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.
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.
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
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.
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.
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).
Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.
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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.
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
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.
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.)
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
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.
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.
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
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.
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.
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.
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.
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
Penalty Algorithm Based on Conjugate Gradient Method for Solving Portfolio Management Problem
Directory of Open Access Journals (Sweden)
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.
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.)
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.
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
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.
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.
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
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
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.
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)
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.
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.
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.
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.
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.
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).
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.
Directory of Open Access Journals (Sweden)
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.
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.
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.
Directory of Open Access Journals (Sweden)
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.
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.
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)).
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.)
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.
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.
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.
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...
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.
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
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
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.
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.
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.
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)
Armstrong, Ian S; Hoffmann, Sandra A
2016-11-01
The interest in quantitative single photon emission computer tomography (SPECT) shows potential in a number of clinical applications and now several vendors are providing software and hardware solutions to allow 'SUV-SPECT' to mirror metrics used in PET imaging. This brief technical report assesses the accuracy of activity concentration measurements using a new algorithm 'xSPECT' from Siemens Healthcare. SPECT/CT data were acquired from a uniform cylinder with 5, 10, 15 and 20 s/projection and NEMA image quality phantom with 25 s/projection. The NEMA phantom had hot spheres filled with an 8 : 1 activity concentration relative to the background compartment. Reconstructions were performed using parameters defined by manufacturer presets available with the algorithm. The accuracy of activity concentration measurements was assessed. A dose calibrator-camera cross-calibration factor (CCF) was derived from the uniform phantom data. In uniform phantom images, a positive bias was observed, ranging from ∼6% in the lower count images to ∼4% in the higher-count images. On the basis of the higher-count data, a CCF of 0.96 was derived. As expected, considerable negative bias was measured in the NEMA spheres using region mean values whereas positive bias was measured in the four largest NEMA spheres. Nonmonotonically increasing recovery curves for the hot spheres suggested the presence of Gibbs edge enhancement from resolution modelling. Sufficiently accurate activity concentration measurements can easily be measured on images reconstructed with the xSPECT algorithm without a CCF. However, the use of a CCF is likely to improve accuracy further. A manual conversion of voxel values into SUV should be possible, provided that the patient weight, injected activity and time between injection and imaging are all known accurately.
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 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.
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. ...
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.
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
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.
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.
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.
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.
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
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.
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.
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 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
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
preconditioning the modified conjugate gradient method
African Journals Online (AJOL)
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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.
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
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
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)
Higher-order force gradient symplectic algorithms
Chin, Siu A.; Kidwell, Donald W.
2000-12-01
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10, and 12, the new algorithms are approximately a factor of 103, 104, 104, and 105 better.
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.
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.
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
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
Gradient algorithm applied to laboratory quantum control
International Nuclear Information System (INIS)
Roslund, Jonathan; Rabitz, Herschel
2009-01-01
The exploration of a quantum control landscape, which is the physical observable as a function of the control variables, is fundamental for understanding the ability to perform observable optimization in the laboratory. For high control variable dimensions, trajectory-based methods provide a means for performing such systematic explorations by exploiting the measured gradient of the observable with respect to the control variables. This paper presents a practical, robust, easily implemented statistical method for obtaining the gradient on a general quantum control landscape in the presence of noise. In order to demonstrate the method's utility, the experimentally measured gradient is utilized as input in steepest-ascent trajectories on the landscapes of three model quantum control problems: spectrally filtered and integrated second harmonic generation as well as excitation of atomic rubidium. The gradient algorithm achieves efficiency gains of up to approximately three times that of the standard genetic algorithm and, as such, is a promising tool for meeting quantum control optimization goals as well as landscape analyses. The landscape trajectories directed by the gradient should aid in the continued investigation and understanding of controlled quantum phenomena.
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.
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.
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
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
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
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)
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)
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
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.
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.
Quasi Gradient Projection Algorithm for Sparse Reconstruction in Compressed Sensing
Directory of Open Access Journals (Sweden)
Xin Meng
2014-02-01
Full Text Available Compressed sensing is a novel signal sampling theory under the condition that the signal is sparse or compressible. The existing recovery algorithms based on the gradient projection can either need prior knowledge or recovery the signal poorly. In this paper, a new algorithm based on gradient projection is proposed, which is referred as Quasi Gradient Projection. The algorithm presented quasi gradient direction and two step sizes schemes along this direction. The algorithm doesn’t need any prior knowledge of the original signal. Simulation results demonstrate that the presented algorithm cans recovery the signal more correctly than GPSR which also don’t need prior knowledge. Meanwhile, the algorithm has a lower computation complexity.
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
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.
Gradient Evolution-based Support Vector Machine Algorithm for Classification
Zulvia, Ferani E.; Kuo, R. J.
2018-03-01
This paper proposes a classification algorithm based on a support vector machine (SVM) and gradient evolution (GE) algorithms. SVM algorithm has been widely used in classification. However, its result is significantly influenced by the parameters. Therefore, this paper aims to propose an improvement of SVM algorithm which can find the best SVMs’ parameters automatically. The proposed algorithm employs a GE algorithm to automatically determine the SVMs’ parameters. The GE algorithm takes a role as a global optimizer in finding the best parameter which will be used by SVM algorithm. The proposed GE-SVM algorithm is verified using some benchmark datasets and compared with other metaheuristic-based SVM algorithms. The experimental results show that the proposed GE-SVM algorithm obtains better results than other algorithms tested in this paper.
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.
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
Gradient Learning Algorithms for Ontology Computing
Gao, Wei; Zhu, Linli
2014-01-01
The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting. PMID:25530752
Gradient Learning Algorithms for Ontology Computing
Directory of Open Access Journals (Sweden)
Wei Gao
2014-01-01
Full Text Available The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting.
The application of projected conjugate gradient solvers on graphical processing units
International Nuclear Information System (INIS)
Lin, Youzuo; Renaut, Rosemary
2011-01-01
Graphical processing units introduce the capability for large scale computation at the desktop. Presented numerical results verify that efficiencies and accuracies of basic linear algebra subroutines of all levels when implemented in CUDA and Jacket are comparable. But experimental results demonstrate that the basic linear algebra subroutines of level three offer the greatest potential for improving efficiency of basic numerical algorithms. We consider the solution of the multiple right hand side set of linear equations using Krylov subspace-based solvers. Thus, for the multiple right hand side case, it is more efficient to make use of a block implementation of the conjugate gradient algorithm, rather than to solve each system independently. Jacket is used for the implementation. Furthermore, including projection from one system to another improves efficiency. A relevant example, for which simulated results are provided, is the reconstruction of a three dimensional medical image volume acquired from a positron emission tomography scanner. Efficiency of the reconstruction is improved by using projection across nearby slices.
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.
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.
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
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.
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.
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
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.
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
Gradient descent learning algorithm overview: a general dynamical systems perspective.
Baldi, P
1995-01-01
Gives a unified treatment of gradient descent learning algorithms for neural networks using a general framework of dynamical systems. This general approach organizes and simplifies all the known algorithms and results which have been originally derived for different problems (fixed point/trajectory learning), for different models (discrete/continuous), for different architectures (forward/recurrent), and using different techniques (backpropagation, variational calculus, adjoint methods, etc.). The general approach can also be applied to derive new algorithms. The author then briefly examines some of the complexity issues and limitations intrinsic to gradient descent learning. Throughout the paper, the author focuses on the problem of trajectory learning.
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.)
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.
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
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.
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.
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
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
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
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.
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
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.
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.
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.
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.
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.
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)
Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization
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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.
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
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.
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.
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)
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....
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
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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.
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.
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
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
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.
Approximated Function Based Spectral Gradient Algorithm for Sparse Signal Recovery
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Weifeng Wang
2014-02-01
Full Text Available Numerical algorithms for the l0-norm regularized non-smooth non-convex minimization problems have recently became a topic of great interest within signal processing, compressive sensing, statistics, and machine learning. Nevertheless, the l0-norm makes the problem combinatorial and generally computationally intractable. In this paper, we construct a new surrogate function to approximate l0-norm regularization, and subsequently make the discrete optimization problem continuous and smooth. Then we use the well-known spectral gradient algorithm to solve the resulting smooth optimization problem. Experiments are provided which illustrate this method is very promising.
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
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.
International Nuclear Information System (INIS)
Cheng Sheng-Yi; Liu Wen-Jin; Chen Shan-Qiu; Dong Li-Zhi; Yang Ping; Xu Bing
2015-01-01
Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n 2 ) ∼ O(n 3 ) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ∼ (O(n) 3/2 ), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. (paper)
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)
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.
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...
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
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
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
Modified cuckoo search: A new gradient free optimisation algorithm
International Nuclear Information System (INIS)
Walton, S.; Hassan, O.; Morgan, K.; Brown, M.R.
2011-01-01
Highlights: → Modified cuckoo search (MCS) is a new gradient free optimisation algorithm. → MCS shows a high convergence rate, able to outperform other optimisers. → MCS is particularly strong at high dimension objective functions. → MCS performs well when applied to engineering problems. - Abstract: A new robust optimisation algorithm, which can be regarded as a modification of the recently developed cuckoo search, is presented. The modification involves the addition of information exchange between the top eggs, or the best solutions. Standard optimisation benchmarking functions are used to test the effects of these modifications and it is demonstrated that, in most cases, the modified cuckoo search performs as well as, or better than, the standard cuckoo search, a particle swarm optimiser, and a differential evolution strategy. In particular the modified cuckoo search shows a high convergence rate to the true global minimum even at high numbers of dimensions.
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.
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.
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 Penalization-Gradient Algorithm for Variational Inequalities
Directory of Open Access Journals (Sweden)
Abdellatif Moudafi
2011-01-01
Full Text Available This paper is concerned with the study of a penalization-gradient algorithm for solving variational inequalities, namely, find x̅∈C such that 〈Ax̅,y-x̅〉≥0 for all y∈C, where A:H→H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ:H→R ∪ {+∞} which acts as a penalization function with respect to the constraint x̅∈C, and a penalization parameter βk, we consider an algorithm which alternates a proximal step with respect to ∂Ψ and a gradient step with respect to A and reads as xk=(I+λkβk∂Ψ-1(xk-1-λkAxk-1. Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing the multivalued operator by its Yosida approximate which is always Lipschitz continuous.
Cheng, Sheng-Yi; Liu, Wen-Jin; Chen, Shan-Qiu; Dong, Li-Zhi; Yang, Ping; Xu, Bing
2015-08-01
Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ˜ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ˜ (O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Provincial Outstanding Youth Academic Technology Leaders Program, China (Grant No. 2012JQ0012).
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.
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.
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.
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.
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
Directory of Open Access Journals (Sweden)
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)
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
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
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
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.
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.
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.
National Research Council Canada - National Science Library
Homaifar, Abdollah; Esterline, Albert; Kimiaghalam, Bahram
2005-01-01
The Hybrid Projected Gradient-Evolutionary Search Algorithm (HPGES) algorithm uses a specially designed evolutionary-based global search strategy to efficiently create candidate solutions in the solution space...
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.
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.
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.
The Physics of Compressive Sensing and the Gradient-Based Recovery Algorithms
Dai, Qi; Sha, Wei
2009-01-01
The physics of compressive sensing (CS) and the gradient-based recovery algorithms are presented. First, the different forms for CS are summarized. Second, the physical meanings of coherence and measurement are given. Third, the gradient-based recovery algorithms and their geometry explanations are provided. Finally, we conclude the report and give some suggestion for future work.
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.
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
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
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).
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.
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
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.
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.
Algorithm for image retrieval based on edge gradient orientation statistical code.
Zeng, Jiexian; Zhao, Yonggang; Li, Weiye; Fu, Xiang
2014-01-01
Image edge gradient direction not only contains important information of the shape, but also has a simple, lower complexity characteristic. Considering that the edge gradient direction histograms and edge direction autocorrelogram do not have the rotation invariance, we put forward the image retrieval algorithm which is based on edge gradient orientation statistical code (hereinafter referred to as EGOSC) by sharing the application of the statistics method in the edge direction of the chain code in eight neighborhoods to the statistics of the edge gradient direction. Firstly, we construct the n-direction vector and make maximal summation restriction on EGOSC to make sure this algorithm is invariable for rotation effectively. Then, we use Euclidean distance of edge gradient direction entropy to measure shape similarity, so that this method is not sensitive to scaling, color, and illumination change. The experimental results and the algorithm analysis demonstrate that the algorithm can be used for content-based image retrieval and has good retrieval results.
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.
A time domain phase-gradient based ISAR autofocus algorithm
CSIR Research Space (South Africa)
Nel, W
2011-10-01
Full Text Available . Results on simulated and measured data show that the algorithm performs well. Unlike many other ISAR autofocus techniques, the algorithm does not make use of several computationally intensive iterations between the data and image domains as part...
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.
Research algorithm for synthesis of double conjugation optical systems in the Gauss region
Directory of Open Access Journals (Sweden)
A. B. Ostrun
2014-01-01
Full Text Available The article focuses on the research of variable magnification optical systems of sophistic class - so-called double conjugation systems. When the magnification changes, they provide two pairs of fixed conjugate planes, namely object and image, as well as entrance and exit pupils. Similar systems are used in microscopy and complex schemes, where it is necessary to conform the pupils of contiguous removable optical components. Synthesis of double conjugation systems in Gauss region is not an easy task. To ensure complete immobility of the exit pupil in the system there should be three movable components or components with variable optical power.Analysis of the literature shows that the design of double conjugation optical system in the paraxial region has been neglected, all methods are not completely universal and suitable for automation.Based on the foregoing, the research and development of a universal method for automated synthesis of double conjugation systems in Gauss region formulated as an objective of the present work seem to be a challenge.To achieve this goal a universal algorithm is used. It is based on the fact that the output coordinates of paraxial rays are multilinear functions of optical surfaces and of axial thicknesses between surfaces. It allows us to create and solve a system of multilinear equations in semi-automatic mode to achieve the chosen values of paraxial characteristics.As a basic scheme for the synthesis a five-component system has been chosen with extreme fixed components and three mobile "internal" ones. The system was considered in two extreme states of moving parts. Initial values of axial thicknesses were taken from Hopkins' patent. Optical force five components were considered unknown. For calculation the system of five equations was created, which allowed us to obtain a certain back focal length, to provide the specified focal length and a fixed position of the exit pupil at a fixed entrance pupil.The scheme
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
TIGER: Development of Thermal Gradient Compensation Algorithms and Techniques
Hereford, James; Parker, Peter A.; Rhew, Ray D.
