Method of Conjugate Radii for Solving Linear and Nonlinear Systems

NASA Technical Reports Server (NTRS)

Nachtsheim, Philip R.

1999-01-01

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

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

PubMed

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 essential.

Dai-Kou type conjugate gradient methods with a line search only using gradient.

PubMed

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.

Approximate error conjugation gradient minimization methods

DOEpatents

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.

Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics

NASA Technical Reports Server (NTRS)

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.

Comparing implementations of penalized weighted least-squares sinogram restoration.

PubMed

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-11-01

A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors' previous penalized-likelihood implementation. Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes.

Application of the conjugate-gradient method to ground-water models

USGS Publications Warehouse

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)

Double diffusive conjugate heat transfer: Part I

NASA Astrophysics Data System (ADS)

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.

Minimizing inner product data dependencies in conjugate gradient iteration

NASA Technical Reports Server (NTRS)

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)).

An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package

NASA Astrophysics Data System (ADS)

Oppe, Thomas C.; Joubert, Wayne D.; Kincaid, David R.

1989-05-01

The most recent research-oriented software package developed as part of the ITPACK Project is called "NSPCG" since it contains many nonsymmetric preconditioned conjugate gradient procedures. It is designed to solve large sparse systems of linear algebraic equations by a variety of different iterative methods. One of the main purposes for the development of the package is to provide a common modular structure for research on iterative methods for nonsymmetric matrices. Another purpose for the development of the package is to investigate the suitability of several iterative methods for vector computers. Since the vectorizability of an iterative method depends greatly on the matrix structure, NSPCG allows great flexibility in the operator representation. The coefficient matrix can be passed in one of several different matrix data storage schemes. These sparse data formats allow matrices with a wide range of structures from highly structured ones such as those with all nonzeros along a relatively small number of diagonals to completely unstructured sparse matrices. Alternatively, the package allows the user to call the accelerators directly with user-supplied routines for performing certain matrix operations. In this case, one can use the data format from an application program and not be required to copy the matrix into one of the package formats. This is particularly advantageous when memory space is limited. Some of the basic preconditioners that are available are point methods such as Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block and multicolor preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner.

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Sonnad, Vijay

1991-01-01

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

A new smoothing modified three-term conjugate gradient method for [Formula: see text]-norm minimization problem.

PubMed

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.

Ionospheric-thermospheric UV tomography: 1. Image space reconstruction algorithms

NASA Astrophysics Data System (ADS)

Dymond, K. F.; Budzien, S. A.; Hei, M. A.

2017-03-01

We present and discuss two algorithms of the class known as Image Space Reconstruction Algorithms (ISRAs) that we are applying to the solution of large-scale ionospheric tomography problems. ISRAs have several desirable features that make them useful for ionospheric tomography. In addition to producing nonnegative solutions, ISRAs are amenable to sparse-matrix formulations and are fast, stable, and robust. We present the results of our studies of two types of ISRA: the Least Squares Positive Definite and the Richardson-Lucy algorithms. We compare their performance to the Multiplicative Algebraic Reconstruction and Conjugate Gradient Least Squares algorithms. We then discuss the use of regularization in these algorithms and present our new approach based on regularization to a partial differential equation.

Comparing implementations of penalized weighted least-squares sinogram restoration

PubMed Central

Forthmann, Peter; Koehler, Thomas; Defrise, Michel; La Riviere, Patrick

2010-01-01

Purpose: A CT scanner measures the energy that is deposited in each channel of a detector array by x rays that have been partially absorbed on their way through the object. The measurement process is complex and quantitative measurements are always and inevitably associated with errors, so CT data must be preprocessed prior to reconstruction. In recent years, the authors have formulated CT sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. The authors have explored both penalized Poisson likelihood (PL) and penalized weighted least-squares (PWLS) objective functions. At low doses, the authors found that the PL approach outperforms PWLS in terms of resolution-noise tradeoffs, but at standard doses they perform similarly. The PWLS objective function, being quadratic, is more amenable to computational acceleration than the PL objective. In this work, the authors develop and compare two different methods for implementing PWLS sinogram restoration with the hope of improving computational performance relative to PL in the standard-dose regime. Sinogram restoration is still significant in the standard-dose regime since it can still outperform standard approaches and it allows for correction of effects that are not usually modeled in standard CT preprocessing. Methods: The authors have explored and compared two implementation strategies for PWLS sinogram restoration: (1) A direct matrix-inversion strategy based on the closed-form solution to the PWLS optimization problem and (2) an iterative approach based on the conjugate-gradient algorithm. Obtaining optimal performance from each strategy required modifying the naive off-the-shelf implementations of the algorithms to exploit the particular symmetry and sparseness of the sinogram-restoration problem. For the closed-form approach, the authors subdivided the large matrix inversion into smaller coupled problems and exploited sparseness to minimize matrix operations. For the conjugate-gradient approach, the authors exploited sparseness and preconditioned the problem to speed up convergence. Results: All methods produced qualitatively and quantitatively similar images as measured by resolution-variance tradeoffs and difference images. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approaches, with a computational burden higher by an order of magnitude or more. The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of the authors’ previous penalized-likelihood implementation. Conclusions: Iterative conjugate-gradient based PWLS sinogram restoration with careful matrix optimizations has computational advantages over direct matrix PWLS inversion and over penalized-likelihood sinogram restoration and can be considered a good alternative in standard-dose regimes. PMID:21158306

Implementation of neural network for color properties of polycarbonates

NASA Astrophysics Data System (ADS)

Saeed, U.; Ahmad, S.; Alsadi, J.; Ross, D.; Rizvi, G.

2014-05-01

In present paper, the applicability of artificial neural networks (ANN) is investigated for color properties of plastics. The neural networks toolbox of Matlab 6.5 is used to develop and test the ANN model on a personal computer. An optimal design is completed for 10, 12, 14,16,18 & 20 hidden neurons on single hidden layer with five different algorithms: batch gradient descent (GD), batch variable learning rate (GDX), resilient back-propagation (RP), scaled conjugate gradient (SCG), levenberg-marquardt (LM) in the feed forward back-propagation neural network model. The training data for ANN is obtained from experimental measurements. There were twenty two inputs including resins, additives & pigments while three tristimulus color values L*, a* and b* were used as output layer. Statistical analysis in terms of Root-Mean-Squared (RMS), absolute fraction of variance (R squared), as well as mean square error is used to investigate the performance of ANN. LM algorithm with fourteen neurons on hidden layer in Feed Forward Back-Propagation of ANN model has shown best result in the present study. The degree of accuracy of the ANN model in reduction of errors is proven acceptable in all statistical analysis and shown in results. However, it was concluded that ANN provides a feasible method in error reduction in specific color tristimulus values.

Multisource least-squares reverse-time migration with structure-oriented filtering

NASA Astrophysics Data System (ADS)

Fan, Jing-Wen; Li, Zhen-Chun; Zhang, Kai; Zhang, Min; Liu, Xue-Tong

2016-09-01

The technology of simultaneous-source acquisition of seismic data excited by several sources can significantly improve the data collection efficiency. However, direct imaging of simultaneous-source data or blended data may introduce crosstalk noise and affect the imaging quality. To address this problem, we introduce a structure-oriented filtering operator as preconditioner into the multisource least-squares reverse-time migration (LSRTM). The structure-oriented filtering operator is a nonstationary filter along structural trends that suppresses crosstalk noise while maintaining structural information. The proposed method uses the conjugate-gradient method to minimize the mismatch between predicted and observed data, while effectively attenuating the interference noise caused by exciting several sources simultaneously. Numerical experiments using synthetic data suggest that the proposed method can suppress the crosstalk noise and produce highly accurate images.

Quantifying the Energy Efficiency of Object Recognition and Optical Flow

DTIC Science & Technology

2014-03-28

other linear solvers, such as conjugate- gradient (CG), preconditioned conjugate-gradient (PCG), and red-black Gauss Seidel (RB). We have also... Seidel , and conjugate gradient solvers. We are interested in the energy it takes to get a given solution quality. In Figure 6, we plot the quality of...in terms of Joules. Conversely, our implementation of red-black Gauss Seidel proves to be very inefficient when we consider Joules instead of just

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

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.

A three-term conjugate gradient method under the strong-Wolfe line search

NASA Astrophysics Data System (ADS)

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.

Transfer-function-parameter estimation from frequency response data: A FORTRAN program

NASA Technical Reports Server (NTRS)

Seidel, R. C.

1975-01-01

A FORTRAN computer program designed to fit a linear transfer function model to given frequency response magnitude and phase data is presented. A conjugate gradient search is used that minimizes the integral of the absolute value of the error squared between the model and the data. The search is constrained to insure model stability. A scaling of the model parameters by their own magnitude aids search convergence. Efficient computer algorithms result in a small and fast program suitable for a minicomputer. A sample problem with different model structures and parameter estimates is reported.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

SAGRAD: A Program for Neural Network Training with Simulated Annealing and the Conjugate Gradient Method.

PubMed

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.

Parallel conjugate gradient algorithms for manipulator dynamic simulation

NASA Technical Reports Server (NTRS)

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).

Conjugate-Gradient Neural Networks in Classification of Multisource and Very-High-Dimensional Remote Sensing Data

NASA Technical Reports Server (NTRS)

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.

Application of augmented-Lagrangian methods in meteorology: Comparison of different conjugate-gradient codes for large-scale minimization

NASA Technical Reports Server (NTRS)

Navon, I. M.

1984-01-01

A Lagrange multiplier method using techniques developed by Bertsekas (1982) was applied to solving the problem of enforcing simultaneous conservation of the nonlinear integral invariants of the shallow water equations on a limited area domain. This application of nonlinear constrained optimization is of the large dimensional type and the conjugate gradient method was found to be the only computationally viable method for the unconstrained minimization. Several conjugate-gradient codes were tested and compared for increasing accuracy requirements. Robustness and computational efficiency were the principal criteria.

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

PubMed

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.

Comparison of genetic algorithms with conjugate gradient methods

NASA Technical Reports Server (NTRS)

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.

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Orderings for conjugate gradient preconditionings

NASA Technical Reports Server (NTRS)

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.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

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.

SAGRAD: A Program for Neural Network Training with Simulated Annealing and the Conjugate Gradient Method

PubMed Central

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. PMID:26958442

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

NASA Astrophysics Data System (ADS)

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

A feasible DY conjugate gradient method for linear equality constraints

NASA Astrophysics Data System (ADS)

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.

Non-preconditioned conjugate gradient on cell and FPGA based hybrid supercomputer nodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubois, David H; Dubois, Andrew J; Boorman, Thomas M

2009-01-01

This work presents a detailed implementation of a double precision, non-preconditioned, Conjugate Gradient algorithm on a Roadrunner heterogeneous supercomputer node. These nodes utilize the Cell Broadband Engine Architecture{sup TM} in conjunction with x86 Opteron{sup TM} processors from AMD. We implement a common Conjugate Gradient algorithm, on a variety of systems, to compare and contrast performance. Implementation results are presented for the Roadrunner hybrid supercomputer, SRC Computers, Inc. MAPStation SRC-6 FPGA enhanced hybrid supercomputer, and AMD Opteron only. In all hybrid implementations wall clock time is measured, including all transfer overhead and compute timings.

Non-preconditioned conjugate gradient on cell and FPCA-based hybrid supercomputer nodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dubois, David H; Dubois, Andrew J; Boorman, Thomas M

2009-03-10

This work presents a detailed implementation of a double precision, Non-Preconditioned, Conjugate Gradient algorithm on a Roadrunner heterogeneous supercomputer node. These nodes utilize the Cell Broadband Engine Architecture{trademark} in conjunction with x86 Opteron{trademark} processors from AMD. We implement a common Conjugate Gradient algorithm, on a variety of systems, to compare and contrast performance. Implementation results are presented for the Roadrunner hybrid supercomputer, SRC Computers, Inc. MAPStation SRC-6 FPGA enhanced hybrid supercomputer, and AMD Opteron only. In all hybrid implementations wall clock time is measured, including all transfer overhead and compute timings.

Comparing direct and iterative equation solvers in a large structural analysis software system

NASA Technical Reports Server (NTRS)

Poole, E. L.

1991-01-01

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

A modified form of conjugate gradient method for unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Ghani, Nur Hamizah Abdul; Rivaie, Mohd.; Mamat, Mustafa

2016-06-01

Conjugate gradient (CG) methods have been recognized as an interesting technique to solve optimization problems, due to the numerical efficiency, simplicity and low memory requirements. In this paper, we propose a new CG method based on the study of Rivaie et al. [7] (Comparative study of conjugate gradient coefficient for unconstrained Optimization, Aus. J. Bas. Appl. Sci. 5(2011) 947-951). Then, we show that our method satisfies sufficient descent condition and converges globally with exact line search. Numerical results show that our proposed method is efficient for given standard test problems, compare to other existing CG methods.

A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems

NASA Astrophysics Data System (ADS)

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.

A least-squares finite element method for 3D incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Gradient optimization and nonlinear control

NASA Technical Reports Server (NTRS)

Hasdorff, L.

1976-01-01

The book represents an introduction to computation in control by an iterative, gradient, numerical method, where linearity is not assumed. The general language and approach used are those of elementary functional analysis. The particular gradient method that is emphasized and used is conjugate gradient descent, a well known method exhibiting quadratic convergence while requiring very little more computation than simple steepest descent. Constraints are not dealt with directly, but rather the approach is to introduce them as penalty terms in the criterion. General conjugate gradient descent methods are developed and applied to problems in control.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

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 minimisation approach to generating holographic traps for ultracold atoms.

PubMed

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.

Conjugate gradient filtering of instantaneous normal modes, saddles on the energy landscape, and diffusion in liquids.

PubMed

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.

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.

PubMed

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.

Conjugate Gradient Algorithms For Manipulator Simulation

NASA Technical Reports Server (NTRS)

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.

Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization.

PubMed

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.

ILUBCG2-11: Solution of 11-banded nonsymmetric linear equation systems by a preconditioned biconjugate gradient routine

NASA Astrophysics Data System (ADS)

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.

Performance comparison of a new hybrid conjugate gradient method under exact and inexact line searches

NASA Astrophysics Data System (ADS)

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.

Efficient method to design RF pulses for parallel excitation MRI using gridding and conjugate gradient

PubMed Central

Feng, Shuo

2014-01-01

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. PMID:24834420

Efficient method to design RF pulses for parallel excitation MRI using gridding and conjugate gradient.

PubMed

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.

Algorithms for parallel and vector computations

NASA Technical Reports Server (NTRS)

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.

Solving large test-day models by iteration on data and preconditioned conjugate gradient.

PubMed

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.

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

NASA Technical Reports Server (NTRS)

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.

Conjugate-Gradient Algorithms For Dynamics Of Manipulators

NASA Technical Reports Server (NTRS)

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.

An M-step preconditioned conjugate gradient method for parallel computation

NASA Technical Reports Server (NTRS)

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.

Navier-Stokes dynamics on a differential one-form

NASA Astrophysics Data System (ADS)

Story, Troy L.

2006-11-01

After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position x^k and the conjugate to the position bk as functions of time. The solution bk is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution bk shows it is bounded since it remains finite as | x^k | ->,, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained.

Conjugate gradient heat bath for ill-conditioned actions.

PubMed

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.

Modelling Schumann resonances from ELF measurements using non-linear optimization methods

NASA Astrophysics Data System (ADS)

Castro, Francisco; Toledo-Redondo, Sergio; Fornieles, Jesús; Salinas, Alfonso; Portí, Jorge; Navarro, Enrique; Sierra, Pablo

2017-04-01

Schumann resonances (SR) can be found in planetary atmospheres, inside the cavity formed by the conducting surface of the planet and the lower ionosphere. They are a powerful tool to investigate both the electric processes that occur in the atmosphere and the characteristics of the surface and the lower ionosphere. In this study, the measurements are obtained in the ELF (Extremely Low Frequency) Juan Antonio Morente station located in the national park of Sierra Nevada. The three first modes, contained in the frequency band between 6 to 25 Hz, will be considered. For each time series recorded by the station, the amplitude spectrum was estimated by using Bartlett averaging. Then, the central frequencies and amplitudes of the SRs were obtained by fitting the spectrum with non-linear functions. In the poster, a study of nonlinear unconstrained optimization methods applied to the estimation of the Schumann Resonances will be presented. Non-linear fit, also known as optimization process, is the procedure followed in obtaining Schumann Resonances from the natural electromagnetic noise. The optimization methods that have been analysed are: Levenberg-Marquardt, Conjugate Gradient, Gradient, Newton and Quasi-Newton. The functions that the different methods fit to data are three lorentzian curves plus a straight line. Gaussian curves have also been considered. The conclusions of this study are outlined in the following paragraphs: i) Natural electromagnetic noise is better fitted using Lorentzian functions; ii) the measurement bandwidth can accelerate the convergence of the optimization method; iii) Gradient method has less convergence and has a highest mean squared error (MSE) between measurement and the fitted function, whereas Levenberg-Marquad, Gradient conjugate method and Cuasi-Newton method give similar results (Newton method presents higher MSE); v) There are differences in the MSE between the parameters that define the fit function, and an interval from 1% to 5% has been found.

Frequency-domain beamformers using conjugate gradient techniques for speech enhancement.

PubMed

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.

Moving force identification based on modified preconditioned conjugate gradient method

NASA Astrophysics Data System (ADS)

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.

Conjugate gradient based projection - A new explicit methodology for frictional contact

NASA Technical Reports Server (NTRS)

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.

M-step preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

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.

Inelastic scattering with Chebyshev polynomials and preconditioned conjugate gradient minimization.

PubMed

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.

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

NASA Technical Reports Server (NTRS)

Christodoulou, C. G.; Kauffman, J. F.

1986-01-01

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Realization of preconditioned Lanczos and conjugate gradient algorithms on optical linear algebra processors.

PubMed

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.

The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.

PubMed

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).

ONRASIA Scientific Information Bulletin. Volume 8, Number 3, July- September 1993

DTIC Science & Technology

1993-09-01

the Ninth Symposium on Preconditioned Conjugate Dr. Steven F. Ashby Gradient Methods , which he organized. Computing Sciences Department Computing...ditioned Conjugate Gradient Methods , held at Keio chines and is currently a topic of considerable University (Yokohama). During this meeting, I interest...in the United States. In Japan, on the other discussed iterative methods for linear systems with hand, this technique does not appear to be too well

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

A family of conjugate gradient methods for large-scale nonlinear equations.

PubMed

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.

High-performance conjugate-gradient benchmark: A new metric for ranking high-performance computing systems

DOE PAGES

Dongarra, Jack; Heroux, Michael A.; Luszczek, Piotr

2015-08-17

Here, we describe a new high-performance conjugate-gradient (HPCG) benchmark. HPCG is composed of computations and data-access patterns commonly found in scientific applications. HPCG strives for a better correlation to existing codes from the computational science domain and to be representative of their performance. Furthermore, HPCG is meant to help drive the computer system design and implementation in directions that will better impact future performance improvement.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

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.

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

USGS Publications Warehouse

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.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

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)β k ≥ 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. PMID:26502409

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

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.

Revisiting the Least-squares Procedure for Gradient Reconstruction on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Thomas, James L. (Technical Monitor)

2003-01-01

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious difficulties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For vertex-based discretizations on triangular and quadrilateral meshes, and cell-centered discretizations on quadrilateral meshes, accuracy can be recovered using an inverse distance weighting in the least-squares construction. For cell-centered discretizations on triangles, both the unweighted and weighted least-squares constructions fail to provide suitable gradient estimates for highly stretched curved meshes. Good overall flow solution accuracy can be retained in spite of poor gradient estimates, due to the presence of flow alignment in exactly the same regions where the poor gradient accuracy is observed. However, the use of entropy fixes has the potential for generating large but subtle discretization errors.

SIERRA - A 3-D device simulator for reliability modeling

NASA Astrophysics Data System (ADS)

Chern, Jue-Hsien; Arledge, Lawrence A., Jr.; Yang, Ping; Maeda, John T.

1989-05-01

SIERRA is a three-dimensional general-purpose semiconductor-device simulation program which serves as a foundation for investigating integrated-circuit (IC) device and reliability issues. This program solves the Poisson and continuity equations in silicon under dc, transient, and small-signal conditions. Executing on a vector/parallel minisupercomputer, SIERRA utilizes a matrix solver which uses an incomplete LU (ILU) preconditioned conjugate gradient square (CGS, BCG) method. The ILU-CGS method provides a good compromise between memory size and convergence rate. The authors have observed a 5x to 7x speedup over standard direct methods in simulations of transient problems containing highly coupled Poisson and continuity equations such as those found in reliability-oriented simulations. The application of SIERRA to parasitic CMOS latchup and dynamic random-access memory single-event-upset studies is described.

[Research on respiration course of human at different postures by electrical impedance tomography].

PubMed

Chen, Xiaoyan; Wu, Jun; Wang, Huaxiang; Li, Da

2010-10-01

In this paper, the respiration courses of human at different postures are reconstructed by electrical impedance tomography (EIT). Conjugate gradient least squares (CGLS) algorithm is applied to reconstruct the resistivity distribution during respiration courses, and the EIT images taken from human at flat lying, left lying, right lying, sitting and prone postures are reconstructed and compared. The relative changes of the resistivity in region of interest (ROI) are analyzed to evidence the influences caused by different postures. Results show that the changes in postures are the most influential factors for the reconstructions, and the EIT images vary with the postures. In human at flat-lying posture, the left and right lungs have larger pulmonary ventilation volume simultaneously, and the EIT-measured data are of lower variability.

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

Albright, N.; Chen, N. F.; Concus, P.; Finn, R.

1977-01-01

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

Experimental study of stochastic noise propagation in SPECT images reconstructed using the conjugate gradient algorithm.

PubMed

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.

Conjugate gradient optimization programs for shuttle reentry

NASA Technical Reports Server (NTRS)

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.

A new family of Polak-Ribiere-Polyak conjugate gradient method with the strong-Wolfe line search

NASA Astrophysics Data System (ADS)

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.

Mechanical Properties of Porous, High Temperature Structural Materials: Sources of Toughness in Reaction Bonded Silicon Nitride.

DTIC Science & Technology

1995-10-15

tensile extension. At each level of externally imposed displacements, internal equilibrium was achieved by a conjugate gradient method of energy...indentation cracks viewed by TEM. This could be due to either weaker grain boundaries or due to grain level internal stresses of misfit. The fact... internally using the conjugate gradient method until the overall elastic strain energy function 4 was minimized for a unit level of border displacement which

Blockwise conjugate gradient methods for image reconstruction in volumetric CT.

PubMed

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.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics

NASA Astrophysics Data System (ADS)

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.

Use of general purpose graphics processing units with MODFLOW

USGS Publications Warehouse

Hughes, Joseph D.; White, Jeremy T.

2013-01-01

To evaluate the use of general-purpose graphics processing units (GPGPUs) to improve the performance of MODFLOW, an unstructured preconditioned conjugate gradient (UPCG) solver has been developed. The UPCG solver uses a compressed sparse row storage scheme and includes Jacobi, zero fill-in incomplete, and modified-incomplete lower-upper (LU) factorization, and generalized least-squares polynomial preconditioners. The UPCG solver also includes options for sequential and parallel solution on the central processing unit (CPU) using OpenMP. For simulations utilizing the GPGPU, all basic linear algebra operations are performed on the GPGPU; memory copies between the central processing unit CPU and GPCPU occur prior to the first iteration of the UPCG solver and after satisfying head and flow criteria or exceeding a maximum number of iterations. The efficiency of the UPCG solver for GPGPU and CPU solutions is benchmarked using simulations of a synthetic, heterogeneous unconfined aquifer with tens of thousands to millions of active grid cells. Testing indicates GPGPU speedups on the order of 2 to 8, relative to the standard MODFLOW preconditioned conjugate gradient (PCG) solver, can be achieved when (1) memory copies between the CPU and GPGPU are optimized, (2) the percentage of time performing memory copies between the CPU and GPGPU is small relative to the calculation time, (3) high-performance GPGPU cards are utilized, and (4) CPU-GPGPU combinations are used to execute sequential operations that are difficult to parallelize. Furthermore, UPCG solver testing indicates GPGPU speedups exceed parallel CPU speedups achieved using OpenMP on multicore CPUs for preconditioners that can be easily parallelized.

Conjugate gradient method for phase retrieval based on the Wirtinger derivative.

PubMed

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.

Reconstruction for limited-projection fluorescence molecular tomography based on projected restarted conjugate gradient normal residual.

PubMed

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

Steepest descent with momentum for quadratic functions is a version of the conjugate gradient method.

PubMed

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.

Weighted graph based ordering techniques for preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

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.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: the square gradient theory and the capillary approach.

PubMed

Wilhelmsen, Øivind; Bedeaux, Dick; Kjelstrup, Signe; Reguera, David

2014-01-14

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wilhelmsen, Øivind, E-mail: oivind.wilhelmsen@ntnu.no; Bedeaux, Dick; Kjelstrup, Signe

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which showsmore » the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.« less

The multigrid preconditioned conjugate gradient method

NASA Technical Reports Server (NTRS)

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.

GPU computing with Kaczmarz’s and other iterative algorithms for linear systems

PubMed Central

Elble, Joseph M.; Sahinidis, Nikolaos V.; Vouzis, Panagiotis

2009-01-01

The graphics processing unit (GPU) is used to solve large linear systems derived from partial differential equations. The differential equations studied are strongly convection-dominated, of various sizes, and common to many fields, including computational fluid dynamics, heat transfer, and structural mechanics. The paper presents comparisons between GPU and CPU implementations of several well-known iterative methods, including Kaczmarz’s, Cimmino’s, component averaging, conjugate gradient normal residual (CGNR), symmetric successive overrelaxation-preconditioned conjugate gradient, and conjugate-gradient-accelerated component-averaged row projections (CARP-CG). Computations are preformed with dense as well as general banded systems. The results demonstrate that our GPU implementation outperforms CPU implementations of these algorithms, as well as previously studied parallel implementations on Linux clusters and shared memory systems. While the CGNR method had begun to fall out of favor for solving such problems, for the problems studied in this paper, the CGNR method implemented on the GPU performed better than the other methods, including a cluster implementation of the CARP-CG method. PMID:20526446

Optimization of non-linear gradient in hydrophobic interaction chromatography for the analytical characterization of antibody-drug conjugates.

PubMed

Bobály, Balázs; Randazzo, Giuseppe Marco; Rudaz, Serge; Guillarme, Davy; Fekete, Szabolcs

2017-01-20

The goal of this work was to evaluate the potential of non-linear gradients in hydrophobic interaction chromatography (HIC), to improve the separation between the different homologous species (drug-to-antibody, DAR) of commercial antibody-drug conjugates (ADC). The selectivities between Brentuximab Vedotin species were measured using three different gradient profiles, namely linear, power function based and logarithmic ones. The logarithmic gradient provides the most equidistant retention distribution for the DAR species and offers the best overall separation of cysteine linked ADC in HIC. Another important advantage of the logarithmic gradient, is its peak focusing effect for the DAR0 species, which is particularly useful to improve the quantitation limit of DAR0. Finally, the logarithmic behavior of DAR species of ADC in HIC was modelled using two different approaches, based on i) the linear solvent strength theory (LSS) and two scouting linear gradients and ii) a new derived equation and two logarithmic scouting gradients. In both cases, the retention predictions were excellent and systematically below 3% compared to the experimental values. Copyright © 2016 Elsevier B.V. All rights reserved.

Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods

NASA Astrophysics Data System (ADS)

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.

Solving large mixed linear models using preconditioned conjugate gradient iteration.

PubMed

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.

Digital transceiver design for two-way AF-MIMO relay systems with imperfect CSI

NASA Astrophysics Data System (ADS)

Hu, Chia-Chang; Chou, Yu-Fei; Chen, Kui-He

2013-09-01

In the paper, combined optimization of the terminal precoders/equalizers and single-relay precoder is proposed for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-way single-relay system with correlated channel uncertainties. Both terminal transceivers and relay precoding matrix are designed based on the minimum mean square error (MMSE) criterion when terminals are unable to erase completely self-interference due to imperfect correlated channel state information (CSI). This robust joint optimization problem of beamforming and precoding matrices under power constraints belongs to neither concave nor convex so that a nonlinear matrix-form conjugate gradient (MCG) algorithm is applied to explore local optimal solutions. Simulation results show that the robust transceiver design is able to overcome effectively the loss of bit-error-rate (BER) due to inclusion of correlated channel uncertainties and residual self-interference.

Particle-in-a-box model of exciton absorption and electroabsorption in conjugated polymers

NASA Astrophysics Data System (ADS)

Pedersen, Thomas G.

2000-12-01

The recently proposed particle-in-a-box model of one-dimensional excitons in conjugated polymers is applied in calculations of optical absorption and electroabsorption spectra. It is demonstrated that for polymers of long conjugation length a superposition of single exciton resonances produces a line shape characterized by a square-root singularity in agreement with experimental spectra near the absorption edge. The effects of finite conjugation length on both absorption and electroabsorption spectra are analyzed.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, G. H.

1985-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90 percent for sufficiently large problems.

Hybrid DFP-CG method for solving unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Osman, Wan Farah Hanan Wan; Asrul Hery Ibrahim, Mohd; Mamat, Mustafa

2017-09-01

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

Finite elements and the method of conjugate gradients on a concurrent processor

NASA Technical Reports Server (NTRS)

Lyzenga, G. A.; Raefsky, A.; Hager, B. H.

1984-01-01

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90% for sufficiently large problems.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

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.

Projection methods for line radiative transfer in spherical media.

NASA Astrophysics Data System (ADS)

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

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

Uncertainty based pressure reconstruction from velocity measurement with generalized least squares

NASA Astrophysics Data System (ADS)

Zhang, Jiacheng; Scalo, Carlo; Vlachos, Pavlos

2017-11-01

A method using generalized least squares reconstruction of instantaneous pressure field from velocity measurement and velocity uncertainty is introduced and applied to both planar and volumetric flow data. Pressure gradients are computed on a staggered grid from flow acceleration. The variance-covariance matrix of the pressure gradients is evaluated from the velocity uncertainty by approximating the pressure gradient error to a linear combination of velocity errors. An overdetermined system of linear equations which relates the pressure and the computed pressure gradients is formulated and then solved using generalized least squares with the variance-covariance matrix of the pressure gradients. By comparing the reconstructed pressure field against other methods such as solving the pressure Poisson equation, the omni-directional integration, and the ordinary least squares reconstruction, generalized least squares method is found to be more robust to the noise in velocity measurement. The improvement on pressure result becomes more remarkable when the velocity measurement becomes less accurate and more heteroscedastic. The uncertainty of the reconstructed pressure field is also quantified and compared across the different methods.

Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics.

PubMed

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.

Local gravity field modeling using spherical radial basis functions and a genetic algorithm

NASA Astrophysics Data System (ADS)

Mahbuby, Hany; Safari, Abdolreza; Foroughi, Ismael

2017-05-01

Spherical Radial Basis Functions (SRBFs) can express the local gravity field model of the Earth if they are parameterized optimally on or below the Bjerhammar sphere. This parameterization is generally defined as the shape of the base functions, their number, center locations, bandwidths, and scale coefficients. The number/location and bandwidths of the base functions are the most important parameters for accurately representing the gravity field; once they are determined, the scale coefficients can then be computed accordingly. In this study, the point-mass kernel, as the simplest shape of SRBFs, is chosen to evaluate the synthesized free-air gravity anomalies over the rough area in Auvergne and GNSS/Leveling points (synthetic height anomalies) are used to validate the results. A two-step automatic approach is proposed to determine the optimum distribution of the base functions. First, the location of the base functions and their bandwidths are found using the genetic algorithm; second, the conjugate gradient least squares method is employed to estimate the scale coefficients. The proposed methodology shows promising results. On the one hand, when using the genetic algorithm, the base functions do not need to be set to a regular grid and they can move according to the roughness of topography. In this way, the models meet the desired accuracy with a low number of base functions. On the other hand, the conjugate gradient method removes the bias between derived quasigeoid heights from the model and from the GNSS/leveling points; this means there is no need for a corrector surface. The numerical test on the area of interest revealed an RMS of 0.48 mGal for the differences between predicted and observed gravity anomalies, and a corresponding 9 cm for the differences in GNSS/leveling points.

Direct and accelerated parameter mapping using the unscented Kalman filter.

PubMed

Zhao, Li; Feng, Xue; Meyer, Craig H

2016-05-01

To accelerate parameter mapping using a new paradigm that combines image reconstruction and model regression as a parameter state-tracking problem. In T2 mapping, the T2 map is first encoded in parameter space by multi-TE measurements and then encoded by Fourier transformation with readout/phase encoding gradients. Using a state transition function and a measurement function, the unscented Kalman filter can describe T2 mapping as a dynamic system and directly estimate the T2 map from the k-space data. The proposed method was validated with a numerical brain phantom and volunteer experiments with a multiple-contrast spin echo sequence. Its performance was compared with a conjugate-gradient nonlinear inversion method at undersampling factors of 2 to 8. An accelerated pulse sequence was developed based on this method to achieve prospective undersampling. Compared with the nonlinear inversion reconstruction, the proposed method had higher precision, improved structural similarity and reduced normalized root mean squared error, with acceleration factors up to 8 in numerical phantom and volunteer studies. This work describes a new perspective on parameter mapping by state tracking. The unscented Kalman filter provides a highly accelerated and efficient paradigm for T2 mapping. © 2015 Wiley Periodicals, Inc.

The truncated conjugate gradient (TCG), a non-iterative/fixed-cost strategy for computing polarization in molecular dynamics: Fast evaluation of analytical forces

NASA Astrophysics Data System (ADS)

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.

The truncated conjugate gradient (TCG), a non-iterative/fixed-cost strategy for computing polarization in molecular dynamics: Fast evaluation of analytical forces.

PubMed

Aviat, Félix; Lagardère, Louis; Piquemal, Jean-Philip

2017-10-28

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.

Compressive sensing of electrocardiogram signals by promoting sparsity on the second-order difference and by using dictionary learning.

PubMed

Pant, Jeevan K; Krishnan, Sridhar

2014-04-01

A new algorithm for the reconstruction of electrocardiogram (ECG) signals and a dictionary learning algorithm for the enhancement of its reconstruction performance for a class of signals are proposed. The signal reconstruction algorithm is based on minimizing the lp pseudo-norm of the second-order difference, called as the lp(2d) pseudo-norm, of the signal. The optimization involved is carried out using a sequential conjugate-gradient algorithm. The dictionary learning algorithm uses an iterative procedure wherein a signal reconstruction and a dictionary update steps are repeated until a convergence criterion is satisfied. The signal reconstruction step is implemented by using the proposed signal reconstruction algorithm and the dictionary update step is implemented by using the linear least-squares method. Extensive simulation results demonstrate that the proposed algorithm yields improved reconstruction performance for temporally correlated ECG signals relative to the state-of-the-art lp(1d)-regularized least-squares and Bayesian learning based algorithms. Also for a known class of signals, the reconstruction performance of the proposed algorithm can be improved by applying it in conjunction with a dictionary obtained using the proposed dictionary learning algorithm.

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix [A projected preconditioned conjugate gradient algorithm for computing a large eigenspace of a Hermitian matrix

DOE PAGES

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

2015-02-25

Here, 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 optimalmore » 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.« less

Conjugate gradient coupled with multigrid for an indefinite problem

NASA Technical Reports Server (NTRS)

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.

Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction.

PubMed

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.

A fast pulse design for parallel excitation with gridding conjugate gradient.

PubMed

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.

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization

PubMed Central

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. PMID:26381742

A Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization.

PubMed

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.

Uniform two-dimensional square assemblies from conjugated block copolymers driven by π–π interactions with controllable sizes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han, Liang; Wang, Meijing; Jia, Xiangmeng

Two-dimensional (2-D) micro- and nano- architectures are attractive because of their unique properties caused by their ultrathin and flat morphologies. However, the formation of 2-D supramolecular highly symmetrical structures with considerable control is still a major challenge. Here, we presented a simple approach for the preparation of regular and homogeneous 2-D fluorescent square noncrystallization micelles with conjugated diblock copolymers PPV12-b-P2VPn through a process of dissolving-cooling-aging. The scale of the formed micelles could be controlled by the ratio of PPV/P2VP blocks and the concentration of the solution. The forming process of the platelet square micelles was analyzed by UV-Vis, DLS andmore » SLS, while the molecular arrangement was characterized by GIXD. The results revealed that the micelles of PPV12-b-P2VPn initially form 1-D structures and then grow into 2-D structures in solution, and the growth is driven by intermolecular π-π interactions with the PPV12 blocks. The formation of 2-D square micelles is induced by herringbone arrangement of the molecules, which is closely related to the presence of the branched alkyl chains attached to conjugated PPV12 cores.« less

Radiofrequency pulse design using nonlinear gradient magnetic fields.

PubMed

Kopanoglu, Emre; Constable, R Todd

2015-09-01

An iterative k-space trajectory and radiofrequency (RF) pulse design method is proposed for excitation using nonlinear gradient magnetic fields. The spatial encoding functions (SEFs) generated by nonlinear gradient fields are linearly dependent in Cartesian coordinates. Left uncorrected, this may lead to flip angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a matching pursuit algorithm, and the RF pulse is designed using a conjugate gradient algorithm. Three variants of the proposed approach are given: the full algorithm, a computationally cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. The method is compared with other iterative (matching pursuit and conjugate gradient) and noniterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity. An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. © 2014 Wiley Periodicals, Inc.

Superlinear convergence estimates for a conjugate gradient method for the biharmonic equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, R.H.; Delillo, T.K.; Horn, M.A.

