calculations that were carried out in support of studies to assess the merits of an EBS
Hargreaves, Brian
2012-01-01
Gradient echo sequences are widely used in magnetic resonance imaging (MRI) for numerous applications ranging from angiography to perfusion to functional MRI. Compared with spin-echo techniques, the very short repetition times of gradient-echo methods enable very rapid 2D and 3D imaging, but also lead to complicated “steady states.” Signal and contrast behavior can be described graphically and mathematically, and depends strongly on the type of spoiling: fully balanced (no spoiling), gradient spoiling, or RF-spoiling. These spoiling options trade off between high signal and pure T1 contrast while the flip angle also affects image contrast in all cases, both of which can be demonstrated theoretically and in image examples. As with spin-echo sequences, magnetization preparation can be added to gradient-echo sequences to alter image contrast. Gradient echo sequences are widely used for numerous applications such as 3D perfusion imaging, functional MRI, cardiac imaging and MR angiography. PMID:23097185
The influence of ALN-Al gradient material gradient index on ballistic performance
International Nuclear Information System (INIS)
Wang Youcong; Liu Qiwen; Li Yao; Shen Qiang
2013-01-01
Ballistic performance of the gradient material is superior to laminated material, and gradient materials have different gradient types. Using ls-dyna to simulate the ballistic performance of ALN-AL gradient target plates which contain three gradient index (b = 1, b = 0.5, b = 2). Through Hopkinson bar numerical simulation to the target plate materials, we obtained the reflection stress wave and transmission stress wave state of gradient material to get the best gradient index. The internal stress state of gradient material is simulated by amplification processing of the target plate model. When the gradient index b is equal to 1, the gradient target plate is best of all.
Analytical characterization of polymer-drug conjugates
International Nuclear Information System (INIS)
Rizzo, V.; Gigli, M.; Pinciroli, V.
1998-01-01
A few polymeric conjugates of antitumor drugs have been recently developed in view of possible therapeutic advantages: solubilization of sparingly soluble drugs in water, improvement of therapeutic index, organ targeting through a second chemical species bound to the same polymeric chain. In this article it's described the analytical approach used in the characterization of the conjugates for chemical identity, purity and strength of the contained active ingredient. The techniques are: high field NMR and size exclusion chromatography with non-aqueous mobile phase for identity; selective hydrolysis and HPLC for strength and purity. A complete and reliable picture is thus obtained both for qualitative and for quantitative aspects. This is an important step forward in the direction of further development and marketing of polymer-drug conjugates [it
Conjugate Meningococcal Vaccines Development: GSK Biologicals Experience
Miller, Jacqueline M.; Mesaros, Narcisa; Van Der Wielen, Marie; Baine, Yaela
2011-01-01
Meningococcal diseases are serious threats to global health, and new vaccines specifically tailored to meet the age-related needs of various geographical areas are required. This paper focuses on the meningococcal conjugate vaccines developed by GSK Biologicals. Two combined conjugate vaccines were developed to help protect infants and young children in countries where the incidence of meningococcal serogroup C or serogroup C and Y disease is important: Hib-MenC-TT vaccine, which offers protection against Haemophilus influenzae type b and Neisseria meningitidis serogroup C diseases, is approved in several countries; and Hib-MenCY-TT vaccine, which adds N. meningitidis serogroup Y antigen, is currently in the final stages of development. Additionally, a tetravalent conjugate vaccine (MenACWY-TT) designed to help protect against four meningococcal serogroups is presently being evaluated for global use in all age groups. All of these vaccines were shown to be highly immunogenic and to have clinically acceptable safety profiles. PMID:21991444
Conjugate Meningococcal Vaccines Development: GSK Biologicals Experience
Directory of Open Access Journals (Sweden)
Jacqueline M. Miller
2011-01-01
Full Text Available Meningococcal diseases are serious threats to global health, and new vaccines specifically tailored to meet the age-related needs of various geographical areas are required. This paper focuses on the meningococcal conjugate vaccines developed by GSK Biologicals. Two combined conjugate vaccines were developed to help protect infants and young children in countries where the incidence of meningococcal serogroup C or serogroup C and Y disease is important: Hib-MenC-TT vaccine, which offers protection against Haemophilus influenzae type b and Neisseria meningitidis serogroup C diseases, is approved in several countries; and Hib-MenCY-TT vaccine, which adds N. meningitidis serogroup Y antigen, is currently in the final stages of development. Additionally, a tetravalent conjugate vaccine (MenACWY-TT designed to help protect against four meningococcal serogroups is presently being evaluated for global use in all age groups. All of these vaccines were shown to be highly immunogenic and to have clinically acceptable safety profiles.