2004-01-01
In a wind tunnel facility, the direct measurement of forces and moments induced on the model are performed by a force measurement balance. The measurement balance is a precision-machined device that has strain gages at strategic locations to measure the strain (i.e., deformations) due to applied forces and moments. The strain gages convert the strain (and hence the applied force) to an electrical voltage that is measured by external instruments. To address the problem of thermal gradients on the force measurement balance NASA-LaRC has initiated a research program called TIGER - Thermally-Induced Gradients Effects Research. The ultimate goals of the TIGER program are to: (a) understand the physics of the thermally-induced strain and its subsequent impact on load measurements and (b) develop a robust thermal gradient compensation technique. This paper will discuss the impact of thermal gradients on force measurement balances, specific aspects of the TIGER program (the design of a special-purpose balance, data acquisition and data analysis challenges), and give an overall summary.
Adaptive Step Size Gradient Ascent ICA Algorithm for Wireless MIMO Systems
Directory of Open Access Journals (Sweden)
Zahoor Uddin
2018-01-01
Full Text Available Independent component analysis (ICA is a technique of blind source separation (BSS used for separation of the mixed received signals. ICA algorithms are classified into adaptive and batch algorithms. Adaptive algorithms perform well in time-varying scenario with high-computational complexity, while batch algorithms have better separation performance in quasistatic channels with low-computational complexity. Amongst batch algorithms, the gradient-based ICA algorithms perform well, but step size selection is critical in these algorithms. In this paper, an adaptive step size gradient ascent ICA (ASS-GAICA algorithm is presented. The proposed algorithm is free from selection of the step size parameter with improved convergence and separation performance. Different performance evaluation criteria are used to verify the effectiveness of the proposed algorithm. Performance of the proposed algorithm is compared with the FastICA and optimum block adaptive ICA (OBAICA algorithms for quasistatic and time-varying wireless channels. Simulation is performed over quadrature amplitude modulation (QAM and binary phase shift keying (BPSK signals. Results show that the proposed algorithm outperforms the FastICA and OBAICA algorithms for a wide range of signal-to-noise ratio (SNR and input data block lengths.
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.
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.
Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals
Cho, Myung
2016-06-24
We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.
Fast alternating projected gradient descent algorithms for recovering spectrally sparse signals
Cho, Myung; Cai, Jian-Feng; Liu, Suhui; Eldar, Yonina C.; Xu, Weiyu
2016-01-01
We propose fast algorithms that speed up or improve the performance of recovering spectrally sparse signals from un-derdetermined measurements. Our algorithms are based on a non-convex approach of using alternating projected gradient descent for structured matrix recovery. We apply this approach to two formulations of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix, and Hankel structured matrix. Our methods provide better recovery performance, and faster signal recovery than existing algorithms, including atomic norm minimization.
International Nuclear Information System (INIS)
Niu Lili; Qian Ming; Yu Wentao; Jin Qiaofeng; Ling Tao; Zheng Hairong; Wan Kun; Gao Shen
2010-01-01
This paper presents a new algorithm for ultrasonic particle image velocimetry (Echo PIV) for improving the flow velocity measurement accuracy and efficiency in regions with high velocity gradients. The conventional Echo PIV algorithm has been modified by incorporating a multiple iterative algorithm, sub-pixel method, filter and interpolation method, and spurious vector elimination algorithm. The new algorithms' performance is assessed by analyzing simulated images with known displacements, and ultrasonic B-mode images of in vitro laminar pipe flow, rotational flow and in vivo rat carotid arterial flow. Results of the simulated images show that the new algorithm produces much smaller bias from the known displacements. For laminar flow, the new algorithm results in 1.1% deviation from the analytically derived value, and 8.8% for the conventional algorithm. The vector quality evaluation for the rotational flow imaging shows that the new algorithm produces better velocity vectors. For in vivo rat carotid arterial flow imaging, the results from the new algorithm deviate 6.6% from the Doppler-measured peak velocities averagely compared to 15% of that from the conventional algorithm. The new Echo PIV algorithm is able to effectively improve the measurement accuracy in imaging flow fields with high velocity gradients.
Directory of Open Access Journals (Sweden)
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.
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.
An Improved Phase Gradient Autofocus Algorithm Used in Real-time Processing
Directory of Open Access Journals (Sweden)
Qing Ji-ming
2015-10-01
Full Text Available The Phase Gradient Autofocus (PGA algorithm can remove the high order phase error effectively, which is of great significance to get high resolution images in real-time processing. While PGA usually needs iteration, which necessitates long working hours. In addition, the performances of the algorithm are not stable in different scene applications. This severely constrains the application of PGA in real-time processing. Isolated scatter selection and windowing are two important algorithmic steps of Phase Gradient Autofocus Algorithm. Therefore, this paper presents an isolated scatter selection method based on sample mean and a windowing method based on pulse envelope. These two methods are highly adaptable to data, which would make the algorithm obtain better stability and need less iteration. The adaptability of the improved PGA is demonstrated with the experimental results of real radar 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
Practical mathematical optimization basic optimization theory and gradient-based algorithms
Snyman, Jan A
2018-01-01
This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and dir...
An Exploration Algorithm for Stochastic Simulators Driven by Energy Gradients
Directory of Open Access Journals (Sweden)
Anastasia S. Georgiou
2017-06-01
Full Text Available In recent work, we have illustrated the construction of an exploration geometry on free energy surfaces: the adaptive computer-assisted discovery of an approximate low-dimensional manifold on which the effective dynamics of the system evolves. Constructing such an exploration geometry involves geometry-biased sampling (through both appropriately-initialized unbiased molecular dynamics and through restraining potentials and, machine learning techniques to organize the intrinsic geometry of the data resulting from the sampling (in particular, diffusion maps, possibly enhanced through the appropriate Mahalanobis-type metric. In this contribution, we detail a method for exploring the conformational space of a stochastic gradient system whose effective free energy surface depends on a smaller number of degrees of freedom than the dimension of the phase space. Our approach comprises two steps. First, we study the local geometry of the free energy landscape using diffusion maps on samples computed through stochastic dynamics. This allows us to automatically identify the relevant coarse variables. Next, we use the information garnered in the previous step to construct a new set of initial conditions for subsequent trajectories. These initial conditions are computed so as to explore the accessible conformational space more efficiently than by continuing the previous, unbiased simulations. We showcase this method on a representative test system.
A gradient based algorithm to solve inverse plane bimodular problems of identification
Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing
2018-02-01
This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.
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)
Data-driven gradient algorithm for high-precision quantum control
Wu, Re-Bing; Chu, Bing; Owens, David H.; Rabitz, Herschel
2018-04-01
In the quest to achieve scalable quantum information processing technologies, gradient-based optimal control algorithms (e.g., grape) are broadly used for implementing high-precision quantum gates, but their performance is often hindered by deterministic or random errors in the system model and the control electronics. In this paper, we show that grape can be taught to be more effective by jointly learning from the design model and the experimental data obtained from process tomography. The resulting data-driven gradient optimization algorithm (d-grape) can in principle correct all deterministic gate errors, with a mild efficiency loss. The d-grape algorithm may become more powerful with broadband controls that involve a large number of control parameters, while other algorithms usually slow down due to the increased size of the search space. These advantages are demonstrated by simulating the implementation of a two-qubit controlled-not gate.
An algorithm for gradient-based dynamic optimization of UV ﬂash processes
DEFF Research Database (Denmark)
Ritschel, Tobias Kasper Skovborg; Capolei, Andrea; Gaspar, Jozsef
2017-01-01
This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor-liquid equilibrium constraints. Such optimal control problems are important in several engineering applications, for instance in control of distillation columns, in certain two...... softwareaswellastheperformanceofdiﬀerentcompilersinaLinuxoperatingsystem. Thesetestsindicatethatreal-timenonlinear model predictive control of UV ﬂash processes is computationally feasible....
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.
Directory of Open Access Journals (Sweden)
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.
On the Strong Convergence of a Sufficient Descent Polak-Ribière-Polyak Conjugate Gradient Method
Directory of Open Access Journals (Sweden)
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.
Dynamic gradient descent learning algorithms for enhanced empirical modeling of power plants
International Nuclear Information System (INIS)
Parlos, A.G.; Atiya, Amir; Chong, K.T.
1991-01-01
A newly developed dynamic gradient descent-based learning algorithm is used to train a recurrent multilayer perceptron network for use in empirical modeling of power plants. The two main advantages of the proposed learning algorithm are its ability to consider past error gradient information for future use and the two forward passes associated with its implementation, instead of one forward and one backward pass of the backpropagation algorithm. The latter advantage results in computational time saving because both passes can be performed simultaneously. The dynamic learning algorithm is used to train a hybrid feedforward/feedback neural network, a recurrent multilayer perceptron, which was previously found to exhibit good interpolation and extrapolation capabilities in modeling nonlinear dynamic systems. One of the drawbacks, however, of the previously reported work has been the long training times associated with accurate empirical models. The enhanced learning capabilities provided by the dynamic gradient descent-based learning algorithm are demonstrated by a case study of a steam power plant. The number of iterations required for accurate empirical modeling has been reduced from tens of thousands to hundreds, thus significantly expediting the learning process
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.
Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm.
Chang, Joshua; Paydarfar, David
2014-12-01
Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.
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.
Image defog algorithm based on open close filter and gradient domain recursive bilateral filter
Liu, Daqian; Liu, Wanjun; Zhao, Qingguo; Fei, Bowen
2017-11-01
To solve the problems of fuzzy details, color distortion, low brightness of the image obtained by the dark channel prior defog algorithm, an image defog algorithm based on open close filter and gradient domain recursive bilateral filter, referred to as OCRBF, was put forward. The algorithm named OCRBF firstly makes use of weighted quad tree to obtain more accurate the global atmospheric value, then exploits multiple-structure element morphological open and close filter towards the minimum channel map to obtain a rough scattering map by dark channel prior, makes use of variogram to correct the transmittance map,and uses gradient domain recursive bilateral filter for the smooth operation, finally gets recovery images by image degradation model, and makes contrast adjustment to get bright, clear and no fog image. A large number of experimental results show that the proposed defog method in this paper can be good to remove the fog , recover color and definition of the fog image containing close range image, image perspective, the image including the bright areas very well, compared with other image defog algorithms,obtain more clear and natural fog free images with details of higher visibility, what's more, the relationship between the time complexity of SIDA algorithm and the number of image pixels is a linear correlation.
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
Dynamic phasing of multichannel cw laser radiation by means of a stochastic gradient algorithm
Energy Technology Data Exchange (ETDEWEB)
Volkov, V A; Volkov, M V; Garanin, S G; Dolgopolov, Yu V; Kopalkin, A V; Kulikov, S M; Starikov, F A; Sukharev, S A; Tyutin, S V; Khokhlov, S V; Chaparin, D A [Russian Federal Nuclear Center ' All-Russian Research Institute of Experimental Physics' , Sarov, Nizhnii Novgorod region (Russian Federation)
2013-09-30
The phasing of a multichannel laser beam by means of an iterative stochastic parallel gradient (SPG) algorithm has been numerically and experimentally investigated. The operation of the SPG algorithm is simulated, the acceptable range of amplitudes of probe phase shifts is found, and the algorithm parameters at which the desired Strehl number can be obtained with a minimum number of iterations are determined. An experimental bench with phase modulators based on lithium niobate, which are controlled by a multichannel electronic unit with a real-time microcontroller, has been designed. Phasing of 16 cw laser beams at a system response bandwidth of 3.7 kHz and phase thermal distortions in a frequency band of about 10 Hz is experimentally demonstrated. The experimental data are in complete agreement with the calculation results. (control of laser radiation parameters)
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
Directory of Open Access Journals (Sweden)
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.
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.
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.
Iris Location Algorithm Based on the CANNY Operator and Gradient Hough Transform
Zhong, L. H.; Meng, K.; Wang, Y.; Dai, Z. Q.; Li, S.
2017-12-01
In the iris recognition system, the accuracy of the localization of the inner and outer edges of the iris directly affects the performance of the recognition system, so iris localization has important research meaning. Our iris data contain eyelid, eyelashes, light spot and other noise, even the gray transformation of the images is not obvious, so the general methods of iris location are unable to realize the iris location. The method of the iris location based on Canny operator and gradient Hough transform is proposed. Firstly, the images are pre-processed; then, calculating the gradient information of images, the inner and outer edges of iris are coarse positioned using Canny operator; finally, according to the gradient Hough transform to realize precise localization of the inner and outer edge of iris. The experimental results show that our algorithm can achieve the localization of the inner and outer edges of the iris well, and the algorithm has strong anti-interference ability, can greatly reduce the location time and has higher accuracy and stability.
Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet
Directory of Open Access Journals (Sweden)
Fang Ye
2017-02-01
Full Text Available In order to improve system performance such as throughput, heterogeneous network (HetNet has become an effective solution in Long Term Evolution-Advanced (LET-A. However, co-channel interference leads to degradation of the HetNet throughput, because femtocells are always arranged to share the spectrum with the macro base station. In this paper, in view of the serious cross-layer interference in double layer HetNet, the Stackelberg game model is adopted to analyze the resource allocation methods of the network. Unlike the traditional system models only focusing on macro base station performance improvement, we take into account the overall system performance and build a revenue function with convexity. System utility functions are defined as the average throughput, which does not adopt frequency spectrum trading method, so as to avoid excessive signaling overhead. Due to the value scope of continuous Nash equilibrium of the built game model, the gradient iterative algorithm is introduced to reduce the computational complexity. As for the solution of Nash equilibrium, one kind of gradient iterative algorithm is proposed, which is able to intelligently choose adjustment factors. The Nash equilibrium can be quickly solved; meanwhile, the step of presetting adjustment factors is avoided according to network parameters in traditional linear iterative model. Simulation results show that the proposed algorithm enhances the overall performance of the system.