1998-01-01

The method of Muskhelishvili for solving the biharmonic equation using conformal mapping is investigated. In [R.H. Chan, T.K. DeLillo, and M.A. Horn, SIAM J. Sci. Comput., 18 (1997), pp. 1571--1582] it was shown, using the Hankel structure, that the linear system in [N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a Hoelder class.

Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

NASA Technical Reports Server (NTRS)

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.

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

Analysis of Artificial Neural Network Backpropagation Using Conjugate Gradient Fletcher Reeves In The Predicting Process

NASA Astrophysics Data System (ADS)

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.

Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

2014-01-01

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

Panel flutter optimization by gradient projection

NASA Technical Reports Server (NTRS)

Pierson, B. L.

1975-01-01

A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.

River suspended sediment estimation by climatic variables implication: Comparative study among soft computing techniques

NASA Astrophysics Data System (ADS)

Kisi, Ozgur; Shiri, Jalal

2012-06-01

Estimating sediment volume carried by a river is an important issue in water resources engineering. This paper compares the accuracy of three different soft computing methods, Artificial Neural Networks (ANNs), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Gene Expression Programming (GEP), in estimating daily suspended sediment concentration on rivers by using hydro-meteorological data. The daily rainfall, streamflow and suspended sediment concentration data from Eel River near Dos Rios, at California, USA are used as a case study. The comparison results indicate that the GEP model performs better than the other models in daily suspended sediment concentration estimation for the particular data sets used in this study. Levenberg-Marquardt, conjugate gradient and gradient descent training algorithms were used for the ANN models. Out of three algorithms, the Conjugate gradient algorithm was found to be better than the others.

A Parallel Nonrigid Registration Algorithm Based on B-Spline for Medical Images.

PubMed

Du, Xiaogang; Dang, Jianwu; Wang, Yangping; Wang, Song; Lei, Tao

2016-01-01

The nonrigid registration algorithm based on B-spline Free-Form Deformation (FFD) plays a key role and is widely applied in medical image processing due to the good flexibility and robustness. However, it requires a tremendous amount of computing time to obtain more accurate registration results especially for a large amount of medical image data. To address the issue, a parallel nonrigid registration algorithm based on B-spline is proposed in this paper. First, the Logarithm Squared Difference (LSD) is considered as the similarity metric in the B-spline registration algorithm to improve registration precision. After that, we create a parallel computing strategy and lookup tables (LUTs) to reduce the complexity of the B-spline registration algorithm. As a result, the computing time of three time-consuming steps including B-splines interpolation, LSD computation, and the analytic gradient computation of LSD, is efficiently reduced, for the B-spline registration algorithm employs the Nonlinear Conjugate Gradient (NCG) optimization method. Experimental results of registration quality and execution efficiency on the large amount of medical images show that our algorithm achieves a better registration accuracy in terms of the differences between the best deformation fields and ground truth and a speedup of 17 times over the single-threaded CPU implementation due to the powerful parallel computing ability of Graphics Processing Unit (GPU).

An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

NASA Astrophysics Data System (ADS)

Mönkölä, Sanna

2013-06-01

This study considers developing numerical solution techniques for the computer simulations of time-harmonic fluid-structure interaction between acoustic and elastic waves. The focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements. We concentrate on the model, in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement. Traditionally, the complex-valued time-harmonic equations are used for solving the time-harmonic problems. Instead of that, we focus on finding periodic solutions without solving the time-harmonic problems directly. The time-dependent equations can be simulated with respect to time until a time-harmonic solution is reached, but the approach suffers from poor convergence. To overcome this challenge, we follow the approach first suggested and developed for the acoustic wave equations by Bristeau, Glowinski, and Périaux. Thus, we accelerate the convergence rate by employing a controllability method. The problem is formulated as a least-squares optimization problem, which is solved with the conjugate gradient (CG) algorithm. Computation of the gradient of the functional is done directly for the discretized problem. A graph-based multigrid method is used for preconditioning the CG algorithm.

RF Pulse Design using Nonlinear Gradient Magnetic Fields

PubMed Central

Kopanoglu, Emre; Constable, R. Todd

2014-01-01

Purpose An iterative k-space trajectory and radio-frequency (RF) pulse design method is proposed for Excitation using Nonlinear Gradient Magnetic fields (ENiGMa). Theory and Methods The spatial encoding functions (SEFs) generated by nonlinear gradient fields (NLGFs) are linearly dependent in Cartesian-coordinates. Left uncorrected, this may lead to flip-angle variations in excitation profiles. In the proposed method, SEFs (k-space samples) are selected using a Matching-Pursuit algorithm, and the RF pulse is designed using a Conjugate-Gradient algorithm. Three variants of the proposed approach are given: the full-algorithm, a computationally-cheaper version, and a third version for designing spoke-based trajectories. The method is demonstrated for various target excitation profiles using simulations and phantom experiments. Results The method is compared to other iterative (Matching-Pursuit and Conjugate Gradient) and non-iterative (coordinate-transformation and Jacobian-based) pulse design methods as well as uniform density spiral and EPI trajectories. The results show that the proposed method can increase excitation fidelity significantly. Conclusion An iterative method for designing k-space trajectories and RF pulses using nonlinear gradient fields is proposed. The method can either be used for selecting the SEFs individually to guide trajectory design, or can be adapted to design and optimize specific trajectories of interest. PMID:25203286

Large-scale computation of incompressible viscous flow by least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Efficient L1 regularization-based reconstruction for fluorescent molecular tomography using restarted nonlinear conjugate gradient.

PubMed

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.

New hybrid conjugate gradient methods with the generalized Wolfe line search.

PubMed

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.

Noise effect in an improved conjugate gradient algorithm to invert particle size distribution and the algorithm amendment.

PubMed

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.

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1990-01-01

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

A conjugate gradient method with descent properties under strong Wolfe line search

NASA Astrophysics Data System (ADS)

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.

Conjugate gradient determination of optimal plane changes for a class of three-impulse transfers between noncoplanar circular orbits

NASA Technical Reports Server (NTRS)

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.

A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search

NASA Astrophysics Data System (ADS)

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.

A modified conjugate gradient coefficient with inexact line search for unconstrained optimization

NASA Astrophysics Data System (ADS)

Aini, Nurul; Rivaie, Mohd; Mamat, Mustafa

2016-11-01

Conjugate gradient (CG) method is a line search algorithm mostly known for its wide application in solving unconstrained optimization problems. Its low memory requirements and global convergence properties makes it one of the most preferred method in real life application such as in engineering and business. In this paper, we present a new CG method based on AMR* and CD method for solving unconstrained optimization functions. The resulting algorithm is proven to have both the sufficient descent and global convergence properties under inexact line search. Numerical tests are conducted to assess the effectiveness of the new method in comparison to some previous CG methods. The results obtained indicate that our method is indeed superior.

Method to create gradient index in a polymer

DOEpatents

Dirk, Shawn M; Johnson, Ross Stefan; Boye, Robert; Descour, Michael R; Sweatt, William C; Wheeler, David R; Kaehr, Bryan James

2014-10-14

Novel photo-writable and thermally switchable polymeric materials exhibit a refractive index change of .DELTA.n.gtoreq.1.0 when exposed to UV light or heat. For example, lithography can be used to convert a non-conjugated precursor polymer to a conjugated polymer having a higher index-of-refraction. Further, two-photon lithography can be used to pattern high-spatial frequency structures.

Luminance gradient at object borders communicates object location to the human oculomotor system.

PubMed

Kilpeläinen, Markku; Georgeson, Mark A

2018-01-25

The locations of objects in our environment constitute arguably the most important piece of information our visual system must convey to facilitate successful visually guided behaviour. However, the relevant objects are usually not point-like and do not have one unique location attribute. Relatively little is known about how the visual system represents the location of such large objects as visual processing is, both on neural and perceptual level, highly edge dominated. In this study, human observers made saccades to the centres of luminance defined squares (width 4 deg), which appeared at random locations (8 deg eccentricity). The phase structure of the square was manipulated such that the points of maximum luminance gradient at the square's edges shifted from trial to trial. The average saccade endpoints of all subjects followed those shifts in remarkable quantitative agreement. Further experiments showed that the shifts were caused by the edge manipulations, not by changes in luminance structure near the centre of the square or outside the square. We conclude that the human visual system programs saccades to large luminance defined square objects based on edge locations derived from the points of maximum luminance gradients at the square's edges.

Primer vector theory and applications

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1975-01-01

A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed.

Computational trigonometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gustafson, K.

1994-12-31

By means of the author`s earlier theory of antieigenvalues and antieigenvectors, a new computational approach to iterative methods is presented. This enables an explicit trigonometric understanding of iterative convergence and provides new insights into the sharpness of error bounds. Direct applications to Gradient descent, Conjugate gradient, GCR(k), Orthomin, CGN, GMRES, CGS, and other matrix iterative schemes will be given.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients.

PubMed

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.

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging.

PubMed

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.

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

NASA Astrophysics Data System (ADS)

Wang, Tai-Han; Huang, Da-Nian; Ma, Guo-Qing; Meng, Zhao-Hai; Li, Ye

2017-06-01

With the continuous development of full tensor gradiometer (FTG) measurement techniques, three-dimensional (3D) inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit (GPU) and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation (SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm (ICCG). Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit (CPU). Real airborne gravity-gradiometry data from Vinton salt dome (southwest Louisiana, USA) are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Conjugate Heat Transfer in Rayleigh-Bénard Convection in a Square Enclosure

PubMed Central

Hashim, Ishak

2014-01-01

Conjugate natural convection-conduction heat transfer in a square enclosure with a finite wall thickness is studied numerically in the present paper. The governing parameters considered are the Rayleigh number (5 × 103 ≤ Ra ≤ 106), the wall-to-fluid thermal conductivity ratio (0.5 ≤ Kr ≤ 10), and the ratio of wall thickness to its height (0.2 ≤ D ≤ 0.4). The staggered grid arrangement together with MAC method was employed to solve the governing equations. It is found that the fluid flow and the heat transfer can be controlled by the thickness of the bottom wall, the thermal conductivity ratio, and the Rayleigh number. PMID:24971390

On the inversion of geodetic integrals defined over the sphere using 1-D FFT

NASA Astrophysics Data System (ADS)

García, R. V.; Alejo, C. A.

2005-08-01

An iterative method is presented which performs inversion of integrals defined over the sphere. The method is based on one-dimensional fast Fourier transform (1-D FFT) inversion and is implemented with the projected Landweber technique, which is used to solve constrained least-squares problems reducing the associated 1-D cyclic-convolution error. The results obtained are as precise as the direct matrix inversion approach, but with better computational efficiency. A case study uses the inversion of Hotine’s integral to obtain gravity disturbances from geoid undulations. Numerical convergence is also analyzed and comparisons with respect to the direct matrix inversion method using conjugate gradient (CG) iteration are presented. Like the CG method, the number of iterations needed to get the optimum (i.e., small) error decreases as the measurement noise increases. Nevertheless, for discrete data given over a whole parallel band, the method can be applied directly without implementing the projected Landweber method, since no cyclic convolution error exists.

Prediction of municipal solid waste generation using nonlinear autoregressive network.

PubMed

Younes, Mohammad K; Nopiah, Z M; Basri, N E Ahmad; Basri, H; Abushammala, Mohammed F M; Maulud, K N A

2015-12-01

Most of the developing countries have solid waste management problems. Solid waste strategic planning requires accurate prediction of the quality and quantity of the generated waste. In developing countries, such as Malaysia, the solid waste generation rate is increasing rapidly, due to population growth and new consumption trends that characterize society. This paper proposes an artificial neural network (ANN) approach using feedforward nonlinear autoregressive network with exogenous inputs (NARX) to predict annual solid waste generation in relation to demographic and economic variables like population number, gross domestic product, electricity demand per capita and employment and unemployment numbers. In addition, variable selection procedures are also developed to select a significant explanatory variable. The model evaluation was performed using coefficient of determination (R(2)) and mean square error (MSE). The optimum model that produced the lowest testing MSE (2.46) and the highest R(2) (0.97) had three inputs (gross domestic product, population and employment), eight neurons and one lag in the hidden layer, and used Fletcher-Powell's conjugate gradient as the training algorithm.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu

2018-05-01

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

Simultaneous travel time tomography for updating both velocity and reflector geometry in triangular/tetrahedral cell model

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; He, Lei-yu; Li, Xing-wang; Sun, Jia-yu

2017-12-01

To conduct forward and simultaneous inversion in a complex geological model, including an irregular topography (or irregular reflector or velocity anomaly), we in this paper combined our previous multiphase arrival tracking method (referred as triangular shortest-path method, TSPM) in triangular (2D) or tetrahedral (3D) cell model and a linearized inversion solver (referred to as damped minimum norms and constrained least squares problem solved using the conjugate gradient method, DMNCLS-CG) to formulate a simultaneous travel time inversion method for updating both velocity and reflector geometry by using multiphase arrival times. In the triangular/tetrahedral cells, we deduced the partial derivative of velocity variation with respective to the depth change of reflector. The numerical simulation results show that the computational accuracy can be tuned to a high precision in forward modeling and the irregular velocity anomaly and reflector geometry can be accurately captured in the simultaneous inversion, because the triangular/tetrahedral cell can be easily used to stitch the irregular topography or subsurface interface.

A conjugate gradient method for solving the non-LTE line radiation transfer problem

NASA Astrophysics Data System (ADS)

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.

Algorithms for accelerated convergence of adaptive PCA.

PubMed

Chatterjee, C; Kang, Z; Roychowdhury, V P

2000-01-01

We derive and discuss new adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja, Sanger, and Xu. It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: 1) gradient descent; 2) steepest descent; 3) conjugate direction; and 4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods.We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.

Three filters for visualization of phase objects with large variations of phase gradients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sagan, Arkadiusz; Antosiewicz, Tomasz J.; Szoplik, Tomasz

2009-02-20

We propose three amplitude filters for visualization of phase objects. They interact with the spectra of pure-phase objects in the frequency plane and are based on tangent and error functions as well as antisymmetric combination of square roots. The error function is a normalized form of the Gaussian function. The antisymmetric square-root filter is composed of two square-root filters to widen its spatial frequency spectral range. Their advantage over other known amplitude frequency-domain filters, such as linear or square-root graded ones, is that they allow high-contrast visualization of objects with large variations of phase gradients.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

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.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

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.

Conjugation of gold nanoparticles and recombinant human endostatin modulates vascular normalization via interruption of anterior gradient 2-mediated angiogenesis.

PubMed

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 vessels by interfering anterior gradient 2-mediated angiogenesis in metastatic colorectal cancer.

Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

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.

Fast conjugate phase image reconstruction based on a Chebyshev approximation to correct for B0 field inhomogeneity and concomitant gradients

PubMed Central

Chen, Weitian; Sica, Christopher T.; Meyer, Craig H.

2008-01-01

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. PMID:18956462

A Parallel Nonrigid Registration Algorithm Based on B-Spline for Medical Images

PubMed Central

Wang, Yangping; Wang, Song

2016-01-01

The nonrigid registration algorithm based on B-spline Free-Form Deformation (FFD) plays a key role and is widely applied in medical image processing due to the good flexibility and robustness. However, it requires a tremendous amount of computing time to obtain more accurate registration results especially for a large amount of medical image data. To address the issue, a parallel nonrigid registration algorithm based on B-spline is proposed in this paper. First, the Logarithm Squared Difference (LSD) is considered as the similarity metric in the B-spline registration algorithm to improve registration precision. After that, we create a parallel computing strategy and lookup tables (LUTs) to reduce the complexity of the B-spline registration algorithm. As a result, the computing time of three time-consuming steps including B-splines interpolation, LSD computation, and the analytic gradient computation of LSD, is efficiently reduced, for the B-spline registration algorithm employs the Nonlinear Conjugate Gradient (NCG) optimization method. Experimental results of registration quality and execution efficiency on the large amount of medical images show that our algorithm achieves a better registration accuracy in terms of the differences between the best deformation fields and ground truth and a speedup of 17 times over the single-threaded CPU implementation due to the powerful parallel computing ability of Graphics Processing Unit (GPU). PMID:28053653

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations.

PubMed

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 algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations

PubMed Central

2016-01-01

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 algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations. PMID:28068773

Conjugate-gradient optimization method for orbital-free density functional calculations.

PubMed

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.

An efficient impedance method for induced field evaluation based on a stabilized Bi-conjugate gradient algorithm.

PubMed

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.

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.

PubMed

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.

High-fidelity phase and amplitude control of phase-only computer generated holograms using conjugate gradient minimisation.

PubMed

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.

LC-NMR Technique in the Analysis of Phytosterols in Natural Extracts

PubMed Central

Horník, Štěpán; Sajfrtová, Marie; Sýkora, Jan; Březinová, Anna; Wimmer, Zdeněk

2013-01-01

The ability of LC-NMR to detect simultaneously free and conjugated phytosterols in natural extracts was tested. The advantages and disadvantages of a gradient HPLC-NMR method were compared to the fast composition screening using SEC-NMR method. Fractions of free and conjugated phytosterols were isolated and analyzed by isocratic HPLC-NMR methods. The results of qualitative and quantitative analyses were in a good agreement with the literature data. PMID:24455424

Distributed Memory Parallel Computing with SEAWAT

NASA Astrophysics Data System (ADS)

Verkaik, J.; Huizer, S.; van Engelen, J.; Oude Essink, G.; Ram, R.; Vuik, K.

2017-12-01

Fresh groundwater reserves in coastal aquifers are threatened by sea-level rise, extreme weather conditions, increasing urbanization and associated groundwater extraction rates. To counteract these threats, accurate high-resolution numerical models are required to optimize the management of these precious reserves. The major model drawbacks are long run times and large memory requirements, limiting the predictive power of these models. Distributed memory parallel computing is an efficient technique for reducing run times and memory requirements, where the problem is divided over multiple processor cores. A new Parallel Krylov Solver (PKS) for SEAWAT is presented. PKS has recently been applied to MODFLOW and includes Conjugate Gradient (CG) and Biconjugate Gradient Stabilized (BiCGSTAB) linear accelerators. Both accelerators are preconditioned by an overlapping additive Schwarz preconditioner in a way that: a) subdomains are partitioned using Recursive Coordinate Bisection (RCB) load balancing, b) each subdomain uses local memory only and communicates with other subdomains by Message Passing Interface (MPI) within the linear accelerator, c) it is fully integrated in SEAWAT. Within SEAWAT, the PKS-CG solver replaces the Preconditioned Conjugate Gradient (PCG) solver for solving the variable-density groundwater flow equation and the PKS-BiCGSTAB solver replaces the Generalized Conjugate Gradient (GCG) solver for solving the advection-diffusion equation. PKS supports the third-order Total Variation Diminishing (TVD) scheme for computing advection. Benchmarks were performed on the Dutch national supercomputer (https://userinfo.surfsara.nl/systems/cartesius) using up to 128 cores, for a synthetic 3D Henry model (100 million cells) and the real-life Sand Engine model ( 10 million cells). The Sand Engine model was used to investigate the potential effect of the long-term morphological evolution of a large sand replenishment and climate change on fresh groundwater resources. Speed-ups up to 40 were obtained with the new PKS solver.

Scintillation Reduction using Conjugate-Plane Imaging

NASA Astrophysics Data System (ADS)

Vander Haagen, Gary A.

2017-06-01

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, f-7 telescope.

New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

PubMed

Bouchard, M

2001-01-01

In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

Ion temperature gradient driven transport in tokamaks with square shaping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Joiner, N.; Dorland, W.

2010-06-15

Advanced tokamak schemes which may offer significant improvement to plasma confinement on the usual large aspect ratio Dee-shaped flux surface configuration are of great interest to the fusion community. One possibility is to introduce square shaping to the flux surfaces. The gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1996)] is used to study linear stability and the resulting nonlinear thermal transport of the ion temperature gradient driven (ITG) mode in tokamak equilibria with square shaping. The maximum linear growth rate of ITG modes is increased by negative squareness (diamond shaping) and reduced by positive values (square shaping).more » The dependence of thermal transport produced by saturated ITG instabilities on squareness is not as clear. The overall trend follows that of the linear instability, heat and particle fluxes increase with negative squareness and decrease with positive squareness. This is contradictory to recent experimental results [Holcomb et al., Phys. Plasmas 16, 056116 (2009)] which show a reduction in transport with negative squareness. This may be reconciled as a reduction in transport (consistent with the experiment) is observed at small negative values of the squareness parameter.« less

Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms

NASA Technical Reports Server (NTRS)

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.

Using Elman recurrent neural networks with conjugate gradient algorithm in determining the anesthetic the amount of anesthetic medicine to be applied.

PubMed

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.

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Poole, E.L.

1986-01-01

This research is concerned with the solution on vector computers of linear systems of equations. Ax = b, where A is a large, sparse symmetric positive definite matrix with non-zero elements lying only along a few diagonals of the matrix. The system is solved using the incomplete Cholesky conjugate gradient method (ICCG). Multi-color orderings are used of the unknowns in the linear system to obtain p-color matrices for which a no-fill block ICCG method is implemented on the CYBER 205 with O(N/p) length vector operations in both the decomposition of A and, more importantly, in the forward and back solvesmore » necessary at each iteration of the method. (N is the number of unknowns and p is a small constant). A p-colored matrix is a matrix that can be partitioned into a p x p block matrix where the diagonal blocks are diagonal matrices. The matrix is stored by diagonals and matrix multiplication by diagonals is used to carry out the decomposition of A and the forward and back solves. Additionally, if the vectors across adjacent blocks line up, then some of the overhead associated with vector startups can be eliminated in the matrix vector multiplication necessary at each conjugate gradient iteration. Necessary and sufficient conditions are given to determine which multi-color orderings of the unknowns correspond to p-color matrices, and a process is indicated for choosing multi-color orderings.« less

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

NASA Technical Reports Server (NTRS)

Madyastha, Raghavendra K.; Aazhang, Behnaam; Henson, Troy F.; Huxhold, Wendy L.

1992-01-01

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

The Atacama Cosmology Telescope: Data Characterization and Map Making

NASA Technical Reports Server (NTRS)

Duenner, Rolando; Hasselfield, Matthew; Marriage, Tobias A.; Sievers, Jon; Acquaviva, Viviana; Addison, Graeme E.; Ade, Peter A. R.; Aguirre, Paula; Amiri, Mandana; Appel, John William;

Scintillation Reduction using Conjugate-Plane Imaging (Abstract)

NASA Astrophysics Data System (ADS)

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.

Evaluation of corrective reconstruction methods using a 3D cardiac-torso phantom and bull's-eye plots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, X.D.; Tsui, B.M.W.; Gregoriou, G.K.

The goal of the investigation was to study the effectiveness of the corrective reconstruction methods in cardiac SPECT using a realistic phantom and to qualitatively and quantitatively evaluate the reconstructed images using bull's-eye plots. A 3D mathematical phantom which realistically models the anatomical structures of the cardiac-torso region of patients was used. The phantom allows simulation of both the attenuation distribution and the uptake of radiopharmaceuticals in different organs. Also, the phantom can be easily modified to simulate different genders and variations in patient anatomy. Two-dimensional projection data were generated from the phantom and included the effects of attenuation andmore » detector response blurring. The reconstruction methods used in the study included the conventional filtered backprojection (FBP) with no attenuation compensation, and the first-order Chang algorithm, an iterative filtered backprojection algorithm (IFBP), the weighted least square conjugate gradient algorithm and the ML-EM algorithm with non-uniform attenuation compensation. The transaxial reconstructed images were rearranged into short-axis slices from which bull's-eye plots of the count density distribution in the myocardium were generated.« less

Hessian-based norm regularization for image restoration with biomedical applications.

PubMed

Lefkimmiatis, Stamatios; Bourquard, Aurélien; Unser, Michael

2012-03-01

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.

Nonnegative least-squares image deblurring: improved gradient projection approaches

NASA Astrophysics Data System (ADS)

Benvenuto, F.; Zanella, R.; Zanni, L.; Bertero, M.

2010-02-01

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the ill-posedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures

NASA Technical Reports Server (NTRS)

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.

Aerodynamic shape optimization using preconditioned conjugate gradient methods

NASA Technical Reports Server (NTRS)

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.

On a concurrent element-by-element preconditioned conjugate gradient algorithm for multiple load cases

NASA Technical Reports Server (NTRS)

Watson, Brian; Kamat, M. P.

1990-01-01

Element-by-element preconditioned conjugate gradient (EBE-PCG) algorithms have been advocated for use in parallel/vector processing environments as being superior to the conventional LDL(exp T) decomposition algorithm for single load cases. Although there may be some advantages in using such algorithms for a single load case, when it comes to situations involving multiple load cases, the LDL(exp T) decomposition algorithm would appear to be decidedly more cost-effective. The authors have outlined an EBE-PCG algorithm suitable for multiple load cases and compared its effectiveness to the highly efficient LDL(exp T) decomposition scheme. The proposed algorithm offers almost no advantages over the LDL(exp T) algorithm for the linear problems investigated on the Alliant FX/8. However, there may be some merit in the algorithm in solving nonlinear problems with load incrementation, but that remains to be investigated.

Rapid and accurate reversed-phase high-performance liquid chromatographic determination of conjugated bile acids in human bile for routine clinical applications. Therapeutic control during gallstone dissolution therapy.

PubMed

Swobodnik, W; Klüppelberg, U; Wechsler, J G; Volz, M; Normandin, G; Ditschuneit, H

1985-05-03

This paper introduces a new method to detect the taurine and glycine conjugates of five different bile acids (cholic acid, deoxycholic acid, chenodeoxycholic acid, ursodeoxycholic acid and lithocholic acid) in human bile. Advantages of this method are sufficient separation of compounds within a short period of time and a high rate of reproducibility. Using a mobile phase gradient of acetonitrile and water, modified with tetrabutylammonium hydrogen sulphate (0.0075 mol/l), we were able to maximize the differentiation between ursodeoxycholic acid and lithocholic acid, which is of primary interest during conservative gallstone dissolution therapy. Use of this gradient reduced analysis time to less than 0.5 h. Recovery rates for this modified method ranged from 94% to 100%, and reproducibility was 98%, sufficient for routine clinical applications.

Improved Conjugate Gradient Bundle Adjustment of Dunhuang Wall Painting Images

NASA Astrophysics Data System (ADS)

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.

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Jin, Jian-Ming; Volakis, John L.

1990-01-01

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates

NASA Astrophysics Data System (ADS)

Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma

2016-10-01

This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.

Low-memory iterative density fitting.

PubMed

Grajciar, Lukáš

2015-07-30

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

Improving Global Mass Flux Solutions from Gravity Recovery and Climate Experiment (GRACE) Through Forward Modeling and Continuous Time Correlation

NASA Technical Reports Server (NTRS)

Sabaka, T. J.; Rowlands, D. D.; Luthcke, S. B.; Boy, J.-P.

2010-01-01

We describe Earth's mass flux from April 2003 through November 2008 by deriving a time series of mas cons on a global 2deg x 2deg equal-area grid at 10 day intervals. We estimate the mass flux directly from K band range rate (KBRR) data provided by the Gravity Recovery and Climate Experiment (GRACE) mission. Using regularized least squares, we take into account the underlying process dynamics through continuous space and time-correlated constraints. In addition, we place the mascon approach in the context of other filtering techniques, showing its equivalence to anisotropic, nonsymmetric filtering, least squares collocation, and Kalman smoothing. We produce mascon time series from KBRR data that have and have not been corrected (forward modeled) for hydrological processes and fmd that the former produce superior results in oceanic areas by minimizing signal leakage from strong sources on land. By exploiting the structure of the spatiotemporal constraints, we are able to use a much more efficient (in storage and computation) inversion algorithm based upon the conjugate gradient method. This allows us to apply continuous rather than piecewise continuous time-correlated constraints, which we show via global maps and comparisons with ocean-bottom pressure gauges, to produce time series with reduced random variance and full systematic signal. Finally, we present a preferred global model, a hybrid whose oceanic portions are derived using forward modeling of hydrology but whose land portions are not, and thus represent a pure GRACE-derived signal.

Two-dimensional phase unwrapping using robust derivative estimation and adaptive integration.

PubMed

Strand, Jarle; Taxt, Torfinn

2002-01-01

The adaptive integration (ADI) method for two-dimensional (2-D) phase unwrapping is presented. The method uses an algorithm for noise robust estimation of partial derivatives, followed by a noise robust adaptive integration process. The ADI method can easily unwrap phase images with moderate noise levels, and the resulting images are congruent modulo 2pi with the observed, wrapped, input images. In a quantitative evaluation, both the ADI and the BLS methods (Strand et al.) were better than the least-squares methods of Ghiglia and Romero (GR), and of Marroquin and Rivera (MRM). In a qualitative evaluation, the ADI, the BLS, and a conjugate gradient version of the MRM method (MRMCG), were all compared using a synthetic image with shear, using 115 magnetic resonance images, and using 22 fiber-optic interferometry images. For the synthetic image and the interferometry images, the ADI method gave consistently visually better results than the other methods. For the MR images, the MRMCG method was best, and the ADI method second best. The ADI method was less sensitive to the mask definition and the block size than the BLS method, and successfully unwrapped images with shears that were not marked in the masks. The computational requirements of the ADI method for images of nonrectangular objects were comparable to only two iterations of many least-squares-based methods (e.g., GR). We believe the ADI method provides a powerful addition to the ensemble of tools available for 2-D phase unwrapping.

Deconvolution of the PSF of a seismic lens

NASA Astrophysics Data System (ADS)

Yu, Jianhua; Wang, Yue; Schuster, Gerard T.

2002-12-01

We show that if seismic data d is related to the migration image by mmig = LTd. then mmig is a blurred version of the actual reflectivity distribution m, i.e., mmig = (LTL)m. Here L is the acoustic forward modeling operator under the Born approximation where d = Lm. The blurring operator (LTL), or point spread function, distorts the image because of defects in the seismic lens, i.e., small source-receiver recording aperture and irregular/coarse geophone-source spacing. These distortions can be partly suppressed by applying the deblurring operator (LTL)-1 to the migration image to get m = (LTL)-1mmig. This deblurred image is known as a least squares migration (LSM) image if (LTL)-1LT is applied to the data d using a conjugate gradient method, and is known as a migration deconvolved (MD) image if (LTL)-1 is directly applied to the migration image mmig in (kx, ky, z) space. The MD algorithm is an order-of-magnitude faster than LSM, but it employs more restrictive assumptions. We also show that deblurring can be used to filter out coherent noise in the data such as multiple reflections. The procedure is to, e.g., decompose the forward modeling operator into both primary and multiple reflection operators d = (Lprim + Lmulti)m, invert for m, and find the primary reflection data by dprim = Lprimm. This method is named least squares migration filtering (LSMF). The above three algorithms (LSM, MD and LSMF) might be useful for attacking problems in optical imaging.

Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations

NASA Technical Reports Server (NTRS)

Elman, Howard C.

1996-01-01

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several two-dimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being both independent of iteration parameters and widely applicable.

Velocity Gradient Power Functional for Brownian Dynamics.

PubMed

de Las Heras, Daniel; Schmidt, Matthias

2018-01-12

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

Velocity Gradient Power Functional for Brownian Dynamics

NASA Astrophysics Data System (ADS)

de las Heras, Daniel; Schmidt, Matthias

2018-01-01

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

Conjugate problems of transport phenomena under quasi-steady microaccelerations in realistic spaceflight.

PubMed

Polezhaev, V I; Nikitin, S A

2009-04-01

A new model for spatial convective transport processes conjugated with the measured or calculated realistic quasi-steady microaccelerations is presented. Rotation around the mass center, including accelerated rotation, gravity gradient, and aerodynamical drag are taken into account. New results of the effect on mixing and concentration inhomogeneities of the elementary convective processes are presented. The mixing problem in spacecraft enclosures, concentration inhomogeneities due to convection induced by body forces in realistic spaceflight, and the coupling of this kind of convection with thermocapillary convection on the basis of this model are discussed.

Preclinical manufacture of anti-HER2 liposome-inserting, scFv-PEG-lipid conjugate. 2. Conjugate micelle identity, purity, stability, and potency analysis.

PubMed

Nellis, David F; Giardina, Steven L; Janini, George M; Shenoy, Shilpa R; Marks, James D; Tsai, Richard; Drummond, Daryl C; Hong, Keelung; Park, John W; Ouellette, Thomas F; Perkins, Shelley C; Kirpotin, Dmitri B

2005-01-01

Analytical methods optimized for micellar F5cys-MP-PEG(2000)-DPSE protein-lipopolymer conjugate are presented. The apparent micelle molecular weight, determined by size exclusion chromatography, ranged from 330 to 960 kDa. The F5cys antibody and conjugate melting points, determined by differential scanning calorimetry, were near 82 degrees C. Traditional methods for characterizing monodisperse protein species were inapplicable to conjugate analysis. The isoelectric point of F5cys (9.2) and the conjugate (8.9) were determined by capillary isoelectric focusing (cIEF) after addition of the zwitterionic detergent CHAPS to the buffer. Conjugate incubation with phospholipase B selectively removed DSPE lipid groups and dispersed the conjugate prior to separation by chromatographic methods. Alternatively, adding 2-propanol (29.4 vol %) and n-butanol (4.5 vol %) to buffers for salt-gradient cation exchange chromatography provided gentler, nonenzymatic dispersion, resulting in well-resolved peaks. This method was used to assess stability, identify contaminants, establish lot-to-lot comparability, and determine the average chromatographic purity (93%) for conjugate lots, described previously. The F5cys amino acid content was confirmed after conjugation. The expected conjugate avidity for immobilized HER-2/neu was measured by bimolecular interaction analysis (BIAcore). Mock therapeutic assemblies were made by conjugate insertion into preformed doxorubicin-encapsulating liposomes for antibody-directed uptake of doxorubicin by HER2-overexpressing cancer cells in vitro. Together these developed assays established that the manufacturing method as described in the first part of this study consistently produced F5cys-MP-PEG(2000)-DSPE having sufficient purity, stability, and functionality for use in preclinical toxicology investigations.

Reactivating dynamics for the susceptible-infected-susceptible model: a simple method to simulate the absorbing phase

NASA Astrophysics Data System (ADS)

Macedo-Filho, A.; Alves, G. A.; Costa Filho, R. N.; Alves, T. F. A.

2018-04-01

We investigated the susceptible-infected-susceptible model on a square lattice in the presence of a conjugated field based on recently proposed reactivating dynamics. Reactivating dynamics consists of reactivating the infection by adding one infected site, chosen randomly when the infection dies out, avoiding the dynamics being trapped in the absorbing state. We show that the reactivating dynamics can be interpreted as the usual dynamics performed in the presence of an effective conjugated field, named the reactivating field. The reactivating field scales as the inverse of the lattice number of vertices n, which vanishes at the thermodynamic limit and does not affect any scaling properties including ones related to the conjugated field.

Polyamine-iron chelator conjugate.

PubMed

Bergeron, Raymond J; McManis, James S; Franklin, April M; Yao, Hua; Weimar, William R

2003-12-04

The current study demonstrates unequivocally that polyamines can serve as vectors for the intracellular delivery of the bidentate chelator 1,2-dimethyl-3-hydroxypyridin-4-one (L1). The polyamine-hydroxypyridinone conjugate 1-(12-amino-4,9-diazadodecyl)-2-methyl-3-hydroxy-4(1H)-pyridinone is assembled from spermine and 3-O-benzylmaltol. The conjugate is shown to form a 3:1 complex with Fe(III) and to be taken up by the polyamine transporter 1900-fold against a concentration gradient. The K(i) of the conjugate is 3.7 microM vs spermidine for the polyamine transporter. The conjugate is also at least 230 times more active in suppressing the growth of L1210 murine leukemia cells than is the parent ligand, decreases the activities of the polyamine biosynthetic enzymes ornithine decarboxylase and S-adenosylmethionine decarboxylase, and upregulates spermidine-spermine N (1)-acetyltransferase. However, the effect on native polyamine pools is a moderate one. These findings are in keeping with the idea that polyamines can also serve as efficient vectors for the intracellular delivery of other iron chelators.

Application of COMSOL to Acoustic Imaging

DTIC Science & Technology

2010-10-01

Marquardt (LM) (2 epochs), followed by Broyden, Fletcher, Goldfarb, and Shannon (BFGS) (2 epochs) followed by scaled conjugate gradient ( SCG )(100...Use Matlab’s excellent Neural Network Toolbox  Optimization techniques considered:  Scaled‏Con jugate‏ Gradient‏ (“ SCG ”)‏ - fast  One‏Step

Aircraft symmetric flight optimization. [gradient techniques for supersonic aircraft control

NASA Technical Reports Server (NTRS)

Falco, M.; Kelley, H. J.

1973-01-01

Review of the development of gradient techniques and their application to aircraft optimal performance computations in the vertical plane of flight. Results obtained using the method of gradients are presented for attitude- and throttle-control programs which extremize the fuel, range, and time performance indices subject to various trajectory and control constraints, including boundedness of engine throttle control. A penalty function treatment of state inequality constraints which generally appear in aircraft performance problems is outlined. Numerical results for maximum-range, minimum-fuel, and minimum-time climb paths for a hypothetical supersonic turbojet interceptor are presented and discussed. In addition, minimum-fuel climb paths subject to various levels of ground overpressure intensity constraint are indicated for a representative supersonic transport. A variant of the Gel'fand-Tsetlin 'method of ravines' is reviewed, and two possibilities for further development of continuous gradient processes are cited - namely, a projection version of conjugate gradients and a curvilinear search.

Adjustment technique without explicit formation of normal equations /conjugate gradient method/

NASA Technical Reports Server (NTRS)

Saxena, N. K.

1974-01-01

For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

A new modified conjugate gradient coefficient for solving system of linear equations

NASA Astrophysics Data System (ADS)

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

Development and applications of algorithms for calculating the transonic flow about harmonically oscillating wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Weatherill, W. H.; Yip, E. L.