125I Radioimmunoassay of serum ursodeoxycholyl conjugates
International Nuclear Information System (INIS)
Hill, A.; Ross, P.E.; Bouchier, I.A.D.
1983-01-01
A radioimmunoassay for serum ursodeoxycholic conjugates using an iodine-125 ligand has been developed. The bile acid was present in normal fasting serum (0.19 +- SD 0.19 μmol/l, n=24) and 2-hour post-prandial serum (0.8 +- SD 0.8 μmol/l, n=16). Gallstone patients undergoing oral ursodeoxycholic acid therapy had significantly higher post-prandial serum levels (21.5 +- SD 14.0 μmol/l, n=15) by radioimmunoassay. Gas liquid chromatography analysis indicated that in normal serum ursodeoxycholic acid was totally conjugated, whereas sera from gallstone patients contained a proportion as the free bile acid (10.2 +- SD 8.1 μmol/l, n=15). Following an oral dose of ursodeoxycholic acid, both unconjugated and conjugated forms of the bile acid appeared in the serum of healthy individuals. (Auth.)
Novel β-cyclodextrin–eosin conjugates
Directory of Open Access Journals (Sweden)
Gábor Benkovics
2017-03-01
Full Text Available Eosin B (EoB and eosin Y (EoY, two xanthene dye derivatives with photosensitizing ability were prepared in high purity through an improved synthetic route. The dyes were grafted to a 6-monoamino-β-cyclodextrin scaffold under mild reaction conditions through a stable amide linkage using the coupling agent 4-(4,6-dimethoxy-1,3,5-triazin-2-yl-4-methylmorpholinium chloride. The molecular conjugates, well soluble in aqueous medium, were extensively characterized by 1D and 2D NMR spectroscopy and mass spectrometry. Preliminary spectroscopic investigations showed that the β-cyclodextrin–EoY conjugate retains both the fluorescence properties and the capability to photogenerate singlet oxygen of the unbound chromophore. In contrast, the corresponding β-cyclodextrin–EoB conjugate did not show either relevant emission or photosensitizing activity probably due to aggregation in aqueous medium, which precludes any response to light excitation.
Novel β-cyclodextrin-eosin conjugates.
Benkovics, Gábor; Afonso, Damien; Darcsi, András; Béni, Szabolcs; Conoci, Sabrina; Fenyvesi, Éva; Szente, Lajos; Malanga, Milo; Sortino, Salvatore
2017-01-01
Eosin B (EoB) and eosin Y (EoY), two xanthene dye derivatives with photosensitizing ability were prepared in high purity through an improved synthetic route. The dyes were grafted to a 6-monoamino-β-cyclodextrin scaffold under mild reaction conditions through a stable amide linkage using the coupling agent 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholinium chloride. The molecular conjugates, well soluble in aqueous medium, were extensively characterized by 1D and 2D NMR spectroscopy and mass spectrometry. Preliminary spectroscopic investigations showed that the β-cyclodextrin-EoY conjugate retains both the fluorescence properties and the capability to photogenerate singlet oxygen of the unbound chromophore. In contrast, the corresponding β-cyclodextrin-EoB conjugate did not show either relevant emission or photosensitizing activity probably due to aggregation in aqueous medium, which precludes any response to light excitation.
Deciphering conjugative plasmid permissiveness in wastewater microbiomes
DEFF Research Database (Denmark)
Jacquiod, Samuel Jehan Auguste; Brejnrod, Asker Daniel; Milani, Stefan Morberg
2017-01-01
Wastewater treatment plants (WWTPs) are designed to robustly treat polluted water. They are characterized by ceaseless flows of organic, chemical and microbial matter, followed by treatment steps before environmental release. WWTPs are hotspots of horizontal gene transfer between bacteria via...... still remains largely uncharted. Furthermore, current in vitro methods used to assess conjugation in complex microbiomes do not include in situ behaviours of recipient cells, resulting in partial understanding of transfers. We investigated the in vitro conjugation capacities of WWTP microbiomes from...... inlet sewage and outlet treated water using the broad-host range IncP-1 conjugative plasmid, pKJK5. A thorough molecular approach coupling metagenomes to 16S rRNA DNA/cDNA amplicon sequencing was established to characterize microbiomes using the ecological concept of functional response groups. A broad...