An optical flow algorithm based on gradient constancy assumption for PIV image processing
International Nuclear Information System (INIS)
Zhong, Qianglong; Yang, Hua; Yin, Zhouping
2017-01-01
Particle image velocimetry (PIV) has matured as a flow measurement technique. It enables the description of the instantaneous velocity field of the flow by analyzing the particle motion obtained from digitally recorded images. Correlation based PIV evaluation technique is widely used because of its good accuracy and robustness. Although very successful, correlation PIV technique has some weakness which can be avoided by optical flow based PIV algorithms. At present, most of the optical flow methods applied to PIV are based on brightness constancy assumption. However, some factors of flow imaging technology and the nature property of the fluids make the brightness constancy assumption less appropriate in real PIV cases. In this paper, an implementation of a 2D optical flow algorithm (GCOF) based on gradient constancy assumption is introduced. The proposed GCOF assumes the edges of the illuminated PIV particles are constant during motion. It comprises two terms: a combined local-global gradient data term and a first-order divergence and vorticity smooth term. The approach can provide accurate dense motion fields. The approach are tested on synthetic images and on two experimental flows. The comparison of GCOF with other optical flow algorithms indicates the proposed method is more accurate especially in conditions of illumination variation. The comparison of GCOF with correlation PIV technique shows that the proposed GCOF has advantages on preserving small divergence and vorticity structures of the motion field and getting less outliers. As a consequence, the GCOF acquire a more accurate and better topological description of the turbulent flow. (paper)
Optimization algorithms and applications
Arora, Rajesh Kumar
2015-01-01
Choose the Correct Solution Method for Your Optimization ProblemOptimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden-Fletcher-Goldfarb-Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible direc
Parametric estimation of the Duffing system by using a modified gradient algorithm
International Nuclear Information System (INIS)
Aguilar-Ibanez, Carlos; Sanchez Herrera, Jorge; Garrido-Moctezuma, Ruben
2008-01-01
The Letter presents a strategy for recovering the unknown parameters of the Duffing oscillator using a measurable output signal. The suggested approach employs the construction of an integral parametrization of one auxiliary output. It is calculated by measuring the difference between the output and its respective delay output. First we estimate the auxiliary output, followed by the application of a modified gradient algorithm, then we adjust the gains of the proposed linear estimator, until this error converges to zero. The convergence of the proposed scheme is shown using Lyapunov method
Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Application
Chambolle, Antonin; Ehrhardt, Matthias J.; Richtarik, Peter; Schö nlieb, Carola-Bibiane
2017-01-01
We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.
Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Application
Chambolle, Antonin
2017-06-15
We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.
Stochastic quasi-gradient based optimization algorithms for dynamic reliability applications
International Nuclear Information System (INIS)
Bourgeois, F.; Labeau, P.E.
2001-01-01
On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the 'best' safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. Stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO 3 supply system
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.
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.
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.
Chugh, Saryu; Arivu Selvan, K.; Nadesh, RK
2017-11-01
Numerous destructive things influence the working arrangement of human body as hypertension, smoking, obesity, inappropriate medication taking which causes many contrasting diseases as diabetes, thyroid, strokes and coronary diseases. The impermanence and horribleness of the environment situation is also the reason for the coronary disease. The structure of Apache start relies on the evolution which requires gathering of the data. To break down the significance of use programming focused on data structure the Apache stop ought to be utilized and it gives various central focuses as it is fast in light as it uses memory worked in preparing. Apache Spark continues running on dispersed environment and chops down the data in bunches giving a high profitability rate. Utilizing mining procedure as a part of the determination of coronary disease has been exhaustively examined indicating worthy levels of precision. Decision trees, Neural Network, Gradient Boosting Algorithm are the various apache spark proficiencies which help in collecting the information.
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)
Grebenkov, Denis S
2011-02-01
A new method for computing the signal attenuation due to restricted diffusion in a linear magnetic field gradient is proposed. A fast random walk (FRW) algorithm for simulating random trajectories of diffusing spin-bearing particles is combined with gradient encoding. As random moves of a FRW are continuously adapted to local geometrical length scales, the method is efficient for simulating pulsed-gradient spin-echo experiments in hierarchical or multiscale porous media such as concrete, sandstones, sedimentary rocks and, potentially, brain or lungs. Copyright © 2010 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
Burt, Adam O.; Tinker, Michael L.
2014-01-01
In this paper, genetic algorithm based and gradient-based topology optimization is presented in application to a real hardware design problem. Preliminary design of a planetary lander mockup structure is accomplished using these methods that prove to provide major weight savings by addressing the structural efficiency during the design cycle. This paper presents two alternative formulations of the topology optimization problem. The first is the widely-used gradient-based implementation using commercially available algorithms. The second is formulated using genetic algorithms and internally developed capabilities. These two approaches are applied to a practical design problem for hardware that has been built, tested and proven to be functional. Both formulations converged on similar solutions and therefore were proven to be equally valid implementations of the process. This paper discusses both of these formulations at a high level.
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
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
A very fast implementation of 2D iterative reconstruction algorithms
DEFF Research Database (Denmark)
Toft, Peter Aundal; Jensen, Peter James
1996-01-01
that iterative reconstruction algorithms can be implemented and run almost as fast as direct reconstruction algorithms. The method has been implemented in a software package that is available for free, providing reconstruction algorithms using ART, EM, and the Least Squares Conjugate Gradient Method...
Energy Technology Data Exchange (ETDEWEB)
Volkov, M V; Garanin, S G; Dolgopolov, Yu V; Kopalkin, A V; Kulikov, S M; Sinyavin, D N; Starikov, F A; Sukharev, S A; Tyutin, S V; Khokhlov, S V; Chaparin, D A [Russian Federal Nuclear Center ' All-Russian Research Institute of Experimental Physics' , Sarov, Nizhnii Novgorod region (Russian Federation)
2014-11-30
A seven-channel fibre laser system operated by the master oscillator – multichannel power amplifier scheme is the phase locked using a stochastic parallel gradient algorithm. The phase modulators on lithium niobate crystals are controlled by a multichannel electronic unit with the microcontroller processing signals in real time. The dynamic phase locking of the laser system with the bandwidth of 14 kHz is demonstrated, the time of phasing is 3 – 4 ms. (fibre and integrated-optical structures)
Gisdon, Florian J; Culka, Martin; Ullmann, G Matthias
2016-10-01
Conjugate peak refinement (CPR) is a powerful and robust method to search transition states on a molecular potential energy surface. Nevertheless, the method was to the best of our knowledge so far only implemented in CHARMM. In this paper, we present PyCPR, a new Python-based implementation of the CPR algorithm within the pDynamo framework. We provide a detailed description of the theory underlying our implementation and discuss the different parts of the implementation. The method is applied to two different problems. First, we illustrate the method by analyzing the gauche to anti-periplanar transition of butane using a semiempirical QM method. Second, we reanalyze the mechanism of a glycyl-radical enzyme, namely of 4-hydroxyphenylacetate decarboxylase (HPD) using QM/MM calculations. In the end, we suggest a strategy how to use our implementation of the CPR algorithm. The integration of PyCPR into the framework pDynamo allows the combination of CPR with the large variety of methods implemented in pDynamo. PyCPR can be used in combination with quantum mechanical and molecular mechanical methods (and hybrid methods) implemented directly in pDynamo, but also in combination with external programs such as ORCA using pDynamo as interface. PyCPR is distributed as free, open source software and can be downloaded from http://www.bisb.uni-bayreuth.de/index.php?page=downloads . Graphical Abstract PyCPR is a search tool for finding saddle points on the potential energy landscape of a molecular system.
Iterative algorithms for large sparse linear systems on parallel computers
Adams, L. M.
1982-01-01
Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.
Streuber, Gregg Mitchell
Environmental and economic factors motivate the pursuit of more fuel-efficient aircraft designs. Aerodynamic shape optimization is a powerful tool in this effort, but is hampered by the presence of multimodality in many design spaces. Gradient-based multistart optimization uses a sampling algorithm and multiple parallel optimizations to reliably apply fast gradient-based optimization to moderately multimodal problems. Ensuring that the sampled geometries remain physically realizable requires manually developing specialized linear constraints for each class of problem. Utilizing free-form deformation geometry control allows these linear constraints to be written in a geometry-independent fashion, greatly easing the process of applying the algorithm to new problems. This algorithm was used to assess the presence of multimodality when optimizing a wing in subsonic and transonic flows, under inviscid and viscous conditions, and a blended wing-body under transonic, viscous conditions. Multimodality was present in every wing case, while the blended wing-body was found to be generally unimodal.
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
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.
Van Kha, Tran; Van Vuong, Hoang; Thanh, Do Duc; Hung, Duong Quoc; Anh, Le Duc
2018-05-01
The maximum horizontal gradient method was first proposed by Blakely and Simpson (1986) for determining the boundaries between geological bodies with different densities. The method involves the comparison of a center point with its eight nearest neighbors in four directions within each 3 × 3 calculation grid. The horizontal location and magnitude of the maximum values are found by interpolating a second-order polynomial through the trio of points provided that the magnitude of the middle point is greater than its two nearest neighbors in one direction. In theoretical models of multiple sources, however, the above condition does not allow the maximum horizontal locations to be fully located, and it could be difficult to correlate the edges of complicated sources. In this paper, the authors propose an additional condition to identify more maximum horizontal locations within the calculation grid. This additional condition will improve the method algorithm for interpreting the boundaries of magnetic and/or gravity sources. The improved algorithm was tested on gravity models and applied to gravity data for the Phu Khanh basin on the continental shelf of the East Vietnam Sea. The results show that the additional locations of the maximum horizontal gradient could be helpful for connecting the edges of complicated source bodies.
González-Recio, O; Jiménez-Montero, J A; Alenda, R
2013-01-01
In the next few years, with the advent of high-density single nucleotide polymorphism (SNP) arrays and genome sequencing, genomic evaluation methods will need to deal with a large number of genetic variants and an increasing sample size. The boosting algorithm is a machine-learning technique that may alleviate the drawbacks of dealing with such large data sets. This algorithm combines different predictors in a sequential manner with some shrinkage on them; each predictor is applied consecutively to the residuals from the committee formed by the previous ones to form a final prediction based on a subset of covariates. Here, a detailed description is provided and examples using a toy data set are included. A modification of the algorithm called "random boosting" was proposed to increase predictive ability and decrease computation time of genome-assisted evaluation in large data sets. Random boosting uses a random selection of markers to add a subsequent weak learner to the predictive model. These modifications were applied to a real data set composed of 1,797 bulls genotyped for 39,714 SNP. Deregressed proofs of 4 yield traits and 1 type trait from January 2009 routine evaluations were used as dependent variables. A 2-fold cross-validation scenario was implemented. Sires born before 2005 were used as a training sample (1,576 and 1,562 for production and type traits, respectively), whereas younger sires were used as a testing sample to evaluate predictive ability of the algorithm on yet-to-be-observed phenotypes. Comparison with the original algorithm was provided. The predictive ability of the algorithm was measured as Pearson correlations between observed and predicted responses. Further, estimated bias was computed as the average difference between observed and predicted phenotypes. The results showed that the modification of the original boosting algorithm could be run in 1% of the time used with the original algorithm and with negligible differences in accuracy
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.
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.
A study of block algorithms for fermion matrix inversion
International Nuclear Information System (INIS)
Henty, D.
1990-01-01
We compare the convergence properties of Lanczos and Conjugate Gradient algorithms applied to the calculation of columns of the inverse fermion matrix for Kogut-Susskind and Wilson fermions in lattice QCD. When several columns of the inverse are required simultaneously, a block version of the Lanczos algorithm is most efficient at small mass, being over 5 times faster than the single algorithms. The block algorithm is also less susceptible to critical slowing down. (orig.)
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.
Directory of Open Access Journals (Sweden)
Sahbi Marrouchi
2014-01-01
Full Text Available Due to the continuous increase of the population and the perpetual progress of industry, the energy management presents nowadays a relevant topic that concerns researchers in electrical engineering. Indeed, in order to establish a good exploitation of the electrical grid, it is necessary to solve technical and economic problems. This can only be done through the resolution of the Unit Commitment Problem. Unit Commitment Problem allows optimizing the combination of the production units’ states and determining their production planning, in order to satisfy the expected consumption with minimal cost during a specified period which varies usually from 24 hours to one week. However, each production unit has some constraints that make this problem complex, combinatorial, and nonlinear. This paper presents a comparative study between a strategy based on hybrid gradient-genetic algorithm method and two strategies based on metaheuristic methods, fuzzy logic, and genetic algorithm, in order to predict the combinations and the unit commitment scheduling of each production unit in one side and to minimize the total production cost in the other side. To test the performance of the optimization proposed strategies, strategies have been applied to the IEEE electrical network 14 busses and the obtained results are very promising.
DEFF Research Database (Denmark)
Rubæk, Tonny; Meaney, P. M.; Meincke, Peter
2007-01-01
is presented which is based on the conjugate gradient least squares (CGLS) algorithm. The iterative CGLS algorithm is capable of solving the update problem by operating on just the Jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations. The new...