1984-01-01

A finite difference method to solve the unsteady transonic flow about harmonically oscillating wings was investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady velocity potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. An alternating direction implicit procedure was investigated, and a pilot program was developed for both two and three dimensional wings. This program provides a relatively efficient relaxation solution without previously encountered solution instability problems. Pressure distributions for two rectangular wings are calculated. Conjugate gradient techniques were developed for the asymmetric, indefinite problem. The conjugate gradient procedure is evaluated for applications to the unsteady transonic problem. Different equations for the alternating direction procedure are derived using a coordinate transformation for swept and tapered wing planforms. Pressure distributions for swept, untaped wings of vanishing thickness are correlated with linear results for sweep angles up to 45 degrees.

Cosmic Microwave Background Mapmaking with a Messenger Field

NASA Astrophysics Data System (ADS)

Huffenberger, Kevin M.; Næss, Sigurd K.

2018-01-01

We apply a messenger field method to solve the linear minimum-variance mapmaking equation in the context of Cosmic Microwave Background (CMB) observations. In simulations, the method produces sky maps that converge significantly faster than those from a conjugate gradient descent algorithm with a diagonal preconditioner, even though the computational cost per iteration is similar. The messenger method recovers large scales in the map better than conjugate gradient descent, and yields a lower overall χ2. In the single, pencil beam approximation, each iteration of the messenger mapmaking procedure produces an unbiased map, and the iterations become more optimal as they proceed. A variant of the method can handle differential data or perform deconvolution mapmaking. The messenger method requires no preconditioner, but a high-quality solution needs a cooling parameter to control the convergence. We study the convergence properties of this new method and discuss how the algorithm is feasible for the large data sets of current and future CMB experiments.

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

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.

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT. [Conjugate Gradient Fast Fourier Transformation

NASA Technical Reports Server (NTRS)

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.

Vacuolar transport of the glutathione conjugate of trans-cinnamic acid.

PubMed

Walczak, H A; Dean, J V

2000-02-01

Red beet (Beta vulgaris L.) tonoplast membrane vesicles and [14C]trans-cinnamic acid-glutatione were used to study the vacuolar transport of phynylpropanoid-glutathione conjugates which are formed in peroxidase-mediated reactions. It was determined that the uptake of [14C]trans-cinnamic acid-glutathione into the tonoplast membrane vesicles was MgATP dependent and was 10-fold faster than the uptake of non-conjugated [14C]trans-cinnamic acid. Uptake of the conjugate in the presence of MgATP was not dependent on a trans-tonoblast H+-electrochemical gradient, because uptake was not affected by the addition of NH4Cl (1 mM; 0% inhibition) and was only slightly affected by gramicidin-D (5 microM; 14% inhibition). Uptake of the conjugate was inhibited 92% by the addition of vanadate (1 mM) and 71% by the addition of the model substrate S-(2,4-dinitrophenyl) glutathione (500 microM). Uptake did not occur when a nonhydrolyzable analog of ATP was used in place of MgATP. The calculated Km and Vmax values for uptake were 142 microM amd 5.95 nmol mg(-1) min(-1), respectively. Based on these results, phenylpropanoid-glutation conjugates formed in peroxidase-mediated reactions appear to be transported into the vacuole by the glutathione S-conjugate pump(s) located in the tonoplast membrane.

Combining the absorptive and radiative loss in metasurfaces for multi-spectral shaping of the electromagnetic scattering.

PubMed

Pan, Wenbo; Huang, Cheng; Pu, Mingbo; Ma, Xiaoliang; Cui, Jianhua; Zhao, Bo; Luo, Xiangang

2016-02-19

The absorptive and radiative losses are two fundamental aspects of the electromagnetic responses, which are widely occurring in many different systems such as waveguides, solar cells, and antennas. Here we proposed a metasurface to realize the control of the absorptive and radiative loss and to reduce the radar cross section (RCS) in multi-frequency bands. The anti-phase gradient and absorptive metasurfaces were designed that consists of metallic square patch and square loop structure inserted with resistors, acting as an phase gradient material in the X and Ku band, while behaving as an absorber in the S band. The simulation and experiment results verified the double-band, wideband and polarization-independent RCS reduction by the absorptive and anti-phase gradient metasurfaces.

Krylov subspace iterative methods for boundary element method based near-field acoustic holography.

PubMed

Valdivia, Nicolas; Williams, Earl G

2005-02-01

The reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods. The solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements. These methods will not require the calculation of the singular value decomposition, which can be expensive when the matrix system is considerably large. Krylov subspace methods are iterative methods that have the phenomena known as "semi-convergence," i.e., the optimal regularization solution is obtained after a few iterations. If the iteration is not stopped, the method converges to a solution that generally is totally corrupted by errors on the measurements. For these methods the number of iterations play the role of the regularization parameter. We will focus our attention to the study of the regularizing properties from the Krylov subspace methods like conjugate gradients, least squares QR and the recently proposed Hybrid method. A discussion and comparison of the available stopping rules will be included. A vibrating plate is considered as an example to validate our results.

An Efficient Augmented Lagrangian Method for Statistical X-Ray CT Image Reconstruction.

PubMed

Li, Jiaojiao; Niu, Shanzhou; Huang, Jing; Bian, Zhaoying; Feng, Qianjin; Yu, Gaohang; Liang, Zhengrong; Chen, Wufan; Ma, Jianhua

2015-01-01

Statistical iterative reconstruction (SIR) for X-ray computed tomography (CT) under the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the nonlinear expression of the objective function, most exiting algorithms related to the SIR unavoidably suffer from heavy computation load and slow convergence rate, especially when an edge-preserving or sparsity-based penalty or regularization is incorporated. In this work, to address abovementioned issues of the general algorithms related to the SIR, we propose an adaptive nonmonotone alternating direction algorithm in the framework of augmented Lagrangian multiplier method, which is termed as "ALM-ANAD". The algorithm effectively combines an alternating direction technique with an adaptive nonmonotone line search to minimize the augmented Lagrangian function at each iteration. To evaluate the present ALM-ANAD algorithm, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present ALM-ANAD algorithm can achieve noticeable gains over the classical nonlinear conjugate gradient algorithm and state-of-the-art split Bregman algorithm in terms of noise reduction, contrast-to-noise ratio, convergence rate, and universal quality index metrics.

Classification of a Driver's cognitive workload levels using artificial neural network on ECG signals.

PubMed

Tjolleng, Amir; Jung, Kihyo; Hong, Wongi; Lee, Wonsup; Lee, Baekhee; You, Heecheon; Son, Joonwoo; Park, Seikwon

2017-03-01

An artificial neural network (ANN) model was developed in the present study to classify the level of a driver's cognitive workload based on electrocardiography (ECG). ECG signals were measured on 15 male participants while they performed a simulated driving task as a primary task with/without an N-back task as a secondary task. Three time-domain ECG measures (mean inter-beat interval (IBI), standard deviation of IBIs, and root mean squared difference of adjacent IBIs) and three frequencydomain ECG measures (power in low frequency, power in high frequency, and ratio of power in low and high frequencies) were calculated. To compensate for individual differences in heart response during the driving tasks, a three-step data processing procedure was performed to ECG signals of each participant: (1) selection of two most sensitive ECG measures, (2) definition of three (low, medium, and high) cognitive workload levels, and (3) normalization of the selected ECG measures. An ANN model was constructed using a feed-forward network and scaled conjugate gradient as a back-propagation learning rule. The accuracy of the ANN classification model was found satisfactory for learning data (95%) and testing data (82%). Copyright © 2016 Elsevier Ltd. All rights reserved.

2.5D complex resistivity modeling and inversion using unstructured grids

NASA Astrophysics Data System (ADS)

Xu, Kaijun; Sun, Jie

2016-04-01

The characteristic of complex resistivity on rock and ore has been recognized by people for a long time. Generally we have used the Cole-Cole Model(CCM) to describe complex resistivity. It has been proved that the electrical anomaly of geologic body can be quantitative estimated by CCM parameters such as direct resistivity(ρ0), chargeability(m), time constant(τ) and frequency dependence(c). Thus it is very important to obtain the complex parameters of geologic body. It is difficult to approximate complex structures and terrain using traditional rectangular grid. In order to enhance the numerical accuracy and rationality of modeling and inversion, we use an adaptive finite-element algorithm for forward modeling of the frequency-domain 2.5D complex resistivity and implement the conjugate gradient algorithm in the inversion of 2.5D complex resistivity. An adaptive finite element method is applied for solving the 2.5D complex resistivity forward modeling of horizontal electric dipole source. First of all, the CCM is introduced into the Maxwell's equations to calculate the complex resistivity electromagnetic fields. Next, the pseudo delta function is used to distribute electric dipole source. Then the electromagnetic fields can be expressed in terms of the primary fields caused by layered structure and the secondary fields caused by inhomogeneities anomalous conductivity. At last, we calculated the electromagnetic fields response of complex geoelectric structures such as anticline, syncline, fault. The modeling results show that adaptive finite-element methods can automatically improve mesh generation and simulate complex geoelectric models using unstructured grids. The 2.5D complex resistivity invertion is implemented based the conjugate gradient algorithm.The conjugate gradient algorithm doesn't need to compute the sensitivity matrix but directly computes the sensitivity matrix or its transpose multiplying vector. In addition, the inversion target zones are segmented with fine grids and the background zones are segmented with big grid, the method can reduce the grid amounts of inversion, it is very helpful to improve the computational efficiency. The inversion results verify the validity and stability of conjugate gradient inversion algorithm. The results of theoretical calculation indicate that the modeling and inversion of 2.5D complex resistivity using unstructured grids are feasible. Using unstructured grids can improve the accuracy of modeling, but the large number of grids inversion is extremely time-consuming, so the parallel computation for the inversion is necessary. Acknowledgments: We thank to the support of the National Natural Science Foundation of China(41304094).

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Generating multiplex gradients of biomolecules for controlling cellular adhesion in parallel microfluidic channels.

PubMed

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.

Quantum dot conjugates in a sub-micrometer fluidic channel

DOEpatents

Stavis, Samuel M.; Edel, Joshua B.; Samiee, Kevan T.; Craighead, Harold G.

2010-04-13

A nanofluidic channel fabricated in fused silica with an approximately 500 nm square cross section was used to isolate, detect and identify individual quantum dot conjugates. The channel enables the rapid detection of every fluorescent entity in solution. A laser of selected wavelength was used to excite multiple species of quantum dots and organic molecules, and the emission spectra were resolved without significant signal rejection. Quantum dots were then conjugated with organic molecules and detected to demonstrate efficient multicolor detection. PCH was used to analyze coincident detection and to characterize the degree of binding. The use of a small fluidic channel to detect quantum dots as fluorescent labels was shown to be an efficient technique for multiplexed single molecule studies. Detection of single molecule binding events has a variety of applications including high throughput immunoassays.

Quantum dot conjugates in a sub-micrometer fluidic channel

DOEpatents

Stavis, Samuel M [Ithaca, NY; Edel, Joshua B [Brookline, MA; Samiee, Kevan T [Ithaca, NY; Craighead, Harold G [Ithaca, NY

2008-07-29

A nanofluidic channel fabricated in fused silica with an approximately 500 nm square cross section was used to isolate, detect and identify individual quantum dot conjugates. The channel enables the rapid detection of every fluorescent entity in solution. A laser of selected wavelength was used to excite multiple species of quantum dots and organic molecules, and the emission spectra were resolved without significant signal rejection. Quantum dots were then conjugated with organic molecules and detected to demonstrate efficient multicolor detection. PCH was used to analyze coincident detection and to characterize the degree of binding. The use of a small fluidic channel to detect quantum dots as fluorescent labels was shown to be an efficient technique for multiplexed single molecule studies. Detection of single molecule binding events has a variety of applications including high throughput immunoassays.

Asymmetry and polarity of the South Atlantic conjugated margins related to the presence of cratons: a numerical study

NASA Astrophysics Data System (ADS)

Andrés-Martínez, Miguel; Pérez-Gussinyé, Marta; de Monserrat Navarro, Albert; Morgan, Jason P.

2015-04-01

Tectonic asymmetry of conjugated passive margins, where one margin is much narrower than the conjugate one, is commonly observed at many passive margins world-wide. Conjugate margin asymmetry has been suggested to be a consequence of lateral changes in rheology, composition, temperature gradient or geometries of the crust and lithosphere. Here we use the South Atlantic margins (from Camamu/Gabon to North Santos/South Kwanza) as a natural laboratory to understand conjugate margin asymmetry. Along this margin sector the polarity of the asymmetry changes. To the North, the Brazilian margin developed in the strong Sao Francisco craton, and this constitutes the narrow side of the conjugate pair. To the South, the Brazilian margin developed in the Ribeira fold belt, and the margin is wide. The opposite is true for the African side. We have thus numerically analysed how the relative distance between the initial location of extension and the craton influences the symmetry/asymmetry and polarity of the conjugate margin system. Our numerical model is 2D visco-elasto-plastic and has a free surface, strain weakening and shear heating. The initial set-up includes a cratonic domain, a mobile belt and a transition area between both. We have run tests with different rheologies, thickness of the lithosphere, and weak seeds at different distances from the craton. Results show asymmetric conjugated margins, where the narrower margin is generally the closest to the craton. Our models also allow us to study how the polarity is controlled by the distance between the initial weakness and the craton, and help to understand how the presence of cratonic domains affects the final architecture of the conjugated margins.

Square-wave voltammetry assays for glycoproteins on nanoporous gold

PubMed Central

Pandey, Binod; Bhattarai, Jay K.; Pornsuriyasak, Papapida; Fujikawa, Kohki; Catania, Rosa; Demchenko, Alexei V.; Stine, Keith J.

2014-01-01

Electrochemical enzyme-linked lectinsorbent assays (ELLA) were developed using nanoporous gold (NPG) as a solid support for protein immobilization and as an electrode for the electrochemical determination of the product of the reaction between alkaline phosphatase (ALP) and p-aminophenyl phosphate (p-APP), which is p-aminophenol (p-AP). Glycoproteins or concanavalin A (Con A) and ALP conjugates were covalently immobilized onto lipoic acid self-assembled monolayers on NPG. The binding of Con A – ALP (or soybean agglutinin – ALP) conjugate to glycoproteins covalently immobilized on NPG and subsequent incubation with p-APP substrate was found to result in square-wave voltammograms whose peak difference current varied with the identity of the glycoprotein. NPG presenting covalently bound glycoproteins was used as the basis for a competitive electrochemical assay for glycoproteins in solution (transferrin and IgG). A kinetic ELLA based on steric hindrance of the enzyme-substrate reaction and hence reduced enzymatic reaction rate after glycoprotein binding is demonstrated using immobilized Con A–ALP conjugates. Using the immobilized Con A-ALP conjugate, the binding affinity of immunoglobulin G (IgG) was found to be 105 nM, and that for transferrin was found to be 650 nM. Minimal interference was observed in the presence of 5 mg mL−1 BSA as a model serum protein in both the kinetic and competitive ELLA. Inhibition studies were performed with methyl D-mannoside for the binding of TSF and IgG to Con A-ALP; IC50 values were found to be 90 μM and 286 μM, respectively. Surface coverages of proteins were estimated using solution depletion and the BCA protein concentration assay. PMID:24611035

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

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.

Exciton intrachain transport induced by interchain packing configurations in conjugated polymers.

PubMed

Meng, Ruixuan; Gao, Kun; Zhang, Gaiyan; Han, Shixuan; Yang, Fujiang; Li, Yuan; Xie, Shijie

2015-07-28

Based on a tight binding model combined with a nonadiabatic dynamics approach, we theoretically investigate the exciton intrachain transport in conjugated polymers with different interchain packing configurations. We construct two different interchain packing configurations, i.e. linear and exponential forms, and simulate the dynamical processes of the exciton transport in these systems. We find that, in both cases, there exists a distribution of driving force for exciton transport, which stems from the gradient of the exciton creation energy along the chains. This finding enriches the picture of exciton transport in polymers and provides a new idea to improve the exciton transport length in polymeric photovoltaic devices.

Directed Self-Assembly of Gradient Concentric Carbon Nanotube Rings

NASA Astrophysics Data System (ADS)

Hong, Suck Won; Jeong, Wonje; Ko, Hyunhyub; Tsukruk, Vladimir; Kessler, Michael; Lin, Zhiqun

2008-03-01

Hundreds of gradient concentric rings of linear conjugated polymer, (poly[2-methoxy-5-(2-ethylhexyloxy)-1,4- phenylenevinylene], i.e., MEH-PPV) with remarkable regularity over large areas were produced by controlled, repetitive ``stick- slip'' motions of the contact line in a confined geometry consisting of a sphere on a flat substrate (i.e., sphere-on-flat geometry). Subsequently, MEH-PPV rings exploited as template to direct the formation of gradient concentric rings of multiwalled carbon nanotubes (MWNTs) with controlled density. This method is simple, cost effective, and robust, combining two consecutive self-assembly processes, namely, evaporation-induced self- assembly of polymers in a sphere-on-flat geometry, followed by subsequent directed self-assembly of MWNTs on the polymer- templated surfaces.

First production of fluorescent anti-ribonucleoproteins conjugate for diagnostic of rabies in Brazil.

PubMed

Medeiros Caporale, Graciane Maria; Rodrigues da Silva, Andréa de Cássia; Peixoto, Zélia Maria Pinheiro; Chaves, Luciana Botelho; Carrieri, Maria Luiza; Vassão, Ruth Camargo

2009-01-01

The laboratory tests recommended by the World Health Organization for detection of rabies virus and evaluation of specific antibodies are performed with fluorescent antibodies against the virus, the ribonucleoproteins (RNPs), or by monoclonal antibodies. In this study, we purified the rabies virus RNPs for the production of a conjugate presenting sensibility and specificity compatible with commercial reagents. The method employed for the purification of RNPs was ultracentrifugation in cesium chloride gradient, the obtained product being used for immunizing rabbits, from which the hyperimmune sera were collected. The serum used for conjugate production was the one presenting the highest titer (1/2,560) when tested by indirect immunofluorescence. The antibodies were purified by anion exchange chromatography (QAE-Sephadex A-50),conjugated to fluorescein isothiocyanate and separated by gel filtration (Sephadex G-50). The resulting conjugate presented titers of 1/400 and 1/500 when assayed by direct immunofluorescence (DIF) and simplified fluorescence inhibition microtest, respectively. Sensibility and specificity tests were performed by DIF in 100 central nervous system samples of different animal species, presenting 100% matches when compared with the commercial reagent used as standard, independent of the conservation state of the samples. The quality reached by our conjugate will enable the standardization of this reagent for use by the laboratories performing diagnosis of rabies in Brazil, contributing to the intensification of the epidemiological vigilance and research on this disease. Copyright 2009 Wiley-Liss, Inc.

Wavelet methods in multi-conjugate adaptive optics

NASA Astrophysics Data System (ADS)

Helin, T.; Yudytskiy, M.

2013-08-01

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.

Gradient metasurface for four-direction anomalous reflection in terahertz

NASA Astrophysics Data System (ADS)

Wang, Jiao; Jiang, Yannan

2018-06-01

In this paper, a four-direction anomalous reflection metasurface is proposed. The basic cells comprise of squares and circles, which are designed at various sizes and arranged in a super cell at regular spacing. Then, properly combining super cells molds a square phase gradient metasurface (PGM). It is mounted on an optical thickness gold mirror, which inhibits all light transmission. Markedly different from previously reported metasurfaces, the square PGM is characterized by four-direction reflection beams. It takes into consideration the normal incidence and the oblique incidence. For the normal incidence, that the degrees of the four reflection angles are identical is due to the x, - x, y and - y directional discontinuous phase gradients, and lies on the symmetric structure in the xoy plane, which is then revealed by the surface current distribution. Incident angles varying from -20° to 20°, the reflection angles are demonstrated in the oblique incidence. Moreover, the PGM is polarization-independent. The performance is attributed to the symmetry of structure, which is verified by Radar cross section. Simulated results prove that our method offers a simple and effective strategy for metasurface design in terahertz. The proposed PGM can aid in focused beams, steering beams, and shaped beams.

An Introduction to the Conjugate Gradient Method that Even an Idiot Can Understand

DTIC Science & Technology

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

Sensitivity calculations for iteratively solved problems

NASA Technical Reports Server (NTRS)

Haftka, R. T.

1985-01-01

The calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated. A modified finite difference procedure is presented which improves the accuracy of the calculated derivatives. The procedure is demonstrated for a simple algebraic example as well as an element-by-element preconditioned conjugate gradient iterative solution technique applied to truss examples.

Self-calibrated multiple-echo acquisition with radial trajectories using the conjugate gradient method (SMART-CG).

PubMed

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.

Self-calibrated Multiple-echo Acquisition with Radial Trajectories using the Conjugate Gradient Method (SMART-CG)

PubMed Central

Jung, Youngkyoo; Samsonov, Alexey A; Bydder, Mark; Block, Walter F.

2011-01-01

Purpose 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. Materials and Methods 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. Results Substantial image quality improvements were demonstrated. Signal dropouts were completely removed and undersampling artifacts were well suppressed. Conclusion 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 3D MRI data acquisition. PMID:21448967

Two-step reconstruction method using global optimization and conjugate gradient for ultrasound-guided diffuse optical tomography.

PubMed

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.

A modified three-term PRP conjugate gradient algorithm for optimization models.

PubMed

Wu, Yanlin

2017-01-01

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the sufficient descent property without any line search technique. They proved the global convergence of the Armijo line search but this fails for the Wolfe line search technique. Inspired by their method, we will make a further study and give a modified three-term PRP CG algorithm. The presented method possesses the following features: (1) The sufficient descent property also holds without any line search technique; (2) the trust region property of the search direction is automatically satisfied; (3) the steplengh is bounded from below; (4) the global convergence will be established under the Wolfe line search. Numerical results show that the new algorithm is more effective than that of the normal method.

A fast mass spring model solver for high-resolution elastic objects

NASA Astrophysics Data System (ADS)

Zheng, Mianlun; Yuan, Zhiyong; Zhu, Weixu; Zhang, Guian

2017-03-01

Real-time simulation of elastic objects is of great importance for computer graphics and virtual reality applications. The fast mass spring model solver can achieve visually realistic simulation in an efficient way. Unfortunately, this method suffers from resolution limitations and lack of mechanical realism for a surface geometry model, which greatly restricts its application. To tackle these problems, in this paper we propose a fast mass spring model solver for high-resolution elastic objects. First, we project the complex surface geometry model into a set of uniform grid cells as cages through *cages mean value coordinate method to reflect its internal structure and mechanics properties. Then, we replace the original Cholesky decomposition method in the fast mass spring model solver with a conjugate gradient method, which can make the fast mass spring model solver more efficient for detailed surface geometry models. Finally, we propose a graphics processing unit accelerated parallel algorithm for the conjugate gradient method. Experimental results show that our method can realize efficient deformation simulation of 3D elastic objects with visual reality and physical fidelity, which has a great potential for applications in computer animation.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Detection of ferromagnetic target based on mobile magnetic gradient tensor system

NASA Astrophysics Data System (ADS)

Gang, Y. I. N.; Yingtang, Zhang; Zhining, Li; Hongbo, Fan; Guoquan, Ren

2016-03-01

Attitude change of mobile magnetic gradient tensor system critically affects the precision of gradient measurements, thereby increasing ambiguity in target detection. This paper presents a rotational invariant-based method for locating and identifying ferromagnetic targets. Firstly, unit magnetic moment vector was derived based on the geometrical invariant, such that the intermediate eigenvector of the magnetic gradient tensor is perpendicular to the magnetic moment vector and the source-sensor displacement vector. Secondly, unit source-sensor displacement vector was derived based on the characteristic that the angle between magnetic moment vector and source-sensor displacement is a rotational invariant. By introducing a displacement vector between two measurement points, the magnetic moment vector and the source-sensor displacement vector were theoretically derived. To resolve the problem of measurement noises existing in the realistic detection applications, linear equations were formulated using invariants corresponding to several distinct measurement points and least square solution of magnetic moment vector and source-sensor displacement vector were obtained. Results of simulation and principal verification experiment showed the correctness of the analytical method, along with the practicability of the least square method.

Monthly evaporation forecasting using artificial neural networks and support vector machines

NASA Astrophysics Data System (ADS)

Tezel, Gulay; Buyukyildiz, Meral

2016-04-01

Evaporation is one of the most important components of the hydrological cycle, but is relatively difficult to estimate, due to its complexity, as it can be influenced by numerous factors. Estimation of evaporation is important for the design of reservoirs, especially in arid and semi-arid areas. Artificial neural network methods and support vector machines (SVM) are frequently utilized to estimate evaporation and other hydrological variables. In this study, usability of artificial neural networks (ANNs) (multilayer perceptron (MLP) and radial basis function network (RBFN)) and ɛ-support vector regression (SVR) artificial intelligence methods was investigated to estimate monthly pan evaporation. For this aim, temperature, relative humidity, wind speed, and precipitation data for the period 1972 to 2005 from Beysehir meteorology station were used as input variables while pan evaporation values were used as output. The Romanenko and Meyer method was also considered for the comparison. The results were compared with observed class A pan evaporation data. In MLP method, four different training algorithms, gradient descent with momentum and adaptive learning rule backpropagation (GDX), Levenberg-Marquardt (LVM), scaled conjugate gradient (SCG), and resilient backpropagation (RBP), were used. Also, ɛ-SVR model was used as SVR model. The models were designed via 10-fold cross-validation (CV); algorithm performance was assessed via mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R 2). According to the performance criteria, the ANN algorithms and ɛ-SVR had similar results. The ANNs and ɛ-SVR methods were found to perform better than the Romanenko and Meyer methods. Consequently, the best performance using the test data was obtained using SCG(4,2,2,1) with R 2 = 0.905.

Neuro-fuzzy and neural network techniques for forecasting sea level in Darwin Harbor, Australia

NASA Astrophysics Data System (ADS)

Karimi, Sepideh; Kisi, Ozgur; Shiri, Jalal; Makarynskyy, Oleg

2013-03-01

Accurate predictions of sea level with different forecast horizons are important for coastal and ocean engineering applications, as well as in land drainage and reclamation studies. The methodology of tidal harmonic analysis, which is generally used for obtaining a mathematical description of the tides, is data demanding requiring processing of tidal observation collected over several years. In the present study, hourly sea levels for Darwin Harbor, Australia were predicted using two different, data driven techniques, adaptive neuro-fuzzy inference system (ANFIS) and artificial neural network (ANN). Multi linear regression (MLR) technique was used for selecting the optimal input combinations (lag times) of hourly sea level. The input combination comprises current sea level as well as five previous level values found to be optimal. For the ANFIS models, five different membership functions namely triangular, trapezoidal, generalized bell, Gaussian and two Gaussian membership function were tested and employed for predicting sea level for the next 1 h, 24 h, 48 h and 72 h. The used ANN models were trained using three different algorithms, namely, Levenberg-Marquardt, conjugate gradient and gradient descent. Predictions of optimal ANFIS and ANN models were compared with those of the optimal auto-regressive moving average (ARMA) models. The coefficient of determination, root mean square error and variance account statistics were used as comparison criteria. The obtained results indicated that triangular membership function was optimal for predictions with the ANFIS models while adaptive learning rate and Levenberg-Marquardt were most suitable for training the ANN models. Consequently, ANFIS and ANN models gave similar forecasts and performed better than the developed for the same purpose ARMA models for all the prediction intervals.

Density interface topography recovered by inversion of satellite gravity gradiometry observations

NASA Astrophysics Data System (ADS)

Ramillien, G. L.

2017-08-01

A radial integration of spherical mass elements (i.e. tesseroids) is presented for evaluating the six components of the second-order gravity gradient (i.e. second derivatives of the Newtonian mass integral for the gravitational potential) created by an uneven spherical topography consisting of juxtaposed vertical prisms. The method uses Legendre polynomial series and takes elastic compensation of the topography by the Earth's surface into account. The speed of computation of the polynomial series increases logically with the observing altitude from the source of anomaly. Such a forward modelling can be easily applied for reduction of observed gravity gradient anomalies by the effects of any spherical interface of density. An iterative least-squares inversion of measured gravity gradient coefficients is also proposed to estimate a regional set of juxtaposed topographic heights. Several tests of recovery have been made by considering simulated gradients created by idealistic conical and irregular Great Meteor seamount topographies, and for varying satellite altitudes and testing different levels of uncertainty. In the case of gravity gradients measured at a GOCE-type altitude of ˜ 300 km, the search converges down to a stable but smooth topography after 10-15 iterations, while the final root-mean-square error is ˜ 100 m that represents only 2 % of the seamount amplitude. This recovery error decreases with the altitude of the gravity gradient observations by revealing more topographic details in the region of survey.

On the null distribution of Bayes factors in linear regression

USDA-ARS?s Scientific Manuscript database

We show that under the null, the 2 log (Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and...

Solar multi-conjugate adaptive optics performance improvement

NASA Astrophysics Data System (ADS)

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.

Ferritin conjugates as specific magnetic labels. Implications for cell separation.

PubMed Central

Odette, L L; McCloskey, M A; Young, S H

1984-01-01

Concanavalin A coupled to the naturally occurring iron storage protein ferritin is used to label rat erythrocytes and increase the cells' magnetic susceptibility. Labeled cells are introduced into a chamber containing spherical iron particles and the chamber is placed in a uniform 5.2 kG (gauss) magnetic field. The trajectory of cells in the inhomogeneous magnetic field around the iron particles and the polar distributions of cells bound to the iron particles compare well with the theoretical predictions for high gradient magnetic systems. On the basis of these findings we suggest that ferritin conjugated ligands can be used for selective magnetic separation of labeled cells. Images FIGURE 2 PMID:6743752

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1984-01-01

The research efforts of University of Virginia students under a NASA sponsored program are summarized and the status of the program is reported. The research includes: testing method evaluations for N version programming; a representation scheme for modeling three dimensional objects; fault tolerant protocols for real time local area networks; performance investigation of Cyber network; XFEM implementation; and vectorizing incomplete Cholesky conjugate gradients.

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Non-linear Multidimensional Optimization for use in Wire Scanner Fitting

NASA Astrophysics Data System (ADS)

Henderson, Alyssa; Terzic, Balsa; Hofler, Alicia; Center Advanced Studies of Accelerators Collaboration

2014-03-01

To ensure experiment efficiency and quality from the Continuous Electron Beam Accelerator at Jefferson Lab, beam energy, size, and position must be measured. Wire scanners are devices inserted into the beamline to produce measurements which are used to obtain beam properties. Extracting physical information from the wire scanner measurements begins by fitting Gaussian curves to the data. This study focuses on optimizing and automating this curve-fitting procedure. We use a hybrid approach combining the efficiency of Newton Conjugate Gradient (NCG) method with the global convergence of three nature-inspired (NI) optimization approaches: genetic algorithm, differential evolution, and particle-swarm. In this Python-implemented approach, augmenting the locally-convergent NCG with one of the globally-convergent methods ensures the quality, robustness, and automation of curve-fitting. After comparing the methods, we establish that given an initial data-derived guess, each finds a solution with the same chi-square- a measurement of the agreement of the fit to the data. NCG is the fastest method, so it is the first to attempt data-fitting. The curve-fitting procedure escalates to one of the globally-convergent NI methods only if NCG fails, thereby ensuring a successful fit. This method allows for the most optimal signal fit and can be easily applied to similar problems.

Magnetic propulsion of a magnetic device using three square-Helmholtz coils and a square-Maxwell coil.

PubMed

Ha, Yong H; Han, Byung H; Lee, Soo Y

2010-02-01

We introduce a square coil system for remote magnetic navigation of a magnetic device without any physical movements of the coils. We used three square-Helmholtz coils and a square-Maxwell coil for magnetic propulsion of a small magnet along the desired path. All the square coils are mountable on a cubic frame that has an opening to accommodate a living subject. The square-Helmholtz coils control the magnetic propulsion direction by generating uniform magnetic field along the desired direction while the square-Maxwell coil controls the propulsion force by generating magnetic gradient field. We performed magnetic propulsion experiments with a down-scaled coil set and a three-channel coil driver. Experimental results demonstrate that we can use the square coil set for magnetic navigation of a magnetic device without any physical movements of the coils.

Limited-memory BFGS based least-squares pre-stack Kirchhoff depth migration

NASA Astrophysics Data System (ADS)

Wu, Shaojiang; Wang, Yibo; Zheng, Yikang; Chang, Xu

2015-08-01

Least-squares migration (LSM) is a linearized inversion technique for subsurface reflectivity estimation. Compared to conventional migration algorithms, it can improve spatial resolution significantly with a few iterative calculations. There are three key steps in LSM, (1) calculate data residuals between observed data and demigrated data using the inverted reflectivity model; (2) migrate data residuals to form reflectivity gradient and (3) update reflectivity model using optimization methods. In order to obtain an accurate and high-resolution inversion result, the good estimation of inverse Hessian matrix plays a crucial role. However, due to the large size of Hessian matrix, the inverse matrix calculation is always a tough task. The limited-memory BFGS (L-BFGS) method can evaluate the Hessian matrix indirectly using a limited amount of computer memory which only maintains a history of the past m gradients (often m < 10). We combine the L-BFGS method with least-squares pre-stack Kirchhoff depth migration. Then, we validate the introduced approach by the 2-D Marmousi synthetic data set and a 2-D marine data set. The results show that the introduced method can effectively obtain reflectivity model and has a faster convergence rate with two comparison gradient methods. It might be significant for general complex subsurface imaging.

Double diffusive conjugate heat transfer: Part II

NASA Astrophysics Data System (ADS)

Azeem, Soudagar, Manzoor Elahi M.

2018-05-01

Conjugate heat transfer in porous medium is an important study involved in many practical applications. The current study is aimed to investigate the double diffusive flow in a square porous cavity subjected to left vertical surface heating and right vertical surface cooling respectively along with left and right surfaces maintained at high and low concentration. The three governing equations are converted into algebraic form of equations by applying finite element method and solved in iterative manner. The study is focused to investigate the effect of presence of solid inside the cavity with respect to varying buoyancy ratio. It is found that the local heat and mass transfer rate decreases along the height of cavity.

Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach

NASA Astrophysics Data System (ADS)

Piretzidis, Dimitrios; Sideris, Michael G.

2017-09-01

Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63-84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10-30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.

HPLC analysis of functionalized poly(amidoamine) dendrimers and the interaction between a folate-dendrimer conjugate and folate binding protein.

PubMed

Shi, Xiangyang; Bi, Xiangdong; Ganser, T Rose; Hong, Seungpyo; Myc, Lukasz A; Desai, Ankur; Holl, Mark M Banaszak; Baker, James R

2006-07-01

Poly(amidoamine) (PAMAM) dendrimers of different generations with carboxyl, acetyl, and hydroxyl terminal groups and a folic acid (FA)-dendrimer conjugate were separated and analyzed using reverse-phase high performance liquid chromatography (HPLC). Analysis of both the individual PAMAM derivatives and the separation of mixed generations can be achieved using a linear gradient 0-50% acetonitrile (ACN) (balance water) within 40 min. We also show that PAMAMs with defined acetylation and carboxylation degrees can be analyzed using HPLC. Furthermore, a generation 5 dendrimer-FA conjugate (G5.75Ac-FA4; Ac denotes acetyl) was analyzed and its specific binding with a bovine folic acid binding protein (FBP) was monitored. The HPLC and sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) results indicate the formation of three complexes after the binding of G5.75Ac-FA4 with FBP. Dendrimers with FA moieties show much higher specific binding capability with FBP than those without FA moieties. Findings from this study indicate that HPLC is an effective technique not only for characterization and separation of functionalized PAMAM dendrimers and conjugates but also for investigation of the interaction between dendrimers and biomolecules.

The role of polymerase III in conjugation between E. coli K12 donor and recipient strains carrying dnaE ts mutation.

PubMed

Blinkowa, A

1976-01-01

The possible role of DNA polimerase III in conjugation was studied in a series of mutants temperature-sensitive for DNA polymerase III synthesis. The temperature-sensitive DNA mutation called dnaE 486 (ts) prohibits vegetative DNA replication at 41-45 degrees. Transfer of episome and chromosome from temperature-sensitive donor, carrying dnaE mutation to wild-type recipient strains, revertants and dnaE recipients was investigated. In the first two cases the number of Lac+ sexductants being even slightly higher at 43 degrees. Conjugational synthesis accompanying transfer involving the combination of dnaE (ts) thymine dependent and thymine independent donor and recipient strains measured by incorporation of 14C thymine was observed at the restrictive temperature. In the case of conjugation with temperaturesensitive recipient strains a drop of Lac+ sexductants and Pro+ recombinants may be as a result of disturbances in the synthesis of complementary strand in recipient, known to be dependent on pol III. However, the episome investigated by centrifugation in neutral CsC1 gradient after its transfer to the recipient with faulty polymerase III was double stranded (replicated) at the restrictive temperature.

Efficient geostatistical inversion of transient groundwater flow using preconditioned nonlinear conjugate gradients

NASA Astrophysics Data System (ADS)

Klein, Ole; Cirpka, Olaf A.; Bastian, Peter; Ippisch, Olaf

2017-04-01

In the geostatistical inverse problem of subsurface hydrology, continuous hydraulic parameter fields, in most cases hydraulic conductivity, are estimated from measurements of dependent variables, such as hydraulic heads, under the assumption that the parameter fields are autocorrelated random space functions. Upon discretization, the continuous fields become large parameter vectors with O (104 -107) elements. While cokriging-like inversion methods have been shown to be efficient for highly resolved parameter fields when the number of measurements is small, they require the calculation of the sensitivity of each measurement with respect to all parameters, which may become prohibitive with large sets of measured data such as those arising from transient groundwater flow. We present a Preconditioned Conjugate Gradient method for the geostatistical inverse problem, in which a single adjoint equation needs to be solved to obtain the gradient of the objective function. Using the autocovariance matrix of the parameters as preconditioning matrix, expensive multiplications with its inverse can be avoided, and the number of iterations is significantly reduced. We use a randomized spectral decomposition of the posterior covariance matrix of the parameters to perform a linearized uncertainty quantification of the parameter estimate. The feasibility of the method is tested by virtual examples of head observations in steady-state and transient groundwater flow. These synthetic tests demonstrate that transient data can reduce both parameter uncertainty and time spent conducting experiments, while the presented methods are able to handle the resulting large number of measurements.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system.

