Acceleration of GPU-based Krylov solvers via data transfer reduction

DOE PAGES

Anzt, Hartwig; Tomov, Stanimire; Luszczek, Piotr; ...

2015-04-08

Krylov subspace iterative solvers are often the method of choice when solving large sparse linear systems. At the same time, hardware accelerators such as graphics processing units continue to offer significant floating point performance gains for matrix and vector computations through easy-to-use libraries of computational kernels. However, as these libraries are usually composed of a well optimized but limited set of linear algebra operations, applications that use them often fail to reduce certain data communications, and hence fail to leverage the full potential of the accelerator. In this study, we target the acceleration of Krylov subspace iterative methods for graphicsmore » processing units, and in particular the Biconjugate Gradient Stabilized solver that significant improvement can be achieved by reformulating the method to reduce data-communications through application-specific kernels instead of using the generic BLAS kernels, e.g. as provided by NVIDIA’s cuBLAS library, and by designing a graphics processing unit specific sparse matrix-vector product kernel that is able to more efficiently use the graphics processing unit’s computing power. Furthermore, we derive a model estimating the performance improvement, and use experimental data to validate the expected runtime savings. Finally, considering that the derived implementation achieves significantly higher performance, we assert that similar optimizations addressing algorithm structure, as well as sparse matrix-vector, are crucial for the subsequent development of high-performance graphics processing units accelerated Krylov subspace iterative methods.« less

Tensor Sparse Coding for Positive Definite Matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikos

2013-08-02

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for e.g., image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Tensor sparse coding for positive definite matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2014-03-01

In recent years, there has been extensive research on sparse representation of vector-valued signals. In the matrix case, the data points are merely vectorized and treated as vectors thereafter (for example, image patches). However, this approach cannot be used for all matrices, as it may destroy the inherent structure of the data. Symmetric positive definite (SPD) matrices constitute one such class of signals, where their implicit structure of positive eigenvalues is lost upon vectorization. This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization. Synthetic and real-world computer vision experiments with region covariance descriptors demonstrate the need for and the applicability of the new sparse coding model. This work serves to bridge the gap between the sparse modeling paradigm and the space of positive definite matrices.

Efficient ICCG on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Hammond, Steven W.; Schreiber, Robert

1989-01-01

Different approaches are discussed for exploiting parallelism in the ICCG (Incomplete Cholesky Conjugate Gradient) method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially.

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.

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Implementation of hierarchical clustering using k-mer sparse matrix to analyze MERS-CoV genetic relationship

NASA Astrophysics Data System (ADS)

Bustamam, A.; Ulul, E. D.; Hura, H. F. A.; Siswantining, T.

2017-07-01

Hierarchical clustering is one of effective methods in creating a phylogenetic tree based on the distance matrix between DNA (deoxyribonucleic acid) sequences. One of the well-known methods to calculate the distance matrix is k-mer method. Generally, k-mer is more efficient than some distance matrix calculation techniques. The steps of k-mer method are started from creating k-mer sparse matrix, and followed by creating k-mer singular value vectors. The last step is computing the distance amongst vectors. In this paper, we analyze the sequences of MERS-CoV (Middle East Respiratory Syndrome - Coronavirus) DNA by implementing hierarchical clustering using k-mer sparse matrix in order to perform the phylogenetic analysis. Our results show that the ancestor of our MERS-CoV is coming from Egypt. Moreover, we found that the MERS-CoV infection that occurs in one country may not necessarily come from the same country of origin. This suggests that the process of MERS-CoV mutation might not only be influenced by geographical factor.

Noniterative MAP reconstruction using sparse matrix representations.