Ghobadi, Kimia; Ghaffari, Hamid R; Aleman, Dionne M; Jaffray, David A; Ruschin, Mark
2012-06-01
The purpose of this work is to develop a framework to the inverse problem for radiosurgery treatment planning on the Gamma Knife(®) Perfexion™ (PFX) for intracranial targets. The approach taken in the present study consists of two parts. First, a hybrid grassfire and sphere-packing algorithm is used to obtain shot positions (isocenters) based on the geometry of the target to be treated. For the selected isocenters, a sector duration optimization (SDO) model is used to optimize the duration of radiation delivery from each collimator size from each individual source bank. The SDO model is solved using a projected gradient algorithm. This approach has been retrospectively tested on seven manually planned clinical cases (comprising 11 lesions) including acoustic neuromas and brain metastases. In terms of conformity and organ-at-risk (OAR) sparing, the quality of plans achieved with the inverse planning approach were, on average, improved compared to the manually generated plans. The mean difference in conformity index between inverse and forward plans was -0.12 (range: -0.27 to +0.03) and +0.08 (range: 0.00-0.17) for classic and Paddick definitions, respectively, favoring the inverse plans. The mean difference in volume receiving the prescribed dose (V(100)) between forward and inverse plans was 0.2% (range: -2.4% to +2.0%). After plan renormalization for equivalent coverage (i.e., V(100)), the mean difference in dose to 1 mm(3) of brainstem between forward and inverse plans was -0.24 Gy (range: -2.40 to +2.02 Gy) favoring the inverse plans. Beam-on time varied with the number of isocenters but for the most optimal plans was on average 33 min longer than manual plans (range: -17 to +91 min) when normalized to a calibration dose rate of 3.5 Gy/min. In terms of algorithm performance, the isocenter selection for all the presented plans was performed in less than 3 s, while the SDO was performed in an average of 215 min. PFX inverse planning can be performed using
Energy Technology Data Exchange (ETDEWEB)
Ghobadi, Kimia; Ghaffari, Hamid R.; Aleman, Dionne M.; Jaffray, David A.; Ruschin, Mark [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S 3G8 (Canada); Department of Radiation Oncology, University of Toronto, Radiation Medicine Program, Princess Margaret Hospital, 610 University Avenue, Toronto, Ontario M5G 2M9 (Canada)
2012-06-15
Purpose: The purpose of this work is to develop a framework to the inverse problem for radiosurgery treatment planning on the Gamma Knife{sup Registered-Sign} Perfexion Trade-Mark-Sign (PFX) for intracranial targets. Methods: The approach taken in the present study consists of two parts. First, a hybrid grassfire and sphere-packing algorithm is used to obtain shot positions (isocenters) based on the geometry of the target to be treated. For the selected isocenters, a sector duration optimization (SDO) model is used to optimize the duration of radiation delivery from each collimator size from each individual source bank. The SDO model is solved using a projected gradient algorithm. This approach has been retrospectively tested on seven manually planned clinical cases (comprising 11 lesions) including acoustic neuromas and brain metastases. Results: In terms of conformity and organ-at-risk (OAR) sparing, the quality of plans achieved with the inverse planning approach were, on average, improved compared to the manually generated plans. The mean difference in conformity index between inverse and forward plans was -0.12 (range: -0.27 to +0.03) and +0.08 (range: 0.00-0.17) for classic and Paddick definitions, respectively, favoring the inverse plans. The mean difference in volume receiving the prescribed dose (V{sub 100}) between forward and inverse plans was 0.2% (range: -2.4% to +2.0%). After plan renormalization for equivalent coverage (i.e., V{sub 100}), the mean difference in dose to 1 mm{sup 3} of brainstem between forward and inverse plans was -0.24 Gy (range: -2.40 to +2.02 Gy) favoring the inverse plans. Beam-on time varied with the number of isocenters but for the most optimal plans was on average 33 min longer than manual plans (range: -17 to +91 min) when normalized to a calibration dose rate of 3.5 Gy/min. In terms of algorithm performance, the isocenter selection for all the presented plans was performed in less than 3 s, while the SDO was performed in an
International Nuclear Information System (INIS)
Ghobadi, Kimia; Ghaffari, Hamid R.; Aleman, Dionne M.; Jaffray, David A.; Ruschin, Mark
2012-01-01
Purpose: The purpose of this work is to develop a framework to the inverse problem for radiosurgery treatment planning on the Gamma Knife ® Perfexion™ (PFX) for intracranial targets. Methods: The approach taken in the present study consists of two parts. First, a hybrid grassfire and sphere-packing algorithm is used to obtain shot positions (isocenters) based on the geometry of the target to be treated. For the selected isocenters, a sector duration optimization (SDO) model is used to optimize the duration of radiation delivery from each collimator size from each individual source bank. The SDO model is solved using a projected gradient algorithm. This approach has been retrospectively tested on seven manually planned clinical cases (comprising 11 lesions) including acoustic neuromas and brain metastases. Results: In terms of conformity and organ-at-risk (OAR) sparing, the quality of plans achieved with the inverse planning approach were, on average, improved compared to the manually generated plans. The mean difference in conformity index between inverse and forward plans was −0.12 (range: −0.27 to +0.03) and +0.08 (range: 0.00–0.17) for classic and Paddick definitions, respectively, favoring the inverse plans. The mean difference in volume receiving the prescribed dose (V 100 ) between forward and inverse plans was 0.2% (range: −2.4% to +2.0%). After plan renormalization for equivalent coverage (i.e., V 100 ), the mean difference in dose to 1 mm 3 of brainstem between forward and inverse plans was −0.24 Gy (range: −2.40 to +2.02 Gy) favoring the inverse plans. Beam-on time varied with the number of isocenters but for the most optimal plans was on average 33 min longer than manual plans (range: −17 to +91 min) when normalized to a calibration dose rate of 3.5 Gy/min. In terms of algorithm performance, the isocenter selection for all the presented plans was performed in less than 3 s, while the SDO was performed in an average of 215 min
Directory of Open Access Journals (Sweden)
Huiru Zhao
2016-09-01
Full Text Available An important goal of China’s electric power system reform is to create a double-side day-ahead wholesale electricity market in the future, where the suppliers (represented by GenCOs and demanders (represented by DisCOs compete simultaneously with each other in one market. Therefore, modeling and simulating the dynamic bidding process and the equilibrium in the double-side day-ahead electricity market scientifically is not only important to some developed countries, but also to China to provide a bidding decision-making tool to help GenCOs and DisCOs obtain more profits in market competition. Meanwhile, it can also provide an economic analysis tool to help government officials design the proper market mechanisms and policies. The traditional dynamic game model and table-based reinforcement learning algorithm have already been employed in the day-ahead electricity market modeling. However, those models are based on some assumptions, such as taking the probability distribution function of market clearing price (MCP and each rival’s bidding strategy as common knowledge (in dynamic game market models, and assuming the discrete state and action sets of every agent (in table-based reinforcement learning market models, which are no longer applicable in a realistic situation. In this paper, a modified reinforcement learning method, called gradient descent continuous Actor-Critic (GDCAC algorithm was employed in the double-side day-ahead electricity market modeling and simulation. This algorithm can not only get rid of the abovementioned unrealistic assumptions, but also cope with the Markov decision-making process with continuous state and action sets just like the real electricity market. Meanwhile, the time complexity of our proposed model is only O(n. The simulation result of employing the proposed model in the double-side day-ahead electricity market shows the superiority of our approach in terms of participant’s profit or social welfare
Directory of Open Access Journals (Sweden)
Shoubin Wang
2017-01-01
Full Text Available Addressing the problem of two-dimensional steady-state thermal boundary recognition, a hybrid algorithm of conjugate gradient method and social particle swarm optimization (CGM-SPSO algorithm is proposed. The global search ability of particle swarm optimization algorithm and local search ability of gradient algorithm are effectively combined, which overcomes the shortcoming that the conjugate gradient method tends to converge to the local solution and relies heavily on the initial approximation of the iterative process. The hybrid algorithm also avoids the problem that the particle swarm optimization algorithm requires a large number of iterative steps and a lot of time. The experimental results show that the proposed algorithm is feasible and effective in solving the problem of two-dimensional steady-state thermal boundary shape.
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)
Indian Academy of Sciences (India)
polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.
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Wen-Xiang Wu
2014-01-01
Full Text Available The cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. We develop a path-based gradient projection algorithm for solving the cost-based system optimum model, based on Goldstein-Levitin-Polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. The Sioux Falls network tested is used to verify the effectiveness of the algorithm.
Indian Academy of Sciences (India)
to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...
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.
A parallel algorithm for solving the integral form of the discrete ordinates equations
International Nuclear Information System (INIS)
Zerr, R. J.; Azmy, Y. Y.
2009-01-01
The integral form of the discrete ordinates equations involves a system of equations that has a large, dense coefficient matrix. The serial construction methodology is presented and properties that affect the execution times to construct and solve the system are evaluated. Two approaches for massively parallel implementation of the solution algorithm are proposed and the current results of one of these are presented. The system of equations May be solved using two parallel solvers-block Jacobi and conjugate gradient. Results indicate that both methods can reduce overall wall-clock time for execution. The conjugate gradient solver exhibits better performance to compete with the traditional source iteration technique in terms of execution time and scalability. The parallel conjugate gradient method is synchronous, hence it does not increase the number of iterations for convergence compared to serial execution, and the efficiency of the algorithm demonstrates an apparent asymptotic decline. (authors)
Phase gradient algorithm based on co-axis two-step phase-shifting interferometry and its application
Wang, Yawei; Zhu, Qiong; Xu, Yuanyuan; Xin, Zhiduo; Liu, Jingye
2017-12-01
A phase gradient method based on co-axis two-step phase-shifting interferometry, is used to reveal the detailed information of a specimen. In this method, the phase gradient distribution can only be obtained by calculating both the first-order derivative and the radial Hilbert transformation of the intensity difference between two phase-shifted interferograms. The feasibility and accuracy of this method were fully verified by the simulation results for a polystyrene sphere and a red blood cell. The empirical results demonstrated that phase gradient is sensitive to changes in the refractive index and morphology. Because phase retrieval and tedious phase unwrapping are not required, the calculation speed is faster. In addition, co-axis interferometry has high spatial resolution.
He, Xiaojun; Ma, Haotong; Luo, Chuanxin
2016-10-01
The optical multi-aperture imaging system is an effective way to magnify the aperture and increase the resolution of telescope optical system, the difficulty of which lies in detecting and correcting of co-phase error. This paper presents a method based on stochastic parallel gradient decent algorithm (SPGD) to correct the co-phase error. Compared with the current method, SPGD method can avoid detecting the co-phase error. This paper analyzed the influence of piston error and tilt error on image quality based on double-aperture imaging system, introduced the basic principle of SPGD algorithm, and discuss the influence of SPGD algorithm's key parameters (the gain coefficient and the disturbance amplitude) on error control performance. The results show that SPGD can efficiently correct the co-phase error. The convergence speed of the SPGD algorithm is improved with the increase of gain coefficient and disturbance amplitude, but the stability of the algorithm reduced. The adaptive gain coefficient can solve this problem appropriately. This paper's results can provide the theoretical reference for the co-phase error correction of the multi-aperture imaging system.
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
Indian Academy of Sciences (India)
ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...
Directory of Open Access Journals (Sweden)
Chen Ming
2017-01-01
Full Text Available To solve the Flexible Job-shop Scheduling Problem (FJSP with different varieties and small batches, a modified meta-heuristic algorithm based on Genetic Algorithm (GA is proposed in which gene encoding is divided into process encoding and machine encoding, and according to the encoding mode, the machine gene fragment is connected with the process gene fragment and can be changed with the alteration of process genes. In order to get the global optimal solutions, the crossover and mutation operation of the process gene fragment and machine gene fragment are carried out respectively. In the initialization operation, the machines with shorter manufacturing time are more likely to be chosen to accelerate the convergence speed and then the tournament selection strategy is applied due to the minimum optimization objective. Meanwhile, a judgment condition of the crossover point quantity is introduced to speed up the population evolution and as an important interaction bridge between the current machine and alternative machines in the incidence matrix, a novel mutation operation of machine genes is proposed to achieve the replacement of manufacturing machines. The benchmark test shows the correctness of proposed algorithm and the case simulation proves the proposed algorithm has better performance compared with existing algorithms.
Directory of Open Access Journals (Sweden)
Donovan H Parks
Full Text Available GenGIS is free and open source software designed to integrate biodiversity data with a digital map and information about geography and habitat. While originally developed with microbial community analyses and phylogeography in mind, GenGIS has been applied to a wide range of datasets. A key feature of GenGIS is the ability to test geographic axes that can correspond to routes of migration or gradients that influence community similarity. Here we introduce GenGIS version 2, which extends the linear gradient tests introduced in the first version to allow comprehensive testing of all possible linear geographic axes. GenGIS v2 also includes a new plugin framework that supports the development and use of graphically driven analysis packages: initial plugins include implementations of linear regression and the Mantel test, calculations of alpha-diversity (e.g., Shannon Index for all samples, and geographic visualizations of dissimilarity matrices. We have also implemented a recently published method for biomonitoring reference condition analysis (RCA, which compares observed species richness and diversity to predicted values to determine whether a given site has been impacted. The newest version of GenGIS supports vector data in addition to raster files. We demonstrate the new features of GenGIS by performing a full gradient analysis of an Australian kangaroo apple data set, by using plugins and embedded statistical commands to analyze human microbiome sample data, and by applying RCA to a set of samples from Atlantic Canada. GenGIS release versions, tutorials and documentation are freely available at http://kiwi.cs.dal.ca/GenGIS, and source code is available at https://github.com/beiko-lab/gengis.
Indian Academy of Sciences (India)
algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).
Indian Academy of Sciences (India)
algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...
Computation of dominant eigenvalues and eigenvectors: A comparative study of algorithms
International Nuclear Information System (INIS)
Nightingale, M.P.; Viswanath, V.S.; Mueller, G.
1993-01-01
We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices---the modified Lanczoes method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods
A comparison of three optimization algorithms for intensity modulated radiation therapy
International Nuclear Information System (INIS)
Pflugfelder, D.; Wilkens, J.J.; Nill, S.; Oelfke, U.
2008-01-01
In intensity modulated treatment techniques, the modulation of each treatment field is obtained using an optimization algorithm. Multiple optimization algorithms have been proposed in the literature, e.g. steepest descent, conjugate gradient, quasi-Newton methods to name a few. The standard optimization algorithm in our in-house inverse planning tool KonRad is a quasi-Newton algorithm. Although this algorithm yields good results, it also has some drawbacks. Thus we implemented an improved optimization algorithm based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) routine. In this paper the improved optimization algorithm is described. To compare the two algorithms, several treatment plans are optimized using both algorithms. This included photon (IMRT) as well as proton (IMPT) intensity modulated therapy treatment plans. To present the results in a larger context the widely used conjugate gradient algorithm was also included into this comparison. On average, the improved optimization algorithm was six times faster to reach the same objective function value. However, it resulted not only in an acceleration of the optimization. Due to the faster convergence, the improved optimization algorithm usually terminates the optimization process at a lower objective function value. The average of the observed improvement in the objective function value was 37%. This improvement is clearly visible in the corresponding dose-volume-histograms. The benefit of the improved optimization algorithm is particularly pronounced in proton therapy plans. The conjugate gradient algorithm ranked in between the other two algorithms with an average speedup factor of two and an average improvement of the objective function value of 30%. (orig.)
Indian Academy of Sciences (India)
will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...
Interpolation algorithm for asynchronous ADC-data
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S. Bramburger
2017-09-01
Full Text Available This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.
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 ...
International Nuclear Information System (INIS)
Molchanov, I.N.; Khimich, A.N.
1984-01-01
This article shows how a reflection method can be used to find the eigenvalues of a matrix by transforming the matrix to tridiagonal form. The method of conjugate gradients is used to find the smallest eigenvalue and the corresponding eigenvector of symmetric positive-definite band matrices. Topics considered include the computational scheme of the reflection method, the organization of parallel calculations by the reflection method, the computational scheme of the conjugate gradient method, the organization of parallel calculations by the conjugate gradient method, and the effectiveness of parallel algorithms. It is concluded that it is possible to increase the overall effectiveness of the multiprocessor electronic computers by either letting the newly available processors of a new problem operate in the multiprocessor mode, or by improving the coefficient of uniform partition of the original information
Okuda, Kyohei; Sakimoto, Shota; Fujii, Susumu; Ida, Tomonobu; Moriyama, Shigeru
The frame-of-reference using computed-tomography (CT) coordinate system on single-photon emission computed tomography (SPECT) reconstruction is one of the advanced characteristics of the xSPECT reconstruction system. The aim of this study was to reveal the influence of the high-resolution frame-of-reference on the xSPECT reconstruction. 99m Tc line-source phantom and National Electrical Manufacturers Association (NEMA) image quality phantom were scanned using the SPECT/CT system. xSPECT reconstructions were performed with the reference CT images in different sizes of the display field-of-view (DFOV) and pixel. The pixel sizes of the reconstructed xSPECT images were close to 2.4 mm, which is acquired as originally projection data, even if the reference CT resolution was varied. The full width at half maximum (FWHM) of the line-source, absolute recovery coefficient, and background variability of image quality phantom were independent on the sizes of DFOV in the reference CT images. The results of this study revealed that the image quality of the reconstructed xSPECT images is not influenced by the resolution of frame-of-reference on SPECT reconstruction.