PubMed

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-21

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

Entropic anomaly and maximal efficiency of microscopic heat engines.

PubMed

Bo, Stefano; Celani, Antonio

2013-05-01

The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We show that-as a consequence of the recently discovered entropic anomaly-quasistatic engines, whose efficiency is maximal in a fluid at uniform temperature, have in fact vanishing efficiency in the presence of temperature gradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured.

TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data.

PubMed

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.

Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods.

PubMed

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.

Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm.

PubMed

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.

Algorithms for the optimization of RBE-weighted dose in particle therapy.

PubMed

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.

Algorithms for the optimization of RBE-weighted dose in particle therapy

NASA Astrophysics Data System (ADS)

Horcicka, M.; Meyer, C.; Buschbacher, A.; Durante, M.; Krämer, M.

2013-01-01

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.

Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions

NASA Technical Reports Server (NTRS)

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.

How cereal grass shoots perceive and respond to gravity

NASA Technical Reports Server (NTRS)

Kaufman, P. B.; Brock, T. G.; Song, I.; Rho, Y. B.; Ghosheh, N. S.

1987-01-01

The leaf-sheath pulvinus of grasses presents a unique system for studying gravitropism, primarily because of its differences from other organs. The mature pulvinus is a discrete organ specialized for gravitropism: it is nongrowing in the absence of gravistimulation and capable of displaying a graviresponse independent of the rest of the plant. In this paper we present a model for gravitropism in pulvini based on recent findings from studies on the mechanisms of graviperception and graviresponse. According to this model, amyloplasts play an essential role in perceiving a change in the orientation of the pulvinus. The perception of this reorientation leads to the enhanced synthesis and release from conjugate of the auxin IAA, and the increased conjugation of gibberellin, on a localized basis. Because there is a graded growth promotion across the gravistimulated pulvinus, it is suggested that the observed hormonal asymmetry is actually an indication of a linear gradient of hormone concentration, as well as hormone response, across the pulvinus. It is further suggested that the linear gradient of hormone concentration may be predominantly the result of local changes in hormone level, rather than a product of hormonal movement into or across the pulvinus.

TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data

DOE PAGES

Yang, Xiaoli; Hofmann, Ralf; Dapp, Robin; ...

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 f 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 themore » 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.« less

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

NASA Astrophysics Data System (ADS)

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.

Solar collector parameter identification from unsteady data by a discrete-gradient optimization algorithm

NASA Technical Reports Server (NTRS)

Hotchkiss, G. B.; Burmeister, L. C.; Bishop, K. A.

1980-01-01

A discrete-gradient optimization algorithm is used to identify the parameters in a one-node and a two-node capacitance model of a flat-plate collector. Collector parameters are first obtained by a linear-least-squares fit to steady state data. These parameters, together with the collector heat capacitances, are then determined from unsteady data by use of the discrete-gradient optimization algorithm with less than 10 percent deviation from the steady state determination. All data were obtained in the indoor solar simulator at the NASA Lewis Research Center.

Rumsey and Walker_AMT_2016_Table 2.xlsx

EPA Pesticide Factsheets

Table summarizes instrument precision assessed by collocating the two sample boxes. Precision is quantified as the standard deviation of the residuals of an orthogonal least squares regression of concentrations from the two sample boxes. This allows for an estimation of gradient precision and ultimately gradient and flux detection limits. This dataset is associated with the following publication:Rumsey, I. Application of an online ion chromatography-based instrument for gradient flux measurements of speciated nitrogen and sulfur. ENVIRONMENTAL SCIENCE & TECHNOLOGY. American Chemical Society, Washington, DC, USA, 9(6): 2581-2592, (2016).

Nonadiabatic excited-state molecular dynamics: modeling photophysics in organic conjugated materials.

PubMed

Nelson, Tammie; Fernandez-Alberti, Sebastian; Roitberg, Adrian E; Tretiak, Sergei

2014-04-15

To design functional photoactive materials for a variety of technological applications, researchers need to understand their electronic properties in detail and have ways to control their photoinduced pathways. When excited by photons of light, organic conjugated materials (OCMs) show dynamics that are often characterized by large nonadiabatic (NA) couplings between multiple excited states through a breakdown of the Born-Oppenheimer (BO) approximation. Following photoexcitation, various nonradiative intraband relaxation pathways can lead to a number of complex processes. Therefore, computational simulation of nonadiabatic molecular dynamics is an indispensable tool for understanding complex photoinduced processes such as internal conversion, energy transfer, charge separation, and spatial localization of excitons. Over the years, we have developed a nonadiabatic excited-state molecular dynamics (NA-ESMD) framework that efficiently and accurately describes photoinduced phenomena in extended conjugated molecular systems. We use the fewest-switches surface hopping (FSSH) algorithm to treat quantum transitions among multiple adiabatic excited state potential energy surfaces (PESs). Extended molecular systems often contain hundreds of atoms and involve large densities of excited states that participate in the photoinduced dynamics. We can achieve an accurate description of the multiple excited states using the configuration interaction single (CIS) formalism with a semiempirical model Hamiltonian. Analytical techniques allow the trajectory to be propagated "on the fly" using the complete set of NA coupling terms and remove computational bottlenecks in the evaluation of excited-state gradients and NA couplings. Furthermore, the use of state-specific gradients for propagation of nuclei on the native excited-state PES eliminates the need for simplifications such as the classical path approximation (CPA), which only uses ground-state gradients. Thus, the NA-ESMD methodology offers a computationally tractable route for simulating hundreds of atoms on ~10 ps time scales where multiple coupled excited states are involved. In this Account, we review recent developments in the NA-ESMD modeling of photoinduced dynamics in extended conjugated molecules involving multiple coupled electronic states. We have successfully applied the outlined NA-ESMD framework to study ultrafast conformational planarization in polyfluorenes where the rate of torsional relaxation can be controlled based on the initial excitation. With the addition of the state reassignment algorithm to identify instances of unavoided crossings between noninteracting PESs, NA-ESMD can now be used to study systems in which these so-called trivial unavoided crossings are expected to predominate. We employ this technique to analyze the energy transfer between poly(phenylene vinylene) (PPV) segments where conformational fluctuations give rise to numerous instances of unavoided crossings leading to multiple pathways and complex energy transfer dynamics that cannot be described using a simple Förster model. In addition, we have investigated the mechanism of ultrafast unidirectional energy transfer in dendrimers composed of poly(phenylene ethynylene) (PPE) chromophores and have demonstrated that differential nuclear motion favors downhill energy transfer in dendrimers. The use of native excited-state gradients allows us to observe this feature.

Application of multivariate chemometric techniques for simultaneous determination of five parameters of cottonseed oil by single bounce attenuated total reflectance Fourier transform infrared spectroscopy.

PubMed

Talpur, M Younis; Kara, Huseyin; Sherazi, S T H; Ayyildiz, H Filiz; Topkafa, Mustafa; Arslan, Fatma Nur; Naz, Saba; Durmaz, Fatih; Sirajuddin

2014-11-01

Single bounce attenuated total reflectance (SB-ATR) Fourier transform infrared (FTIR) spectroscopy in conjunction with chemometrics was used for accurate determination of free fatty acid (FFA), peroxide value (PV), iodine value (IV), conjugated diene (CD) and conjugated triene (CT) of cottonseed oil (CSO) during potato chips frying. Partial least square (PLS), stepwise multiple linear regression (SMLR), principal component regression (PCR) and simple Beer׳s law (SBL) were applied to develop the calibrations for simultaneous evaluation of five stated parameters of cottonseed oil (CSO) during frying of French frozen potato chips at 170°C. Good regression coefficients (R(2)) were achieved for FFA, PV, IV, CD and CT with value of >0.992 by PLS, SMLR, PCR, and SBL. Root mean square error of prediction (RMSEP) was found to be less than 1.95% for all determinations. Result of the study indicated that SB-ATR FTIR in combination with multivariate chemometrics could be used for accurate and simultaneous determination of different parameters during the frying process without using any toxic organic solvent. Copyright © 2014 Elsevier B.V. All rights reserved.

The Gemini-South MCAO operational model: insights on a new era of telescope operation

NASA Astrophysics Data System (ADS)

Trancho, Gelys; Bec, Matthieu; Artigau, Etienne; d'Orgeville, Celine; Gratadour, Damien; Rigaut, Francois J.; Walls, Brian

2008-07-01

The Gemini Observatory is implementing a Multi-Conjugate Adaptive Optics (MCAO) system as a facility instrument for the Gemini South telescope (GeMS). The system will include 5 Laser Guide Stars, 3 Natural Guide Stars, and 3 deformable mirrors, optically conjugated at different altitudes, to achieve near-uniform atmospheric compensation over a one arc minute square field of view. This setup implies some level of operational complexity. In this paper we describe how GeMS will be integrated into the flow of Gemini operations, from the observing procedures necessary to execute the programs in the queue (telescope control software, observing tools, sequence executor) to the safety implementation needed such as spotters/ASCAM, space command and laser traffic control software.

Method and apparatus for second-rank tensor generation

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang (Inventor)

1991-01-01

A method and apparatus are disclosed for generation of second-rank tensors using a photorefractive crystal to perform the outer-product between two vectors via four-wave mixing, thereby taking 2n input data to a control n squared output data points. Two orthogonal amplitude modulated coherent vector beams x and y are expanded and then parallel sides of the photorefractive crystal in exact opposition. A beamsplitter is used to direct a coherent pumping beam onto the crystal at an appropriate angle so as to produce a conjugate beam that is the matrix product of the vector beam that propagates in the exact opposite direction from the pumping beam. The conjugate beam thus separated is the tensor output xy (sup T).

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1986-01-01

Various graduate research activities in the field of computer science are reported. Among the topics discussed are: (1) failure probabilities in multi-version software; (2) Gaussian Elimination on parallel computers; (3) three dimensional Poisson solvers on parallel/vector computers; (4) automated task decomposition for multiple robot arms; (5) multi-color incomplete cholesky conjugate gradient methods on the Cyber 205; and (6) parallel implementation of iterative methods for solving linear equations.

A Fast Deep Learning System Using GPU

DTIC Science & Technology

2014-06-01

hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and...widely used in data modeling until three decades later when efficient training algorithm for RBM is invented by Hinton [3] and the computing power is...be trained using most of optimization algorithms , such as BP, conjugate gradient descent (CGD) or Levenberg-Marquardt (LM). The advantage of this

Conference Proceedings: 7th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, California, March 18-22, 1991

DTIC Science & Technology

1991-03-01

34Volume integral Equations and Conjugate Gradient Methods in Electromagnetic Non destructive Evaluation’ by Dr. Harold P.. Sabbagh, Sabbagh Associates...8217 Experimental Demonstrations far teaching Electroamgnetic Folods and Energy’ M. Zathn, J. Mectrer...8217-....................................... . ...................................................... 329 ’PoalarimetrIc Scattering and Control at Radar Crass Section of Chirat Targets at Simple

Analysis and diagnosis of basal cell carcinoma (BCC) via infrared imaging

NASA Astrophysics Data System (ADS)

Flores-Sahagun, J. H.; Vargas, J. V. C.; Mulinari-Brenner, F. A.

2011-09-01

In this work, a structured methodology is proposed and tested through infrared imaging temperature measurements of a healthy control group to establish expected normality ranges and of basal cell carcinoma patients (a type of skin cancer) previously diagnosed through biopsies of the affected regions. A method of conjugated gradients is proposed to compare measured dimensionless temperature difference values (Δ θ) between two symmetric regions of the patient's body, that takes into account the skin, the surrounding ambient and the individual core temperatures and doing so, the limitation of the results interpretation for different individuals become simple and nonsubjective. The range of normal temperatures in different regions of the body for seven healthy individuals was determined, and admitting that the human skin exhibits a unimodal normal distribution, the normal range for each region was considered to be the mean dimensionless temperature difference plus/minus twice the standard deviation of the measurements (Δθ±2σ) in order to represent 95% of the population. Eleven patients with previously diagnosed basal cell carcinoma through biopsies were examined with the method, which was capable of detecting skin abnormalities in all cases. Therefore, the conjugated gradients method was considered effective in the identification of the basal cell carcinoma through infrared imaging even with the use of a low optical resolution camera (160 × 120 pixels) and a thermal resolution of 0.1 °C. The method could also be used to scan a larger area around the lesion in order to detect the presence of other lesions still not perceptible in the clinical exam. However, it is necessary that a temperature differences mesh-like mapping of the healthy human body skin is produced, so that the comparison of the patient Δ θ could be made with the exact region of such mapping in order to possibly make a more effective diagnosis. Finally, the infrared image analyzed through the conjugated gradients method could be useful in the definition of a better safety margin in the surgery for the removal of the lesion, both minimizing esthetics damage to the patient and possibly avoiding basal cell carcinoma recurrence.

A biconjugate gradient type algorithm on massively parallel architectures

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Hochbruck, Marlis

1991-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. Recently, Freund and Nachtigal have proposed a novel BCG type approach, the quasi-minimal residual method (QMR), which overcomes the problems of BCG. Here, an implementation is presented of QMR based on an s-step version of the nonsymmetric look-ahead Lanczos algorithm. The main feature of the s-step Lanczos algorithm is that, in general, all inner products, except for one, can be computed in parallel at the end of each block; this is unlike the other standard Lanczos process where inner products are generated sequentially. The resulting implementation of QMR is particularly attractive on massively parallel SIMD architectures, such as the Connection Machine.

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Environmental gradients explain species richness and community composition of coastal breeding birds in the Baltic Sea.

PubMed

Nord, Maria; Forslund, Pär

2015-01-01

Scientifically-based systematic conservation planning for reserve design requires knowledge of species richness patterns and how these are related to environmental gradients. In this study, we explore a large inventory of coastal breeding birds, in total 48 species, sampled in 4646 1 km2 squares which covered a large archipelago in the Baltic Sea on the east coast of Sweden. We analysed how species richness (α diversity) and community composition (β diversity) of two groups of coastal breeding birds (specialists, i.e. obligate coastal breeders; generalists, i.e. facultative coastal breeders) were affected by distance to open sea, land area, shoreline length and archipelago width. The total number of species per square increased with increasing shoreline length, but increasing land area counteracted this effect in specialists. The number of specialist bird species per square increased with decreasing distance to open sea, while the opposite was true for the generalists. Differences in community composition between squares were associated with differences in land area and distance to open sea, both when considering all species pooled and each group separately. Fourteen species were nationally red-listed, and showed similar relationships to the environmental gradients as did all species, specialists and generalists. We suggest that availability of suitable breeding habitats, and probably also proximity to feeding areas, explain much of the observed spatial distributions of coastal birds in this study. Our findings have important implications for systematic conservation planning of coastal breeding birds. In particular, we provide information on where coastal breeding birds occur and which environments they seem to prefer. Small land areas with long shorelines are highly valuable both in general and for red-listed species. Thus, such areas should be prioritized for protection against human disturbance and used by management in reserve selection.

Environmental Gradients Explain Species Richness and Community Composition of Coastal Breeding Birds in the Baltic Sea

PubMed Central

Nord, Maria; Forslund, Pär

2015-01-01

Scientifically-based systematic conservation planning for reserve design requires knowledge of species richness patterns and how these are related to environmental gradients. In this study, we explore a large inventory of coastal breeding birds, in total 48 species, sampled in 4646 1 km2 squares which covered a large archipelago in the Baltic Sea on the east coast of Sweden. We analysed how species richness (α diversity) and community composition (β diversity) of two groups of coastal breeding birds (specialists, i.e. obligate coastal breeders; generalists, i.e. facultative coastal breeders) were affected by distance to open sea, land area, shoreline length and archipelago width. The total number of species per square increased with increasing shoreline length, but increasing land area counteracted this effect in specialists. The number of specialist bird species per square increased with decreasing distance to open sea, while the opposite was true for the generalists. Differences in community composition between squares were associated with differences in land area and distance to open sea, both when considering all species pooled and each group separately. Fourteen species were nationally red-listed, and showed similar relationships to the environmental gradients as did all species, specialists and generalists. We suggest that availability of suitable breeding habitats, and probably also proximity to feeding areas, explain much of the observed spatial distributions of coastal birds in this study. Our findings have important implications for systematic conservation planning of coastal breeding birds. In particular, we provide information on where coastal breeding birds occur and which environments they seem to prefer. Small land areas with long shorelines are highly valuable both in general and for red-listed species. Thus, such areas should be prioritized for protection against human disturbance and used by management in reserve selection. PMID:25714432

Finite-temperature stress calculations in atomic models using moments of position.

PubMed

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-04

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

Finite-temperature stress calculations in atomic models using moments of position

NASA Astrophysics Data System (ADS)

Parthasarathy, Ranganathan; Misra, Anil; Ouyang, Lizhi

2018-07-01

Continuum modeling of finite temperature mechanical behavior of atomic systems requires refined description of atomic motions. In this paper, we identify additional kinematical quantities that are relevant for a more accurate continuum description as the system is subjected to step-wise loading. The presented formalism avoids the necessity for atomic trajectory mapping with deformation, provides the definitions of the kinematic variables and their conjugates in real space, and simplifies local work conjugacy. The total work done on an atom under deformation is decomposed into the work corresponding to changing its equilibrium position and work corresponding to changing its second moment about equilibrium position. Correspondingly, we define two kinematic variables: a deformation gradient tensor and a vibration tensor, and derive their stress conjugates, termed here as static and vibration stresses, respectively. The proposed approach is validated using MD simulation in NVT ensembles for fcc aluminum subjected to uniaxial extension. The observed evolution of second moments in the MD simulation with macroscopic deformation is not directly related to the transformation of atomic trajectories through the deformation gradient using generator functions. However, it is noteworthy that deformation leads to a change in the second moment of the trajectories. Correspondingly, the vibration part of the Piola stress becomes particularly significant at high temperature and high tensile strain as the crystal approaches the softening limit. In contrast to the eigenvectors of the deformation gradient, the eigenvectors of the vibration tensor show strong spatial heterogeneity in the vicinity of softening. More importantly, the elliptic distribution of local atomic density transitions to a dumbbell shape, before significant non-affinity in equilibrium positions has occurred.

Numerical algorithms for scatter-to-attenuation reconstruction in PET: empirical comparison of convergence, acceleration, and the effect of subsets.

PubMed

Berker, Yannick; Karp, Joel S; Schulz, Volkmar

2017-09-01

The use of scattered coincidences for attenuation correction of positron emission tomography (PET) data has recently been proposed. For practical applications, convergence speeds require further improvement, yet there exists a trade-off between convergence speed and the risk of non-convergence. In this respect, a maximum-likelihood gradient-ascent (MLGA) algorithm and a two-branch back-projection (2BP), which was previously proposed, were evaluated. MLGA was combined with the Armijo step size rule; and accelerated using conjugate gradients, Nesterov's momentum method, and data subsets of different sizes. In 2BP, we varied the subset size, an important determinant of convergence speed and computational burden. We used three sets of simulation data to evaluate the impact of a spatial scale factor. The Armijo step size allowed 10-fold increased step sizes compared to native MLGA. Conjugate gradients and Nesterov momentum lead to slightly faster, yet non-uniform convergence; improvements were mostly confined to later iterations, possibly due to the non-linearity of the problem. MLGA with data subsets achieved faster, uniform, and predictable convergence, with a speed-up factor equivalent to the number of subsets and no increase in computational burden. By contrast, 2BP computational burden increased linearly with the number of subsets due to repeated evaluation of the objective function, and convergence was limited to the case of many (and therefore small) subsets, which resulted in high computational burden. Possibilities of improving 2BP appear limited. While general-purpose acceleration methods appear insufficient for MLGA, results suggest that data subsets are a promising way of improving MLGA performance.

The relationship between tree canopy and crime rates across an urban-rural gradient in the greater Baltimore region

Treesearch

Austin Troy; J. Morgan Grove; Jarlath O' Neill-Dunne

2012-01-01

The extent to which urban tree cover influences crime is in debate in the literature. This research took advantage of geocoded crime point data and high resolution tree canopy data to address this question in Baltimore City and County, MD, an area that includes a significant urban-rural gradient. Using ordinary least squares and spatially adjusted regression and...

Nucleus detection using gradient orientation information and linear least squares regression

NASA Astrophysics Data System (ADS)

Kwak, Jin Tae; Hewitt, Stephen M.; Xu, Sheng; Pinto, Peter A.; Wood, Bradford J.

2015-03-01

Computerized histopathology image analysis enables an objective, efficient, and quantitative assessment of digitized histopathology images. Such analysis often requires an accurate and efficient detection and segmentation of histological structures such as glands, cells and nuclei. The segmentation is used to characterize tissue specimens and to determine the disease status or outcomes. The segmentation of nuclei, in particular, is challenging due to the overlapping or clumped nuclei. Here, we propose a nuclei seed detection method for the individual and overlapping nuclei that utilizes the gradient orientation or direction information. The initial nuclei segmentation is provided by a multiview boosting approach. The angle of the gradient orientation is computed and traced for the nuclear boundaries. Taking the first derivative of the angle of the gradient orientation, high concavity points (junctions) are discovered. False junctions are found and removed by adopting a greedy search scheme with the goodness-of-fit statistic in a linear least squares sense. Then, the junctions determine boundary segments. Partial boundary segments belonging to the same nucleus are identified and combined by examining the overlapping area between them. Using the final set of the boundary segments, we generate the list of seeds in tissue images. The method achieved an overall precision of 0.89 and a recall of 0.88 in comparison to the manual segmentation.

Supplemental optical specifications for imaging systems: parameters of phase gradient

NASA Astrophysics Data System (ADS)

Xuan, Bin; Li, Jun-Feng; Wang, Peng; Chen, Xiao-Ping; Song, Shu-Mei; Xie, Jing-Jiang

2009-12-01

Specifications of phase error, peak to valley (PV), and root mean square (rms) are not able to represent the properties of a wavefront reasonably because of their irresponsibility for spatial frequencies. Power spectral density is a parameter that is especially effective to indicate the frequency regime. However, it seems not convenient for opticians to implement. Parameters of phase gradient, PV gradient, and rms gradient are most correlated with a point-spread function of an imaging system, and they can provide clear instruction of manufacture. The algorithms of gradient parameters have been modified in order to represent the image quality better. In order to demonstrate the analyses, an experimental spherical mirror has been worked out. It is clear that imaging performances can be maintained while manufacture difficulties are decreased when a reasonable trade-off between specifications of phase error and phase gradient is made.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

PubMed Central

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-01

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer’s Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26-cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients. PMID:28033119

L-Valine appended PLGA nanoparticles for oral insulin delivery.

PubMed

Jain, Ashish; Jain, Sanjay K

2015-08-01

Oral insulin delivery has been the major research issue, since many decades, due to several obvious advantages over other routes. However, this route poses several constraints for the delivery of peptides and proteins which are to be worked upon. The small intestine has been shown to be able to transport the L-forms of amino acids against a concentration gradient and that they compete for the mechanism concerned. So, L-valine was used as a ligand for carrier-mediated transport of insulin-loaded polylactic-co-glycolic acid (PLGA) nanoparticles (NPs). L-Valine-conjugated PLGA nanoparticles were prepared using double emulsion solvent evaporation method. The NPs and conjugated NPs were characterized for their size, drug entrapment efficiency, zeta potential, polydispersity index and in vitro insulin release. Ex vivo studies on intestine revealed that conjugated nanoparticles showed greater insulin uptake as compared to non-conjugated nanoparticles. In vivo studies were performed on streptozotocin-induced diabetic rabbits. Oral suspension of insulin-loaded PLGA nanoparticles reduced blood glucose level from 265.4 ± 8.5 to 246.6 ± 2.4 mg/dL within 4 h which further decreased to 198.7 ± 7.1 mg/dL value after 8 h. The ligand-conjugated formulation on oral administration produced hypoglycaemic effect (216.9 ± 1.9 mg/dL) within 4 h of administration, and the hypoglycaemic effect prolonged till 12 h of oral administration. Simultaneously, the insulin concentration in withdrawn samples was also assessed and found that profile of insulin level is in compliance with the blood glucose reduction profile. Hence, it is concluded that the L-valine-conjugated NPs bearing insulin are the promising carrier for the transportation of insulin across the intestine on oral administration.

Non-linear Multidimensional Optimization for use in Wire Scanner Fitting

NASA Astrophysics Data System (ADS)

Henderson, Alyssa; Terzic, Balsa; Hofler, Alicia; CASA and Accelerator Ops Collaboration

2013-10-01

To ensure experiment efficiency and quality from the Continuous Electron Beam Accelerator at Jefferson Lab, beam energy, size, and position must be measured. Wire scanners are devices inserted into the beamline to produce measurements which are used to obtain beam properties. Extracting physical information from the wire scanner measurements begins by fitting Gaussian curves to the data. This study focuses on optimizing and automating this curve-fitting procedure. We use a hybrid approach combining the efficiency of Newton Conjugate Gradient (NCG) method with the global convergence of three nature-inspired (NI) optimization approaches: genetic algorithm, differential evolution, and particle-swarm. In this Python-implemented approach, augmenting the locally-convergent NCG with one of the globally-convergent methods ensures the quality, robustness, and automation of curve-fitting. After comparing the methods, we establish that given an initial data-derived guess, each finds a solution with the same chi-square- a measurement of the agreement of the fit to the data. NCG is the fastest method, so it is the first to attempt data-fitting. The curve-fitting procedure escalates to one of the globally-convergent NI methods only if NCG fails, thereby ensuring a successful fit. This method allows for the most optimal signal fit and can be easily applied to similar problems. Financial support from DoE, NSF, ODU, DoD, and Jefferson Lab.

An experimental study of interstitial lung tissue classification in HRCT images using ANN and role of cost functions

NASA Astrophysics Data System (ADS)

Dash, Jatindra K.; Kale, Mandar; Mukhopadhyay, Sudipta; Khandelwal, Niranjan; Prabhakar, Nidhi; Garg, Mandeep; Kalra, Naveen

2017-03-01

In this paper, we investigate the effect of the error criteria used during a training phase of the artificial neural network (ANN) on the accuracy of the classifier for classification of lung tissues affected with Interstitial Lung Diseases (ILD). Mean square error (MSE) and the cross-entropy (CE) criteria are chosen being most popular choice in state-of-the-art implementations. The classification experiment performed on the six interstitial lung disease (ILD) patterns viz. Consolidation, Emphysema, Ground Glass Opacity, Micronodules, Fibrosis and Healthy from MedGIFT database. The texture features from an arbitrary region of interest (AROI) are extracted using Gabor filter. Two different neural networks are trained with the scaled conjugate gradient back propagation algorithm with MSE and CE error criteria function respectively for weight updation. Performance is evaluated in terms of average accuracy of these classifiers using 4 fold cross-validation. Each network is trained for five times for each fold with randomly initialized weight vectors and accuracies are computed. Significant improvement in classification accuracy is observed when ANN is trained by using CE (67.27%) as error function compared to MSE (63.60%). Moreover, standard deviation of the classification accuracy for the network trained with CE (6.69) error criteria is found less as compared to network trained with MSE (10.32) criteria.

Density Functional Theory Calculations of the Dissociation of H[2] on (100) 2H-MoS[2] Surfaces: A Key Step in the Hydroprocessing of Crude Oil

ERIC Educational Resources Information Center

Todorova, Teodora; Alexiev, Valentin; Weber, Thomas

2006-01-01

Hydrogen activation on the (100) surface of MoS[2] structures was investigated by means of density functional theory calculations. Linear and quadratic synchronous transit methods with a conjugate gradient refinement of the saddle point were used to localize transition states. The calculations include heterolytic and homolytic dissociation of…

A technique for accelerating the convergence of restarted GMRES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, A H; Jessup, E R; Manteuffel, T

2004-03-09

We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.

A modified conjugate gradient method based on the Tikhonov system for computerized tomography (CT).

PubMed

Wang, Qi; Wang, Huaxiang

2011-04-01

During the past few decades, computerized tomography (CT) was widely used for non-destructive testing (NDT) and non-destructive examination (NDE) in the industrial area because of its characteristics of non-invasiveness and visibility. Recently, CT technology has been applied to multi-phase flow measurement. Using the principle of radiation attenuation measurements along different directions through the investigated object with a special reconstruction algorithm, cross-sectional information of the scanned object can be worked out. It is a typical inverse problem and has always been a challenge for its nonlinearity and ill-conditions. The Tikhonov regulation method is widely used for similar ill-posed problems. However, the conventional Tikhonov method does not provide reconstructions with qualities good enough, the relative errors between the reconstructed images and the real distribution should be further reduced. In this paper, a modified conjugate gradient (CG) method is applied to a Tikhonov system (MCGT method) for reconstructing CT images. The computational load is dominated by the number of independent measurements m, and a preconditioner is imported to lower the condition number of the Tikhonov system. Both simulation and experiment results indicate that the proposed method can reduce the computational time and improve the quality of image reconstruction. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

USGS Publications Warehouse

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.

Bundle block adjustment of large-scale remote sensing data with Block-based Sparse Matrix Compression combined with Preconditioned Conjugate Gradient

NASA Astrophysics Data System (ADS)

Zheng, Maoteng; Zhang, Yongjun; Zhou, Shunping; Zhu, Junfeng; Xiong, Xiaodong

2016-07-01

In recent years, new platforms and sensors in photogrammetry, remote sensing and computer vision areas have become available, such as Unmanned Aircraft Vehicles (UAV), oblique camera systems, common digital cameras and even mobile phone cameras. Images collected by all these kinds of sensors could be used as remote sensing data sources. These sensors can obtain large-scale remote sensing data which consist of a great number of images. Bundle block adjustment of large-scale data with conventional algorithm is very time and space (memory) consuming due to the super large normal matrix arising from large-scale data. In this paper, an efficient Block-based Sparse Matrix Compression (BSMC) method combined with the Preconditioned Conjugate Gradient (PCG) algorithm is chosen to develop a stable and efficient bundle block adjustment system in order to deal with the large-scale remote sensing data. The main contribution of this work is the BSMC-based PCG algorithm which is more efficient in time and memory than the traditional algorithm without compromising the accuracy. Totally 8 datasets of real data are used to test our proposed method. Preliminary results have shown that the BSMC method can efficiently decrease the time and memory requirement of large-scale data.

Modeling of Field-Aligned Guided Echoes in the Plasmasphere

NASA Technical Reports Server (NTRS)

Fung, Shing F.; Green, James L.

2004-01-01

The conditions under which high frequency (f>>f(sub uh)) long-range extraordinary-mode discrete field-aligned echoes observed by the Radio Plasma Imager (RPI) on board the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) satellite in the plasmasphere are investigated by ray tracing modeling. Field-aligned discrete echoes are most commonly observed by RPI in the plasmasphere although they are also observed over the polar cap region. The plasmasphere field-aligned echoes appearing as multiple echo traces at different virtual ranges are attributed to signals reflected successively between conjugate hemispheres that propagate along or nearly along closed geomagnetic field lines. The ray tracing simulations show that field-aligned ducts with as little as 1% density perturbations (depletions) and less than 10 wavelengths wide can guide nearly field-aligned propagating high frequency X mode waves. Effective guidance of wave at a given frequency and wave normal angle (Psi) depends on the cross-field density scale of the duct, such that ducts with stronger density depletions need to be wider in order to maintain the same gradient of refractive index across the magnetic field. While signal guidance by field aligned density gradient without ducting is possible only over the polar region, conjugate field-aligned echoes that have traversed through the equatorial region are most likely guided by ducting.

Uptake and intracellular fate of [14C]sucrose-insulin in perfused rat livers.

PubMed

Surmacz, C A; Wert, J J; Ward, W F; Mortimore, G E

1988-07-01

Insulin was covalently linked to [14C]sucrose by means of cyanuric chloride to provide a label that would remain entrapped within the vacuolar system. The uptake of the conjugate by the perfused rat liver was rapid (half-life = 2.9 min), competitively inhibited by native insulin, and abolished by alkali denaturation. As assessed by its distribution on self-generating gradients of colloidal silica-povidone, label in lysosome-enriched samples of liver taken at different times after the addition of the conjugate moved progressively during 15 min from the plasma membrane into an intermediate peak and then to dense lysosomal fractions. After 30-60 min, the label had equilibrated throughout the lysosomal-vacuolar system. The initial movement from the plasma membrane to the intermediate peak occurred between 2 and 5 min. Because label in the peak could be physically separated from the lysosomal marker, beta-acetylglucosaminidase, by dispersing the sample through the gradient mixture before centrifugation rather than layering it, we concluded that the intermediate particles in question were not lysosomal in nature. On gel-filtration chromatography, label extracted from the intermediate peak did not move with insulin but rather as a broad band of lower molecular weight products, suggesting that insulin is subject to early proteolytic attack within a nonlysosomal compartment.

Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion

NASA Astrophysics Data System (ADS)

Dehiya, Rahul; Singh, Arun; Gupta, Pravin K.; Israil, M.

2017-01-01

We present the features and results of a newly developed code, based on Gauss-Newton optimization technique, for solving three-dimensional Controlled-Source Electromagnetic inverse problem. In this code a special emphasis has been put on representing the operations by block matrices for conjugate gradient iteration. We show how in the computation of Jacobian, the matrix formed by differentiation of system matrix can be made independent of frequency to optimize the operations at conjugate gradient step. The coarse level parallel computing, using OpenMP framework, is used primarily due to its simplicity in implementation and accessibility of shared memory multi-core computing machine to almost anyone. We demonstrate how the coarseness of modeling grid in comparison to source (comp`utational receivers) spacing can be exploited for efficient computing, without compromising the quality of the inverted model, by reducing the number of adjoint calls. It is also demonstrated that the adjoint field can even be computed on a grid coarser than the modeling grid without affecting the inversion outcome. These observations were reconfirmed using an experiment design where the deviation of source from straight tow line is considered. Finally, a real field data inversion experiment is presented to demonstrate robustness of the code.

Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Wang, Jun; Luo, Ray

2009-01-01

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

TV-based conjugate gradient method and discrete L-curve for few-view CT reconstruction of X-ray in vivo data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaoli; Hofmann, Ralf; Dapp, Robin

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 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 numbermore » 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. (C) 2015 Optical Society of America« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stavis, Samuel M; Edel, Joshua B; Samiee, Kevan T

A nanofluidic channel fabricated in fused silica with an approximately 500 nm square cross section was used to isolate, detect and identify individual quantum dot conjugates. The channel enables the rapid detection of every fluorescent entity in solution. A laser of selected wavelength was used to excite multiple species of quantum dots and organic molecules, and the emission spectra were resolved without significant signal rejection. Quantum dots were then conjugated with organic molecules and detected to demonstrate efficient multicolor detection. PCH was used to analyze coincident detection and to characterize the degree of binding. The use of a small fluidicmore » channel to detect quantum dots as fluorescent labels was shown to be an efficient technique for multiplexed single molecule studies. Detection of single molecule binding events has a variety of applications including high throughput immunoassays.« less

An historical survey of computational methods in optimal control.

NASA Technical Reports Server (NTRS)

Polak, E.

1973-01-01

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Fine-scale features in the far-field of a turbulent jet

NASA Astrophysics Data System (ADS)

Buxton, Oliver; Ganapathisubramani, Bharathram

2008-11-01

The structure of a fully turbulent axisymmetric jet, at Reynolds number based on jet exit conditions of 5000, is investigated with cinematographic (1 kHz) stereoscopic PIV in a plane normal to the jet axis. Taylor's hypothesis is employed to calculate all three velocity gradients in the axial direction. The technique's resolution allows all terms of the velocity gradient tensor, hence strain rate tensor and kinetic energy dissipation, to be computed at each point within the plane. The data reveals that the vorticity field is dominated by high enstrophy tube-like structures. Conversely, the dissipation field appears to consist of sheet-like structures. Several criteria for isolating these strongly swirling vortical structures from the background turbulence were employed. One such technique involves isolating points in which the velocity gradient tensor has a real and a pair of complex conjugate eigenvectors. Once identified, the alignment of the various structures with relation to the vorticity vector and the real velocity gradient tensor eigenvector is investigated. The effect of the strain field on the geometry of the structures is also examined.

Statistical Characterization of Altitude Matrices by Computer. Report 4. Frequency Distributions of Gradient.

DTIC Science & Technology

1977-01-01

balanced at the mean, with the central part steeper ( platykurtic : broad mode or truncated tails) -r flatter (leptokurtic: peaked mode or extended...and NUPUR, have negative kurtosis (they are platykurtic , with truncated tails and/or broad modes relative to their standard deviations) FERRO, on the...the other areas, and its gradients are platykurtic but almost unskewed. Hence the square root of sine transformation (Fig,15) and the log tangent

Performance analysis of structured gradient algorithm. [for adaptive beamforming linear arrays

NASA Technical Reports Server (NTRS)

Godara, Lal C.

1990-01-01

The structured gradient algorithm uses a structured estimate of the array correlation matrix (ACM) to estimate the gradient required for the constrained least-mean-square (LMS) algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied.

Gradient pattern analysis applied to galaxy morphology

NASA Astrophysics Data System (ADS)

Rosa, R. R.; de Carvalho, R. R.; Sautter, R. A.; Barchi, P. H.; Stalder, D. H.; Moura, T. C.; Rembold, S. B.; Morell, D. R. F.; Ferreira, N. C.