Theoretical and computational studies of excitons in conjugated polymers
Barford, William; Bursill, Robert J.; Smith, Richard W.
2002-09-01
We present a theoretical and computational analysis of excitons in conjugated polymers. We use a tight-binding model of π-conjugated electrons, with 1/r interactions for large r. In both the weak-coupling limit (defined by W>>U) and the strong-coupling limit (defined by Wparticle models. We compare these to density matrix renormalization group (DMRG) calculations, and find good agreement in the extreme limits. We use these analytical results to interpret the DMRG calculations in the intermediate-coupling regime (defined by W~U), most applicable to conjugated polymers. We make the following conclusions. (1) In the weak-coupling limit the bound states are Mott-Wannier excitons, i.e., conduction-band electrons bound to valence-band holes. Singlet and triplet excitons whose relative wave functions are odd under a reflection of the relative coordinate are degenerate. Thus, the 2 1A+g and 1 3A-g states are degenerate in this limit. (2) In the strong-coupling limit the bound states are Mott-Hubbard excitons, i.e., particles in the upper Hubbard band bound to holes in the lower Hubbard band. These bound states occur in doublets of even and odd parity excitons. Triplet excitons are magnons bound to the singlet excitons, and hence are degenerate with their singlet counterparts. (3) In the intermediate-coupling regime Mott-Wannier excitons are the more appropriate description for large dimerization, while for the undimerized chain Mott-Hubbard excitons are the correct description. For dimerizations relevant to polyacetylene and polydiacetylene both Mott-Hubbard and Mott-Wannier excitons are present. (4) For all coupling strengths an infinite number of bound states exist for 1/r interactions for an infinite polymer. As a result of the discreteness of the lattice and the restrictions on the exciton wave functions in one dimension, the progression of states does not follow the Rydberg series. In practice, excitons whose particle-hole separation exceeds the length of the polymer
Optimization of Coil Element Configurations for a Matrix Gradient Coil.
Kroboth, Stefan; Layton, Kelvin J; Jia, Feng; Littin, Sebastian; Yu, Huijun; Hennig, Jurgen; Zaitsev, Maxim
2018-01-01
Recently, matrix gradient coils (also termed multi-coils or multi-coil arrays) were introduced for imaging and B 0 shimming with 24, 48, and even 84 coil elements. However, in imaging applications, providing one amplifier per coil element is not always feasible due to high cost and technical complexity. In this simulation study, we show that an 84-channel matrix gradient coil (head insert for brain imaging) is able to create a wide variety of field shapes even if the number of amplifiers is reduced. An optimization algorithm was implemented that obtains groups of coil elements, such that a desired target field can be created by driving each group with an amplifier. This limits the number of amplifiers to the number of coil element groups. Simulated annealing is used due to the NP-hard combinatorial nature of the given problem. A spherical harmonic basis set up to the full third order within a sphere of 20-cm diameter in the center of the coil was investigated as target fields. We show that the median normalized least squares error for all target fields is below approximately 5% for 12 or more amplifiers. At the same time, the dissipated power stays within reasonable limits. With a relatively small set of amplifiers, switches can be used to sequentially generate spherical harmonics up to third order. The costs associated with a matrix gradient coil can be lowered, which increases the practical utility of matrix gradient coils.