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
ILUCG algorithm which minimizes in the Euclidean norm
International Nuclear Information System (INIS)
Petravic, M.; Kuo-Petravic, G.
1978-07-01
An algroithm is presented which solves sparse systems of linear equations of the form Ax = Y, where A is non-symmetric, by the Incomplete LU Decomposition-Conjugate Gradient (ILUCG) method. The algorithm minimizes the error in the Euclidean norm vertical bar x/sub i/ - x vertical bar 2 , where x/sub i/ is the solution vector after the i/sup th/ iteration and x the exact solution vector. The results of a test on one real problem indicate that the algorithm is likely to be competitive with the best existing algorithms of its type
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.
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.
Itoh, Shoji; Sugihara, Masaaki
2016-01-01
We present a theorem that defines the direction of a preconditioned system for the bi-conjugate gradient (BiCG) method, and we extend it to preconditioned bi-Lanczos-type algorithms. We show that the direction of a preconditioned system is switched by construction and by the settings of the initial shadow residual vector. We analyze and compare the polynomial structures of four preconditioned BiCG algorithms.
A quasi-Newton algorithm for large-scale nonlinear equations
Directory of Open Access Journals (Sweden)
Linghua Huang
2017-02-01
Full Text Available Abstract In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i a conjugate gradient (CG algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm’s initial point does not have any restrictions; (ii a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length α k $\\alpha_{k}$ . The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the 1 + q $1+q$ -order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.
Directory of Open Access Journals (Sweden)
OMER MAHMOUD
2007-08-01
Full Text Available One of the essential factors that affect the performance of Artificial Neural Networks is the learning algorithm. The performance of Multilayer Feed Forward Artificial Neural Network performance in image compression using different learning algorithms is examined in this paper. Based on Gradient Descent, Conjugate Gradient, Quasi-Newton techniques three different error back propagation algorithms have been developed for use in training two types of neural networks, a single hidden layer network and three hidden layers network. The essence of this study is to investigate the most efficient and effective training methods for use in image compression and its subsequent applications. The obtained results show that the Quasi-Newton based algorithm has better performance as compared to the other two algorithms.
An efficient parallel algorithm for matrix-vector multiplication
Energy Technology Data Exchange (ETDEWEB)
Hendrickson, B.; Leland, R.; Plimpton, S.
1993-03-01
The multiplication of a vector by a matrix is the kernel computation of many algorithms in scientific computation. A fast parallel algorithm for this calculation is therefore necessary if one is to make full use of the new generation of parallel supercomputers. This paper presents a high performance, parallel matrix-vector multiplication algorithm that is particularly well suited to hypercube multiprocessors. For an n x n matrix on p processors, the communication cost of this algorithm is O(n/[radical]p + log(p)), independent of the matrix sparsity pattern. The performance of the algorithm is demonstrated by employing it as the kernel in the well-known NAS conjugate gradient benchmark, where a run time of 6.09 seconds was observed. This is the best published performance on this benchmark achieved to date using a massively parallel supercomputer.
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.
Algorithms for parallel and vector computations
Ortega, James M.
1995-01-01
This is a final report on work performed under NASA grant NAG-1-1112-FOP during the period March, 1990 through February 1995. Four major topics are covered: (1) solution of nonlinear poisson-type equations; (2) parallel reduced system conjugate gradient method; (3) orderings for conjugate gradient preconditioners, and (4) SOR as a preconditioner.
Directory of Open Access Journals (Sweden)
Andreea Koreanschi
2017-02-01
Full Text Available In this paper, an ‘in-house’ genetic algorithm is described and applied to an optimization problem for improving the aerodynamic performances of an aircraft wing tip through upper surface morphing. The algorithm’s performances were studied from the convergence point of view, in accordance with design conditions. The algorithm was compared to two other optimization methods, namely the artificial bee colony and a gradient method, for two optimization objectives, and the results of the optimizations with each of the three methods were plotted on response surfaces obtained with the Monte Carlo method, to show that they were situated in the global optimum region. The optimization results for 16 wind tunnel test cases and 2 objective functions were presented. The 16 cases used for the optimizations were included in the experimental test plan for the morphing wing-tip demonstrator, and the results obtained using the displacements given by the optimizations were evaluated.
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
Prodhan, Suryoday; Ramasesha, S.
2018-05-01
The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.
Unterkircher, A
2005-01-01
We propose methods for parallel assembling and iterative equation solving based on graph algorithms. The assembling technique is independent of dimension, element type and model shape. As a parallel solving technique we construct a multiplicative symmetric Schwarz preconditioner for the conjugate gradient method. Both methods have been incorporated into a non-linear FE code to simulate 3D metal extrusion processes. We illustrate the efficiency of these methods on shared memory computers by realistic examples.
Algorithms for the optimization of RBE-weighted dose in particle therapy.
Horcicka, M; Meyer, C; Buschbacher, A; Durante, M; Krämer, M
2013-01-21
We report on various algorithms used for the nonlinear optimization of RBE-weighted dose in particle therapy. Concerning the dose calculation carbon ions are considered and biological effects are calculated by the Local Effect Model. Taking biological effects fully into account requires iterative methods to solve the optimization problem. We implemented several additional algorithms into GSI's treatment planning system TRiP98, like the BFGS-algorithm and the method of conjugated gradients, in order to investigate their computational performance. We modified textbook iteration procedures to improve the convergence speed. The performance of the algorithms is presented by convergence in terms of iterations and computation time. We found that the Fletcher-Reeves variant of the method of conjugated gradients is the algorithm with the best computational performance. With this algorithm we could speed up computation times by a factor of 4 compared to the method of steepest descent, which was used before. With our new methods it is possible to optimize complex treatment plans in a few minutes leading to good dose distributions. At the end we discuss future goals concerning dose optimization issues in particle therapy which might benefit from fast optimization solvers.
Maximum entropy algorithm and its implementation for the neutral beam profile measurement
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Wook; Cho, Gyu Seong [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Cho, Yong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1997-12-31
A tomography algorithm to maximize the entropy of image using Lagrangian multiplier technique and conjugate gradient method has been designed for the measurement of 2D spatial distribution of intense neutral beams of KSTAR NBI (Korea Superconducting Tokamak Advanced Research Neutral Beam Injector), which is now being designed. A possible detection system was assumed and a numerical simulation has been implemented to test the reconstruction quality of given beam profiles. This algorithm has the good applicability for sparse projection data and thus, can be used for the neutral beam tomography. 8 refs., 3 figs. (Author)
Maximum entropy algorithm and its implementation for the neutral beam profile measurement
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Wook; Cho, Gyu Seong [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of); Cho, Yong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
A tomography algorithm to maximize the entropy of image using Lagrangian multiplier technique and conjugate gradient method has been designed for the measurement of 2D spatial distribution of intense neutral beams of KSTAR NBI (Korea Superconducting Tokamak Advanced Research Neutral Beam Injector), which is now being designed. A possible detection system was assumed and a numerical simulation has been implemented to test the reconstruction quality of given beam profiles. This algorithm has the good applicability for sparse projection data and thus, can be used for the neutral beam tomography. 8 refs., 3 figs. (Author)
Directory of Open Access Journals (Sweden)
A. J. Hind
2011-01-01
Full Text Available Dimethyl sulphide (DMS is an important precursor of cloud condensation nuclei (CCN, particularly in the remote marine atmosphere. The SE Pacific is consistently covered with a persistent stratocumulus layer that increases the albedo over this large area. It is not certain whether the source of CCN to these clouds is natural and oceanic or anthropogenic and terrestrial. This unknown currently limits our ability to reliably model either the cloud behaviour or the oceanic heat budget of the region. In order to better constrain the marine source of CCN, it is necessary to have an improved understanding of the sea-air flux of DMS. Of the factors that govern the magnitude of this flux, the greatest unknown is the surface seawater DMS concentration. In the study area, there is a paucity of such data, although previous measurements suggest that the concentration can be substantially variable. In order to overcome such data scarcity, a number of climatologies and algorithms have been devised in the last decade to predict seawater DMS. Here we test some of these in the SE Pacific by comparing predictions with measurements of surface seawater made during the Vamos Ocean-Cloud-Atmosphere-Land Study Regional Experiment (VOCALS-REx in October and November of 2008. We conclude that none of the existing algorithms reproduce local variability in seawater DMS in this region very well. From these findings, we recommend the best algorithm choice for the SE Pacific and suggest lines of investigation for future work.
Projective block Lanczos algorithm for dense, Hermitian eigensystems
International Nuclear Information System (INIS)
Webster, F.; Lo, G.C.
1996-01-01
Projection operators are used to effect open-quotes deflation by restrictionclose quotes and it is argued that this is an optimal Lanczos algorithm for memory minimization. Algorithmic optimization is constrained to dense, Hermitian eigensystems where a significant number of the extreme eigenvectors must be obtained reliably and completely. The defining constraints are operator algebra without a matrix representation and semi-orthogonalization without storage of Krylov vectors. other semi-orthogonalization strategies for Lanczos algorithms and conjugate gradient techniques are evaluated within these constraints. Large scale, sparse, complex numerical experiments are performed on clusters of magnetic dipoles, a quantum many-body system that is not block-diagonalizable. Plane-wave, density functional theory of beryllium clusters provides examples of dense complex eigensystems. Use of preconditioners and spectral transformations is evaluated in a preprocessor prior to a high accuracy self-consistent field calculation. 25 refs., 3 figs., 5 tabs
Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images
International Nuclear Information System (INIS)
Mumcuglu, E.U.; Leahy, R.; Zhou, Z.; Cherry, S.R.
1994-01-01
The authors describe conjugate gradient algorithms for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation, where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure nonnegativity of the solution, a penalty function is used to convert the problem to one of unconstrained optimization. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15--25 iterations. Reconstructions are presented of an 18 FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors
Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis
Chiou, Jin-Chern
1990-01-01
Computational procedures for kinematic and dynamic analysis of three-dimensional multibody dynamic (MBD) systems are developed from the differential-algebraic equations (DAE's) viewpoint. Constraint violations during the time integration process are minimized and penalty constraint stabilization techniques and partitioning schemes are developed. The governing equations of motion, a two-stage staggered explicit-implicit numerical algorithm, are treated which takes advantage of a partitioned solution procedure. A robust and parallelizable integration algorithm is developed. This algorithm uses a two-stage staggered central difference algorithm to integrate the translational coordinates and the angular velocities. The angular orientations of bodies in MBD systems are then obtained by using an implicit algorithm via the kinematic relationship between Euler parameters and angular velocities. It is shown that the combination of the present solution procedures yields a computationally more accurate solution. To speed up the computational procedures, parallel implementation of the present constraint treatment techniques, the two-stage staggered explicit-implicit numerical algorithm was efficiently carried out. The DAE's and the constraint treatment techniques were transformed into arrowhead matrices to which Schur complement form was derived. By fully exploiting the sparse matrix structural analysis techniques, a parallel preconditioned conjugate gradient numerical algorithm is used to solve the systems equations written in Schur complement form. A software testbed was designed and implemented in both sequential and parallel computers. This testbed was used to demonstrate the robustness and efficiency of the constraint treatment techniques, the accuracy of the two-stage staggered explicit-implicit numerical algorithm, and the speed up of the Schur-complement-based parallel preconditioned conjugate gradient algorithm on a parallel computer.
Zeng, Fa; Tan, Qiaofeng; Yan, Yingbai; Jin, Guofan
2007-10-01
Study of phase retrieval technology is quite meaningful, for its wide applications related to many domains, such as adaptive optics, detection of laser quality, precise measurement of optical surface, and so on. Here a hybrid iterative phase retrieval algorithm is proposed, based on fusion of the intensity information in three defocused planes. First the conjugate gradient algorithm is adapted to achieve a coarse solution of phase distribution in the input plane; then the iterative angular spectrum method is applied in succession for better retrieval result. This algorithm is still applicable even when the exact shape and size of the aperture in the input plane are unknown. Moreover, this algorithm always exhibits good convergence, i.e., the retrieved results are insensitive to the chosen positions of the three defocused planes and the initial guess of complex amplitude in the input plane, which has been proved by both simulations and further experiments.
Neural Network Blind Equalization Algorithm Applied in Medical CT Image Restoration
Directory of Open Access Journals (Sweden)
Yunshan Sun
2013-01-01
Full Text Available A new algorithm for iterative blind image restoration is presented in this paper. The method extends blind equalization found in the signal case to the image. A neural network blind equalization algorithm is derived and used in conjunction with Zigzag coding to restore the original image. As a result, the effect of PSF can be removed by using the proposed algorithm, which contributes to eliminate intersymbol interference (ISI. In order to obtain the estimation of the original image, what is proposed in this method is to optimize constant modulus blind equalization cost function applied to grayscale CT image by using conjugate gradient method. Analysis of convergence performance of the algorithm verifies the feasibility of this method theoretically; meanwhile, simulation results and performance evaluations of recent image quality metrics are provided to assess the effectiveness of the proposed method.
Quantitative tomography simulations and reconstruction algorithms
International Nuclear Information System (INIS)
Martz, H.E.; Aufderheide, M.B.; Goodman, D.; Schach von Wittenau, A.; Logan, C.; Hall, J.; Jackson, J.; Slone, D.