2018-06-01

Gradient pattern analysis (GPA) is a well-established technique for measuring gradient bilateral asymmetries of a square numerical lattice. This paper introduces an improved version of GPA designed for galaxy morphometry. We show the performance of the new method on a selected sample of 54 896 objects from the SDSS-DR7 in common with Galaxy Zoo 1 catalogue. The results suggest that the second gradient moment, G2, has the potential to dramatically improve over more conventional morphometric parameters. It separates early- from late-type galaxies better (˜ 90 per cent) than the CAS system (C˜ 79 per cent, A˜ 50 per cent, S˜ 43 per cent) and a benchmark test shows that it is applicable to hundreds of thousands of galaxies using typical processing systems.

Gradient Pattern Analysis Applied to Galaxy Morphology

NASA Astrophysics Data System (ADS)

Rosa, R. R.; de Carvalho, R. R.; Sautter, R. A.; Barchi, P. H.; Stalder, D. H.; Moura, T. C.; Rembold, S. B.; Morell, D. R. F.; Ferreira, N. C.

2018-04-01

Gradient pattern analysis (GPA) is a well-established technique for measuring gradient bilateral asymmetries of a square numerical lattice. This paper introduces an improved version of GPA designed for galaxy morphometry. We show the performance of the new method on a selected sample of 54,896 objects from the SDSS-DR7 in common with Galaxy Zoo 1 catalog. The results suggest that the second gradient moment, G2, has the potential to dramatically improve over more conventional morphometric parameters. It separates early from late type galaxies better (˜90%) than the CAS system (C ˜ 79%, A ˜ 50%, S ˜ 43%) and a benchmark test shows that it is applicable to hundreds of thousands of galaxies using typical processing systems.

Inhomogeneous field induced magnetoelectric effect in Mott insulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boulaevskii, Lev N; Batista, Cristian D

2008-01-01

We consider a Mott insulator like HoMnO{sub 3} whose magnetic lattice is geometrically frustrated and comprises a 3D array of triangular layers with magnetic moments ordered in a 120{sup o} structure. We show that the effect of a uniform magnetic field gradient, {gradient}H, is to redistribute the electronic charge of the magnetically ordered phase leading to a unfirom electric field gradient. The resulting voltage difference between the crystal edges is proportional to the square of the crystal thickness, or inter-edge distance, L. It can reach values of several volts for |{gradient}H| {approx} 0.01 T/cm and L {approx_equal} 1mm, as longmore » as the crystal is free of antiferromagnetic domain walls.« less

Phase-unwrapping algorithm by a rounding-least-squares approach

NASA Astrophysics Data System (ADS)

Juarez-Salazar, Rigoberto; Robledo-Sanchez, Carlos; Guerrero-Sanchez, Fermin

2014-02-01

A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm's performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.

Influence of Turbulence Parameters, Reynolds Number, and Body Shape on Stagnation-Region Heat Transfer

NASA Technical Reports Server (NTRS)

Vanfossen, G. James; Simoneau, Robert J.; Ching, Chan Y.

1994-01-01

The purpose of the present work was threefold: (1) to determine if a free-stream turbulence length scale existed that would cause the greatest augmentation in stagnation-region heat transfer over laminar levels; (2) to investigate the effect of velocity gradient on stagnation-region heat transfer augmentation by free-stream turbulence; and (3) to develop a prediction tool for stagnation heat transfer in the presence of free-stream turbulence. Heat transfer was measured in the stagnation region of four models with elliptical leading edges that had ratios of major to minor axes of 1:1, 1.5:1, 2.25:1, and 3:1. Five turbulence-generating grids were fabricated; four were square mesh, biplane grids made from square bars. The fifth grid was an array of fine parallel wires that were perpendicular to the model spanwise direction. Heat transfer data were taken at Reynolds numbers ranging from 37 000 to 228 000. Turbulence intensities were in the range of 1.1 to 15.9% while the ratio of integral length scale to leading-edge diameter ranged from 0.05 to 0.30. Stagnation-point velocity gradient was varied by nearly 50%. Stagnation-region heat transfer augmentation was found to increase with decreasing length scale but no optimum length scale was found. Heat transfer augmentation due to turbulence was found to be unaffected by the velocity gradient near the leading edge. A correlation was developed that fit heat transfer data for the square-bar grids to within +/- 4%.

Ambiguity resolution for satellite Doppler positioning systems

NASA Technical Reports Server (NTRS)

Argentiero, P.; Marini, J.

1979-01-01

The implementation of satellite-based Doppler positioning systems frequently requires the recovery of transmitter position from a single pass of Doppler data. The least-squares approach to the problem yields conjugate solutions on either side of the satellite subtrack. It is important to develop a procedure for choosing the proper solution which is correct in a high percentage of cases. A test for ambiguity resolution which is the most powerful in the sense that it maximizes the probability of a correct decision is derived. When systematic error sources are properly included in the least-squares reduction process to yield an optimal solution the test reduces to choosing the solution which provides the smaller valuation of the least-squares loss function. When systematic error sources are ignored in the least-squares reduction, the most powerful test is a quadratic form comparison with the weighting matrix of the quadratic form obtained by computing the pseudoinverse of a reduced-rank square matrix. A formula for computing the power of the most powerful test is provided. Numerical examples are included in which the power of the test is computed for situations that are relevant to the design of a satellite-aided search and rescue system.

Calixarene-Mediated Liquid-Membrane Transport of Choline Conjugates.

PubMed

Adhikari, Birendra Babu; Fujii, Ayu; Schramm, Michael P

2014-05-01

A series of supramolecular calixarenes efficiently transport distinct molecular species through a liquid membrane when attached to a receptor-complementary choline handle. Calix-[6]arene hexacarboxylic acid was highly effective at transporting different target molecules against a pH gradient. Both carboxylic- and phosphonic-acid-functionalized calix[4]arenes effect transport without requiring a pH or ion gradient. NMR binding studies, two-phase solvent extraction, and three-phase transport experiments reveal the necessary and subtle parameters to effect the transport of molecules attached to a choline "handle". On the other hand, rescorin[4]arene cavitands, which have similar guest recognition profiles, did not transport guest molecules. These developments reveal new approaches towards attempting synthetic-receptor-mediated selective small-molecule transport in vesicular and cellular systems.

Deep Restricted Kernel Machines Using Conjugate Feature Duality.

PubMed

Suykens, Johan A K

2017-08-01

The aim of this letter is to propose a theory of deep restricted kernel machines offering new foundations for deep learning with kernel machines. From the viewpoint of deep learning, it is partially related to restricted Boltzmann machines, which are characterized by visible and hidden units in a bipartite graph without hidden-to-hidden connections and deep learning extensions as deep belief networks and deep Boltzmann machines. From the viewpoint of kernel machines, it includes least squares support vector machines for classification and regression, kernel principal component analysis (PCA), matrix singular value decomposition, and Parzen-type models. A key element is to first characterize these kernel machines in terms of so-called conjugate feature duality, yielding a representation with visible and hidden units. It is shown how this is related to the energy form in restricted Boltzmann machines, with continuous variables in a nonprobabilistic setting. In this new framework of so-called restricted kernel machine (RKM) representations, the dual variables correspond to hidden features. Deep RKM are obtained by coupling the RKMs. The method is illustrated for deep RKM, consisting of three levels with a least squares support vector machine regression level and two kernel PCA levels. In its primal form also deep feedforward neural networks can be trained within this framework.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant.

PubMed

Eidi, Zahra; Mohammad-Rafiee, Farshid; Khorrami, Mohammad; Gholami, Azam

2017-11-15

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

Accelerated gradient based diffuse optical tomographic image reconstruction.

PubMed

Biswas, Samir Kumar; Rajan, K; Vasu, R M

2011-01-01

Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, B; Southern Medical University, Guangzhou, Guangdong; Shen, C

Purpose: Multi-energy computed tomography (MECT) is an emerging application in medical imaging due to its ability of material differentiation and potential for molecular imaging. In MECT, image correlations at different spatial and channels exist. It is desirable to incorporate these correlations in reconstruction to improve image quality. For this purpose, this study proposes a MECT reconstruction technique that employes spatial spectral non-local means (ssNLM) regularization. Methods: We consider a kVp-switching scanning method in which source energy is rapidly switched during data acquisition. For each energy channel, this yields projection data acquired at a number of angles, whereas projection angles amongmore » channels are different. We formulate the reconstruction task as an optimziation problem. A least square term enfores data fidelity. A ssNLM term is used as regularization to encourage similarities among image patches at different spatial locations and channels. When comparing image patches at different channels, intensity difference were corrected by a transformation estimated via histogram equalization during the reconstruction process. Results: We tested our method in a simulation study with a NCAT phantom and an experimental study with a Gammex phantom. For comparison purpose, we also performed reconstructions using conjugate-gradient least square (CGLS) method and conventional NLM method that only considers spatial correlation in an image. ssNLM is able to better suppress streak artifacts. The streaks are along different projection directions in images at different channels. ssNLM discourages this dissimilarity and hence removes them. True image structures are preserved in this process. Measurements in regions of interests yield 1.1 to 3.2 and 1.5 to 1.8 times higher contrast to noise ratio than the NLM approach. Improvements over CGLS is even more profound due to lack of regularization in the CGLS method and hence amplified noise. Conclusion: The proposed ssNLM method for kVp-switching MECT reconstruction can achieve high quality MECT images.« less

Quantification and Reconstruction in Photoacoustic Tomography

NASA Astrophysics Data System (ADS)

Guo, Zijian

Optical absorption is closely associated with many physiological important parameters, such as the concentration and oxygen saturation of hemoglobin. Conventionally, accurate quantification in PAT requires knowledge of the optical fluence attenuation, acoustic pressure attenuation, and detection bandwidth. We circumvent this requirement by quantifying the optical absorption coefficients from the acoustic spectra of PA signals acquired at multiple optical wavelengths. We demonstrate the method using the optical-resolution photoacoustic microscopy (OR-PAM) and the acoustical-resolution photoacoustic microscopy (AR-PAM) in the optical ballistic regime and in the optical diffusive regime, respectively. The data acquisition speed in photoacoustic computed tomography (PACT) is limited by the laser repetition rate and the number of parallel ultrasound detecting channels. Reconstructing an image with fewer measurements can effectively accelerate the data acquisition and reduce the system cost. We adapted Compressed Sensing (CS) for the reconstruction in PACT. CS-based PACT was implemented as a non-linear conjugate gradient descent algorithm and tested with both phantom and in vivo experiments. Speckles have been considered ubiquitous in all scattering-based coherent imaging technologies. As a coherent imaging modality based on optical absorption, photoacoustic (PA) tomography (PAT) is generally devoid of speckles. PAT suppresses speckles by building up prominent boundary signals, via a mechanism similar to that of specular reflection. When imaging smooth boundary absorbing targets, the speckle visibility in PAT, which is defined as the ratio of the square root of the average power of speckles to that of boundaries, is inversely proportional to the square root of the absorber density. If the surfaces of the absorbing targets have uncorrelated height fluctuations, however, the boundary features may become fully developed speckles. The findings were validated by simulations and experiments. The first- and second-order statistics of PAT speckles were also studied experimentally. While the amplitude of the speckles follows a Gaussian distribution, the autocorrelation of the speckle patterns tracks that of the system point spread function.

Phase-space finite elements in a least-squares solution of the transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

MODFLOW-2000, The U.S. Geological Survey Modular Ground-Water Model -- GMG Linear Equation Solver Package Documentation

USGS Publications Warehouse

Wilson, John D.; Naff, Richard L.

2004-01-01

A geometric multigrid solver (GMG), based in the preconditioned conjugate gradient algorithm, has been developed for solving systems of equations resulting from applying the cell-centered finite difference algorithm to flow in porous media. This solver has been adapted to the U.S. Geological Survey ground-water flow model MODFLOW-2000. The documentation herein is a description of the solver and the adaptation to MODFLOW-2000.

Toward an Integrated Framwork for Data-Efficient Parametric Adaptive Detection

DTIC Science & Technology

2012-02-27

any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a ...SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON a . REPORT...2012-0534 Distribution A - Approved for Public Release The conjugate-gradient (CG) algorithm is investigated for reduced-rank STAP detection. A family

Conjugate Gradient Parametric Detection of Multichannel Signals (Preprint)

DTIC Science & Technology

2012-05-01

aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information...if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YY) 2...processing (STAP) detection is re- examined in this paper. Originally, the PAMF detector was introduced by using a multichannel autoregressive (AR

Estimation of the zeta potential and the dielectric constant using velocity measurements in the electroosmotic flows.

PubMed

Park, H M; Hong, S M

2006-12-15

In this paper we develop a method for the determination of the zeta potential zeta and the dielectric constant epsilon by exploiting velocity measurements of the electroosmotic flow in microchannels. The inverse problem is solved through the minimization of a performance function utilizing the conjugate gradient method. The present method is found to estimate zeta and epsilon with reasonable accuracy even with noisy velocity measurements.

Benchmarking and tuning the MILC code on clusters and supercomputers

NASA Astrophysics Data System (ADS)

Gottlieb, Steven

2002-03-01

Recently, we have benchmarked and tuned the MILC code on a number of architectures including Intel Itanium and Pentium IV (PIV), dual-CPU Athlon, and the latest Compaq Alpha nodes. Results will be presented for many of these, and we shall discuss some simple code changes that can result in a very dramatic speedup of the KS conjugate gradient on processors with more advanced memory systems such as PIV, IBM SP and Alpha.

Benchmarking and tuning the MILC code on clusters and supercomputers

NASA Astrophysics Data System (ADS)

Gottlieb, Steven

Recently, we have benchmarked and tuned the MILC code on a number of architectures including Intel Itanium and Pentium IV (PIV), dual-CPU Athlon, and the latest Compaq Alpha nodes. Results will be presented for many of these, and we shall discuss some simple code changes that can result in a very dramatic speedup of the KS conjugate gradient on processors with more advanced memory systems such as PIV, IBM SP and Alpha.

Automatic correction of intensity nonuniformity from sparseness of gradient distribution in medical images.

PubMed

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P; Gee, James C

2009-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities.

Automatic Correction of Intensity Nonuniformity from Sparseness of Gradient Distribution in Medical Images

PubMed Central

Zheng, Yuanjie; Grossman, Murray; Awate, Suyash P.; Gee, James C.

2013-01-01

We propose to use the sparseness property of the gradient probability distribution to estimate the intensity nonuniformity in medical images, resulting in two novel automatic methods: a non-parametric method and a parametric method. Our methods are easy to implement because they both solve an iteratively re-weighted least squares problem. They are remarkably accurate as shown by our experiments on images of different imaged objects and from different imaging modalities. PMID:20426191

Evolution of passive scalar statistics in a spatially developing turbulence

NASA Astrophysics Data System (ADS)

Paul, I.; Papadakis, G.; Vassilicos, J. C.

2018-02-01

We investigate the evolution of passive scalar statistics in a spatially developing turbulence using direct numerical simulation. Turbulence is generated by a square grid element, which is heated continuously, and the passive scalar is temperature. The square element is the fundamental building block for both regular and fractal grids. We trace the dominant mechanisms responsible for the dynamical evolution of scalar-variance and its dissipation along the bar and grid-element centerlines. The scalar-variance is generated predominantly by the action of the mean scalar gradient behind the bar and is transported laterally by turbulent fluctuations to the grid-element centerline. The scalar-variance dissipation (proportional to the scalar-gradient variance) is produced primarily by the compression of the fluctuating scalar-gradient vector by the turbulent strain rate, while the contribution of mean velocity and scalar fields is negligible. Close to the grid element the scalar spectrum exhibits a well-defined -5 /3 power-law, even though the basic premises of the Kolmogorov-Obukhov-Corrsin theory are not satisfied (the fluctuating scalar field is highly intermittent, inhomogeneous, and anisotropic, and the local Corrsin-microscale-Péclet number is small). At this location, the PDF of scalar gradient production is only slightly skewed towards positive, and the fluctuating scalar-gradient vector aligns only with the compressive strain-rate eigenvector. The scalar-gradient vector is stretched or compressed stronger than the vorticity vector by turbulent strain rate throughout the grid-element centerline. However, the alignment of the former changes much earlier in space than that of the latter, resulting in scalar-variance dissipation to decay earlier along the grid-element centerline compared to the turbulent kinetic energy dissipation. The universal alignment behavior of the scalar-gradient vector is found far downstream, although the local Reynolds and Péclet numbers (based on the Taylor and Corrsin length scales, respectively) are low.

A Least Squares Collocation Approach with GOCE gravity gradients for regional Moho-estimation

NASA Astrophysics Data System (ADS)

Rieser, Daniel; Mayer-Guerr, Torsten

2014-05-01

The depth of the Moho discontinuity is commonly derived by either seismic observations, gravity measurements or combinations of both. In this study, we aim to use the gravity gradient measurements of the GOCE satellite mission in a Least Squares Collocation (LSC) approach for the estimation of the Moho depth on regional scale. Due to its mission configuration and measurement setup, GOCE is able to contribute valuable information in particular in the medium wavelengths of the gravity field spectrum, which is also of special interest for the crust-mantle boundary. In contrast to other studies we use the full information of the gradient tensor in all three dimensions. The problem outline is formulated as isostatically compensated topography according to the Airy-Heiskanen model. By using a topography model in spherical harmonics representation the topographic influences can be reduced from the gradient observations. Under the assumption of constant mantle and crustal densities, surface densities are directly derived by LSC on regional scale, which in turn are converted in Moho depths. First investigations proofed the ability of this method to resolve the gravity inversion problem already with a small amount of GOCE data and comparisons with other seismic and gravitmetric Moho models for the European region show promising results. With the recently reprocessed GOCE gradients, an improved data set shall be used for the derivation of the Moho depth. In this contribution the processing strategy will be introduced and the most recent developments and results using the currently available GOCE data shall be presented.

Full Gradient Solution to Adaptive Hybrid Control

NASA Technical Reports Server (NTRS)

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.

Full Gradient Solution to Adaptive Hybrid Control

NASA Technical Reports Server (NTRS)

Bean, Jacob; Schiller, Noah H.; Fuller, Chris

2016-01-01

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.

Comments on Different techniques for finding best-fit parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fenimore, Edward E.; Triplett, Laurie A.

2014-07-01

A common data analysis problem is to find best-fit parameters through chi-square minimization. Levenberg-Marquardt is an often used system that depends on gradients and converges when successive iterations do not change chi-square more than a specified amount. We point out in cases where the sought-after parameter weakly affects the fit and cases where the overall scale factor is a parameter, that a Golden Search technique can often do better. The Golden Search converges when the best-fit point is within a specified range and that range can be made arbitrarily small. It does not depend on the value of chi-square.

Natural convection in binary gases driven by combined horizontal thermal and vertical solutal gradients

NASA Technical Reports Server (NTRS)

Weaver, J. A.; Viskanta, Raymond

1992-01-01

An investigation of natural convection is presented to examine the influence of a horizontal temperature gradient and a concentration gradient occurring from the bottom to the cold wall in a cavity. As the solutal buoyancy force changes from augmenting to opposing the thermal buoyancy force, the fluid motion switches from unicellular to multicellular flow (fluid motion is up the cold wall and down the hot wall for the bottom counterrotating flow cell). Qualitatively, the agreement between predicted streamlines and smoke flow patterns is generally good. In contrast, agreement between measured and predicted temperature and concentration distributions ranges from fair to poor. Part of the discrepancy can be attributed to experimental error. However, there remains considerable discrepancy between data and predictions due to the idealizations of the mathematical model, which examines only first-order physical effects. An unsteady flow, variable thermophysical properties, conjugate effects, species interdiffusion, and radiation were not accounted for in the model.

Intrinsically stretchable and healable semiconducting polymer for organic transistors

NASA Astrophysics Data System (ADS)

Oh, Jin Young; Rondeau-Gagné, Simon; Chiu, Yu-Cheng; Chortos, Alex; Lissel, Franziska; Wang, Ging-Ji Nathan; Schroeder, Bob C.; Kurosawa, Tadanori; Lopez, Jeffrey; Katsumata, Toru; Xu, Jie; Zhu, Chenxin; Gu, Xiaodan; Bae, Won-Gyu; Kim, Yeongin; Jin, Lihua; Chung, Jong Won; Tok, Jeffrey B.-H.; Bao, Zhenan

2016-11-01

Thin-film field-effect transistors are essential elements of stretchable electronic devices for wearable electronics. All of the materials and components of such transistors need to be stretchable and mechanically robust. Although there has been recent progress towards stretchable conductors, the realization of stretchable semiconductors has focused mainly on strain-accommodating engineering of materials, or blending of nanofibres or nanowires into elastomers. An alternative approach relies on using semiconductors that are intrinsically stretchable, so that they can be fabricated using standard processing methods. Molecular stretchability can be enhanced when conjugated polymers, containing modified side-chains and segmented backbones, are infused with more flexible molecular building blocks. Here we present a design concept for stretchable semiconducting polymers, which involves introducing chemical moieties to promote dynamic non-covalent crosslinking of the conjugated polymers. These non-covalent crosslinking moieties are able to undergo an energy dissipation mechanism through breakage of bonds when strain is applied, while retaining high charge transport abilities. As a result, our polymer is able to recover its high field-effect mobility performance (more than 1 square centimetre per volt per second) even after a hundred cycles at 100 per cent applied strain. Organic thin-film field-effect transistors fabricated from these materials exhibited mobility as high as 1.3 square centimetres per volt per second and a high on/off current ratio exceeding a million. The field-effect mobility remained as high as 1.12 square centimetres per volt per second at 100 per cent strain along the direction perpendicular to the strain. The field-effect mobility of damaged devices can be almost fully recovered after a solvent and thermal healing treatment. Finally, we successfully fabricated a skin-inspired stretchable organic transistor operating under deformations that might be expected in a wearable device.

Intrinsically stretchable and healable semiconducting polymer for organic transistors.

PubMed

Oh, Jin Young; Rondeau-Gagné, Simon; Chiu, Yu-Cheng; Chortos, Alex; Lissel, Franziska; Wang, Ging-Ji Nathan; Schroeder, Bob C; Kurosawa, Tadanori; Lopez, Jeffrey; Katsumata, Toru; Xu, Jie; Zhu, Chenxin; Gu, Xiaodan; Bae, Won-Gyu; Kim, Yeongin; Jin, Lihua; Chung, Jong Won; Tok, Jeffrey B-H; Bao, Zhenan

2016-11-17

Thin-film field-effect transistors are essential elements of stretchable electronic devices for wearable electronics. All of the materials and components of such transistors need to be stretchable and mechanically robust. Although there has been recent progress towards stretchable conductors, the realization of stretchable semiconductors has focused mainly on strain-accommodating engineering of materials, or blending of nanofibres or nanowires into elastomers. An alternative approach relies on using semiconductors that are intrinsically stretchable, so that they can be fabricated using standard processing methods. Molecular stretchability can be enhanced when conjugated polymers, containing modified side-chains and segmented backbones, are infused with more flexible molecular building blocks. Here we present a design concept for stretchable semiconducting polymers, which involves introducing chemical moieties to promote dynamic non-covalent crosslinking of the conjugated polymers. These non-covalent crosslinking moieties are able to undergo an energy dissipation mechanism through breakage of bonds when strain is applied, while retaining high charge transport abilities. As a result, our polymer is able to recover its high field-effect mobility performance (more than 1 square centimetre per volt per second) even after a hundred cycles at 100 per cent applied strain. Organic thin-film field-effect transistors fabricated from these materials exhibited mobility as high as 1.3 square centimetres per volt per second and a high on/off current ratio exceeding a million. The field-effect mobility remained as high as 1.12 square centimetres per volt per second at 100 per cent strain along the direction perpendicular to the strain. The field-effect mobility of damaged devices can be almost fully recovered after a solvent and thermal healing treatment. Finally, we successfully fabricated a skin-inspired stretchable organic transistor operating under deformations that might be expected in a wearable device.

Atmospheric gradients from very long baseline interferometry observations

NASA Technical Reports Server (NTRS)

Macmillan, D. S.

1995-01-01

Azimuthal asymmetries in the atmospheric refractive index can lead to errors in estimated vertical and horizontal station coordinates. Daily average gradient effects can be as large as 50 mm of delay at a 7 deg elevation. To model gradients, the constrained estimation of gradient paramters was added to the standard VLBI solution procedure. Here the analysis of two sets of data is summarized: the set of all geodetic VLBI experiments from 1990-1993 and a series of 12 state-of-the-art R&D experiments run on consecutive days in January 1994. In both cases, when the gradient parameters are estimated, the overall fit of the geodetic solution is improved at greater than the 99% confidence level. Repeatabilities of baseline lengths ranging up to 11,000 km are improved by 1 to 8 mm in a root-sum-square sense. This varies from about 20% to 40% of the total baseline length scatter without gradient modeling for the 1990-1993 series and 40% to 50% for the January series. Gradients estimated independently for each day as a piecewise linear function are mostly continuous from day to day within their formal uncertainties.

Estimating locations and total magnetization vectors of compact magnetic sources from scalar, vector, or tensor magnetic measurements through combined Helbig and Euler analysis

USGS Publications Warehouse

Phillips, J.D.; Nabighian, M.N.; Smith, D.V.; Li, Y.

2007-01-01

The Helbig method for estimating total magnetization directions of compact sources from magnetic vector components is extended so that tensor magnetic gradient components can be used instead. Depths of the compact sources can be estimated using the Euler equation, and their dipole moment magnitudes can be estimated using a least squares fit to the vector component or tensor gradient component data. ?? 2007 Society of Exploration Geophysicists.

Investigation of Photographic Image Quality Estimators

DTIC Science & Technology

1980-04-01

WORDS (Conltnu* wi r« y «f •• »iä* ll n«c»*aarr «M läm’lly by ftloc* nuwWo Resolving Power Acutance SENTINEL SIGMA Math Model Modulation Transfer...Bibeman (1973) describes acutance as being "expressed in terms of the mean square of the gradient of . . . density (in a photographic image) with...the density difference AD. for each interval from the (smoothed) microdensitometer trace (calibrated in density units). 4. Compute the gradient -77

Isothermal magnetostatic atmospheres. III - Similarity solutions with current proportional to the magnetic potential squared. [in solar corona

NASA Technical Reports Server (NTRS)

Webb, G. M.

1988-01-01

A family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is considered. It is assumed that the current (J) is proportional to the square of the magnetostatic potential and falls off exponentially with distance. Results are presented for the contributions of the anisotropic J x B force (where B is the magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

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.

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1985-01-01

Synopses are given for NASA supported work in computer science at the University of Virginia. Some areas of research include: error seeding as a testing method; knowledge representation for engineering design; analysis of faults in a multi-version software experiment; implementation of a parallel programming environment; two computer graphics systems for visualization of pressure distribution and convective density particles; task decomposition for multiple robot arms; vectorized incomplete conjugate gradient; and iterative methods for solving linear equations on the Flex/32.

Calixarene-Mediated Liquid-Membrane Transport of Choline Conjugates

PubMed Central

Adhikari, Birendra Babu; Fujii, Ayu

2015-01-01

A series of supramolecular calixarenes efficiently transport distinct molecular species through a liquid membrane when attached to a receptor-complementary choline handle. Calix-[6]arene hexacarboxylic acid was highly effective at transporting different target molecules against a pH gradient. Both carboxylic- and phosphonic-acid-functionalized calix[4]arenes effect transport without requiring a pH or ion gradient. NMR binding studies, two-phase solvent extraction, and three-phase transport experiments reveal the necessary and subtle parameters to effect the transport of molecules attached to a choline “handle”. On the other hand, rescorin[4]arene cavitands, which have similar guest recognition profiles, did not transport guest molecules. These developments reveal new approaches towards attempting synthetic-receptor-mediated selective small-molecule transport in vesicular and cellular systems. PMID:26161034

User intent prediction with a scaled conjugate gradient trained artificial neural network for lower limb amputees using a powered prosthesis.

PubMed

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.

Practical method development for the separation of monoclonal antibodies and antibody-drug-conjugate species in hydrophobic interaction chromatography, part 1: optimization of the mobile phase.

PubMed

Rodriguez-Aller, Marta; Guillarme, Davy; Beck, Alain; Fekete, Szabolcs

2016-01-25

The goal of this work is to provide some recommendations for method development in HIC using monoclonal antibodies (mAbs) and antibody-drug conjugates (ADCs) as model drug candidates. The effects of gradient steepness, mobile phase pH, salt concentration and type, as well as organic modifier were evaluated for tuning selectivity and retention in HIC. Except the nature of the stationary phase, which was not discussed in this study, the most important parameter for modifying selectivity was the gradient steepness. The addition of organic solvent (up to 15% isopropanol) in the mobile phase was also found to be useful for mAbs analysis, since it could provide some changes in elution order, in some cases. On the contrary, isopropanol was not beneficial with ADCs, since the most hydrophobic DAR species (DAR6 and DAR8) cannot be eluted from the stationary phase under these conditions. This study also illustrates the possibility to perform HIC method development using optimization software, such as Drylab. The optimum conditions suggested by the software were tested using therapeutic mAbs and commercial cysteine linked ADC (brentuximab-vedotin) and the average retention time errors between predicted and experimental retention times were ∼ 1%. Copyright © 2015 Elsevier B.V. All rights reserved.

A finite element: Boundary integral method for electromagnetic scattering. Ph.D. Thesis Technical Report, Feb. - Sep. 1992

NASA Technical Reports Server (NTRS)

Collins, J. D.; Volakis, John L.

1992-01-01

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Modeling of field-aligned guided echoes in the plasmasphere

NASA Astrophysics Data System (ADS)

Fung, Shing F.; Green, James L.

2005-01-01

Ray tracing modeling is used to investigate the plasma conditions under which high-frequency (f ≫ fuh) extraordinary mode waves can be guided along geomagnetic field lines. These guided signals have often been observed as long-range discrete echoes in the plasmasphere by the Radio Plasma Imager (RPI) onboard the Imager for Magnetopause-to-Aurora Global Exploration satellite. Field-aligned discrete echoes are most commonly observed by RPI in the plasmasphere, although they are also observed over the polar cap region. The plasmasphere field-aligned echoes appearing as multiple echo traces at different virtual ranges are attributed to signals reflected successively between conjugate hemispheres that propagate along or nearly along closed geomagnetic field lines. The ray tracing simulations show that field-aligned ducts with as little as 1% density perturbations (depletions) and <10 wavelengths wide can guide nearly field-aligned propagating high-frequency X mode waves. Effective guidance of a wave at a given frequency and wave normal angle (Ψ) depends on the cross-field density scale of the duct, such that ducts with stronger density depletions need to be wider in order to maintain the same gradient of refractive index across the magnetic field. While signal guidance by field aligned density gradient without ducting is possible only over the polar region, conjugate field-aligned echoes that have traversed through the equatorial region are most likely guided by ducting.

Parallel processors and nonlinear structural dynamics algorithms and software

NASA Technical Reports Server (NTRS)

Belytschko, Ted

1990-01-01

Techniques are discussed for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a 3-D nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling. A significant reduction in the number of iterations required for convergence is shown for a statically loaded rigid bar suspended by three equally spaced springs.

Pixel-based OPC optimization based on conjugate gradients.

PubMed

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.

Ordering effects of conjugate thermal fields in simulations of molecular liquids: Carbon dioxide and water

NASA Astrophysics Data System (ADS)

Dittmar, Harro R.; Kusalik, Peter G.

2016-10-01

As shown previously, it is possible to apply configurational and kinetic thermostats simultaneously in order to induce a steady thermal flux in molecular dynamics simulations of many-particle systems. This flux appears to promote motion along potential gradients and can be utilized to enhance the sampling of ordered arrangements, i.e., it can facilitate the formation of a critical nucleus. Here we demonstrate that the same approach can be applied to molecular systems, and report a significant enhancement of the homogeneous crystal nucleation of a carbon dioxide (EPM2 model) system. Quantitative ordering effects and reduction of the particle mobilities were observed in water (TIP4P-2005 model) and carbon dioxide systems. The enhancement of the crystal nucleation of carbon dioxide was achieved with relatively small conjugate thermal fields. The effect is many orders of magnitude bigger at milder supercooling, where the forward flux sampling method was employed, than at a lower temperature that enabled brute force simulations of nucleation events. The behaviour exhibited implies that the effective free energy barrier of nucleation must have been reduced by the conjugate thermal field in line with our interpretation of previous results for atomic systems.

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

On the role and value of β in incompressible MHD simulations

NASA Astrophysics Data System (ADS)

Chahine, Robert; Bos, Wouter J. T.

2018-04-01

The parameter β, defined as the ratio of the pressure to the square of the magnetic field, is widely used to characterize astrophysical and fusion plasmas. However, in the dynamics of a plasma flow, it is the pressure gradient which is important rather than the value of the pressure itself. It is shown that if one is interested in the influence of the pressure gradient on the dynamics of a plasma, it is not the quantity β which should be considered, but a similar quantity depending on the pressure gradient. The scaling of this newly defined quantity is investigated using incompressible magnetohydrodynamic simulations in a periodic cylinder in the Reversed Field Pinch flow regime.

A frequency dependent preconditioned wavelet method for atmospheric tomography

NASA Astrophysics Data System (ADS)

Yudytskiy, Mykhaylo; Helin, Tapio; Ramlau, Ronny

2013-12-01

Atmospheric tomography, i.e. the reconstruction of the turbulence in the atmosphere, is a main task for the adaptive optics systems of the next generation telescopes. For extremely large telescopes, such as the European Extremely Large Telescope, this problem becomes overly complex and an efficient algorithm is needed to reduce numerical costs. Recently, a conjugate gradient method based on wavelet parametrization of turbulence layers was introduced [5]. An iterative algorithm can only be numerically efficient when the number of iterations required for a sufficient reconstruction is low. A way to achieve this is to design an efficient preconditioner. In this paper we propose a new frequency-dependent preconditioner for the wavelet method. In the context of a multi conjugate adaptive optics (MCAO) system simulated on the official end-to-end simulation tool OCTOPUS of the European Southern Observatory we demonstrate robustness and speed of the preconditioned algorithm. We show that three iterations are sufficient for a good reconstruction.

Development and application of a UPLC-MS/MS method for the pharmacokinetic study of 10-hydroxy camptothecin and hydroxyethyl starch conjugate in rats.

PubMed

Li, Guofei; Cai, Cuifang; Ren, Tianyang; Tang, Xing

2014-01-01

With the purpose to carry out the pharmacokinetic studies of 10-hydroxy camptothecin (10-HCPT) and hydroxyethyl starch (10-HCPT-HES) conjugate, an ultraperformance liquid chromatography tandem mass spectrometry (UPLC-MS/MS) method has been developed and validated. The analytes, 10-HCPT and the internal standard, Diphenhydramine hydrochloride were extracted with ethyl acetate-isopropanol (95:5, v/v) and separated on an ACQUITY UPLC™ BEH C18 column using a mobile phase composed of acetonitrile and water (containing 0.1% formic acid) with a linear gradient program. With positive ion electrospray ionization (ESI), the analytes were monitored on a triple quadrupole mass spectrometer in the multiple reaction monitoring (MRM) mode. Linear calibration curves were obtained over the concentration ranges of 0.5-2500ng/mL. The intra- and inter-day precisions were less than 9.8% and 10.8%, respectively. The accuracy was within 12.1%. The mean recoveries of 10-HCPT at three concentrations of 2.5, 100, 2000ng/mL were higher than 87.2%. Commercial 10-HCPT injection and 10-HCPT-HES conjugate were administered intravenously at an equal dose of 10-HCPT at 0.5mg/kg. The biological half-life of conjugate was increased significantly from 10min to 3.15h and the bioavailability was 40 times higher than 10-HCPT injection. Consequently, the proposed UPLC-ESI-MS/MS method was proved to be sensitive, specific and reliable to analyze 10-HCPT in biological samples; 10-HCPT and HES conjugate is a promising strategy for delivery of 10-HCPT with prolonged half time and improved bioavailability. Copyright © 2013 Elsevier B.V. All rights reserved.

Grafting PNIPAAm from β-barrel shaped transmembrane nanopores.

PubMed

Charan, Himanshu; Kinzel, Julia; Glebe, Ulrich; Anand, Deepak; Garakani, Tayebeh Mirzaei; Zhu, Leilei; Bocola, Marco; Schwaneberg, Ulrich; Böker, Alexander

2016-11-01

The research on protein-polymer conjugates by grafting from the surface of proteins has gained significant interest in the last decade. While there are many studies with globular proteins, membrane proteins have remained untouched to the best of our knowledge. In this study, we established the conjugate formation with a class of transmembrane proteins and grow polymer chains from the ferric hydroxamate uptake protein component A (FhuA; a β-barrel transmembrane protein of Escherichia coli). As the lysine residues of naturally occurring FhuA are distributed over the whole protein, FhuA was reengineered to have up to 11 lysines, distributed symmetrically in a rim on the membrane exposed side (outside) of the protein channel and exclusively above the hydrophobic region. Reengineering of FhuA ensures a polymer growth only on the outside of the β-barrel and prevents blockage of the channel as a result of the polymerization. A water-soluble initiator for controlled radical polymerization (CRP) was consecutively linked to the lysine residues of FhuA and N-isopropylacrylamide (NIPAAm) polymerized under copper-mediated CRP conditions. The conjugate formation was analyzed by using MALDI-ToF mass spectrometry, SDS-PAGE, circular dichroism spectroscopy, analytical ultracentrifugation, dynamic light scattering, transmission electron microscopy and size exclusion chromatography. Such conjugates combine the specific functions of the transmembrane proteins, like maintaining membrane potential gradients or translocation of substrates with the unique properties of synthetic polymers such as temperature and pH stimuli handles. FhuA-PNIPAAm conjugates will serve as functional nanosized building blocks for applications in targeted drug delivery, self-assembly systems, functional membranes and transmembrane protein gated nanoreactors. Copyright © 2016 Elsevier Ltd. All rights reserved.