METHOD OF CONJUGATED CIRCULAR ARCS TRACING
Directory of Open Access Journals (Sweden)
N. Ageyev Vladimir
2017-01-01
Full Text Available The geometric properties of conjugated circular arcs connecting two points on the plane with set directions of tan- gent vectors are studied in the work. It is shown that pairs of conjugated circular arcs with the same conditions in frontier points create one-parameter set of smooth curves tightly filling all the plane. One of the basic properties of this set is the fact that all coupling points of circular arcs are on the circular curve going through the initially given points. The circle radius depends on the direction of tangent vectors. Any point of the circle curve, named auxiliary in this work, determines a pair of conjugated arcs with given boundary conditions. One more condition of the auxiliary circle curve is that it divides the plane into two parts. The arcs going from the initial point are out of the circle limited by this circle curve and the arcs coming to the final point are inside it. These properties are the basis for the method of conjugated circular arcs tracing pro- posed in this article. The algorithm is rather simple and allows to fulfill all the needed plottings using only the divider and ruler. Two concrete examples are considered. The first one is related to the problem of tracing of a pair of conjugated arcs with the minimal curve jump when going through the coupling point. The second one demonstrates the possibility of trac- ing of the smooth curve going through any three points on the plane under condition that in the initial and final points the directions of tangent vectors are given. The proposed methods of conjugated circular arcs tracing can be applied in solving of a wide variety of problems connected with the tracing of cam contours, for example pattern curves in textile industry or in computer-aided-design systems when programming of looms with numeric control.
Computational logic with square rings of nanomagnets
Arava, Hanu; Derlet, Peter M.; Vijayakumar, Jaianth; Cui, Jizhai; Bingham, Nicholas S.; Kleibert, Armin; Heyderman, Laura J.
2018-06-01
Nanomagnets are a promising low-power alternative to traditional computing. However, the successful implementation of nanomagnets in logic gates has been hindered so far by a lack of reliability. Here, we present a novel design with dipolar-coupled nanomagnets arranged on a square lattice to (i) support transfer of information and (ii) perform logic operations. We introduce a thermal protocol, using thermally active nanomagnets as a means to perform computation. Within this scheme, the nanomagnets are initialized by a global magnetic field and thermally relax on raising the temperature with a resistive heater. We demonstrate error-free transfer of information in chains of up to 19 square rings and we show a high level of reliability with successful gate operations of ∼94% across more than 2000 logic gates. Finally, we present a functionally complete prototype NAND/NOR logic gate that could be implemented for advanced logic operations. Here we support our experiments with simulations of the thermally averaged output and determine the optimal gate parameters. Our approach provides a new pathway to a long standing problem concerning reliability in the use of nanomagnets for computation.
Conjugated Polymers as Actuators: Modes of Actuation
DEFF Research Database (Denmark)
Skaarup, Steen
2004-01-01
The physical and chemical properties of conjugated polymers often depend very strongly on the degree of doping with anions or cations. The movement of ions in and out of the polymer matrix as it is redox cycled is also accompanied by mechanical changes. Both the volume and the stiffness can exhibit...... significant differences between the oxidized and reduced states. These effects form the basis of the use of conjugated polymers as actuators (or “artificial muscles”) controllable by a small (1-10 V) voltage. Three basic modes of actuation (bending, linear extension and stiffness change) have been proposed...
Conjugated polymers as actuators: modes of actuation
DEFF Research Database (Denmark)
Skaarup, Steen
2007-01-01
The physical and chemical properties of conjugated polymers often depend very strongly on the degree of doping with anions or cations. The movement of ions in and out of the polymer matrix as it is redox cycled is also accompanied by mechanical changes. Both the volume and the stiffness can exhibit...... significant differences between the oxidized and reduced states. These effects form the basis of the use of conjugated polymers as actuators (or “artificial muscles”) controllable by a small (1-10 V) voltage. Three basic modes of actuation (bending, linear extension and stiffness change) have been proposed...
Functionalized conjugated polyelectrolytes design and biomedical applications
Wang, Shu
2014-01-01
Functionalized Conjugated Polyelectrolytes presents a comprehensive review of these polyelectrolytes and their biomedical applications. Basic aspects like molecular design and optoelectronic properties are covered in the first chapter. Emphasis is placed on the various applications including sensing (chemical and biological), disease diagnosis, cell imaging, drug/gene delivery and disease treatment. This book explores a multi-disciplinary topic of interest to researchers working in the fields of chemistry, materials, biology and medicine. It also offers an integrated perspective on both basic research and application issues. Functionalized conjugated polyelectrolyte materials, which have already drawn considerable interest, will become a major new direction for biomedicine development.
Phase-unwrapping algorithm by a rounding-least-squares approach
Juarez-Salazar, Rigoberto; Robledo-Sanchez, Carlos; Guerrero-Sanchez, Fermin
2014-02-01
A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm's performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.