2000-01-01
X-ray, neutron and proton transmission radiography and computed tomography (CT) are important diagnostic tools that are at the heart of LLNL's effort to meet the goals of the DOE's Advanced Radiography Campaign. This campaign seeks to improve radiographic simulation and analysis so that radiography can be a useful quantitative diagnostic tool for stockpile stewardship. Current radiographic accuracy does not allow satisfactory separation of experimental effects from the true features of an object's tomographically reconstructed image. This can lead to difficult and sometimes incorrect interpretation of the results. By improving our ability to simulate the whole radiographic and CT system, it will be possible to examine the contribution of system components to various experimental effects, with the goal of removing or reducing them. In this project, we are merging this simulation capability with a maximum-likelihood (constrained-conjugate-gradient-CCG) reconstruction technique yielding a physics-based, forward-model image-reconstruction code. In addition, we seek to improve the accuracy of computed tomography from transmission radiographs by studying what physics is needed in the forward model. During FY 2000, an improved version of the LLNL ray-tracing code called HADES has been coupled with a recently developed LLNL CT algorithm known as CCG. The problem of image reconstruction is expressed as a large matrix equation relating a model for the object being reconstructed to its projections (radiographs). Using a constrained-conjugate-gradient search algorithm, a maximum likelihood solution is sought. This search continues until the difference between the input measured radiographs or projections and the simulated or calculated projections is satisfactorily small
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.
Three-dimensional Gravity Inversion with a New Gradient Scheme on Unstructured Grids
Sun, S.; Yin, C.; Gao, X.; Liu, Y.; Zhang, B.
2017-12-01
Stabilized gradient-based methods have been proved to be efficient for inverse problems. Based on these methods, setting gradient close to zero can effectively minimize the objective function. Thus the gradient of objective function determines the inversion results. By analyzing the cause of poor resolution on depth in gradient-based gravity inversion methods, we find that imposing depth weighting functional in conventional gradient can improve the depth resolution to some extent. However, the improvement is affected by the regularization parameter and the effect of the regularization term becomes smaller with increasing depth (shown as Figure 1 (a)). In this paper, we propose a new gradient scheme for gravity inversion by introducing a weighted model vector. The new gradient can improve the depth resolution more efficiently, which is independent of the regularization parameter, and the effect of regularization term will not be weakened when depth increases. Besides, fuzzy c-means clustering method and smooth operator are both used as regularization terms to yield an internal consecutive inverse model with sharp boundaries (Sun and Li, 2015). We have tested our new gradient scheme with unstructured grids on synthetic data to illustrate the effectiveness of the algorithm. Gravity forward modeling with unstructured grids is based on the algorithm proposed by Okbe (1979). We use a linear conjugate gradient inversion scheme to solve the inversion problem. The numerical experiments show a great improvement in depth resolution compared with regular gradient scheme, and the inverse model is compact at all depths (shown as Figure 1 (b)). AcknowledgeThis research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900). ReferencesSun J, Li Y. 2015. Multidomain petrophysically constrained inversion and
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...
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.
Algorithms and Their Explanations
Benini, M.; Gobbo, F.; Beckmann, A.; Csuhaj-Varjú, E.; Meer, K.
2014-01-01
By analysing the explanation of the classical heapsort algorithm via the method of levels of abstraction mainly due to Floridi, we give a concrete and precise example of how to deal with algorithmic knowledge. To do so, we introduce a concept already implicit in the method, the ‘gradient of
Energy Technology Data Exchange (ETDEWEB)
Llacer, Jorge [EC Engineering Consultants, LLC, Los Gatos, CA (United States)]. E-mail: jllacer@home.com; Solberg, Timothy D. [Department of Radiation Oncology, University of California, Los Angeles, CA (United States)]. E-mail: Solberg@radonc.ucla.edu; Promberger, Claus [BrainLAB AG, Heimstetten (Germany)]. E-mail: promberg@brainlab.com
2001-10-01
This paper presents a description of tests carried out to compare the behaviour of five algorithms in inverse radiation therapy planning: (1) The Dynamically Penalized Likelihood (DPL), an algorithm based on statistical estimation theory; (2) an accelerated version of the same algorithm; (3) a new fast adaptive simulated annealing (ASA) algorithm; (4) a conjugate gradient method; and (5) a Newton gradient method. A three-dimensional mathematical phantom and two clinical cases have been studied in detail. The phantom consisted of a U-shaped tumour with a partially enclosed 'spinal cord'. The clinical examples were a cavernous sinus meningioma and a prostate case. The algorithms have been tested in carefully selected and controlled conditions so as to ensure fairness in the assessment of results. It has been found that all five methods can yield relatively similar optimizations, except when a very demanding optimization is carried out. For the easier cases, the differences are principally in robustness, ease of use and optimization speed. In the more demanding case, there are significant differences in the resulting dose distributions. The accelerated DPL emerges as possibly the algorithm of choice for clinical practice. An appendix describes the differences in behaviour between the new ASA method and the one based on a patent by the Nomos Corporation. (author)
Sochi, Taha
2016-09-01
Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.
Introduction: a brief overview of iterative algorithms in X-ray computed tomography.
Soleimani, M; Pengpen, T
2015-06-13
This paper presents a brief overview of some basic iterative algorithms, and more sophisticated methods are presented in the research papers in this issue. A range of algebraic iterative algorithms are covered here including ART, SART and OS-SART. A major limitation of the traditional iterative methods is their computational time. The Krylov subspace based methods such as the conjugate gradients (CG) algorithm and its variants can be used to solve linear systems of equations arising from large-scale CT with possible implementation using modern high-performance computing tools. The overall aim of this theme issue is to stimulate international efforts to develop the next generation of X-ray computed tomography (CT) image reconstruction software. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Shao, Jiaxin; Rapacchi, Stanislas; Nguyen, Kim-Lien; Hu, Peng
2016-02-01
To develop an accurate and precise myocardial T1 mapping technique using an inversion recovery spoiled gradient echo readout at 3.0 Tesla (T). The modified Look-Locker inversion-recovery (MOLLI) sequence was modified to use fast low angle shot (FLASH) readout, incorporating a BLESSPC (Bloch Equation Simulation with Slice Profile Correction) T1 estimation algorithm, for accurate myocardial T1 mapping. The FLASH-MOLLI with BLESSPC fitting was compared with different approaches and sequences with regards to T1 estimation accuracy, precision and image artifact based on simulation, phantom studies, and in vivo studies of 10 healthy volunteers and three patients at 3.0 Tesla. The FLASH-MOLLI with BLESSPC fitting yields accurate T1 estimation (average error = -5.4 ± 15.1 ms, percentage error = -0.5% ± 1.2%) for T1 from 236-1852 ms and heart rate from 40-100 bpm in phantom studies. The FLASH-MOLLI sequence prevented off-resonance artifacts in all 10 healthy volunteers at 3.0T. In vivo, there was no significant difference between FLASH-MOLLI-derived myocardial T1 values and "ShMOLLI+IE" derived values (1458.9 ± 20.9 ms versus 1464.1 ± 6.8 ms, P = 0.50); However, the average precision by FLASH-MOLLI was significantly better than that generated by "ShMOLLI+IE" (1.84 ± 0.36% variance versus 3.57 ± 0.94%, P < 0.001). The FLASH-MOLLI with BLESSPC fitting yields accurate and precise T1 estimation, and eliminates banding artifacts associated with bSSFP at 3.0T. © 2015 Wiley Periodicals, Inc.
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
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
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.
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.
Acceleration of the direct reconstruction of linear parametric images using nested algorithms
International Nuclear Information System (INIS)
Wang Guobao; Qi Jinyi
2010-01-01
Parametric imaging using dynamic positron emission tomography (PET) provides important information for biological research and clinical diagnosis. Indirect and direct methods have been developed for reconstructing linear parametric images from dynamic PET data. Indirect methods are relatively simple and easy to implement because the image reconstruction and kinetic modeling are performed in two separate steps. Direct methods estimate parametric images directly from raw PET data and are statistically more efficient. However, the convergence rate of direct algorithms can be slow due to the coupling between the reconstruction and kinetic modeling. Here we present two fast gradient-type algorithms for direct reconstruction of linear parametric images. The new algorithms decouple the reconstruction and linear parametric modeling at each iteration by employing the principle of optimization transfer. Convergence speed is accelerated by running more sub-iterations of linear parametric estimation because the computation cost of the linear parametric modeling is much less than that of the image reconstruction. Computer simulation studies demonstrated that the new algorithms converge much faster than the traditional expectation maximization (EM) and the preconditioned conjugate gradient algorithms for dynamic PET.
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.
Conjugate schema and basis representation of crossover and mutation operators.
Kazadi, S T
1998-01-01
In genetic search algorithms and optimization routines, the representation of the mutation and crossover operators are typically defaulted to the canonical basis. We show that this can be influential in the usefulness of the search algorithm. We then pose the question of how to find a basis for which the search algorithm is most useful. The conjugate schema is introduced as a general mathematical construct and is shown to separate a function into smaller dimensional functions whose sum is the original function. It is shown that conjugate schema, when used on a test suite of functions, improves the performance of the search algorithm on 10 out of 12 of these functions. Finally, a rigorous but abbreviated mathematical derivation is given in the appendices.
Genetic Algorithm for Opto-thermal Skin Hydration Depth Profiling Measurements
Cui, Y.; Xiao, Perry; Imhof, R. E.
2013-09-01
Stratum corneum is the outermost skin layer, and the water content in stratum corneum plays a key role in skin cosmetic properties as well as skin barrier functions. However, to measure the water content, especially the water concentration depth profile, within stratum corneum is very difficult. Opto-thermal emission radiometry, or OTTER, is a promising technique that can be used for such measurements. In this paper, a study on stratum corneum hydration depth profiling by using a genetic algorithm (GA) is presented. The pros and cons of a GA compared against other inverse algorithms such as neural networks, maximum entropy, conjugate gradient, and singular value decomposition will be discussed first. Then, it will be shown how to use existing knowledge to optimize a GA for analyzing the opto-thermal signals. Finally, these latest GA results on hydration depth profiling of stratum corneum under different conditions, as well as on the penetration profiles of externally applied solvents, will be shown.
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.
An algorithm for online optimization of accelerators
Energy Technology Data Exchange (ETDEWEB)
Huang, Xiaobiao [SLAC National Accelerator Lab., Menlo Park, CA (United States); Corbett, Jeff [SLAC National Accelerator Lab., Menlo Park, CA (United States); Safranek, James [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wu, Juhao [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2013-10-01
We developed a general algorithm for online optimization of accelerator performance, i.e., online tuning, using the performance measure as the objective function. This method, named robust conjugate direction search (RCDS), combines the conjugate direction set approach of Powell's method with a robust line optimizer which considers the random noise in bracketing the minimum and uses parabolic fit of data points that uniformly sample the bracketed zone. Moreover, it is much more robust against noise than traditional algorithms and is therefore suitable for online application. Simulation and experimental studies have been carried out to demonstrate the strength of the new algorithm.
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
Zhang, Xiao-bo; Tan, Jun; Song, Peng; Li, Jin-shan; Xia, Dong-ming; Liu, Zhao-lun
2017-01-01
The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge storage consumption in the gradient preconditioning algorithms based on Hessian matrices in time-domain full waveform inversion (FWI), but the accuracy
Algorithms for computational fluid dynamics n parallel processors
International Nuclear Information System (INIS)
Van de Velde, E.F.
1986-01-01
A study of parallel algorithms for the numerical solution of partial differential equations arising in computational fluid dynamics is presented. The actual implementation on parallel processors of shared and nonshared memory design is discussed. The performance of these algorithms is analyzed in terms of machine efficiency, communication time, bottlenecks and software development costs. For elliptic equations, a parallel preconditioned conjugate gradient method is described, which has been used to solve pressure equations discretized with high order finite elements on irregular grids. A parallel full multigrid method and a parallel fast Poisson solver are also presented. Hyperbolic conservation laws were discretized with parallel versions of finite difference methods like the Lax-Wendroff scheme and with the Random Choice method. Techniques are developed for comparing the behavior of an algorithm on different architectures as a function of problem size and local computational effort. Effective use of these advanced architecture machines requires the use of machine dependent programming. It is shown that the portability problems can be minimized by introducing high level operations on vectors and matrices structured into program libraries
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...
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.
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
Adaptive Gradient Multiobjective Particle Swarm Optimization.
Han, Honggui; Lu, Wei; Zhang, Lu; Qiao, Junfei
2017-10-09
An adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm, based on a multiobjective gradient (stocktickerMOG) method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance in this paper. In this AGMOPSO algorithm, the stocktickerMOG method is devised to update the archive to improve the convergence speed and the local exploitation in the evolutionary process. Meanwhile, the self-adaptive flight parameters mechanism, according to the diversity information of the particles, is then established to balance the convergence and diversity of AGMOPSO. Attributed to the stocktickerMOG method and the self-adaptive flight parameters mechanism, this AGMOPSO algorithm not only has faster convergence speed and higher accuracy, but also its solutions have better diversity. Additionally, the convergence is discussed to confirm the prerequisite of any successful application of AGMOPSO. Finally, with regard to the computation performance, the proposed AGMOPSO algorithm is compared with some other multiobjective particle swarm optimization algorithms and two state-of-the-art multiobjective algorithms. The results demonstrate that the proposed AGMOPSO algorithm can find better spread of solutions and have faster convergence to the true Pareto-optimal front.
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
Directory of Open Access Journals (Sweden)
Jide Julius Popoola
2015-11-01
Full Text Available This paper proposes two new classifiers that automatically recognise twelve combined analog and digital modulated signals without any a priori knowledge of the modulation schemes and the modulation parameters. The classifiers are developed using pattern recognition approach. Feature keys extracted from the instantaneous amplitude, instantaneous phase and the spectrum symmetry of the simulated signals are used as inputs to the artificial neural network employed in developing the classifiers. The two developed classifiers are trained using scaled conjugate gradient (SCG and conjugate gradient (CONJGRAD training algorithms. Sample results of the two classifiers show good success recognition performance with an average overall recognition rate above 99.50% at signal-to-noise ratio (SNR value from 0 dB and above with the two training algorithms employed and an average overall recognition rate slightly above 99.00% and 96.40% respectively at - 5 dB SNR value for SCG and CONJGRAD training algorithms. The comparative performance evaluation of the two developed classifiers using the two training algorithms shows that the two training algorithms have different effects on both the response rate and efficiency of the two developed artificial neural networks classifiers. In addition, the result of the performance evaluation carried out on the overall success recognition rates between the two developed classifiers in this study using pattern recognition approach with the two training algorithms and one reported classifier in surveyed literature using decision-theoretic approach shows that the classifiers developed in this study perform favourably with regard to accuracy and performance probability as compared to classifier presented in previous study.