Imperfect coupling between northern and southern ionospheres: asymmetry in TEC anomalies before earthquakes

NASA Astrophysics Data System (ADS)

Jhuang, Hau-Kun; Ho, Yi-Ying; Lee, Lou-Chuang

2016-04-01

The northern ionosphere is coupled to the conjugate southern ionosphere through the highly conducting geomagenetic field lines. The coupling is very strong or "perfect" if the geomagnetic field lines are equipotential (the parallel electric field E||=0) and hence the perpendicular electric field (E⊥) at the conjugate sites of both ionospheres are equal. The coupling is "imperfect" if some of the geomagnetic field lines are non-equipotential (E||≠0). The field-aligned electric field E|| can be associated with electron inertia, pressure gradient and collisions appearing in the form of double layer, kinetic Alfvén waves and finite field-aligned conductivity σ||. We use the Global Ionospheric Maps (GIM) data to examine the conjugate effect of total electron content (TEC) for six significant earthquakes. The anomalous (ΔTEC)source in the source ionosphere and (ΔTEC)conjugate in the conjugate ionosphere are obtained for 85 events before the six earthquakes. The ΔTEC ratio β = (ΔTEC)conjugate / (ΔTEC)source is calculated for each anomaly. For a "perfect" coupling, β=1. There are 85 anomalous events before the six significant earthquakes, with 62 events occurring in the daytime (07-18 LT) and 23 events in the nighttime (19-06 LT). The average value of daytime (07-18 LT) TEC variations in the source ionosphere is |ΔTEC|source =20.13 TECu, while the average value in the nighttime (19-06 LT) ionosphere is |ΔTEC|source=14.43 TECu. The value of ΔTEC ratio β ranges from 0.05 (very weak coupling) to 0.98 (nearly perfect coupling) with an average of 0.52. There are 14 strong coupling cases with β ≥0.8, which take place from 11 LT to 19 LT. The daytime (07-18 LT) β average value is 0.57 and the nighttime (19-06 LT) β average is 0.37. The south-north ionosphere coupling is stronger (weaker) in the daytime (nighttime).

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.

PubMed

Davids, Mathias; Schad, Lothar R; Wald, Lawrence L; Guérin, Bastien

2016-10-01

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns. We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels. Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax  = 40 mT/m, Smax  = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions. Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Reversible ratchet effects for vortices in conformal pinning arrays

DOE PAGES

Reichhardt, Charles; Ray, Dipanjan; Reichhardt, Cynthia Jane Olson

2015-05-04

A conformal transformation of a uniform triangular pinning array produces a structure called a conformal crystal which preserves the sixfold ordering of the original lattice but contains a gradient in the pinning density. Here we use numerical simulations to show that vortices in type-II superconductors driven with an ac drive over gradient pinning arrays produce the most pronounced ratchet effect over a wide range of parameters for a conformal array, while square gradient or random gradient arrays with equivalent pinning densities give reduced ratchet effects. In the conformal array, the larger spacing of the pinning sites in the direction transversemore » to the ac drive permits easy funneling of interstitial vortices for one driving direction, producing the enhanced ratchet effect. In the square array, the transverse spacing between pinning sites is uniform, giving no asymmetry in the funneling of the vortices as the driving direction switches, while in the random array, there are numerous easy-flow channels present for either direction of drive. We find multiple ratchet reversals in the conformal arrays as a function of vortex density and ac amplitude, and correlate the features with a reversal in the vortex ordering, which is greater for motion in the ratchet direction. In conclusion, the enhanced conformal pinning ratchet effect can also be realized for colloidal particles moving over a conformal array, indicating the general usefulness of conformal structures for controlling the motion of particles.« less

Least squares collocation applied to local gravimetric solutions from satellite gravity gradiometry data

NASA Technical Reports Server (NTRS)

Robbins, J. W.

1985-01-01

An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.

One day prediction of nighttime VLF amplitudes using nonlinear autoregression and neural network modeling

NASA Astrophysics Data System (ADS)

Santosa, H.; Hobara, Y.

2017-01-01

The electric field amplitude of very low frequency (VLF) transmitter from Hawaii (NPM) has been continuously recorded at Chofu (CHF), Tokyo, Japan. The VLF amplitude variability indicates lower ionospheric perturbation in the D region (60-90 km altitude range) around the NPM-CHF propagation path. We carried out the prediction of daily nighttime mean VLF amplitude by using Nonlinear Autoregressive with Exogenous Input Neural Network (NARX NN). The NARX NN model, which was built based on the daily input variables of various physical parameters such as stratospheric temperature, total column ozone, cosmic rays, Dst, and Kp indices possess good accuracy during the model building. The fitted model was constructed within the training period from 1 January 2011 to 4 February 2013 by using three algorithms, namely, Bayesian Neural Network (BRANN), Levenberg Marquardt Neural Network (LMANN), and Scaled Conjugate Gradient (SCG). The LMANN has the largest Pearson correlation coefficient (r) of 0.94 and smallest root-mean-square error (RMSE) of 1.19 dB. The constructed models by using LMANN were applied to predict the VLF amplitude from 5 February 2013 to 31 December 2013. As a result the one step (1 day) ahead predicted nighttime VLF amplitude has the r of 0.93 and RMSE of 2.25 dB. We conclude that the model built according to the proposed methodology provides good predictions of the electric field amplitude of VLF waves for NPM-CHF (midlatitude) propagation path.

Fast implementation for compressive recovery of highly accelerated cardiac cine MRI using the balanced sparse model.

PubMed

Ting, Samuel T; Ahmad, Rizwan; Jin, Ning; Craft, Jason; Serafim da Silveira, Juliana; Xue, Hui; Simonetti, Orlando P

2017-04-01

Sparsity-promoting regularizers can enable stable recovery of highly undersampled magnetic resonance imaging (MRI), promising to improve the clinical utility of challenging applications. However, lengthy computation time limits the clinical use of these methods, especially for dynamic MRI with its large corpus of spatiotemporal data. Here, we present a holistic framework that utilizes the balanced sparse model for compressive sensing and parallel computing to reduce the computation time of cardiac MRI recovery methods. We propose a fast, iterative soft-thresholding method to solve the resulting ℓ1-regularized least squares problem. In addition, our approach utilizes a parallel computing environment that is fully integrated with the MRI acquisition software. The methodology is applied to two formulations of the multichannel MRI problem: image-based recovery and k-space-based recovery. Using measured MRI data, we show that, for a 224 × 144 image series with 48 frames, the proposed k-space-based approach achieves a mean reconstruction time of 2.35 min, a 24-fold improvement compared a reconstruction time of 55.5 min for the nonlinear conjugate gradient method, and the proposed image-based approach achieves a mean reconstruction time of 13.8 s. Our approach can be utilized to achieve fast reconstruction of large MRI datasets, thereby increasing the clinical utility of reconstruction techniques based on compressed sensing. Magn Reson Med 77:1505-1515, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

On the robustness of a Bayes estimate. [in reliability theory

NASA Technical Reports Server (NTRS)

Canavos, G. C.

1974-01-01

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

Non-classical continuum theory for fluids incorporating internal and Cosserat rotation rates

NASA Astrophysics Data System (ADS)

Surana, K. S.; Joy, A. D.; Reddy, J. N.

2017-11-01

This paper presents a non-classical continuum theory for fluent continua in which the conservation and balance laws are derived by incorporating both internal rotation rates arising from the velocity gradient tensor and the rotation rates of the Cosserats. Specifically, in this non-classical continuum theory we have (1) the usual velocities (\\bar{ ±b {\\varvec{v }}}), (2) the three internal rotation rates ({}_i^t\\bar{ ±b {\\varvec{Θ }}}) about the axes of a fixed triad whose axes are parallel to the x-frame arising from the velocity gradient tensor (\\bar{ ±b {\\varvec{L }}}) that are completely defined by the antisymmetric part of the velocity gradient tensor, and (3) three additional rotation rates ({}_e^t\\bar{ ±b {\\varvec{Θ }}}) about the axes of the same triad located at each material point as additional three unknown degrees of freedom, referred to as Cosserat rotation rates. This gives rise to \\bar{ ±b {\\varvec{v }}} and {}_e^t\\bar{ ±b {\\varvec{Θ }}} as six degrees of freedom at a material point. The internal rotation rates {}_i^t\\bar{ ±b {\\varvec{Θ }}}, often neglected in classical fluid mechanics, exist in all deforming fluent continua as these are due to velocity gradient tensor. When the internal rotation rates {}_i^t\\bar{ ±b {\\varvec{Θ }}} are resisted by deforming fluent continua, conjugate moment tensor arises that together with {}_i^t\\bar{ ±b {\\varvec{Θ }}} may result in energy storage and/or dissipation, which must be considered in the conservation and balance laws. The Cosserat rotation rations {}_e^t\\bar{ ±b {\\varvec{Θ }}} also result in conjugate moment tensor that together with {}_e^t\\bar{ ±b {\\varvec{Θ }}} may also result in energy storage and/or dissipation. The main focus of this paper is a consistent derivation of conservation and balance laws for fluent continua that incorporate the aforementioned physics and associated constitutive theories for thermofluids using the conditions resulting from the entropy inequality. The material coefficients derived in the constitutive theories are clearly defined and discussed.

New Langevin and gradient thermostats for rigid body dynamics.

PubMed

Davidchack, R L; Ouldridge, T E; Tretyakov, M V

2015-04-14

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.

Interpolation algorithm for asynchronous ADC-data

NASA Astrophysics Data System (ADS)

Bramburger, Stefan; Zinke, Benny; Killat, Dirk

2017-09-01

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.

Identification of the Thermal Conductivity Coefficient for Quasi-Stationary Two-Dimensional Heat Conduction Equations

NASA Astrophysics Data System (ADS)

Matsevityi, Yu. M.; Alekhina, S. V.; Borukhov, V. T.; Zayats, G. M.; Kostikov, A. O.

2017-11-01

The problem of identifying the time-dependent thermal conductivity coefficient in the initial-boundary-value problem for the quasi-stationary two-dimensional heat conduction equation in a bounded cylinder is considered. It is assumed that the temperature field in the cylinder is independent of the angular coordinate. To solve the given problem, which is related to a class of inverse problems, a mathematical approach based on the method of conjugate gradients in a functional form is being developed.

Curved-line search algorithm for ab initio atomic structure relaxation

NASA Astrophysics Data System (ADS)

Chen, Zhanghui; Li, Jingbo; Li, Shushen; Wang, Lin-Wang

2017-09-01

Ab initio atomic relaxations often take large numbers of steps and long times to converge, especially when the initial atomic configurations are far from the local minimum or there are curved and narrow valleys in the multidimensional potentials. An atomic relaxation method based on on-the-flight force learning and a corresponding curved-line search algorithm is presented to accelerate this process. Results demonstrate the superior performance of this method for metal and magnetic clusters when compared with the conventional conjugate-gradient method.

D4Z - a new renumbering for iterative solution of ground-water flow and solute- transport equations

USGS Publications Warehouse

Kipp, K.L.; Russell, T.F.; Otto, J.S.

1992-01-01

D4 zig-zag (D4Z) is a new renumbering scheme for producing a reduced matrix to be solved by an incomplete LU preconditioned, restarted conjugate-gradient iterative solver. By renumbering alternate diagonals in a zig-zag fashion, a very low sensitivity of convergence rate to renumbering direction is obtained. For two demonstration problems involving groundwater flow and solute transport, iteration counts are related to condition numbers and spectra of the reduced matrices.

Mapping the Conjugate Gradient Algorithm onto High Performance Heterogeneous Computers

DTIC Science & Technology

2014-05-01

Matrix Storage Formats According to J . Dongarra (Dongerra 2000), the efficiency of most iterative methods, such as CG, can be attributed to the...valh = aij) ⇒ (colh = j ). The ptr integer vector is of length n + 1 and contains the index in val where each matrix row starts. For example, the...first nonzero element of matrix rowm is found at index ptrm of val. By convention, ptrn+1 ≡ nz + 1. Notice that (aij) ⇒ (ptri ≤ j < ptri+1) for all i. An

Image Understanding Workshop. Proceedings of a Workshop Held in Los Angeles, California on 23-25 February 1987. Volume 2

DTIC Science & Technology

1987-02-25

Modellierung von Kanten bei unregel. Navigation within a building, to be published in IEEE mifliger Rasterung in Bildverarbeitun uand Muster...converted them into equivalent machine cycles in Table 3-1. We took into account of 100 nanosecond 0 - 0, machine cycle time of the MPP. In MPP, NON- VON ...We show the result for the conjugate gradient method in of NON- VON . We assumed that the instructions which carry Table 4-4. The computation of four

Image reconstruction from few-view CT data by gradient-domain dictionary learning.

PubMed

Hu, Zhanli; Liu, Qiegen; Zhang, Na; Zhang, Yunwan; Peng, Xi; Wu, Peter Z; Zheng, Hairong; Liang, Dong

2016-05-21

Decreasing the number of projections is an effective way to reduce the radiation dose exposed to patients in medical computed tomography (CT) imaging. However, incomplete projection data for CT reconstruction will result in artifacts and distortions. In this paper, a novel dictionary learning algorithm operating in the gradient-domain (Grad-DL) is proposed for few-view CT reconstruction. Specifically, the dictionaries are trained from the horizontal and vertical gradient images, respectively and the desired image is reconstructed subsequently from the sparse representations of both gradients by solving the least-square method. Since the gradient images are sparser than the image itself, the proposed approach could lead to sparser representations than conventional DL methods in the image-domain, and thus a better reconstruction quality is achieved. To evaluate the proposed Grad-DL algorithm, both qualitative and quantitative studies were employed through computer simulations as well as real data experiments on fan-beam and cone-beam geometry. The results show that the proposed algorithm can yield better images than the existing algorithms.

Designing in vivo concentration gradients with discrete controlled release: a computational model

NASA Astrophysics Data System (ADS)

Walker, Edgar Y.; Barbour, Dennis L.

2010-08-01

One promising neurorehabilitation therapy involves presenting neurotrophins directly into the brain to induce growth of new neural connections. The precise control of neurotrophin concentration gradients deep within neural tissue that would be necessary for such a therapy is not currently possible, however. Here we evaluate the theoretical potential of a novel method of drug delivery, discrete controlled release (DCR), to control effective neurotrophin concentration gradients in an isotropic region of neocortex. We do so by constructing computational models of neurotrophin concentration profiles resulting from discrete release locations into the cortex and then optimizing their design for uniform concentration gradients. The resulting model indicates that by rationally selecting initial neurotrophin concentrations for drug-releasing electrode coatings in a square 16-electrode array, nearly uniform concentration gradients (i.e. planar concentration profiles) from one edge of the electrode array to the other should be obtainable. DCR therefore represents a promising new method of precisely directing neuronal growth in vivo over a wider spatial profile than would be possible with single release points.

Optimized phase gradient measurements and phase-amplitude interplay in optical coherence elastography

NASA Astrophysics Data System (ADS)

Zaitsev, Vladimir Y.; Matveyev, Alexander L.; Matveev, Lev A.; Gelikonov, Grigory V.; Sovetsky, Aleksandr A.; Vitkin, Alex

2016-11-01

In compressional optical coherence elastography, phase-variation gradients are used for estimating quasistatic strains created in tissue. Using reference and deformed optical coherence tomography (OCT) scans, one typically compares phases from pixels with the same coordinates in both scans. Usually, this limits the allowable strains to fairly small values < to 10-3, with the caveat that such weak phase gradients may become corrupted by stronger measurement noises. Here, we extend the OCT phase-resolved elastographic methodology by (1) showing that an order of magnitude greater strains can significantly increase the accuracy of derived phase-gradient differences, while also avoiding error-phone phase-unwrapping procedures and minimizing the influence of decorrelation noise caused by suprapixel displacements, (2) discussing the appearance of artifactual stiff inclusions in resultant OCT elastograms in the vicinity of bright scatterers due to the amplitude-phase interplay in phase-variation measurements, and (3) deriving/evaluating methods of phase-gradient estimation that can outperform conventionally used least-square gradient fitting. We present analytical arguments, numerical simulations, and experimental examples to demonstrate the advantages of the proposed optimized phase-variation methodology.

Superconducting gravity gradiometer and a test of inverse square law

NASA Technical Reports Server (NTRS)

Moody, M. V.; Paik, Ho Jung

1989-01-01

The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth.

Observation and simulation of flow on soap film induced by concentration gradient

NASA Astrophysics Data System (ADS)

Ohnishi, Mitsuru; Yoshihara, Shoichi; Azuma, Hisao

The behavior of the flow and capillary wave induced on the film surface by the surfactant concentration difference is studied. Flat soap film is used as a model of thin film. The result is applicable to the case of flow by thermal gradient. The Schlieren method is used to observe the flow and the wave on the soap film. It is found that the wave velocities, in the case of a high surface tension difference, are linearly related to the square root of the surface tension difference.

Algorithms for Nonlinear Least-Squares Problems

DTIC Science & Technology

1988-09-01

O -,i(x) 2 , where each -,(x) is a smooth function mapping Rn to R. J - The m x n Jacobian matrix of f. ... x g - The gradient of the nonlinear least...V211f(X*)I112~ l~ l) J(xk)T J(xk) 2 + O(k - X*) For more convergence results and detailed convergence analysis for the Gauss-Newton method, see, e. g ...for a class of nonlinear least-squares problems that includes zero-residual prob- lems. The function Jt is the pseudo-inverse of Jk (see, e. g

Parameter estimation for terrain modeling from gradient data. [navigation system for Martian rover

NASA Technical Reports Server (NTRS)

Dangelo, K. R.

1974-01-01

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

Sewall Wright's equation Deltaq=(q(1-q) partial differentialw/ partial differentialq)/2w.

PubMed

Edwards, A W

2000-02-01

An equation of Sewall Wright's expresses the change in the frequency of an allele under selection at a multiallelic locus as a function of the gradient of the mean fitness "surface" in the direction in which the relative proportions of the other alleles do not change. An attempt to derive this equation using conventional vector calculus shows that this description leads to a different equation and that the purported gradient in Wright's equation is not a gradient of the mean fitness surface except in the diallelic case, where the two equations are the same. It is further shown that if Fisher's angular transformation is applied to the diallelic case the genic variance is exactly equal to one-eighth of the square of the gradient of the mean fitness with respect to the transformed gene frequency. Copyright 2000 Academic Press.

Method of determining effects of heat-induced irregular refractive index on an optical system.

PubMed

Song, Xifa; Li, Lin; Huang, Yifan

2015-09-01

The effects of an irregular refractive index on optical performance are examined. A method was developed to express a lens's irregular refractive index distribution. An optical system and its mountings were modeled by a thermomechanical finite element (FE) program in the predicted operating temperature range, -45°C-50°C. FE outputs were elaborated using a MATLAB optimization routine; a nonlinear least squares algorithm was adopted to determine which gradient equation best fit each lens's refractive index distribution. The obtained gradient data were imported into Zemax for sequential ray-tracing analysis. The root mean square spot diameter, modulation transfer function, and diffraction ensquared energy were computed for an optical system under an irregular refractive index and under thermoelastic deformation. These properties are greatly reduced by the irregular refractive index effect, which is one-third to five-sevenths the size of the thermoelastic deformation effect. Thus, thermal analyses of optical systems should consider not only thermoelastic deformation but also refractive index irregularities caused by inhomogeneous temperature.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Heat flow and geothermal potential of the East Mesa KGRA, Imperial Valley, California

NASA Technical Reports Server (NTRS)

Swanberg, C. A.

1974-01-01

The East Mesa KGRA (Known Geothermal Resource Area) is located in the southeast part of the Imperial Valley, California, and is roughly 150 kilometers square in areal extent. A new heat flow technique which utilizes temperature gradient measurements across best clays is presented and shown to be as accurate as conventional methods for the present study area. Utilizing the best clay gradient technique, over 70 heat flow determinations have been completed within and around the East Mesa KGRA. Background heat flow values range from 1.4 to 2.4 hfu (1 hfu = .000001 cal. per square centimeter-second) and are typical of those throughout the Basin and Range province. Heat flow values for the northwest lobe of the KGRA (Mesa anomaly) are as high as 7.9 hfu, with the highest values located near gravity and seismic noise maxima and electrical resistivity minima. An excellent correlation exists between heat flow contours and faults defined by remote sensing and microearthquake monitoring.

Estimation of liver T₂ in transfusion-related iron overload in patients with weighted least squares T₂ IDEAL.

PubMed

Vasanawala, Shreyas S; Yu, Huanzhou; Shimakawa, Ann; Jeng, Michael; Brittain, Jean H

2012-01-01

MRI imaging of hepatic iron overload can be achieved by estimating T(2) values using multiple-echo sequences. The purpose of this work is to develop and clinically evaluate a weighted least squares algorithm based on T(2) Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) technique for volumetric estimation of hepatic T(2) in the setting of iron overload. The weighted least squares T(2) IDEAL technique improves T(2) estimation by automatically decreasing the impact of later, noise-dominated echoes. The technique was evaluated in 37 patients with iron overload. Each patient underwent (i) a standard 2D multiple-echo gradient echo sequence for T(2) assessment with nonlinear exponential fitting, and (ii) a 3D T(2) IDEAL technique, with and without a weighted least squares fit. Regression and Bland-Altman analysis demonstrated strong correlation between conventional 2D and T(2) IDEAL estimation. In cases of severe iron overload, T(2) IDEAL without weighted least squares reconstruction resulted in a relative overestimation of T(2) compared with weighted least squares. Copyright © 2011 Wiley-Liss, Inc.

A simple microgravity table for the Orbiter or Space Station

NASA Technical Reports Server (NTRS)

Garriott, O. K.; Debra, D. B.

1985-01-01

Methods of limiting perturbations in microgravity experiments are proposed. An acceleration level below 10 to the -4th m/s-squared is necessary to maintain an undisturbed microgravity environment. Machinery vibrations, crew motion, and the firing of vernier thrusters produce acceleration levels greate than 10 to the -4th m/s-squared. The use of a weak spring system or simple electromagnets to isolate an experimental table from these factors is described. The manners in which crew motion and vernier firing are countered by the springs are examined. The steady acceleration caused by atmospheric drag, gravity gradient force, and steady rotation can be maintained below 10 to the -th m/s-squared; however, the springs can protect the table from these accelerations if required.

Energy minimization in medical image analysis: Methodologies and applications.

PubMed

Zhao, Feng; Xie, Xianghua

2016-02-01

Energy minimization is of particular interest in medical image analysis. In the past two decades, a variety of optimization schemes have been developed. In this paper, we present a comprehensive survey of the state-of-the-art optimization approaches. These algorithms are mainly classified into two categories: continuous method and discrete method. The former includes Newton-Raphson method, gradient descent method, conjugate gradient method, proximal gradient method, coordinate descent method, and genetic algorithm-based method, while the latter covers graph cuts method, belief propagation method, tree-reweighted message passing method, linear programming method, maximum margin learning method, simulated annealing method, and iterated conditional modes method. We also discuss the minimal surface method, primal-dual method, and the multi-objective optimization method. In addition, we review several comparative studies that evaluate the performance of different minimization techniques in terms of accuracy, efficiency, or complexity. These optimization techniques are widely used in many medical applications, for example, image segmentation, registration, reconstruction, motion tracking, and compressed sensing. We thus give an overview on those applications as well. Copyright © 2015 John Wiley & Sons, Ltd.

Fast Quantitative Susceptibility Mapping with L1-Regularization and Automatic Parameter Selection

PubMed Central

Bilgic, Berkin; Fan, Audrey P.; Polimeni, Jonathan R.; Cauley, Stephen F.; Bianciardi, Marta; Adalsteinsson, Elfar; Wald, Lawrence L.; Setsompop, Kawin

2014-01-01

Purpose To enable fast reconstruction of quantitative susceptibility maps with Total Variation penalty and automatic regularization parameter selection. Methods ℓ1-regularized susceptibility mapping is accelerated by variable-splitting, which allows closed-form evaluation of each iteration of the algorithm by soft thresholding and FFTs. This fast algorithm also renders automatic regularization parameter estimation practical. A weighting mask derived from the magnitude signal can be incorporated to allow edge-aware regularization. Results Compared to the nonlinear Conjugate Gradient (CG) solver, the proposed method offers 20× speed-up in reconstruction time. A complete pipeline including Laplacian phase unwrapping, background phase removal with SHARP filtering and ℓ1-regularized dipole inversion at 0.6 mm isotropic resolution is completed in 1.2 minutes using Matlab on a standard workstation compared to 22 minutes using the Conjugate Gradient solver. This fast reconstruction allows estimation of regularization parameters with the L-curve method in 13 minutes, which would have taken 4 hours with the CG algorithm. Proposed method also permits magnitude-weighted regularization, which prevents smoothing across edges identified on the magnitude signal. This more complicated optimization problem is solved 5× faster than the nonlinear CG approach. Utility of the proposed method is also demonstrated in functional BOLD susceptibility mapping, where processing of the massive time-series dataset would otherwise be prohibitive with the CG solver. Conclusion Online reconstruction of regularized susceptibility maps may become feasible with the proposed dipole inversion. PMID:24259479

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Deconvolution of astronomical images using SOR with adaptive relaxation.

PubMed

Vorontsov, S V; Strakhov, V N; Jefferies, S M; Borelli, K J

2011-07-04

We address the potential performance of the successive overrelaxation technique (SOR) in image deconvolution, focusing our attention on the restoration of astronomical images distorted by atmospheric turbulence. SOR is the classical Gauss-Seidel iteration, supplemented with relaxation. As indicated by earlier work, the convergence properties of SOR, and its ultimate performance in the deconvolution of blurred and noisy images, can be made competitive to other iterative techniques, including conjugate gradients, by a proper choice of the relaxation parameter. The question of how to choose the relaxation parameter, however, remained open, and in the practical work one had to rely on experimentation. In this paper, using constructive (rather than exact) arguments, we suggest a simple strategy for choosing the relaxation parameter and for updating its value in consecutive iterations to optimize the performance of the SOR algorithm (and its positivity-constrained version, +SOR) at finite iteration counts. We suggest an extension of the algorithm to the notoriously difficult problem of "blind" deconvolution, where both the true object and the point-spread function have to be recovered from the blurred image. We report the results of numerical inversions with artificial and real data, where the algorithm is compared with techniques based on conjugate gradients. In all of our experiments +SOR provides the highest quality results. In addition +SOR is found to be able to detect moderately small changes in the true object between separate data frames: an important quality for multi-frame blind deconvolution where stationarity of the object is a necesessity.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

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.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

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.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Multi-GPU Accelerated Admittance Method for High-Resolution Human Exposure Evaluation.

PubMed

Xiong, Zubiao; Feng, Shi; Kautz, Richard; Chandra, Sandeep; Altunyurt, Nevin; Chen, Ji

2015-12-01

A multi-graphics processing unit (GPU) accelerated admittance method solver is presented for solving the induced electric field in high-resolution anatomical models of human body when exposed to external low-frequency magnetic fields. In the solver, the anatomical model is discretized as a three-dimensional network of admittances. The conjugate orthogonal conjugate gradient (COCG) iterative algorithm is employed to take advantage of the symmetric property of the complex-valued linear system of equations. Compared against the widely used biconjugate gradient stabilized method, the COCG algorithm can reduce the solving time by 3.5 times and reduce the storage requirement by about 40%. The iterative algorithm is then accelerated further by using multiple NVIDIA GPUs. The computations and data transfers between GPUs are overlapped in time by using asynchronous concurrent execution design. The communication overhead is well hidden so that the acceleration is nearly linear with the number of GPU cards. Numerical examples show that our GPU implementation running on four NVIDIA Tesla K20c cards can reach 90 times faster than the CPU implementation running on eight CPU cores (two Intel Xeon E5-2603 processors). The implemented solver is able to solve large dimensional problems efficiently. A whole adult body discretized in 1-mm resolution can be solved in just several minutes. The high efficiency achieved makes it practical to investigate human exposure involving a large number of cases with a high resolution that meets the requirements of international dosimetry guidelines.

Separation of antibody drug conjugate species by RPLC: A generic method development approach.

PubMed

Fekete, Szabolcs; Molnár, Imre; Guillarme, Davy

2017-04-15

This study reports the use of modelling software for the successful method development of IgG1 cysteine conjugated antibody drug conjugate (ADC) in RPLC. The goal of such a method is to be able to calculate the average drug to antibody ratio (DAR) of and ADC product. A generic method development strategy was proposed including the optimization of mobile phase temperature, gradient profile and mobile phase ternary composition. For the first time, a 3D retention modelling was presented for large therapeutic protein. Based on a limited number of preliminary experiments, a fast and efficient separation of the DAR species of a commercial ADC sample, namely brentuximab vedotin, was achieved. The prediction offered by the retention model was found to be highly reliable, with an average error of retention time prediction always lower than 0.5% using a 2D or 3D retention models. For routine purpose, four to six initial experiments were required to build the 2D retention models, while 12 experiments were recommended to create the 3D model. At the end, RPLC can therefore be considered as a good method for estimating the average DAR of an ADC, based on the observed peak area ratios of RPLC chromatogram of the reduced ADC sample. Copyright © 2017 Elsevier B.V. All rights reserved.

X-ray computed tomography imaging of a tumor with high sensitivity using gold nanoparticles conjugated to a cancer-specific antibody via polyethylene glycol chains on their surface

NASA Astrophysics Data System (ADS)

Nakagawa, Tomohiko; Gonda, Kohsuke; Kamei, Takashi; Cong, Liman; Hamada, Yoh; Kitamura, Narufumi; Tada, Hiroshi; Ishida, Takanori; Aimiya, Takuji; Furusawa, Naoko; Nakano, Yasushi; Ohuchi, Noriaki

2016-01-01

Contrast agents are often used to enhance the contrast of X-ray computed tomography (CT) imaging of tumors to improve diagnostic accuracy. However, because the iodine-based contrast agents currently used in hospitals are of low molecular weight, the agent is rapidly excreted from the kidney or moves to extravascular tissues through the capillary vessels, depending on its concentration gradient. This leads to nonspecific enhancement of contrast images for tissues. Here, we created gold (Au) nanoparticles as a new contrast agent to specifically image tumors with CT using an enhanced permeability and retention (EPR) effect. Au has a higher X-ray absorption coefficient than does iodine. Au nanoparticles were supported with polyethylene glycol (PEG) chains on their surface to increase the blood retention and were conjugated with a cancer-specific antibody via terminal PEG chains. The developed Au nanoparticles were injected into tumor-bearing mice, and the distribution of Au was examined with CT imaging, transmission electron microscopy, and elemental analysis using inductively coupled plasma optical emission spectrometry. The results show that specific localization of the developed Au nanoparticles in the tumor is affected by a slight difference in particle size and enhanced by the conjugation of a specific antibody against the tumor.

Simple method for RF pulse measurement using gradient reversal.

PubMed

Landes, Vanessa L; Nayak, Krishna S

2018-05-01

To develop and evaluate a simple method for measuring the envelope of small-tip radiofrequency (RF) excitation waveforms in MRI, without extra hardware or synchronization. Gradient reversal approach to evaluate RF (GRATER) involves RF excitation with a constant gradient and reversal of that gradient during signal reception to acquire the time-reversed version of an RF envelope. An outer-volume suppression prepulse is used optionally to preselect a uniform volume. GRATER was evaluated in phantom and in vivo experiments. It was compared with the programmed waveform and the traditional pick-up coil method. In uniform phantom experiments, pick-up coil, GRATER, and outer-volume suppression + GRATER matched the programmed waveforms to less than 2.1%, less than 6.1%, and less than 2.4% normalized root mean square error, respectively, for real RF pulses with flip angle less than or equal to 30°, time-bandwidth product 2 to 8, and two to five excitation bands. For flip angles greater than 30°, GRATER measurement error increased as predicted by Bloch simulation. Fat-water phantom and in vivo experiments with outer-volume suppression + GRATER demonstrated less than 6.4% normalized root mean square error. The GRATER sequence measures small-tip RF envelopes without extra hardware or synchronization in just over two times the RF duration. The sequence may be useful in prescan calibration and for measurement and precompensation of RF amplifier nonlinearity. Magn Reson Med 79:2642-2651, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Self-assembly of pi-conjugated peptides in aqueous environments leading to energy-transporting bioelectronic nanostructures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tavor, John

The realization of new supramolecular pi-conjugated organic structures inspired and driven by peptide-based self-assembly will offer a new approach to interface with the biotic environment in a way that will help to meet many DOE-recognized grand challenges. Previously, we developed pi-conjugated peptides that undergo supramolecular self-assembly into one-dimensional (1-D) organic electronic nanomaterials under benign aqueous conditions. The intermolecular interactions among the pi-conjugated organic segments within these nanomaterials lead to defined perturbations of their optoelectronic properties and yield nanoscale conduits that support energy transport within individual nanostructures and throughout bulk macroscopic collections of nanomaterials. Our objectives for future research are tomore » construct and study biomimetic electronic materials for energy-related technology optimized for harsher non-biological environments where peptide-driven self-assembly enhances pi-stacking within nanostructured biomaterials, as detailed in the following specific tasks: (1) synthesis and detailed optoelectronic characterization of new pi-electron units to embed within homogeneous self assembling peptides, (2) molecular and data-driven modeling of the nanomaterial aggregates and their higher-order assemblies, and (3) development of new hierarchical assembly paradigms to organize multiple electronic subunits within the nanomaterials leading to heterogeneous electronic properties (i.e. gradients and localized electric fields). These intertwined research tasks will lead to the continued development and fundamental mechanistic understanding of a powerful bioinspired materials set capable of making connections between nanoscale electronic materials and macroscopic bulk interfaces, be they those of a cell, a protein or a device.« less

High resolution separations of charge variants and disulfide isomers of monoclonal antibodies and antibody drug conjugates using ultra-high voltage capillary electrophoresis with high electric field strength.

PubMed

Henley, W Hampton; He, Yan; Mellors, J Scott; Batz, Nicholas G; Ramsey, J Michael; Jorgenson, James W

2017-11-10

Ultra-high voltage capillary electrophoresis with high electric field strength has been applied to the separation of the charge variants, drug conjugates, and disulfide isomers of monoclonal antibodies. Samples composed of many closely related species are difficult to resolve and quantify using traditional analytical instrumentation. High performance instrumentation can often save considerable time and effort otherwise spent on extensive method development. Ideally, the resolution obtained for a given CE buffer system scales with the square root of the applied voltage. Currently available commercial CE instrumentation is limited to an applied voltage of approximately 30kV and a maximum electric field strength of 1kV/cm due to design limitations. The instrumentation described here is capable of safely applying potentials of at least 120kV with electric field strengths over 2000V/cm, potentially doubling the resolution of the best conventional CE buffer/capillary systems while decreasing analysis time in some applications. Separations of these complex mixtures using this new instrumentation demonstrate the potential of ultra-high voltage CE to identify the presence of previously unresolved components and to reduce analysis time for complex mixtures of antibody variants and drug conjugates. Copyright © 2017 Elsevier B.V. All rights reserved.

Nanoporous gold as a solid support for protein immobilization and development of an electrochemical immunoassay for prostate specific antigen and carcinoembryonic antigen

PubMed Central

Pandey, Binod; Demchenko, Alexei V.; Stine, Keith J.

2013-01-01

Nanoporous gold (NPG) was utilized as a support for immobilizing alkaline phosphatase (ALP) conjugated to monoclonal antibodies against either prostate specific antigen (PSA) or carcinoembryonic antigen (CEA). The antibody-ALP conjugates were coupled to self-assembled monolayers of lipoic acid and used in direct kinetic assays. Using the enzyme substrate p-aminophenylphosphate, the product p-aminophenol was detected by its oxidation near 0.1 V (vs. Ag|AgCl) using square wave voltammetry. The difference in peak current arising from oxidation of p-aminophenol before and after incubation with biomarker increased with biomarker concentration. The response to these two biomarkers was linear up to 10 ng mL-1 for CEA and up to 30 ng mL-1 for PSA. The effect of interference on the PSA assay was studied using bovine serum albumin (BSA) as a model albumin protein. The effect of interference from a serum matrix was examined for the PSA assay using newborn calf serum. A competitive version of the immunoassay using antigen immobilized onto the NPG surface was highly sensitive at lower antigen concentration. Estimates of the surface coverage of the antibody-ALP conjugates on the NPG surface are presented. PMID:23935216

How PEGylation enhances the stability and potency of insulin: a molecular dynamics simulation.

PubMed

Yang, Cheng; Lu, Diannan; Liu, Zheng

2011-04-05

While the effectiveness of PEGylation in enhancing the stability and potency of protein pharmaceuticals has been validated for years, the underlying mechanism remains poorly understood, particularly at the molecular level. A molecular dynamics simulation was developed using an annealing procedure that allowed an all-atom level examination of the interaction between PEG polymers of different chain lengths and a conjugated protein represented by insulin. It was shown that PEG became entangled around the protein surface through hydrophobic interaction and concurrently formed hydrogen bonds with the surrounding water molecules. In addition to enhancing its structural stability, as indicated by the root-mean-square difference (rmsd) and secondary structure analyses, conjugation increased the size of the protein drug while decreasing the solvent accessible surface area of the protein. All these thus led to prolonged circulation life despite kidney filtration, proteolysis, and immunogenic side effects, as experimentally demonstrated elsewhere. Moreover, the simulation results indicated that an optimal chain length exists that would maximize drug potency underpinned by the parameters mentioned above. The simulation provided molecular insight into the interaction between PEG and the conjugated protein at the all-atom level and offered a tool that would allow for the design of PEGylated protein pharmaceuticals for given applications.