Vapor-liquid equilibrium and critical asymmetry of square well and short square well chain fluids.
Li, Liyan; Sun, Fangfang; Chen, Zhitong; Wang, Long; Cai, Jun
2014-08-07
The critical behavior of square well fluids with variable interaction ranges and of short square well chain fluids have been investigated by grand canonical ensemble Monte Carlo simulations. The critical temperatures and densities were estimated by a finite-size scaling analysis with the help of histogram reweighting technique. The vapor-liquid coexistence curve in the near-critical region was determined using hyper-parallel tempering Monte Carlo simulations. The simulation results for coexistence diameters show that the contribution of |t|(1-α) to the coexistence diameter dominates the singular behavior in all systems investigated. The contribution of |t|(2β) to the coexistence diameter is larger for the system with a smaller interaction range λ. While for short square well chain fluids, longer the chain length, larger the contribution of |t|(2β). The molecular configuration greatly influences the critical asymmetry: a short soft chain fluid shows weaker critical asymmetry than a stiff chain fluid with same chain length.
Cichocki, A; Unbehauen, R
1994-01-01
In this paper a new class of simplified low-cost analog artificial neural networks with on chip adaptive learning algorithms are proposed for solving linear systems of algebraic equations in real time. The proposed learning algorithms for linear least squares (LS), total least squares (TLS) and data least squares (DLS) problems can be considered as modifications and extensions of well known algorithms: the row-action projection-Kaczmarz algorithm and/or the LMS (Adaline) Widrow-Hoff algorithms. The algorithms can be applied to any problem which can be formulated as a linear regression problem. The correctness and high performance of the proposed neural networks are illustrated by extensive computer simulation results.
Commutative discrete filtering on unstructured grids based on least-squares techniques
International Nuclear Information System (INIS)
Haselbacher, Andreas; Vasilyev, Oleg V.
2003-01-01
The present work is concerned with the development of commutative discrete filters for unstructured grids and contains two main contributions. First, building on the work of Marsden et al. [J. Comp. Phys. 175 (2002) 584], a new commutative discrete filter based on least-squares techniques is constructed. Second, a new analysis of the discrete commutation error is carried out. The analysis indicates that the discrete commutation error is not only dependent on the number of vanishing moments of the filter weights, but also on the order of accuracy of the discrete gradient operator. The results of the analysis are confirmed by grid-refinement studies
Directory of Open Access Journals (Sweden)
Ibrahim Mohd Tarmizi
2017-01-01
Full Text Available Theories are developed to explain an observed phenomenon in an effort to understand why and how things happen. Theories thus, use latent variables to estimate conceptual parameters. The level of abstraction depends, partly on the complexity of the theoretical model explaining the phenomenon. The conjugation of directly-measured variables leads to a formation of a first-order factor. A combination of theoretical underpinnings supporting an existence of a higher-order components, and statistical evidence pointing to such presence adds advantage for the researchers to investigate a phenomenon both at an aggregated and disjointed dimensions. As partial least square (PLS gains its tractions in theory development, behavioural accounting discipline in general should exploit the flexibility of PLS to work with the higher-order factors. However, technical guides are scarcely available. Therefore, this article presents a PLS approach to validate a higher-order factor on a statistical ground using accounting information system dataset.
Wang, Yun-Peng; Li, Xiang-Guo; Liu, Shuang-Long; Fry, James N.; Cheng, Hai-Ping
2018-03-01
We investigate theoretically magnetism and magnetic phase transitions induced by electrostatic gating of two-dimensional square metal-organic framework compounds. We find that electrostatic gating can induce phase transitions between homogeneous ferromagnetic and various spin-textured antiferromagnetic states. Electronic structure and Wannier function analysis can reveal hybridizations between transition-metal d orbitals and conjugated π orbitals in the organic framework. Mn-containing compounds exhibit a strong d -π hybridization that leads to partially occupied spin-minority bands, in contrast to compounds containing transition-metal ions other than Mn, for which electronic structure around the Fermi energy is only slightly spin split due to weak d -π hybridization and the magnetic interaction is of the Ruderman-Kittel-Kasuya-Yosida type. We use a ferromagnetic Kondo lattice model to understand the phase transition in Mn-containing compounds in terms of carrier density and illuminate the complexity and the potential to control two-dimensional magnetization.