International Nuclear Information System (INIS)
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-01-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated
Duan, Jizhong; Liu, Yu; Jing, Peiguang
2018-02-01
Self-consistent parallel imaging (SPIRiT) is an auto-calibrating model for the reconstruction of parallel magnetic resonance imaging, which can be formulated as a regularized SPIRiT problem. The Projection Over Convex Sets (POCS) method was used to solve the formulated regularized SPIRiT problem. However, the quality of the reconstructed image still needs to be improved. Though methods such as NonLinear Conjugate Gradients (NLCG) can achieve higher spatial resolution, these methods always demand very complex computation and converge slowly. In this paper, we propose a new algorithm to solve the formulated Cartesian SPIRiT problem with the JTV and JL1 regularization terms. The proposed algorithm uses the operator splitting (OS) technique to decompose the problem into a gradient problem and a denoising problem with two regularization terms, which is solved by our proposed split Bregman based denoising algorithm, and adopts the Barzilai and Borwein method to update step size. Simulation experiments on two in vivo data sets demonstrate that the proposed algorithm is 1.3 times faster than ADMM for datasets with 8 channels. Especially, our proposal is 2 times faster than ADMM for the dataset with 32 channels. Copyright © 2017 Elsevier Inc. All rights reserved.
DEFF Research Database (Denmark)
Mahnke, Martina; Uprichard, Emma
2014-01-01
Imagine sailing across the ocean. The sun is shining, vastness all around you. And suddenly [BOOM] you’ve hit an invisible wall. Welcome to the Truman Show! Ever since Eli Pariser published his thoughts on a potential filter bubble, this movie scenario seems to have become reality, just with slight...... changes: it’s not the ocean, it’s the internet we’re talking about, and it’s not a TV show producer, but algorithms that constitute a sort of invisible wall. Building on this assumption, most research is trying to ‘tame the algorithmic tiger’. While this is a valuable and often inspiring approach, we...
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.
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
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
Final report for “Extreme-scale Algorithms and Solver Resilience”
Energy Technology Data Exchange (ETDEWEB)
Gropp, William Douglas [Univ. of Illinois, Urbana-Champaign, IL (United States)
2017-06-30
This is a joint project with principal investigators at Oak Ridge National Laboratory, Sandia National Laboratories, the University of California at Berkeley, and the University of Tennessee. Our part of the project involves developing performance models for highly scalable algorithms and the development of latency tolerant iterative methods. During this project, we extended our performance models for the Multigrid method for solving large systems of linear equations and conducted experiments with highly scalable variants of conjugate gradient methods that avoid blocking synchronization. In addition, we worked with the other members of the project on alternative techniques for resilience and reproducibility. We also presented an alternative approach for reproducible dot-products in parallel computations that performs almost as well as the conventional approach by separating the order of computation from the details of the decomposition of vectors across the processes.
Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing
Directory of Open Access Journals (Sweden)
Radu Mutihac
2009-06-01
Full Text Available Basics of Bayesian statistics in inverse problems using the maximum entropy principle are summarized in connection with the restoration of positive, additive images from various types of data like X-ray digital mammograms. An efficient iterative algorithm for image restoration from large data sets based on the conjugate gradient method and Lagrange multipliers in nonlinear optimization of a specific potential function was developed. The point spread function of the imaging system was determined by numerical simulations of inhomogeneous breast-like tissue with microcalcification inclusions of various opacities. The processed digital and digitized mammograms resulted superior in comparison with their raw counterparts in terms of contrast, resolution, noise, and visibility of details.
RES: Regularized Stochastic BFGS Algorithm
Mokhtari, Aryan; Ribeiro, Alejandro
2014-12-01
RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.
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.
Stereo vision with distance and gradient recognition
Kim, Soo-Hyun; Kang, Suk-Bum; Yang, Tae-Kyu
2007-12-01
Robot vision technology is needed for the stable walking, object recognition and the movement to the target spot. By some sensors which use infrared rays and ultrasonic, robot can overcome the urgent state or dangerous time. But stereo vision of three dimensional space would make robot have powerful artificial intelligence. In this paper we consider about the stereo vision for stable and correct movement of a biped robot. When a robot confront with an inclination plane or steps, particular algorithms are needed to go on without failure. This study developed the recognition algorithm of distance and gradient of environment by stereo matching process.
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.
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...
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.
De Götzen , Amalia; Mion , Luca; Tache , Olivier
2007-01-01
International audience; We call sound algorithms the categories of algorithms that deal with digital sound signal. Sound algorithms appeared in the very infancy of computer. Sound algorithms present strong specificities that are the consequence of two dual considerations: the properties of the digital sound signal itself and its uses, and the properties of auditory perception.
Wang, Lui; Bayer, Steven E.
1991-01-01
Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.
Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim
2014-01-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using
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...
Nachtigal, Noel M.
1991-01-01
The Lanczos algorithm can be used both for eigenvalue problems and to solve linear systems. However, when applied to non-Hermitian matrices, the classical Lanczos algorithm is susceptible to breakdowns and potential instabilities. In addition, the biconjugate gradient (BCG) algorithm, which is the natural generalization of the conjugate gradient algorithm to non-Hermitian linear systems, has a second source of breakdowns, independent of the Lanczos breakdowns. Here, we present two new results. We propose an implementation of a look-ahead variant of the Lanczos algorithm which overcomes the breakdowns by skipping over those steps where a breakdown or a near-breakdown would occur. The new algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products per step as the classical Lanczos algorithm without look-ahead. Based on the proposed look-ahead Lanczos algorithm, we then present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which avoids the second source of breakdowns in the BCG algorithm. We present details of the new method and discuss some of its properties. In particular, we discuss the relationship between QMR and BCG, showing how one can recover the BCG iterates, when they exist, from the QMR iterates. We also present convergence results for QMR, showing the connection between QMR and the generalized minimal residual (GMRES) algorithm, the optimal method in this class of methods. Finally, we give some numerical examples, both for eigenvalue computations and for non-Hermitian linear systems.
Canonical trivialization of gravitational gradients
International Nuclear Information System (INIS)
Niedermaier, Max
2017-01-01
A one-parameter family of canonical transformations is constructed that reduces the Hamiltonian form of the Einstein–Hilbert action to its strong coupling limit where dynamical spatial gradients are absent. The parameter can alternatively be viewed as the overall scale of the spatial metric or as a fractional inverse power of Newton’s constant. The generating function of the canonical transformation is constructed iteratively as a powerseries in the parameter to all orders. The algorithm draws on Lie–Deprit transformation theory and defines a ‘trivialization map’ with several bonus properties: (i) Trivialization of the Hamiltonian constraint implies that of the action while the diffeomorphism constraint is automatically co-transformed. (ii) Only a set of ordinary differential equations needs to be solved to drive the iteration via a homological equation where no gauge fixing is required. (iii) In contrast to (the classical limit of) a Lagrangian trivialization map the algorithm also produces series solutions of the field equations. (iv) In the strong coupling theory temporal gauge variations are abelian, nevertheless the map intertwines with the respective gauge symmetries on the action, the field equations, and their solutions. (paper)
Canonical trivialization of gravitational gradients
Niedermaier, Max
2017-06-01
A one-parameter family of canonical transformations is constructed that reduces the Hamiltonian form of the Einstein-Hilbert action to its strong coupling limit where dynamical spatial gradients are absent. The parameter can alternatively be viewed as the overall scale of the spatial metric or as a fractional inverse power of Newton’s constant. The generating function of the canonical transformation is constructed iteratively as a powerseries in the parameter to all orders. The algorithm draws on Lie-Deprit transformation theory and defines a ‘trivialization map’ with several bonus properties: (i) Trivialization of the Hamiltonian constraint implies that of the action while the diffeomorphism constraint is automatically co-transformed. (ii) Only a set of ordinary differential equations needs to be solved to drive the iteration via a homological equation where no gauge fixing is required. (iii) In contrast to (the classical limit of) a Lagrangian trivialization map the algorithm also produces series solutions of the field equations. (iv) In the strong coupling theory temporal gauge variations are abelian, nevertheless the map intertwines with the respective gauge symmetries on the action, the field equations, and their solutions.
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.
Joux, Antoine
2009-01-01
Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic
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)
Hougardy, Stefan
2016-01-01
Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.
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.
Tel, G.
We define the notion of total algorithms for networks of processes. A total algorithm enforces that a "decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of
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…
Conditionally-uniform Feasible Grid Search Algorithm
DEFF Research Database (Denmark)
Dziubinski, Matt P.
We present and evaluate a numerical optimization method (together with an algorithm for choosing the starting values) pertinent to the constrained optimization problem arising in the estimation of the GARCH models with inequality constraints, in particular the Simplied Component GARCH Model...... (SCGARCH), together with algorithms for the objective function and analytical gradient computation for SCGARCH....
International Nuclear Information System (INIS)
Li Yongjie; Yao Dezhong; Yao, Jonathan; Chen Wufan
2005-01-01
Automatic beam angle selection is an important but challenging problem for intensity-modulated radiation therapy (IMRT) planning. Though many efforts have been made, it is still not very satisfactory in clinical IMRT practice because of overextensive computation of the inverse problem. In this paper, a new technique named BASPSO (Beam Angle Selection with a Particle Swarm Optimization algorithm) is presented to improve the efficiency of the beam angle optimization problem. Originally developed as a tool for simulating social behaviour, the particle swarm optimization (PSO) algorithm is a relatively new population-based evolutionary optimization technique first introduced by Kennedy and Eberhart in 1995. In the proposed BASPSO, the beam angles are optimized using PSO by treating each beam configuration as a particle (individual), and the beam intensity maps for each beam configuration are optimized using the conjugate gradient (CG) algorithm. These two optimization processes are implemented iteratively. The performance of each individual is evaluated by a fitness value calculated with a physical objective function. A population of these individuals is evolved by cooperation and competition among the individuals themselves through generations. The optimization results of a simulated case with known optimal beam angles and two clinical cases (a prostate case and a head-and-neck case) show that PSO is valid and efficient and can speed up the beam angle optimization process. Furthermore, the performance comparisons based on the preliminary results indicate that, as a whole, the PSO-based algorithm seems to outperform, or at least compete with, the GA-based algorithm in computation time and robustness. In conclusion, the reported work suggested that the introduced PSO algorithm could act as a new promising solution to the beam angle optimization problem and potentially other optimization problems in IMRT, though further studies need to be investigated
Azami, Hamed; Escudero, Javier
2015-08-01
Breast cancer is one of the most common types of cancer in women all over the world. Early diagnosis of this kind of cancer can significantly increase the chances of long-term survival. Since diagnosis of breast cancer is a complex problem, neural network (NN) approaches have been used as a promising solution. Considering the low speed of the back-propagation (BP) algorithm to train a feed-forward NN, we consider a number of improved NN trainings for the Wisconsin breast cancer dataset: BP with momentum, BP with adaptive learning rate, BP with adaptive learning rate and momentum, Polak-Ribikre conjugate gradient algorithm (CGA), Fletcher-Reeves CGA, Powell-Beale CGA, scaled CGA, resilient BP (RBP), one-step secant and quasi-Newton methods. An NN ensemble, which is a learning paradigm to combine a number of NN outputs, is used to improve the accuracy of the classification task. Results demonstrate that NN ensemble-based classification methods have better performance than NN-based algorithms. The highest overall average accuracy is 97.68% obtained by NN ensemble trained by RBP for 50%-50% training-test evaluation method.
Parallel Implementation and Scaling of an Adaptive Mesh Discrete Ordinates Algorithm for Transport
International Nuclear Information System (INIS)
Howell, L H
2004-01-01
Block-structured adaptive mesh refinement (AMR) uses a mesh structure built up out of locally-uniform rectangular grids. In the BoxLib parallel framework used by the Raptor code, each processor operates on one or more of these grids at each refinement level. The decomposition of the mesh into grids and the distribution of these grids among processors may change every few timesteps as a calculation proceeds. Finer grids use smaller timesteps than coarser grids, requiring additional work to keep the system synchronized and ensure conservation between different refinement levels. In a paper for NECDC 2002 I presented preliminary results on implementation of parallel transport sweeps on the AMR mesh, conjugate gradient acceleration, accuracy of the AMR solution, and scalar speedup of the AMR algorithm compared to a uniform fully-refined mesh. This paper continues with a more in-depth examination of the parallel scaling properties of the scheme, both in single-level and multi-level calculations. Both sweeping and setup costs are considered. The algorithm scales with acceptable performance to several hundred processors. Trends suggest, however, that this is the limit for efficient calculations with traditional transport sweeps, and that modifications to the sweep algorithm will be increasingly needed as job sizes in the thousands of processors become common
International Nuclear Information System (INIS)
Xiao, Liye; Qian, Feng; Shao, Wei
2017-01-01
Highlights: • Propose a hybrid architecture based on a modified bat algorithm for multi-step wind speed forecasting. • Improve the accuracy of multi-step wind speed forecasting. • Modify bat algorithm with CG to improve optimized performance. - Abstract: As one of the most promising sustainable energy sources, wind energy plays an important role in energy development because of its cleanliness without causing pollution. Generally, wind speed forecasting, which has an essential influence on wind power systems, is regarded as a challenging task. Analyses based on single-step wind speed forecasting have been widely used, but their results are insufficient in ensuring the reliability and controllability of wind power systems. In this paper, a new forecasting architecture based on decomposing algorithms and modified neural networks is successfully developed for multi-step wind speed forecasting. Four different hybrid models are contained in this architecture, and to further improve the forecasting performance, a modified bat algorithm (BA) with the conjugate gradient (CG) method is developed to optimize the initial weights between layers and thresholds of the hidden layer of neural networks. To investigate the forecasting abilities of the four models, the wind speed data collected from four different wind power stations in Penglai, China, were used as a case study. The numerical experiments showed that the hybrid model including the singular spectrum analysis and general regression neural network with CG-BA (SSA-CG-BA-GRNN) achieved the most accurate forecasting results in one-step to three-step wind speed forecasting.
Dynamic training algorithm for dynamic neural networks
International Nuclear Information System (INIS)
Tan, Y.; Van Cauwenberghe, A.; Liu, Z.