Speed and convergence properties of gradient algorithms for optimization of IMRT.

PubMed

Zhang, Xiaodong; Liu, Helen; Wang, Xiaochun; Dong, Lei; Wu, Qiuwen; Mohan, Radhe

2004-05-01

Gradient algorithms are the most commonly employed search methods in the routine optimization of IMRT plans. It is well known that local minima can exist for dose-volume-based and biology-based objective functions. The purpose of this paper is to compare the relative speed of different gradient algorithms, to investigate the strategies for accelerating the optimization process, to assess the validity of these strategies, and to study the convergence properties of these algorithms for dose-volume and biological objective functions. With these aims in mind, we implemented Newton's, conjugate gradient (CG), and the steepest decent (SD) algorithms for dose-volume- and EUD-based objective functions. Our implementation of Newton's algorithm approximates the second derivative matrix (Hessian) by its diagonal. The standard SD algorithm and the CG algorithm with "line minimization" were also implemented. In addition, we investigated the use of a variation of the CG algorithm, called the "scaled conjugate gradient" (SCG) algorithm. To accelerate the optimization process, we investigated the validity of the use of a "hybrid optimization" strategy, in which approximations to calculated dose distributions are used during most of the iterations. Published studies have indicated that getting trapped in local minima is not a significant problem. To investigate this issue further, we first obtained, by trial and error, and starting with uniform intensity distributions, the parameters of the dose-volume- or EUD-based objective functions which produced IMRT plans that satisfied the clinical requirements. Using the resulting optimized intensity distributions as the initial guess, we investigated the possibility of getting trapped in a local minimum. For most of the results presented, we used a lung cancer case. To illustrate the generality of our methods, the results for a prostate case are also presented. For both dose-volume and EUD based objective functions, Newton's method far outperforms other algorithms in terms of speed. The SCG algorithm, which avoids expensive "line minimization," can speed up the standard CG algorithm by at least a factor of 2. For the same initial conditions, all algorithms converge essentially to the same plan. However, we demonstrate that for any of the algorithms studied, starting with previously optimized intensity distributions as the initial guess but for different objective function parameters, the solution frequently gets trapped in local minima. We found that the initial intensity distribution obtained from IMRT optimization utilizing objective function parameters, which favor a specific anatomic structure, would lead to a local minimum corresponding to that structure. Our results indicate that from among the gradient algorithms tested, Newton's method appears to be the fastest by far. Different gradient algorithms have the same convergence properties for dose-volume- and EUD-based objective functions. The hybrid dose calculation strategy is valid and can significantly accelerate the optimization process. The degree of acceleration achieved depends on the type of optimization problem being addressed (e.g., IMRT optimization, intensity modulated beam configuration optimization, or objective function parameter optimization). Under special conditions, gradient algorithms will get trapped in local minima, and reoptimization, starting with the results of previous optimization, will lead to solutions that are generally not significantly different from the local minimum.

SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Reconstruction of vector physical fields by optical tomography

NASA Astrophysics Data System (ADS)

Kulchin, Yurii N.; Vitrik, O. B.; Kamenev, O. T.; Kirichenko, O. V.; Petrov, Yu S.

1995-10-01

Reconstruction of vector physical fields by optical tomography, with the aid of a system of fibre-optic measuring lines, is considered. The reported experimental results are used to reconstruct the distribution of the square of the gradient of transverse displacements of a flat membrane.

Introductory Linear Regression Programs in Undergraduate Chemistry.

ERIC Educational Resources Information Center

Gale, Robert J.

1982-01-01

Presented are simple programs in BASIC and FORTRAN to apply the method of least squares. They calculate gradients and intercepts and express errors as standard deviations. An introduction of undergraduate students to such programs in a chemistry class is reviewed, and issues instructors should be aware of are noted. (MP)

Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.; Wang, Qiqi

2018-02-01

Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic systems, including simulations of chaotic vortex shedding and homogeneous isotropic turbulence. However, this gradient information comes at a very high computational cost. This paper presents multiple shooting shadowing (MSS), a more computationally efficient shadowing approach than the original LSS approach. Through an analysis of the convergence rate of MSS, it is shown that MSS can have lower memory usage and run time than LSS.

Three-dimensional Gravity Inversion with a New Gradient Scheme on Unstructured Grids

NASA Astrophysics Data System (ADS)

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 geology differentiation using guided fuzzy c-means clustering. Geophysics, 80(4): ID1-ID18. Okabe M. 1979. Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies. Geophysics, 44(4), 730-741.

A nonrecursive 'Order N' preconditioned conjugate gradient/range space formulation of MDOF dynamics

NASA Technical Reports Server (NTRS)

Kurdila, A. J.; Menon, R.; Sunkel, John

1991-01-01

This paper addresses the requirements of present-day mechanical system simulations of algorithms that induce parallelism on a fine scale and of transient simulation methods which must be automatically load balancing for a wide collection of system topologies and hardware configurations. To this end, a combination range space/preconditioned conjugage gradient formulation of multidegree-of-freedon dynamics is developed, which, by employing regular ordering of the system connectivity graph, makes it possible to derive an extremely efficient preconditioner from the range space metric (as opposed to the system coefficient matrix). Because of the effectiveness of the preconditioner, the method can achieve performance rates that depend linearly on the number of substructures. The method, termed 'Order N' does not require the assembly of system mass or stiffness matrices, and is therefore amenable to implementation on work stations. Using this method, a 13-substructure model of the Space Station was constructed.

DenInv3D: a geophysical software for three-dimensional density inversion of gravity field data

NASA Astrophysics Data System (ADS)

Tian, Yu; Ke, Xiaoping; Wang, Yong

2018-04-01

This paper presents a three-dimensional density inversion software called DenInv3D that operates on gravity and gravity gradient data. The software performs inversion modelling, kernel function calculation, and inversion calculations using the improved preconditioned conjugate gradient (PCG) algorithm. In the PCG algorithm, due to the uncertainty of empirical parameters, such as the Lagrange multiplier, we use the inflection point of the L-curve as the regularisation parameter. The software can construct unequally spaced grids and perform inversions using such grids, which enables changing the resolution of the inversion results at different depths. Through inversion of airborne gradiometry data on the Australian Kauring test site, we discovered that anomalous blocks of different sizes are present within the study area in addition to the central anomalies. The software of DenInv3D can be downloaded from http://159.226.162.30.

Multimodal magnetic nano-carriers for cancer treatment: Challenges and advancements

NASA Astrophysics Data System (ADS)

Aadinath, W.; Ghosh, Triroopa; Anandharamakrishnan, C.

2016-03-01

Iron oxide nanoparticles (IONPs) have been a propitious topic for cancer treatment in recent years because of its multifunctional theranostic applications under magnetic field. Two such widely used applications in cancer biology are gradient magnetic field guided targeting and alternative magnetic field (AMF) induced local hyperthermia. Gradient magnetic field guided targeting is a mode of active targeting of therapeutics conjugated with iron oxide nanoparticles. These particles also dissipate heat in presence of AMF which causes thermal injury to the cells of interest, for example tumour cells and subsequent death. Clinical trials divulge the feasibility of such magnetic nano-carrier as a promising candidate in cancer biology. However, these techniques need further investigations to curtail certain limitations manifested. Recent progresses in response have shrunken the barricade to certain extent. In this context, principles, challenges associated with these applications and recent efforts made in response will be discussed.

Generation of Plasma Density Irregularities in the Midlatitude/Subauroral F Region

NASA Astrophysics Data System (ADS)

Mishin, E. V.

2017-12-01

A concise review is given of the current state of the theoretical understanding of the creation of small- and meso-scale plasma density irregularities in the midlatitude/subauroral F region during quiet and disturbed periods. The former are discussed in terms of the temperature gradient instability (TGI) in the vicinity of the ionospheric projection of the plasmapause and the Perkins instability. During active conditions some part of the midlatitude ionosphere becomes the subauroral region dominated by enhanced westward flows (SAPS and SAID) driven by poleward electric fields. Their irregular, often nonlinear wave structure leads to the formation of plasma density irregularities in the plasmasphere and conjugate ionosphere. Here, meso-scale irregularities are due to the positive feedback magnetosphere-ionosphere coupling instability, while small scales resulted from the gradient drift instability (GDI), temperature GDI, and the ion frictional heating instability. The theoretical predictions are compared with satellite observations in the perturbed subauroral geospace.

Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

NASA Astrophysics Data System (ADS)

Muldoon, F. H.

2018-04-01

Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.

Operation regimes of a dielectric laser accelerator

NASA Astrophysics Data System (ADS)

Hanuka, Adi; Schächter, Levi

2018-04-01

We investigate three operation regimes in dielectric laser driven accelerators: maximum efficiency, maximum charge, and maximum loaded gradient. We demonstrate, using a self-consistent approach, that loaded gradients of the order of 1 to 6 [GV/m], efficiencies of 20% to 80%, and electrons flux of 1014 [el/s] are feasible, without significant concerns regarding damage threshold fluence. The latter imposes that the total charge per squared wavelength is constant (a total of 106 per μm2). We conceive this configuration as a zero-order design that should be considered for the road map of future accelerators.

Image Edge Extraction via Fuzzy Reasoning

NASA Technical Reports Server (NTRS)

Dominquez, Jesus A. (Inventor); Klinko, Steve (Inventor)

2008-01-01

A computer-based technique for detecting edges in gray level digital images employs fuzzy reasoning to analyze whether each pixel in an image is likely on an edge. The image is analyzed on a pixel-by-pixel basis by analyzing gradient levels of pixels in a square window surrounding the pixel being analyzed. An edge path passing through the pixel having the greatest intensity gradient is used as input to a fuzzy membership function, which employs fuzzy singletons and inference rules to assigns a new gray level value to the pixel that is related to the pixel's edginess degree.

Global grids of gravity anomalies and vertical gravity gradients at 10 km altitude from GOCE gradient data 2009-2011 and polar gravity.

NASA Astrophysics Data System (ADS)

Tscherning, Carl Christian; Arabelos, Dimitrios; Reguzzoni, Mirko

2013-04-01

The GOCE satellite measures gravity gradients which are filtered and transformed to gradients into an Earth-referenced frame by the GOCE High Level processing Facility. More than 80000000 data with 6 components are available from the period 2009-2011. IAG Arctic gravity was used north of 83 deg., while data at the Antarctic was not used due to bureaucratic restrictions by the data-holders. Subsets of the data have been used to produce gridded values at 10 km altitude of gravity anomalies and vertical gravity gradients in 20 deg. x 20 deg. blocks with 10' spacing. Various combinations and densities of data were used to obtain values in areas with known gravity anomalies. The (marginally) best choice was vertical gravity gradients selected with an approximately 0.125 deg spacing. Using Least-Squares Collocation, error-estimates were computed and compared to the difference between the GOCE-grids and grids derived from EGM2008 to deg. 512. In general a good agreement was found, however with some inconsistencies in certain areas. The computation time on a usual server with 24 processors was typically 100 minutes for a block with generally 40000 GOCE vertical gradients as input. The computations will be updated with new Wiener-filtered data in the near future.

Stepwise Assembly and Characterization of DNA Linked Two-Color Quantum Dot Clusters.

PubMed

Coopersmith, Kaitlin; Han, Hyunjoo; Maye, Mathew M

2015-07-14

The DNA-mediated self-assembly of multicolor quantum dot (QD) clusters via a stepwise approach is described. The CdSe/ZnS QDs were synthesized and functionalized with an amphiphilic copolymer, followed by ssDNA conjugation. At each functionalization step, the QDs were purified via gradient ultracentrifugation, which was found to remove excess polymer and QD aggregates, allowing for improved conjugation yields and assembly reactivity. The QDs were then assembled and disassembled in a stepwise manner at a ssDNA functionalized magnetic colloid, which provided a convenient way to remove unreacted QDs and ssDNA impurities. After assembly/disassembly, the clusters' optical characteristics were studied by fluorescence spectroscopy and the assembly morphology and stoichiometry was imaged via electron microscopy. The results indicate that a significant amount of QD-to-QD energy transfer occurred in the clusters, which was studied as a function of increasing acceptor-to-donor ratios, resulting in increased QD acceptor emission intensities compared to controls.

Hamiltonian and Thermodynamic Modeling of Quantum Turbulence

NASA Astrophysics Data System (ADS)

Grmela, Miroslav

2010-10-01

The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in 4He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.

COVARIANCE ESTIMATION USING CONJUGATE GRADIENT FOR 3D CLASSIFICATION IN CRYO-EM.

PubMed

Andén, Joakim; Katsevich, Eugene; Singer, Amit

2015-04-01

Classifying structural variability in noisy projections of biological macromolecules is a central problem in Cryo-EM. In this work, we build on a previous method for estimating the covariance matrix of the three-dimensional structure present in the molecules being imaged. Our proposed method allows for incorporation of contrast transfer function and non-uniform distribution of viewing angles, making it more suitable for real-world data. We evaluate its performance on a synthetic dataset and an experimental dataset obtained by imaging a 70S ribosome complex.

Research in computer science

NASA Technical Reports Server (NTRS)

Ortega, J. M.

1984-01-01

Several short summaries of the work performed during this reporting period are presented. Topics discussed in this document include: (1) resilient seeded errors via simple techniques; (2) knowledge representation for engineering design; (3) analysis of faults in a multiversion software experiment; (4) implementation of parallel programming environment; (5) symbolic execution of concurrent programs; (6) two computer graphics systems for visualization of pressure distribution and convective density particles; (7) design of a source code management system; (8) vectorizing incomplete conjugate gradient on the Cyber 203/205; (9) extensions of domain testing theory and; (10) performance analyzer for the pisces system.

A superlinear convergence estimate for an iterative method for the biharmonic equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horn, M.A.

In [CDH] a method for the solution of boundary value problems for the biharmonic equation using conformal mapping was investigated. The method is an implementation of the classical method of Muskhelishvili. In [CDH] it was shown, using the Hankel structure, that the linear system in [Musk] is the discretization of the identify plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. The purpose of this paper is to give an estimate of the superlinear convergence in the case when the boundary curve is in a Hoelder class.

Optimal control of population and coherence in three-level Λ systems

NASA Astrophysics Data System (ADS)

Kumar, Praveen; Malinovskaya, Svetlana A.; Malinovsky, Vladimir S.

2011-08-01

Optimal control theory (OCT) implementations for an efficient population transfer and creation of maximum coherence in a three-level system are considered. We demonstrate that the half-stimulated Raman adiabatic passage scheme for creation of the maximum Raman coherence is the optimal solution according to the OCT. We also present a comparative study of several implementations of OCT applied to the complete population transfer and creation of the maximum coherence. Performance of the conjugate gradient method, the Zhu-Rabitz method and the Krotov method has been analysed.

Lattice QCD calculation using VPP500

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Seyong; Ohta, Shigemi

1995-02-01

A new vector parallel supercomputer, Fujitsu VPP500, was installed at RIKEN earlier this year. It consists of 30 vector computers, each with 1.6 GFLOPS peak speed and 256 MB memory, connected by a crossbar switch with 400 MB/s peak data transfer rate each way between any pair of nodes. The authors developed a Fortran lattice QCD simulation code for it. It runs at about 1.1 GFLOPS sustained per node for Metropolis pure-gauge update, and about 0.8 GFLOPS sustained per node for conjugate gradient inversion of staggered fermion matrix.

News on Seeking Gaia's Astrometric Core Solution with AGIS

NASA Astrophysics Data System (ADS)

Lammers, U.; Lindegren, L.

We report on recent new developments around the Astrometric Global Iterative Solution system. This includes the availability of an efficient Conjugate Gradient solver and the Generic Astrometric Calibration scheme that had been proposed a while ago. The number of primary stars to be included in the core solution is now believed to be significantly higher than the 100 Million that served as baseline until now. Cloud computing services are being studied as a possible cost-effective alternative to running AGIS on dedicated computing hardware at ESAC during the operational phase.

Design and characterization of nanomaterial-biomolecule conjugates

NASA Astrophysics Data System (ADS)

Yim, Tae-Jin

In the field of nanobiotechnology, nanoscale dimensions result in physical properties that differ from more conventional bulk material state. The integration of nanomaterials with biomolecules has begun to be used for unique physical properties, and for biological specific recognition, thereby leading to novel nanomaterial-biomolecule conjugates. The direction of this dissertation is to develop biocatalytic nanomaterial-biomolecule conjugates and to characterize them. For this, biological catalysts are employed to combine with nanomaterials. Two large parts include functional ization of nanomaterials with biomolecules and assembly of nanomaterials using a biological catalyst. First part of this thesis work is the exploration of the biocatalytic properties of nanomaterial-biomolecule conjugates. Si nanocolumns have higher surface area which leads more amount of biocatalytis immobilization than flat Si wafer with the same projected area. The enhanced activity of soybean peroxidase (SBP) immobilized onto Si nanocolumns as novel nanostructured supports is focused. Next, the catalytic activity of immobilized DNAzyme onto multiwalled carbon nanotubes (MWNTs) is compared to that in solution phase, and multiple turnovers are examined. The relationship between hybridization efficiency and activity is investigated as a function of surface density of DNAzyme on MWNTs. Then, cellular delivery of silica nanoparticle-protein conjugates is visually confirmed and therefore the intracellular function of a protein delivered by silica nanoparticle-protein conjugates is proved. For one example of the intracellular function, stable SBP immobilized onto silica nanoparticles to activate a prodrug is demonstrated. Second part of this thesis work is the formation of nanostructured materials through the enzymatic assembly of single-walled carbon nanotubes (SWNTs). Enzymatic polymerization of a phenol compound is applied to the bridging of two or more SWNTs functionalized with phenol monomers. Next, future work based on previous works is proposed; first, the cellular delivery of DNAzyme using SWNTs is proposed to be a promising nonviral nanovehicle for gene silencing. Second, hydrophobic/hydrophilic switchable surface using DNAzyme is suggested to expand its usage to hydrophobically gradient surface. Finally, reversible assembly and disassembly of poly-L-histidine coated MWNTs can be applied to a reversible nanotube patterning on surface. And, the expansion of the works presented in this thesis to "nanomedicine" is suggested.

Optical fringe-reflection deflectometry with sparse representation

NASA Astrophysics Data System (ADS)

Xiao, Yong-Liang; Li, Sikun; Zhang, Qican; Zhong, Jianxin; Su, Xianyu; You, Zhisheng

2018-05-01

Optical fringe-reflection deflectometry is a surprisingly attractive scratch detection technique for specular surfaces owing to its unparalleled local sensibility. Full-field surface topography is obtained from a measured normal field using gradient integration. However, there may not be an ideal measured gradient field for deflectometry reconstruction in practice. Both the non-integrability condition and various kinds of image noise distributions, which are present in the indirect measured gradient field, may lead to ambiguity about the scratches on specular surfaces. In order to reduce misjudgment of scratches, sparse representation is introduced into the Southwell curl equation for deflectometry. The curl can be represented as a linear combination of the given redundant dictionary for curl and the sparsest solution for gradient refinement. The non-integrability condition and noise permutation can be overcome with sparse representation for gradient refinement. Numerical simulations demonstrate that the accuracy rate of judgment of scratches can be enhanced with sparse representation compared to the standard least-squares integration. Preliminary experiments are performed with the application of practical measured deflectometric data to verify the validity of the algorithm.

Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm.

PubMed

Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

2013-12-07

The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence.

Phase discrepancy induced from least squares wavefront reconstruction of wrapped phase measurements with high noise or large localized wavefront gradients

NASA Astrophysics Data System (ADS)

Steinbock, Michael J.; Hyde, Milo W.

2012-10-01

Adaptive optics is used in applications such as laser communication, remote sensing, and laser weapon systems to estimate and correct for atmospheric distortions of propagated light in real-time. Within an adaptive optics system, a reconstruction process interprets the raw wavefront sensor measurements and calculates an estimate for the unwrapped phase function to be sent through a control law and applied to a wavefront correction device. This research is focused on adaptive optics using a self-referencing interferometer wavefront sensor, which directly measures the wrapped wavefront phase. Therefore, its measurements must be reconstructed for use on a continuous facesheet deformable mirror. In testing and evaluating a novel class of branch-point- tolerant wavefront reconstructors based on the post-processing congruence operation technique, an increase in Strehl ratio compared to a traditional least squares reconstructor was noted even in non-scintillated fields. To investigate this further, this paper uses wave-optics simulations to eliminate many of the variables from a hardware adaptive optics system, so as to focus on the reconstruction techniques alone. The simulation results along with a discussion of the physical reasoning for this phenomenon are provided. For any applications using a self-referencing interferometer wavefront sensor with low signal levels or high localized wavefront gradients, understanding this phenomena is critical when applying a traditional least squares wavefront reconstructor.

Bird community specialization, bird conservation and disturbance: the role of wildfires.

PubMed

Clavero, Miguel; Brotons, Lluís; Herrando, Sergi

2011-01-01

1. Although niche theory predicts that disturbance should favour generalist species, the community-level implications of this pattern have been sparsely analysed. Here, we test the hypothesis that disturbance favours generalist species within communities, analysing effects of wildfires in bird communities in a Mediterranean climate area as a case study. 2. We use bird occurrence data in more than 500 1 × 1 km squares forming a gradient running from forest to completely burnt areas. The level of specialization of bird communities was estimated by means of three complementary species specialization indices, calculated for different landscape gradients and averaged at the community level (i.e. 1 × 1 km squares), and mean species rarity. 3. We also calculated mean habitat preferences along landscape gradients, as well as an index of conservation value and total species richness. 4. Different estimators of bird community specialization varied in contrasting fashion along the wildfire disturbance gradient, and thus we conclude that it is not justified to expect unique community responses to the sharp variations in habitat characteristics brought by wildfire disturbances. 5. Burnt areas tended to have rarer and urban-avoider bird species, whereas unburnt forests tended to have larger proportions of forest specialist species. 6. The mean conservation value of communities clearly increased towards the burnt extreme of the wildfire disturbance gradient, while this had a negligible effect on species richness. 7. Wildfires seem to play an important role for the maintenance of open-habitat, urban-avoider bird populations in Mediterranean landscapes and also to benefit a set of bird species of unfavourable European conservation status. 8. In this context, it cannot be unambiguously concluded that fire disturbance, even in a context in which fires are greatly favoured by human-related activities, leads to more functionally simplified communities dominated by generalist species. © 2010 The Authors. Journal compilation © 2010 British Ecological Society.

Quantum critical phase with infinite projected entangled paired states

NASA Astrophysics Data System (ADS)

Poilblanc, Didier; Mambrini, Matthieu

2017-07-01

A classification of SU(2)-invariant projected entangled paired states (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al. [M. Mambrini, R. Orús, and D. Poilblanc, Phys. Rev. B 94, 205124 (2016), 10.1103/PhysRevB.94.205124]. It is not clear whether such SU(2)-invariant PEPS can either (i) exhibit long-range magnetic order (such as in the Néel phase) or (ii) describe a genuine quantum critical point (QCP) or quantum critical phase (QCPh) separating two ordered phases. Here, we identify a specific family of SU(2)-invariant PEPS of the classification which provides excellent variational energies for the J1-J2 frustrated Heisenberg model, especially at J2=0.5 , corresponding to the approximate location of the QCP or QCPh separating the Néel phase from a dimerized phase. The PEPS are built from virtual states belonging to the 1/2⊗N⊕0 SU(2) representation, i.e., with N "colors" of virtual spin-1/2 . Using a full-update infinite-PEPS approach directly in the thermodynamic limit, based on the corner transfer matrix renormalization algorithm supplemented by a conjugate gradient optimization scheme, we provide evidence of (i) the absence of magnetic order and of (ii) diverging correlation lengths (i.e., showing no sign of saturation with increasing environment dimension) in both the singlet and triplet channels, when the number of colors N ≥3 . We argue that such a PEPS gives a qualitative description of the QCP or QCPh of the J1-J2 model.

Simultaneous elastic parameter inversion in 2-D/3-D TTI medium combined later arrival times

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; Wang, Tao; Yang, Shang-bei; Li, Xing-wang; Huang, Guo-jiao

2016-04-01

Traditional traveltime inversion for anisotropic medium is, in general, based on a "weak" assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both "weak" and "strong") anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including "strong") anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.

3-compartment talaporfin sodium pharmacokinetic model by optimization using fluorescence measurement data from canine skin to estimate the concentration in interstitial space

NASA Astrophysics Data System (ADS)

Uno, Yuko; Ogawa, Emiyu; Aiyoshi, Eitaro; Arai, Tsunenori

2018-02-01

We constructed the 3-compartment talaporfin sodium pharmacokinetic model for canine by an optimization using the fluorescence measurement data from canine skin to estimate the concentration in the interstitial space. It is difficult to construct the 3-compartment model consisted of plasma, interstitial space, and cell because there is a lack of the dynamic information. Therefore, we proposed the methodology to construct the 3-compartment model using the measured talaporfin sodium skin fluorescence change considering originated tissue part by a histological observation. In a canine animal experiment, the talaporfin sodium concentration time history in plasma was measured by a spectrophotometer with a prepared calibration curve. The time history of talaporfin sodium Q-band fluorescence on left femoral skin of a beagle dog excited by talaporfin sodium Soret-band of 409 nm was measured in vivo by our previously constructed measurement system. The measured skin fluorescence was classified to its source, that is, specific ratio of plasma, interstitial space, and cell. We represented differential rate equations of the talaporfin sodium concentration in plasma, interstitial space, cell. The specific ratios and a converting constant to obtain absolute value of skin concentration were arranged. Minimizing the squared error of the difference between the measured fluorescence data and calculated concentration by the conjugate gradient method in MATLAB, the rate constants in the 3-compartment model were determined. The accuracy of the fitting operation was confirmed with determination coefficient of 0.98. We could construct the 3-compartment pharmacokinetic model for canine using the measured talaporfin sodium fluorescence change from canine skin.

On-Surface Synthesis and Characterization of Honeycombene Oligophenylene Macrocycles.

PubMed

Chen, Min; Shang, Jian; Wang, Yongfeng; Wu, Kai; Kuttner, Julian; Hilt, Gerhard; Hieringer, Wolfgang; Gottfried, J Michael

2017-01-24

We report the on-surface formation and characterization of [30]-honeycombene, a cyclotriacontaphenylene, which consists of 30 phenyl rings (C 180 H 120 ) and has a diameter of 4.0 nm. This shape-persistent, conjugated, and unsubstituted hexagonal hydrocarbon macrocycle was obtained by solvent-free synthesis on a silver (111) single-crystal surface, making solubility-enhancing alkyl side groups unnecessary. Side products include strained macrocycles with square, pentagonal, and heptagonal shape. The molecules were characterized by scanning tunneling microscopy and density functional theory (DFT) calculations. On the Ag(111) surface, the macrocycles act as molecular quantum corrals and lead to the confinement of surface-state electrons inside the central cavity. The energy of the confined surface state correlates with the size of the macrocycle and is well described by a particle-in-the-box model. Tunneling spectroscopy suggests conjugation within the planar rings and reveals influences of self-assembly on the electronic structure. While the adsorbed molecules appear to be approximately planar, the free molecules have nonplanar conformation, according to DFT.

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

Parameter estimation of extended free-burning electric arc within 1 kA

NASA Astrophysics Data System (ADS)

Sun, Qiuqin; Liu, Hao; Wang, Feng; Chen, She; Zhai, Yujia

2018-05-01

A long electric arc, as a common phenomenon in the power system, not only damages the electrical equipment but also threatens the safety of the system. In this work, a series of tests on a long electric arc in free air have been conducted. The arc voltage and current data were obtained, and the arc trajectories were captured using a high speed camera. The arc images were digitally processed by means of edge detection, and the length is formulated and achieved. Based on the experimental data, the characteristics of the long arc are discussed. It shows that the arc voltage waveform is close to the square wave with high-frequency components, whereas the current is almost sinusoidal. As the arc length elongates, the arc voltage and the resistance increase sharply. The arc takes a spiral shape with the effect of magnetic forces. The arc length will shorten briefly with the occurrence of the short-circuit phenomenon. Based on the classical Mayr model, the parameters of the long electric arc, including voltage gradient and time constant, with different lengths and current amplitudes are estimated using the linear least-square method. To reduce the computational error, segmentation interpolation is also employed. The results show that the voltage gradient of the long arc is mainly determined by the current amplitude but almost independent of the arc length. However, the time constant is jointly governed by these two variables. The voltage gradient of the arc with the current amplitude at 200-800 A is in the range of 3.9 V/cm-20 V/cm, and the voltage gradient decreases with the increase in current.

Conjugated linolenic acid (CLnA), conjugated linoleic acid (CLA) and other biohydrogenation intermediates in plasma and milk fat of cows fed raw or extruded linseed.

PubMed

Akraim, F; Nicot, M C; Juaneda, P; Enjalbert, F

2007-07-01

Thirty lactating dairy cows were used in a 3 × 3 Latin-square design to investigate the effects of a raw or extruded blend of linseed and wheat bran (70:30) on plasma and milk fatty-acids (FA). Linseed diets, containing 16.6% linseed blend on a dry-matter basis, decreased milk yield and protein percentage. They decreased the proportions of FA with less than 18 carbons in plasma and milk and resulted in cis-9, cis-12, cis-15 18:3 proportions that were more than three and four times higher in plasma and milk, respectively, whereas cis-9, cis-12 18:2 proportions were decreased by 10-15%. The cis-9, trans-11, cis-15 18:3 isomer of conjugated linolenic acid was not detected in the milk of control cows, but was over 0.15% of total FA in the milk fat of linseed-supplemented cows. Similarly, linseed increased plasma and milk proportions of all biohydrogenation (BH) intermediates in plasma and milk, including the main isomer of conjugated linoleic acid cis-9, trans-11 18:2, except trans-4 18:1 and cis-11, trans-15 18:2 in plasma lipids. In milk fat, compared with raw linseed, extruded linseed further reduced 6:0-16:0 even-chain FA, did not significantly affect the proportions of 18:0, cis-9 18:1 and cis-9, cis-12 18:2, tended to increase cis-9, cis-12, cis-15 18:3, and resulted in an additional increase in the proportions of most BH intermediates. It was concluded that linseed addition can improve the proportion of conjugated linoleic and linolenic acids, and that extrusion further increases the proportions of intermediates of ruminal BH in milk fat.

Numerical Simulations of Aero-Optical Distortions Around Various Turret Geometries

DTIC Science & Technology

2013-06-12

arbi trary cell topologies. The spatial operator uses the exact Riemann Solver of Gottlieb and Groth, least squares gradient cal- culations using QR...Unstructured Euler/Navier-Stokes Flow Solver ," in A/AA Paper 1999-0786, 1999. [9] J. J. Gottlieb and C. P. T. Groth, "Assessment of Riemann Solvers

Hysteresis modeling of magnetic shape memory alloy actuator based on Krasnosel'skii-Pokrovskii model.

PubMed

Zhou, Miaolei; Wang, Shoubin; Gao, Wei

2013-01-01

As a new type of intelligent material, magnetically shape memory alloy (MSMA) has a good performance in its applications in the actuator manufacturing. Compared with traditional actuators, MSMA actuator has the advantages as fast response and large deformation; however, the hysteresis nonlinearity of the MSMA actuator restricts its further improving of control precision. In this paper, an improved Krasnosel'skii-Pokrovskii (KP) model is used to establish the hysteresis model of MSMA actuator. To identify the weighting parameters of the KP operators, an improved gradient correction algorithm and a variable step-size recursive least square estimation algorithm are proposed in this paper. In order to demonstrate the validity of the proposed modeling approach, simulation experiments are performed, simulations with improved gradient correction algorithm and variable step-size recursive least square estimation algorithm are studied, respectively. Simulation results of both identification algorithms demonstrate that the proposed modeling approach in this paper can establish an effective and accurate hysteresis model for MSMA actuator, and it provides a foundation for improving the control precision of MSMA actuator.

Stagnation Region Heat Transfer: The Influence of Turbulence Parameters, Reynolds Number and Body Shape

NASA Technical Reports Server (NTRS)

Vanfossen, G. James; Simoneau, Robert J.

1994-01-01

The effect of velocity gradient on stagnation region heat transfer augmentation by free stream turbulence was investigated. Heat transfer was measured in the stagnation region of four models with elliptical leading edges with ratios of major to minor axes of 1:1, 1.5:1, 2.25:1, and 3:1. Four geometrically similar, square bar, square mesh, biplane grids were used to generate free stream turbulence with different intensities and length. Heat transfer measurements were made for the following ranges of parameters: Reynolds number, based on leading edge diameter, 37,000 to 228,000; dimensionless leading edge velocity gradient, 1.20 to 1.80; turbulence intensity, 1.1 to 15.9%; and length scale to leading edge diameter ratio, 0.05 to 0.30. Stagnation point heat transfer augmentation by free stream turbulence can be predicted using a modified version of a previously developed correlation for a circular leading edge. Heat transfer augmentation was independent of body shape at the stagnation point. The heat transfer distribution down-stream from the stagnation point can be predicted using the normalized laminar heat transfer distribution.

An optimization approach for fitting canonical tensor decompositions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methodsmore » have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.« less

Hysteresis Modeling of Magnetic Shape Memory Alloy Actuator Based on Krasnosel'skii-Pokrovskii Model

PubMed Central

Wang, Shoubin; Gao, Wei

2013-01-01

As a new type of intelligent material, magnetically shape memory alloy (MSMA) has a good performance in its applications in the actuator manufacturing. Compared with traditional actuators, MSMA actuator has the advantages as fast response and large deformation; however, the hysteresis nonlinearity of the MSMA actuator restricts its further improving of control precision. In this paper, an improved Krasnosel'skii-Pokrovskii (KP) model is used to establish the hysteresis model of MSMA actuator. To identify the weighting parameters of the KP operators, an improved gradient correction algorithm and a variable step-size recursive least square estimation algorithm are proposed in this paper. In order to demonstrate the validity of the proposed modeling approach, simulation experiments are performed, simulations with improved gradient correction algorithm and variable step-size recursive least square estimation algorithm are studied, respectively. Simulation results of both identification algorithms demonstrate that the proposed modeling approach in this paper can establish an effective and accurate hysteresis model for MSMA actuator, and it provides a foundation for improving the control precision of MSMA actuator. PMID:23737730

Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes.

PubMed

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.

Constraint treatment techniques and parallel algorithms for multibody dynamic analysis. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

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.

A microfluidic chip with a staircase pH gradient generator, a packed column and a fraction collector for chromatofocusing of proteins.

PubMed

Rho, Hoon Suk; Hanke, Alexander Thomas; Ottens, Marcel; Gardeniers, Han J G E

2018-04-01

A microfluidic device for pH gradient chromatofocusing is presented, which performs creation of a micro-column, pH gradient generation, and fraction collection in a single device. Using a sieve micro-valve, anion exchange particles were packed into a microchannel in order to realize a solid-phase absorption column. To fractionate proteins according to their isoelectric points, elution buffer solutions with a stepwise pH gradient were prepared in 16 parallel mixing reactors and flowed through the micro-column, wherein a protein mixture was previously loaded. The volume of the column is only 20 nL, hence it allows extremely low sample consumption and fast analysis compared with a conventional system. We demonstrated separation of two proteins, albumin-fluorescein isothiocyanate conjugate (FITC-BSA) and R-Phycoerythrin (R-PE), by using a microcolumn of commercial charged polymeric particles (Source 15Q). The microfluidic device can be used as a rapid diagnostic tool to analyse crude mixtures of proteins or nucleic acids and determine adsorption/desorption characteristics of various biochemical products, which can be helpful for scientific fundamental understanding as well as instrumental in various industrial applications, especially in early stage screening and process development. © 2018 The Authors Electrophoresis Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On the evolution of the invariants of the velocity gradient tensor in single-square-grid-generated turbulence

NASA Astrophysics Data System (ADS)

Zhou, Yi; Nagata, Koji; Sakai, Yasuhiko; Ito, Yasumasa; Hayase, Toshiyuki

2015-07-01

Direct numerical simulations were performed to investigate the topological evolution of turbulence generated by a single square grid. Immediately behind the single square grid (i.e., in the irrotational dissipation region), the conditional mean trajectories (CMTs) of R and Q are distinctly different from those in homogeneous isotropic turbulence (HIT), where R and Q are the third and second invariants, respectively, of the velocity gradient tensor. In this region, the non-local influence of the pressure Hessian is dominant, which causes irrotational viscous dissipation. The anisotropic part of the pressure Hessian may be responsible for the irrotational viscous dissipation found at the turbulent/nonturbulent interface in turbulent jets [C. B. da Silva and J. C. F. Pereira, "Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets," Phys. Fluids 20, 055101 (2008) and Watanabe et al., "Vortex stretching and compression near the turbulent/non-turbulent interface in a planar jet," J. Fluid Mech. 758, 754 (2014)]. In the transition region, the CMTs of R and Q gradually acquire an evolution pattern similar to that in HIT. The expansion of the (R, Q) map at Q > 0 is associated with the effects of the restricted Euler term. Finally, in the fully turbulent region, the CMTs of R and Q demonstrate a clockwise evolution toward a point close to the origin. However, the cyclic spiraling seen in HIT is not found. The lack of the cyclic evolution may be attributed to the considerably large effect of the viscous term owing to the relatively small local Reynolds number. On average, the combined influences of the restricted Euler term and anisotropic part of the pressure Hessian contribute to the generation of small-scale motions, and the viscous term tends to remove small-scale motions.

A directional model of tropospheric horizontal gradients in Global Positioning System and its application for particular weather scenarios

NASA Astrophysics Data System (ADS)

Masoumi, Salim; McClusky, Simon; Koulali, Achraf; Tregoning, Paul

2017-04-01

Improper modeling of horizontal tropospheric gradients in GPS analysis induces errors in estimated parameters, with the largest impact on heights and tropospheric zenith delays. The conventional two-axis tilted plane model of horizontal gradients fails to provide an accurate representation of tropospheric gradients under weather conditions with asymmetric horizontal changes of refractivity. A new parametrization of tropospheric gradients whereby an arbitrary number of gradients are estimated as discrete directional wedges is shown via simulations to significantly improve the accuracy of recovered tropospheric zenith delays in asymmetric gradient scenarios. In a case study of an extreme rain event that occurred in September 2002 in southern France, the new directional parametrization is able to isolate the strong gradients in particular azimuths around the GPS stations consistent with the "V" shape spatial pattern of the observed precipitation. In another study of a network of GPS stations in the Sierra Nevada region where highly asymmetric tropospheric gradients are known to exist, the new directional model significantly improves the repeatabilities of the stations in asymmetric gradient situations while causing slightly degraded repeatabilities for the stations in normal symmetric gradient conditions. The average improvement over the entire network is ˜31%, while the improvement for one of the worst affected sites P631 is ˜49% (from 8.5 mm to 4.3 mm) in terms of weighted root-mean-square (WRMS) error and ˜82% (from -1.1 to -0.2) in terms of skewness. At the same station, the use of the directional model changes the estimates of zenith wet delay by 15 mm (˜25%).

Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Yongfeng; Qu, Shaobo; Wang, Jiafu

2014-06-02

Phase gradient metasurface (PGMs) are artificial surfaces that can provide pre-defined in-plane wave-vectors to manipulate the directions of refracted/reflected waves. In this Letter, we propose to achieve wideband radar cross section (RCS) reduction using two-dimensional (2D) PGMs. A 2D PGM was designed using a square combination of 49 split-ring sub-unit cells. The PGM can provide additional wave-vectors along the two in-plane directions simultaneously, leading to either surface wave conversion, deflected reflection, or diffuse reflection. Both the simulation and experiment results verified the wide-band, polarization-independent, high-efficiency RCS reduction induced by the 2D PGM.

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms. PMID:24077658

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks.

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

Optimization in Quaternion Dynamic Systems: Gradient, Hessian, and Learning Algorithms.

PubMed

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.

Importance of Ionospheric Gradients for error Correction

NASA Astrophysics Data System (ADS)

Ravula, Ramprasad

Importance of Ionospheric Gradients for error Correction R. Ram Prasad1, P.Nagasekhar2 1Sai Spurthi Institute of Technology-JNTU Hyderabad,2Sai Spurthi Institute of Technology-JNTU Hyderabad Email ID:rams.ravula@gmail.com In India, Indian Space Research Organization (ISRO) has established with an objective to develop space technology and its application to various national tasks. To cater to the needs of civil aviation applications, GPS Aided Geo Augmented Navigation (GAGAN) system is being jointly implemented along with Airports Authority of India (AAI) over the Indian region. The most predominant parameter affecting the navigation accuracy of GAGAN is ionospheric delay which is a function of total number of electrons present in one square meter cylindrical cross sectional area in the line of site direction between the satellite and the user on the earth i.e. Total Electron Content (TEC).The irregular distribution of electron densities i.e. rate of TEC variation, causes Ionospheric gradients such as spatial gradients (Expressed in TECu/km) and temporal gradients (Expressed in TECu /minute). Among the satellite signals arriving to the earth in multiple directions, the signals which suffer from severe ionospheric gradients can be estimated i.e. Rate of TEC Index (ROTI) and Rate of TEC (ROT). These aspects which contribute to errors can be treated for improving GAGAN positional accuracy.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Guiding neuron development with planar surface gradients of substrate cues deposited using microfluidic devices.

PubMed

Millet, Larry J; Stewart, Matthew E; Nuzzo, Ralph G; Gillette, Martha U

2010-06-21

Wiring the nervous system relies on the interplay of intrinsic and extrinsic signaling molecules that control neurite extension, neuronal polarity, process maturation and experience-dependent refinement. Extrinsic signals establish and enrich neuron-neuron interactions during development. Understanding how such extrinsic cues direct neurons to establish neural connections in vitro will facilitate the development of organized neural networks for investigating the development and function of nervous system networks. Producing ordered networks of neurons with defined connectivity in vitro presents special technical challenges because the results must be compliant with the biological requirements of rewiring neural networks. Here we demonstrate the ability to form stable, instructive surface-bound gradients of laminin that guide postnatal hippocampal neuron development in vitro. Our work uses a three-channel, interconnected microfluidic device that permits the production of adlayers of planar substrates through the combination of laminar flow, diffusion and physisorption. Through simple flow modifications, a variety of patterns and gradients of laminin (LN) and fluorescein isothiocyanate-conjugated poly-l-lysine (FITC-PLL) were deposited to present neurons with an instructive substratum to guide neuronal development. We present three variations in substrate design that produce distinct growth regimens for postnatal neurons in dispersed cell cultures. In the first approach, diffusion-mediated gradients of LN were formed on cover slips to guide neurons toward increasing LN concentrations. In the second approach, a combined gradient of LN and FITC-PLL was produced using aspiration-driven laminar flow to restrict neuronal growth to a 15 microm wide growth zone at the center of the two superimposed gradients. The last approach demonstrates the capacity to combine binary lines of FITC-PLL in conjunction with surface gradients of LN and bovine serum albumin (BSA) to produce substrate adlayers that provide additional levels of control over growth. This work demonstrates the advantages of spatio-temporal fluid control for patterning surface-bound gradients using a simple microfluidics-based substrate deposition procedure. We anticipate that this microfluidics-based patterning approach will provide instructive patterns and surface-bound gradients to enable a new level of control in guiding neuron development and network formation.

A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods

NASA Astrophysics Data System (ADS)

Syrakos, Alexandros; Varchanis, Stylianos; Dimakopoulos, Yannis; Goulas, Apostolos; Tsamopoulos, John

2017-12-01

Finite volume methods (FVMs) constitute a popular class of methods for the numerical simulation of fluid flows. Among the various components of these methods, the discretisation of the gradient operator has received less attention despite its fundamental importance with regards to the accuracy of the FVM. The most popular gradient schemes are the divergence theorem (DT) (or Green-Gauss) scheme and the least-squares (LS) scheme. Both are widely believed to be second-order accurate, but the present study shows that in fact the common variant of the DT gradient is second-order accurate only on structured meshes whereas it is zeroth-order accurate on general unstructured meshes, and the LS gradient is second-order and first-order accurate, respectively. This is explained through a theoretical analysis and is confirmed by numerical tests. The schemes are then used within a FVM to solve a simple diffusion equation on unstructured grids generated by several methods; the results reveal that the zeroth-order accuracy of the DT gradient is inherited by the FVM as a whole, and the discretisation error does not decrease with grid refinement. On the other hand, use of the LS gradient leads to second-order accurate results, as does the use of alternative, consistent, DT gradient schemes, including a new iterative scheme that makes the common DT gradient consistent at almost no extra cost. The numerical tests are performed using both an in-house code and the popular public domain partial differential equation solver OpenFOAM.

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

NASA Technical Reports Server (NTRS)

Thomas, James

2008-01-01

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Local invariants vanishing on stationary horizons: a diagnostic for locating black holes.

PubMed

Page, Don N; Shoom, Andrey A

2015-04-10

Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime.

Dual Fine Tracking Control of a Satellite Laser Communication Uplink

DTIC Science & Technology

2006-09-14

rejec- tion results for LQG control compared with adaptive least mean squares (LMS) and gradient adaptive lattice (GAL) algorithms , however, both...period [7, page 256]. The steady-state Kalman filter, defined by the predictor / corrector form, is implemented for each beam respectively as [7, page...Disturbance Environment . . . . . . . . . . . . . . . . . 97 B.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Appendix C . Aircraft

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Subauditory Speech Recognition based on EMG/EPG Signals

NASA Technical Reports Server (NTRS)

Jorgensen, Charles; Lee, Diana Dee; Agabon, Shane; Lau, Sonie (Technical Monitor)

2003-01-01

Sub-vocal electromyogram/electro palatogram (EMG/EPG) signal classification is demonstrated as a method for silent speech recognition. Recorded electrode signals from the larynx and sublingual areas below the jaw are noise filtered and transformed into features using complex dual quad tree wavelet transforms. Feature sets for six sub-vocally pronounced words are trained using a trust region scaled conjugate gradient neural network. Real time signals for previously unseen patterns are classified into categories suitable for primitive control of graphic objects. Feature construction, recognition accuracy and an approach for extension of the technique to a variety of real world application areas are presented.

Numerical Simulation of Convective Heat and Mass Transfer in a Two-Layer System

NASA Astrophysics Data System (ADS)

Myznikova, B. I.; Kazaryan, V. A.; Tarunin, E. L.; Wertgeim, I. I.

The results are presented of mathematical and computer modeling of natural convection in the “liquid-gas” two-layer system, filling a vertical cylinder surrounded by solid heat conductive tract. The model describes approximately the conjugate heat and mass transfer in the underground oil product storage, filled partially by a hydrocarbon liquid, with natural gas layer above the liquid surface. The geothermal gradient in a rock mass gives rise to the intensive convection in the liquid-gas system. The consideration is worked out for laminar flows, laminar-turbulent transitional regimes, and developed turbulent flows.

3D near-to-surface conductivity reconstruction by inversion of VETEM data using the distorted Born iterative method

USGS Publications Warehouse

Wang, G.L.; Chew, W.C.; Cui, T.J.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.

2004-01-01

Three-dimensional (3D) subsurface imaging by using inversion of data obtained from the very early time electromagnetic system (VETEM) was discussed. The study was carried out by using the distorted Born iterative method to match the internal nonlinear property of the 3D inversion problem. The forward solver was based on the total-current formulation bi-conjugate gradient-fast Fourier transform (BCCG-FFT). It was found that the selection of regularization parameter follow a heuristic rule as used in the Levenberg-Marquardt algorithm so that the iteration is stable.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

NASA Technical Reports Server (NTRS)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gropp, W.D.; Keyes, D.E.

1988-03-01

The authors discuss the parallel implementation of preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions on several architectures. The complexity of these methods is described on a variety of message-passing parallel computers as a function of the size of the problem, number of processors and relative communication speeds of the processors. They show that communication startups are very important, and that even the small amount of global communication in these methods can significantly reduce the performance of many message-passing architectures.

Programming Probabilistic Structural Analysis for Parallel Processing Computer

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Chen, Heh-Chyun; Twisdale, Lawrence A.; Chamis, Christos C.; Murthy, Pappu L. N.

1991-01-01

The ultimate goal of this research program is to make Probabilistic Structural Analysis (PSA) computationally efficient and hence practical for the design environment by achieving large scale parallelism. The paper identifies the multiple levels of parallelism in PSA, identifies methodologies for exploiting this parallelism, describes the development of a parallel stochastic finite element code, and presents results of two example applications. It is demonstrated that speeds within five percent of those theoretically possible can be achieved. A special-purpose numerical technique, the stochastic preconditioned conjugate gradient method, is also presented and demonstrated to be extremely efficient for certain classes of PSA problems.

Gradient-based interpolation method for division-of-focal-plane polarimeters.

PubMed

Gao, Shengkui; Gruev, Viktor

2013-01-14

Recent advancements in nanotechnology and nanofabrication have allowed for the emergence of the division-of-focal-plane (DoFP) polarization imaging sensors. These sensors capture polarization properties of the optical field at every imaging frame. However, the DoFP polarization imaging sensors suffer from large registration error as well as reduced spatial-resolution output. These drawbacks can be improved by applying proper image interpolation methods for the reconstruction of the polarization results. In this paper, we present a new gradient-based interpolation method for DoFP polarimeters. The performance of the proposed interpolation method is evaluated against several previously published interpolation methods by using visual examples and root mean square error (RMSE) comparison. We found that the proposed gradient-based interpolation method can achieve better visual results while maintaining a lower RMSE than other interpolation methods under various dynamic ranges of a scene ranging from dim to bright conditions.

Remote Sensing techniques used to characterize soil erosion in southwestern Sao Paulo state. M.S. Thesis - 29 Sep. 1982; [Brazil

NASA Technical Reports Server (NTRS)

Parada, N. D. J. (Principal Investigator); Pinto, S. D. A. F.

1983-01-01

Within randomly sampled squares of a 1 km x 1 km grid, rill/gullies frequency, land cover/land use type and shape of the slopes were extracted from aerial photographs of the Ribeirao Anhumas drainage basin. Mean slope gradient, stream frequency and slope length were calculated on topographic maps. Ground truth data on fine sand/coarse sand ratio and vegetation cover densities were obtained. The MSS-LANDSAT-2 data (CCTs) were analyzed using single-cell, cluster synthesis and slicer algorithms. Graphical and statistical analyses of the data indicate that different slope gradients and land cover/land use types are the most significant factors related to the soil erosion process. The digital analysis of MSS data allowed the association among gray level classes and vegetation cover classes, which defined seven classes. These gray level classes and slope gradient classes were used to rank erosion risk.

Development of a gradient elution high-performance liquid chromatography assay with ultraviolet detection for the determination in plasma of the anticancer peptide [Arg6, D-Trp7,9, mePhe8]-substance P (6-11) (antagonist G), its major metabolites and a C-terminal pyrene-labelled conjugate.

PubMed

Cummings, J; MacLellan, A J; Mark, M; Jodrell, D I

1999-09-24

[Arg6, D-Trp7,9 mePhe8]-substance P (6-11), code-named antagonist G, is a novel peptide currently undergoing early clinical trials as an anticancer drug. A sensitive, high efficiency high-performance liquid chromatography (HPLC) method is described for the determination in human plasma of antagonist G and its three major metabolites, deamidated-G (M1), G-minus Met11 (M2) and G[Met11(O)] (M3). Gradient elution was employed using 40 mM ammonium acetate in 0.15% trifluoroacetic acid as buffer A and acetonitrile as solvent B, with a linear gradient increasing from 30 to 100% B over 15 min, together with a microbore analytical column (microBondapak C18, 30 cm X 2 mm I.D.). Detection was by UV at 280 nm and the column was maintained at 40 degrees C. Retention times varied by <1% throughout the day and were as follows: G, 13.0 min; M1, 12.2 min; M2, 11.2 min; M3, 10.8 min, and 18.1 min for a pyrene conjugate of G (G-P). The limit of detection on column (LOD) was 2.5 ng for antagonist G, M1-3 and G-P and the limit of quantitation (LOQ) was 20 ng/ml for G and 100 ng/ml for M1-3. Sample clean-up by solid-phase extraction using C2-bonded 40 microm silica particles (Bond Elut, 1 ml reservoirs) resulted in elimination of interference from plasma constituents. Within-day and between-day precision and accuracy over a broad range of concentrations (100 ng/ml-100 microg/ml) normally varied by < 10%, although at the highest concentrations of M1 and M2 studied (50 microg/ml), increased variability and reduced recovery were observed. The new assay will aid in the clinical development of antagonist G.

Double diffusive conjugate heat transfer: Part III

NASA Astrophysics Data System (ADS)

Soudagar, Manzoor Elahi M.; Azeem

2018-05-01

The placement of a small solid wall towards cold surface of square porous cavity affects the heat transfer behavior of porous region due to restriction of fluid motion in the region occupied by solid wall. An investigation of heat transfer is carried out to understand the fluid flow and heat transfer behavior in porous cavity by solving the governing partial differential equations. Galerkin's approach is used to convert the partial differential equations into algebraic form of equations by applying finite element method. The heat transfer increases for solid towards right surface as compared to the case of solid at center of cavity.

Effectiveness of tobramycin conjugated to iron oxide nanoparticles in treating infection in cystic fibrosis

NASA Astrophysics Data System (ADS)

Brandt, Yekaterina I.; Armijo, Leisha M.; Rivera, Antonio C.; Plumley, John B.; Cook, Nathaniel C.; Smolyakov, Gennady A.; Smyth, Hugh D. C.; Osiński, Marek

2013-02-01

Cystic fibrosis (CF) is an inherited childhood-onset life-shortening disease. It is characterized by increased respiratory production, leading to airway obstruction, chronic lung infection and inflammatory reactions. The most common bacteria causing persisting infections in people with CF is Pseudomonas aeruginosa. Superparamagnetic Fe3O4 iron oxide nanoparticles (NPs) conjugated to the antibiotic (tobramycin), guided by a gradient of the magnetic field or subjected to an oscillating magnetic field, show promise in improving the drug delivery across the mucus and P. aeruginosa biofilm to the bacteria. The question remains whether tobramycin needs to be released from the NPs after the penetration of the mucus barrier in order to act upon the pathogenic bacteria. We used a zero-length 1-ethyl-3-[3-dimethylaminopropyl] carbodiimide hydrochloride (EDC) crosslinking agent to couple tobramycin, via its amine groups, to the carboxyl groups on Fe3O4 NPs capped with citric acid. The therapeutic efficiency of Fe3O4 NPs attached to the drug versus that of the free drug was investigated in P. aeruginosa culture.

Demonstration of nuclear compartmentalization of glutathione in hepatocytes.

PubMed Central

Bellomo, G; Vairetti, M; Stivala, L; Mirabelli, F; Richelmi, P; Orrenius, S

1992-01-01

The intracellular distribution of glutathione (GSH) in cultured hepatocytes has been investigated by using the compound monochlorobimane (BmCl), which interacts specifically with GSH to form a highly fluorescent adduct. Image analysis of BmCl-labeled hepatocytes predominantly localized the fluorescence in the nucleus; the nuclear/cytoplasmic concentration gradient was approximately three. This concentration gradient was collapsed by treatment of the cells with ATP-depleting agents. The uneven distribution of BmCl fluorescence was not attributable to (i) nonspecific interaction of BmCl with protein sulfhydryl groups, (ii) any selective nuclear localization of the GSH transferase(s) catalyzing formation of the GSH-BmCl conjugate, or (iii) any apparent alterations in cell morphology from culture conditions, suggesting that this distribution did, indeed, reflect a nuclear compartmentalization of GSH. That the nuclear pool of GSH was found more resistant to depletion by several agents than the cytoplasmic pool supports the assumption that GSH is essential in protecting DNA and other nuclear structures from chemical injury. Images PMID:1584774

Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method.

PubMed

Wang, Qi; Wang, Huaxiang; Cui, Ziqiang; Yang, Chengyi

2012-11-01

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

The unidirectional motion of two heat-conducting liquids in a flat channel

NASA Astrophysics Data System (ADS)

Andreev, V. K.; Cheremnykh, E. N.

2017-10-01

The unidirectional motion of two viscous incompressible liquids in a flat channel is studied. Liquids contact on a flat interface. External boundaries are fixed solid walls, on which the non-stationary temperature gradients are given. The motion is induced by a joint action of thermogravitational and thermocapillary forces and given total non - stationary fluid flow rate in layers. The corresponding initial boundary value problem is conjugate and inverse because the pressure gradients along axes channel have to be determined together with the velocity and temperature field. For this problem the exact stationary solution is found and a priori estimates of non - stationary solutions are obtained. In Laplace images the solution of the non - stationary problem is found in quadratures. It is proved, that the solution converges to a steady regime with time, if the temperature on the walls and the fluid flow rate are stabilized. The numerical calculations for specific liquid media good agree with the theoretical results.

Ion-exchange chromatography for the characterization of biopharmaceuticals.

PubMed

Fekete, Szabolcs; Beck, Alain; Veuthey, Jean-Luc; Guillarme, Davy

2015-09-10

Ion-exchange chromatography (IEX) is a historical technique widely used for the detailed characterization of therapeutic proteins and can be considered as a reference and powerful technique for the qualitative and quantitative evaluation of charge heterogeneity. The goal of this review is to provide an overview of theoretical and practical aspects of modern IEX applied for the characterization of therapeutic proteins including monoclonal antibodies (Mabs) and antibody drug conjugates (ADCs). The section on method development describes how to select a suitable stationary phase chemistry and dimensions, the mobile phase conditions (pH, nature and concentration of salt), as well as the temperature and flow rate, considering proteins isoelectric point (pI). In addition, both salt-gradient and pH-gradient approaches were critically reviewed and benefits as well as limitations of these two strategies were provided. Finally, several applications, mostly from pharmaceutical industries, illustrate the potential of IEX for the characterization of charge variants of various types of biopharmaceutical products. Copyright © 2015 Elsevier B.V. All rights reserved.

Point-spread function reconstruction in ground-based astronomy by l(1)-l(p) model.

PubMed

Chan, Raymond H; Yuan, Xiaoming; Zhang, Wenxing

2012-11-01

In ground-based astronomy, images of objects in outer space are acquired via ground-based telescopes. However, the imaging system is generally interfered by atmospheric turbulence, and hence images so acquired are blurred with unknown point-spread function (PSF). To restore the observed images, the wavefront of light at the telescope's aperture is utilized to derive the PSF. A model with the Tikhonov regularization has been proposed to find the high-resolution phase gradients by solving a least-squares system. Here we propose the l(1)-l(p) (p=1, 2) model for reconstructing the phase gradients. This model can provide sharper edges in the gradients while removing noise. The minimization models can easily be solved by the Douglas-Rachford alternating direction method of a multiplier, and the convergence rate is readily established. Numerical results are given to illustrate that the model can give better phase gradients and hence a more accurate PSF. As a result, the restored images are much more accurate when compared to the traditional Tikhonov regularization model.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Won, Yoo Jai; Ki, Hyungson

A novel picosecond-laser pulsed laser deposition method has been developed for fabricating functionally graded films with pre-designed gradient profiles. Theoretically, the developed method is capable of precisely fabricating films with any thicknesses and any gradient profiles by controlling the laser beam powers for the two different targets based on the film composition profiles. As an implementation example, we have successfully constructed functionally graded diamond-like carbon films with six different gradient profiles: linear, quadratic, cubic, square root, cubic root, and sinusoidal. Energy dispersive X-ray spectroscopy is employed for investigating the chemical composition along the thickness of the film, and the depositionmore » profile and thickness errors are found to be less than 3% and 1.04%, respectively. To the best of the authors' knowledge, this is the first method for fabricating films with designed gradient profiles and has huge potential in many areas of coatings and films, including multifunctional optical films. We believe that this method is not only limited to the example considered in this study, but also can be applied to all material combinations as long as they can be deposited using the pulsed laser deposition technique.« less

Myocardial perfusion magnetic resonance imaging using sliding-window conjugate-gradient highly constrained back-projection reconstruction for detection of coronary artery disease.

PubMed

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.

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach

PubMed Central

Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M.; El Fakhri, Georges

2013-01-01

Purpose: 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. Methods: 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. Results: At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%–29% and 32%–70% for 50 × 106 and 10 × 106 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. Conclusions: 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. PMID:24089922

First Applications of the New Parallel Krylov Solver for MODFLOW on a National and Global Scale

NASA Astrophysics Data System (ADS)

Verkaik, J.; Hughes, J. D.; Sutanudjaja, E.; van Walsum, P.

2016-12-01

Integrated high-resolution hydrologic models are increasingly being used for evaluating water management measures at field scale. Their drawbacks are large memory requirements and long run times. Examples of such models are The Netherlands Hydrological Instrument (NHI) model and the PCRaster Global Water Balance (PCR-GLOBWB) model. Typical simulation periods are 30-100 years with daily timesteps. The NHI model predicts water demands in periods of drought, supporting operational and long-term water-supply decisions. The NHI is a state-of-the-art coupling of several models: a 7-layer MODFLOW groundwater model ( 6.5M 250m cells), a MetaSWAP model for the unsaturated zone (Richards emulator of 0.5M cells), and a surface water model (MOZART-DM). The PCR-GLOBWB model provides a grid-based representation of global terrestrial hydrology and this work uses the version that includes a 2-layer MODFLOW groundwater model ( 4.5M 10km cells). The Parallel Krylov Solver (PKS) speeds up computation by both distributed memory parallelization (Message Passing Interface) and shared memory parallelization (Open Multi-Processing). PKS includes conjugate gradient, bi-conjugate gradient stabilized, and generalized minimal residual linear accelerators that use an overlapping additive Schwarz domain decomposition preconditioner. PKS can be used for both structured and unstructured grids and has been fully integrated in MODFLOW-USG using METIS partitioning and in iMODFLOW using RCB partitioning. iMODFLOW is an accelerated version of MODFLOW-2005 that is implicitly and online coupled to MetaSWAP. Results for benchmarks carried out on the Cartesius Dutch supercomputer (https://userinfo.surfsara.nl/systems/cartesius) for the PCRGLOB-WB model and on a 2x16 core Windows machine for the NHI model show speedups up to 10-20 and 5-10, respectively.

A nonrecursive order N preconditioned conjugate gradient: Range space formulation of MDOF dynamics

NASA Technical Reports Server (NTRS)

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.

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach.

PubMed

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.

Multigrid Methods for the Computation of Propagators in Gauge Fields

NASA Astrophysics Data System (ADS)

Kalkreuter, Thomas

Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.

The two-phase method for finding a great number of eigenpairs of the symmetric or weakly non-symmetric large eigenvalue problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dul, F.A.; Arczewski, K.

1994-03-01

Although it has been stated that [open quotes]an attempt to solve (very large problems) by subspace iterations seems futile[close quotes], we will show that the statement is not true, especially for extremely large eigenproblems. In this paper a new two-phase subspace iteration/Rayleigh quotient/conjugate gradient method for generalized, large, symmetric eigenproblems Ax = [lambda]Bx is presented. It has the ability of solving extremely large eigenproblems, N = 216,000, for example, and finding a large number of leftmost or rightmost eigenpairs, up to 1000 or more. Multiple eigenpairs, even those with multiplicity 100, can be easily found. The use of the proposedmore » method for solving the big full eigenproblems (N [approximately] 10[sup 3]), as well as for large weakly non-symmetric eigenproblems, have been considered also. The proposed method is fully iterative; thus the factorization of matrices ins avoided. The key idea consists in joining two methods: subspace and Rayleigh quotient iterations. The systems of indefinite and almost singular linear equations (a - [sigma]B)x = By are solved by various iterative conjugate gradient method can be used without danger of breaking down due to its property that may be called [open quotes]self-correction towards the eigenvector,[close quotes] discovered recently by us. The use of various preconditioners (SSOR and IC) has also been considered. The main features of the proposed method have been analyzed in detail. Comparisons with other methods, such as, accelerated subspace iteration, Lanczos, Davidson, TLIME, TRACMN, and SRQMCG, are presented. The results of numerical tests for various physical problems (acoustic, vibrations of structures, quantum chemistry) are presented as well. 40 refs., 12 figs., 2 tabs.« less

Functionalization of quantum rods with oligonucleotides for programmable assembly with DNA origami

NASA Astrophysics Data System (ADS)

Doane, Tennyson L.; Alam, Rabeka; Maye, Mathew M.

2015-02-01

The DNA-mediated self-assembly of CdSe/CdS quantum rods (QRs) onto DNA origami is described. Two QR types with unique optical emission and high polarization were synthesized, and then functionalized with oligonucleotides (ssDNA) using a novel protection-deprotection approach, which harnessed ssDNA's tailorable rigidity and denaturation temperature to increase DNA coverage by reducing non-specific coordination and wrapping. The QR assembly was programmable, and occurred at two different assembly zones that had capture strands in parallel alignment. QRs with different optical properties were assembled, opening up future studies on orientation dependent QR FRET. The QR-origami conjugates could be purified via gel electrophoresis and sucrose gradient ultracentrifugation. Assembly yields, QR stoichiometry and orientation, as well as energy transfer implications were studied in light of QR distances, origami flexibility, and conditions.The DNA-mediated self-assembly of CdSe/CdS quantum rods (QRs) onto DNA origami is described. Two QR types with unique optical emission and high polarization were synthesized, and then functionalized with oligonucleotides (ssDNA) using a novel protection-deprotection approach, which harnessed ssDNA's tailorable rigidity and denaturation temperature to increase DNA coverage by reducing non-specific coordination and wrapping. The QR assembly was programmable, and occurred at two different assembly zones that had capture strands in parallel alignment. QRs with different optical properties were assembled, opening up future studies on orientation dependent QR FRET. The QR-origami conjugates could be purified via gel electrophoresis and sucrose gradient ultracentrifugation. Assembly yields, QR stoichiometry and orientation, as well as energy transfer implications were studied in light of QR distances, origami flexibility, and conditions. Electronic supplementary information (ESI) available: Experimental conditions, DNA origami blueprint and sequences, FRET calculations. Additional Fig. S1-S13. See DOI: 10.1039/c4nr07662a

Technical note: Avoiding the direct inversion of the numerator relationship matrix for genotyped animals in single-step genomic best linear unbiased prediction solved with the preconditioned conjugate gradient.

PubMed

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 smoothing algorithm using cubic spline functions

NASA Technical Reports Server (NTRS)

Smith, R. E., Jr.; Price, J. M.; Howser, L. M.

1974-01-01

Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

A simulation of dielectrophoresis force actuated liquid lens

NASA Astrophysics Data System (ADS)

Yao, Xiaoyin; Xia, Jun

2009-11-01

Dielectrophoresis (DEP) and electrowetting on dielectric (EWOD) are based on the electrokinetic mechanisms which have great potential in microfluidic manipulation. DEP dominate the movement of particles induced by polarization effects in nonuniform electric field ,while EWOD has become one of the most widely used tools for manipulating tiny amounts of liquids on solid surfaces. Liquid lens driven by EWOD have been well studied and developed. But liquid lens driven by DEP has not been studied adequately. This paper focuses on modeling liquid lens driven by DEP force. A simulation of DEP driven droplet dynamics was performed by coupling of the electrostatic field and the two-phase flow field. Two incompressible and dielectric liquids with different permittivity were chosen in the two-phase flow field. The DEP force density, in direct proportion to gradient of the square of the electric field intensity, was used as a body force density in Navier-Stokes equation. When voltage applied, the liquid with high permittivity flowed to the place where the gradient of the square of the electric field intensity was higher, and thus change the curvature of interface between two immiscible liquid. The differences between DEP and EWOD liquid lens were also presented.

Identification of integrated airframe: Propulsion effects on an F-15 aircraft for application to drag minimization

NASA Technical Reports Server (NTRS)

Schkolnik, Gerard S.

1993-01-01

The application of an adaptive real-time measurement-based performance optimization technique is being explored for a future flight research program. The key technical challenge of the approach is parameter identification, which uses a perturbation-search technique to identify changes in performance caused by forced oscillations of the controls. The controls on the NASA F-15 highly integrated digital electronic control (HIDEC) aircraft were perturbed using inlet cowl rotation steps at various subsonic and supersonic flight conditions to determine the effect on aircraft performance. The feasibility of the perturbation-search technique for identifying integrated airframe-propulsion system performance effects was successfully shown through flight experiments and postflight data analysis. Aircraft response and control data were analyzed postflight to identify gradients and to determine the minimum drag point. Changes in longitudinal acceleration as small as 0.004 g were measured, and absolute resolution was estimated to be 0.002 g or approximately 50 lbf of drag. Two techniques for identifying performance gradients were compared: a least-squares estimation algorithm and a modified maximum likelihood estimator algorithm. A complementary filter algorithm was used with the least squares estimator.

Identification of integrated airframe-propulsion effects on an F-15 aircraft for application to drag minimization

NASA Technical Reports Server (NTRS)

Schkolnik, Gerald S.

1993-01-01

The application of an adaptive real-time measurement-based performance optimization technique is being explored for a future flight research program. The key technical challenge of the approach is parameter identification, which uses a perturbation-search technique to identify changes in performance caused by forced oscillations of the controls. The controls on the NASA F-15 highly integrated digital electronic control (HIDEC) aircraft were perturbed using inlet cowl rotation steps at various subsonic and supersonic flight conditions to determine the effect on aircraft performance. The feasibility of the perturbation-search technique for identifying integrated airframe-propulsion system performance effects was successfully shown through flight experiments and postflight data analysis. Aircraft response and control data were analyzed postflight to identify gradients and to determine the minimum drag point. Changes in longitudinal acceleration as small as 0.004 g were measured, and absolute resolution was estimated to be 0.002 g or approximately 50 lbf of drag. Two techniques for identifying performance gradients were compared: a least-squares estimation algorithm and a modified maximum likelihood estimator algorithm. A complementary filter algorithm was used with the least squares estimator.

Translation-aware semantic segmentation via conditional least-square generative adversarial networks

NASA Astrophysics Data System (ADS)

Zhang, Mi; Hu, Xiangyun; Zhao, Like; Pang, Shiyan; Gong, Jinqi; Luo, Min

2017-10-01

Semantic segmentation has recently made rapid progress in the field of remote sensing and computer vision. However, many leading approaches cannot simultaneously translate label maps to possible source images with a limited number of training images. The core issue is insufficient adversarial information to interpret the inverse process and proper objective loss function to overcome the vanishing gradient problem. We propose the use of conditional least squares generative adversarial networks (CLS-GAN) to delineate visual objects and solve these problems. We trained the CLS-GAN network for semantic segmentation to discriminate dense prediction information either from training images or generative networks. We show that the optimal objective function of CLS-GAN is a special class of f-divergence and yields a generator that lies on the decision boundary of discriminator that reduces possible vanished gradient. We also demonstrate the effectiveness of the proposed architecture at translating images from label maps in the learning process. Experiments on a limited number of high resolution images, including close-range and remote sensing datasets, indicate that the proposed method leads to the improved semantic segmentation accuracy and can simultaneously generate high quality images from label maps.

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

Geohydrology of, and simulation of ground-water flow in, the Milford-Souhegan glacial-drift aquifer, Milford, New Hampshire

USGS Publications Warehouse

Harte, P.T.; Mack, Thomas J.

1992-01-01

Hydrogeologic data collected since 1990 were assessed and a ground-water-flow model was refined in this study of the Milford-Souhegan glacial-drift aquifer in Milford, New Hampshire. The hydrogeologic data collected were used to refine estimates of hydraulic conductivity and saturated thickness of the aquifer, which were previously calculated during 1988-90. In October 1990, water levels were measured at 124 wells and piezometers, and at 45 stream-seepage sites on the main stem of the Souhegan River, and on small tributary streams overlying the aquifer to improve an understanding of ground-water-flow patterns and stream-seepage gains and losses. Refinement of the ground-water-flow model included a reduction in the number of active cells in layer 2 in the central part of the aquifer, a revision of simulated hydraulic conductivity in model layers 2 and representing the aquifer, incorporation of a new block-centered finite-difference ground-water-flow model, and incorporation of a new solution algorithm and solver (a preconditioned conjugate-gradient algorithm). Refinements to the model resulted in decreases in the difference between calculated and measured heads at 22 wells. The distribution of gains and losses of stream seepage calculated in simulation with the refined model is similar to that calculated in the previous model simulation. The contributing area to the Savage well, under average pumping conditions, decreased by 0.021 square miles from the area calculated in the previous model simulation. The small difference in the contrib- uting recharge area indicates that the additional data did not enhance model simulation and that the conceptual framework for the previous model is accurate.

Computationally efficient algorithms for Brownian dynamics simulation of long flexible macromolecules modeled as bead-rod chains

NASA Astrophysics Data System (ADS)

Moghani, Mahdy Malekzadeh; Khomami, Bamin

2017-02-01

The computational efficiency of Brownian dynamics (BD) simulation of the constrained model of a polymeric chain (bead-rod) with n beads and in the presence of hydrodynamic interaction (HI) is reduced to the order of n2 via an efficient algorithm which utilizes the conjugate-gradient (CG) method within a Picard iteration scheme. Moreover, the utility of the Barnes and Hut (BH) multipole method in BD simulation of polymeric solutions in the presence of HI, with regard to computational cost, scaling, and accuracy, is discussed. Overall, it is determined that this approach leads to a scaling of O (n1.2) . Furthermore, a stress algorithm is developed which accurately captures the transient stress growth in the startup of flow for the bead-rod model with HI and excluded volume (EV) interaction. Rheological properties of the chains up to n =350 in the presence of EV and HI are computed via the former algorithm. The result depicts qualitative differences in shear thinning behavior of the polymeric solutions in the intermediate values of the Weissenburg number (10

Quantification of susceptibility change at high-concentrated SPIO-labeled target by characteristic phase gradient recognition.

PubMed

Zhu, Haitao; Nie, Binbin; Liu, Hua; Guo, Hua; Demachi, Kazuyuki; Sekino, Masaki; Shan, Baoci

2016-05-01

Phase map cross-correlation detection and quantification may produce highlighted signal at superparamagnetic iron oxide nanoparticles, and distinguish them from other hypointensities. The method may quantify susceptibility change by performing least squares analysis between a theoretically generated magnetic field template and an experimentally scanned phase image. Because characteristic phase recognition requires the removal of phase wrap and phase background, additional steps of phase unwrapping and filtering may increase the chance of computing error and enlarge the inconsistence among algorithms. To solve problem, phase gradient cross-correlation and quantification method is developed by recognizing characteristic phase gradient pattern instead of phase image because phase gradient operation inherently includes unwrapping and filtering functions. However, few studies have mentioned the detectable limit of currently used phase gradient calculation algorithms. The limit may lead to an underestimation of large magnetic susceptibility change caused by high-concentrated iron accumulation. In this study, mathematical derivation points out the value of maximum detectable phase gradient calculated by differential chain algorithm in both spatial and Fourier domain. To break through the limit, a modified quantification method is proposed by using unwrapped forward differentiation for phase gradient generation. The method enlarges the detectable range of phase gradient measurement and avoids the underestimation of magnetic susceptibility. Simulation and phantom experiments were used to quantitatively compare different methods. In vivo application performs MRI scanning on nude mice implanted by iron-labeled human cancer cells. Results validate the limit of detectable phase gradient and the consequent susceptibility underestimation. Results also demonstrate the advantage of unwrapped forward differentiation compared with differential chain algorithms for susceptibility quantification at high-concentrated iron accumulation. Copyright © 2015 Elsevier Inc. All rights reserved.