1996-01-01
The widely used backpropagation algorithm for training neural networks based on the gradient descent has a significant drawback of slow convergence. A Gauss-Newton method based recursive least squares (RLS) type algorithm with dynamic error backpropagation is presented to speed-up the learning procedure of neural networks with local recurrent terms. Finally, simulation examples concerning the applications of the RLS type algorithm to identification of nonlinear processes using a local recurrent neural network are also included in this paper
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
Gradient descent learning in and out of equilibrium
International Nuclear Information System (INIS)
Caticha, Nestor; Araujo de Oliveira, Evaldo
2001-01-01
Relations between the off thermal equilibrium dynamical process of on-line learning and the thermally equilibrated off-line learning are studied for potential gradient descent learning. The approach of Opper to study on-line Bayesian algorithms is used for potential based or maximum likelihood learning. We look at the on-line learning algorithm that best approximates the off-line algorithm in the sense of least Kullback-Leibler information loss. The closest on-line algorithm works by updating the weights along the gradient of an effective potential, which is different from the parent off-line potential. A few examples are analyzed and the origin of the potential annealing is discussed
Gradient Optimization for Analytic conTrols - GOAT
Assémat, Elie; Machnes, Shai; Tannor, David; Wilhelm-Mauch, Frank
Quantum optimal control becomes a necessary step in a number of studies in the quantum realm. Recent experimental advances showed that superconducting qubits can be controlled with an impressive accuracy. However, most of the standard optimal control algorithms are not designed to manage such high accuracy. To tackle this issue, a novel quantum optimal control algorithm have been introduced: the Gradient Optimization for Analytic conTrols (GOAT). It avoids the piecewise constant approximation of the control pulse used by standard algorithms. This allows an efficient implementation of very high accuracy optimization. It also includes a novel method to compute the gradient that provides many advantages, e.g. the absence of backpropagation or the natural route to optimize the robustness of the control pulses. This talk will present the GOAT algorithm and a few applications to transmons systems.
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
Innovative applications of genetic algorithms to problems in accelerator physics
Directory of Open Access Journals (Sweden)
Alicia Hofler
2013-01-01
Full Text Available The genetic algorithm (GA is a powerful technique that implements the principles nature uses in biological evolution to optimize a multidimensional nonlinear problem. The GA works especially well for problems with a large number of local extrema, where traditional methods (such as conjugate gradient, steepest descent, and others fail or, at best, underperform. The field of accelerator physics, among others, abounds with problems which lend themselves to optimization via GAs. In this paper, we report on the successful application of GAs in several problems related to the existing Continuous Electron Beam Accelerator Facility nuclear physics machine, the proposed Medium-energy Electron-Ion Collider at Jefferson Lab, and a radio frequency gun-based injector. These encouraging results are a step forward in optimizing accelerator design and provide an impetus for application of GAs to other problems in the field. To that end, we discuss the details of the GAs used, include a newly devised enhancement which leads to improved convergence to the optimum, and make recommendations for future GA developments and accelerator applications.
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.
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...
The evolving approach to the evaluation of low-gradient aortic stenosis.
Cutting, William B; Bavry, Anthony A
2018-04-07
Severe aortic stenosis (AS) is typically identified by a low valve area (≤1.0 cm 2 ) and high mean gradient (≥40 mm Hg). A subset of patients are found to have a less than severe mean gradient (gradient AS (stage D2) or normal ejection fraction with low-gradient AS (stage D3). Determining the true severity of disease within these categories has proved difficult. In this review we illustrate both traditional and novel techniques that can be used for further valvular assessment. We also propose a simple algorithm that can be used to evaluate low-gradient AS. Published by Elsevier Inc.
Seismic noise attenuation using an online subspace tracking algorithm
Zhou, Yatong; Li, Shuhua; Zhang, D.; Chen, Yangkang
2018-01-01
We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient
Developing operation algorithms for vision subsystems in autonomous mobile robots
Shikhman, M. V.; Shidlovskiy, S. V.
2018-05-01
The paper analyzes algorithms for selecting keypoints on the image for the subsequent automatic detection of people and obstacles. The algorithm is based on the histogram of oriented gradients and the support vector method. The combination of these methods allows successful selection of dynamic and static objects. The algorithm can be applied in various autonomous mobile robots.
Directory of Open Access Journals (Sweden)
Zeng-Rong Hao
2014-11-01
Full Text Available The performance of modern heavy-duty gas turbines is greatly determined by the accurate numerical predictions of thermal loading on the hot-end components. The purpose of this paper is: (1 to present an approach applying a novel numerical technique—the discontinuous Galerkin (DG method—to conjugate heat transfer (CHT simulations, develop the engineering-oriented numerical platform, and validate the feasibility of the methodology and tool preliminarily; and (2 to utilize the constructed platform to investigate the aerothermodynamic features of a typical transonic turbine vane with convection cooling. Fluid dynamic and solid heat conductive equations are discretized into explicit DG formulations. A centroid-expanded Taylor basis is adopted for various types of elements. The Bassi-Rebay method is used in the computation of gradients. A coupled strategy based on a data exchange process via numerical flux on interface quadrature points is simply devised. Additionally, various turbulence Reynolds-Averaged-Navier-Stokes (RANS models and the local-variable-based transition model γ-Reθ are assimilated into the integral framework, combining sophisticated modelling with the innovative algorithm. Numerical tests exhibit good consistency between computational and analytical or experimental results, demonstrating that the presented approach and tool can handle well general CHT simulations. Application and analysis in the turbine vane, focusing on features around where there in cluster exist shock, separation and transition, illustrate the effects of Bradshaw’s shear stress limitation and separation-induced-transition modelling. The general overestimation of heat transfer intensity behind shock is conjectured to be associated with compressibility effects on transition modeling. This work presents an unconventional formulation in CHT problems and achieves its engineering applications in gas turbines.
Accelerated gradient methods for constrained image deblurring
International Nuclear Information System (INIS)
Bonettini, S; Zanella, R; Zanni, L; Bertero, M
2008-01-01
In this paper we propose a special gradient projection method for the image deblurring problem, in the framework of the maximum likelihood approach. We present the method in a very general form and we give convergence results under standard assumptions. Then we consider the deblurring problem and the generality of the proposed algorithm allows us to add a energy conservation constraint to the maximum likelihood problem. In order to improve the convergence rate, we devise appropriate scaling strategies and steplength updating rules, especially designed for this application. The effectiveness of the method is evaluated by means of a computational study on astronomical images corrupted by Poisson noise. Comparisons with standard methods for image restoration, such as the expectation maximization algorithm, are also reported.
Eigen-Gradients for Traffic Sign Recognition
Directory of Open Access Journals (Sweden)
Sheila Esmeralda Gonzalez-Reyna
2013-01-01
Full Text Available Traffic sign detection and recognition systems include a variety of applications like autonomous driving, road sign inventory, and driver support systems. Machine learning algorithms provide useful tools for traffic sign identification tasks. However, classification algorithms depend on the preprocessing stage to obtain high accuracy rates. This paper proposes a road sign characterization method based on oriented gradient maps and the Karhunen-Loeve transform in order to improve classification performance. Dimensionality reduction may be important for portable applications on resource constrained devices like FPGAs; therefore, our approach focuses on achieving a good classification accuracy by using a reduced amount of attributes compared to some state-of-the-art methods. The proposed method was tested using German Traffic Sign Recognition Benchmark, reaching a dimensionality reduction of 99.3% and a classification accuracy of 95.9% with a Multi-Layer Perceptron.
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
Bayesian posterior sampling via stochastic gradient Fisher scoring
Ahn, S.; Korattikara, A.; Welling, M.; Langford, J.; Pineau, J.
2012-01-01
In this paper we address the following question: "Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?". An algorithm based on the Langevin equation with stochastic gradients (SGLD) was
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.
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.
A new simple iterative reconstruction algorithm for SPECT transmission measurement
International Nuclear Information System (INIS)
Hwang, D.S.; Zeng, G.L.
2005-01-01
This paper proposes a new iterative reconstruction algorithm for transmission tomography and compares this algorithm with several other methods. The new algorithm is simple and resembles the emission ML-EM algorithm in form. Due to its simplicity, it is easy to implement and fast to compute a new update at each iteration. The algorithm also always guarantees non-negative solutions. Evaluations are performed using simulation studies and real phantom data. Comparisons with other algorithms such as convex, gradient, and logMLEM show that the proposed algorithm is as good as others and performs better in some cases
DEFF Research Database (Denmark)
Sadegh, Payman
1997-01-01
This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....
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…
Automated gravity gradient tensor inversion for underwater object detection
International Nuclear Information System (INIS)
Wu, Lin; Tian, Jinwen
2010-01-01
Underwater abnormal object detection is a current need for the navigation security of autonomous underwater vehicles (AUVs). In this paper, an automated gravity gradient tensor inversion algorithm is proposed for the purpose of passive underwater object detection. Full-tensor gravity gradient anomalies induced by an object in the partial area can be measured with the technique of gravity gradiometry on an AUV. Then the automated algorithm utilizes the anomalies, using the inverse method to estimate the mass and barycentre location of the arbitrary-shaped object. A few tests on simple synthetic models will be illustrated, in order to evaluate the feasibility and accuracy of the new algorithm. Moreover, the method is applied to a complicated model of an abnormal object with gradiometer and AUV noise, and interference from a neighbouring illusive smaller object. In all cases tested, the estimated mass and barycentre location parameters are found to be in good agreement with the actual values
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...
DEFF Research Database (Denmark)
Boiroux, Dimitri; Juhl, Rune; Madsen, Henrik
2016-01-01
This paper addresses maximum likelihood parameter estimation of continuous-time nonlinear systems with discrete-time measurements. We derive an efficient algorithm for the computation of the log-likelihood function and its gradient, which can be used in gradient-based optimization algorithms....... This algorithm uses UD decomposition of symmetric matrices and the array algorithm for covariance update and gradient computation. We test our algorithm on the Lotka-Volterra equations. Compared to the maximum likelihood estimation based on finite difference gradient computation, we get a significant speedup...
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.
Novel algorithm of large-scale simultaneous linear equations
International Nuclear Information System (INIS)
Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L
2010-01-01
We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.
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
Spectral edge: gradient-preserving spectral mapping for image fusion.
Connah, David; Drew, Mark S; Finlayson, Graham D
2015-12-01
This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.
International Nuclear Information System (INIS)
Creutz, M.
1987-11-01
A large variety of Monte Carlo algorithms are being used for lattice gauge simulations. For purely bosonic theories, present approaches are generally adequate; nevertheless, overrelaxation techniques promise savings by a factor of about three in computer time. For fermionic fields the situation is more difficult and less clear. Algorithms which involve an extrapolation to a vanishing step size are all quite closely related. Methods which do not require such an approximation tend to require computer time which grows as the square of the volume of the system. Recent developments combining global accept/reject stages with Langevin or microcanonical updatings promise to reduce this growth to V/sup 4/3/
Hu, T C
2002-01-01
Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9
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
General approach for solving the density gradient theory in the interfacial tension calculations
DEFF Research Database (Denmark)
Liang, Xiaodong; Michelsen, Michael Locht
2017-01-01
Within the framework of the density gradient theory, the interfacial tension can be calculated by finding the density profiles that minimize an integral of two terms over the system of infinite width. It is found that the two integrands exhibit a constant difference along the interface for a finite...... property evaluations compared to other methods. The performance of the algorithm with recommended parameters is analyzed for various systems, and the efficiency is further compared with the geometric-mean density gradient theory, which only needs to solve nonlinear algebraic equations. The results show...... that the algorithm is only 5-10 times less efficient than solving the geometric-mean density gradient theory....
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.
Directory of Open Access Journals (Sweden)
Anna Bourmistrova
2011-02-01
Full Text Available The autodriver algorithm is an intelligent method to eliminate the need of steering by a driver on a well-defined road. The proposed method performs best on a four-wheel steering (4WS vehicle, though it is also applicable to two-wheel-steering (TWS vehicles. The algorithm is based on coinciding the actual vehicle center of rotation and road center of curvature, by adjusting the kinematic center of rotation. The road center of curvature is assumed prior information for a given road, while the dynamic center of rotation is the output of dynamic equations of motion of the vehicle using steering angle and velocity measurements as inputs. We use kinematic condition of steering to set the steering angles in such a way that the kinematic center of rotation of the vehicle sits at a desired point. At low speeds the ideal and actual paths of the vehicle are very close. With increase of forward speed the road and tire characteristics, along with the motion dynamics of the vehicle cause the vehicle to turn about time-varying points. By adjusting the steering angles, our algorithm controls the dynamic turning center of the vehicle so that it coincides with the road curvature center, hence keeping the vehicle on a given road autonomously. The position and orientation errors are used as feedback signals in a closed loop control to adjust the steering angles. The application of the presented autodriver algorithm demonstrates reliable performance under different driving conditions.
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...
Applying Gradient Descent in Convolutional Neural Networks
Cui, Nan
2018-04-01
With the development of the integrated circuit and computer science, people become caring more about solving practical issues via information technologies. Along with that, a new subject called Artificial Intelligent (AI) comes up. One popular research interest of AI is about recognition algorithm. In this paper, one of the most common algorithms, Convolutional Neural Networks (CNNs) will be introduced, for image recognition. Understanding its theory and structure is of great significance for every scholar who is interested in this field. Convolution Neural Network is an artificial neural network which combines the mathematical method of convolution and neural network. The hieratical structure of CNN provides it reliable computer speed and reasonable error rate. The most significant characteristics of CNNs are feature extraction, weight sharing and dimension reduction. Meanwhile, combining with the Back Propagation (BP) mechanism and the Gradient Descent (GD) method, CNNs has the ability to self-study and in-depth learning. Basically, BP provides an opportunity for backwardfeedback for enhancing reliability and GD is used for self-training process. This paper mainly discusses the CNN and the related BP and GD algorithms, including the basic structure and function of CNN, details of each layer, the principles and features of BP and GD, and some examples in practice with a summary in the end.
The Dropout Learning Algorithm
Baldi, Pierre; Sadowski, Peter
2014-01-01
Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations. PMID:24771879
Quality measures for HRR alignment based ISAR imaging algorithms
CSIR Research Space (South Africa)
Janse van Rensburg, V
2013-05-01
Full Text Available Some Inverse Synthetic Aperture Radar (ISAR) algorithms form the image in a two-step process of range alignment and phase conjugation. This paper discusses a comprehensive set of measures used to quantify the quality of range alignment, with the aim...
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
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.
DEFF Research Database (Denmark)
Markham, Annette
This paper takes an actor network theory approach to explore some of the ways that algorithms co-construct identity and relational meaning in contemporary use of social media. Based on intensive interviews with participants as well as activity logging and data tracking, the author presents a richly...... layered set of accounts to help build our understanding of how individuals relate to their devices, search systems, and social network sites. This work extends critical analyses of the power of algorithms in implicating the social self by offering narrative accounts from multiple perspectives. It also...... contributes an innovative method for blending actor network theory with symbolic interaction to grapple with the complexity of everyday sensemaking practices within networked global information flows....
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.
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