PubMed

Cao, Guangzhi; Bouman, Charles A; Webb, Kevin J

2009-09-01

We present a method for noniterative maximum a posteriori (MAP) tomographic reconstruction which is based on the use of sparse matrix representations. Our approach is to precompute and store the inverse matrix required for MAP reconstruction. This approach has generally not been used in the past because the inverse matrix is typically large and fully populated (i.e., not sparse). In order to overcome this problem, we introduce two new ideas. The first idea is a novel theory for the lossy source coding of matrix transformations which we refer to as matrix source coding. This theory is based on a distortion metric that reflects the distortions produced in the final matrix-vector product, rather than the distortions in the coded matrix itself. The resulting algorithms are shown to require orthonormal transformations of both the measurement data and the matrix rows and columns before quantization and coding. The second idea is a method for efficiently storing and computing the required orthonormal transformations, which we call a sparse-matrix transform (SMT). The SMT is a generalization of the classical FFT in that it uses butterflies to compute an orthonormal transform; but unlike an FFT, the SMT uses the butterflies in an irregular pattern, and is numerically designed to best approximate the desired transforms. We demonstrate the potential of the noniterative MAP reconstruction with examples from optical tomography. The method requires offline computation to encode the inverse transform. However, once these offline computations are completed, the noniterative MAP algorithm is shown to reduce both storage and computation by well over two orders of magnitude, as compared to a linear iterative reconstruction methods.

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

NASA Technical Reports Server (NTRS)

David, R. E.

1984-01-01

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

Improved analysis of SP and CoSaMP under total perturbations

NASA Astrophysics Data System (ADS)

Li, Haifeng

2016-12-01

Practically, in the underdetermined model y= A x, where x is a K sparse vector (i.e., it has no more than K nonzero entries), both y and A could be totally perturbed. A more relaxed condition means less number of measurements are needed to ensure the sparse recovery from theoretical aspect. In this paper, based on restricted isometry property (RIP), for subspace pursuit (SP) and compressed sampling matching pursuit (CoSaMP), two relaxed sufficient conditions are presented under total perturbations to guarantee that the sparse vector x is recovered. Taking random matrix as measurement matrix, we also discuss the advantage of our condition. Numerical experiments validate that SP and CoSaMP can provide oracle-order recovery performance.

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

DOE PAGES

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel; ...

2017-06-01

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations

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

Aktulga, Hasan Metin; Afibuzzaman, Md.; Williams, Samuel

As on-node parallelism increases and the performance gap between the processor and the memory system widens, achieving high performance in large-scale scientific applications requires an architecture-aware design of algorithms and solvers. We focus on the eigenvalue problem arising in nuclear Configuration Interaction (CI) calculations, where a few extreme eigenpairs of a sparse symmetric matrix are needed. Here, we consider a block iterative eigensolver whose main computational kernels are the multiplication of a sparse matrix with multiple vectors (SpMM), and tall-skinny matrix operations. We then present techniques to significantly improve the SpMM and the transpose operation SpMM T by using themore » compressed sparse blocks (CSB) format. We achieve 3-4× speedup on the requisite operations over good implementations with the commonly used compressed sparse row (CSR) format. We develop a performance model that allows us to correctly estimate the performance of our SpMM kernel implementations, and we identify cache bandwidth as a potential performance bottleneck beyond DRAM. We also analyze and optimize the performance of LOBPCG kernels (inner product and linear combinations on multiple vectors) and show up to 15× speedup over using high performance BLAS libraries for these operations. The resulting high performance LOBPCG solver achieves 1.4× to 1.8× speedup over the existing Lanczos solver on a series of CI computations on high-end multicore architectures (Intel Xeons). We also analyze the performance of our techniques on an Intel Xeon Phi Knights Corner (KNC) processor.« less

Exact recovery of sparse multiple measurement vectors by [Formula: see text]-minimization.

PubMed

Wang, Changlong; Peng, Jigen

2018-01-01

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile [Formula: see text]-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., [Formula: see text]-minimization [Formula: see text] Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant [Formula: see text] such that the original unique sparse solution also can be recovered from a minimization in [Formula: see text] quasi-norm subject to matrixes whenever [Formula: see text]. The other one is showing an analytic expression of such [Formula: see text]. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for [Formula: see text]-minimization by using our results.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Gutknecht, Martin H.; Nachtigal, Noel M.

1991-01-01

The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. An implementation is presented of a look-ahead version of the Lanczos algorithm that, except for the very special situation of an incurable breakdown, overcomes these problems by skipping over those steps in which a breakdown or near-breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.

Discriminative Dictionary Learning With Two-Level Low Rank and Group Sparse Decomposition for Image Classification.

PubMed

Wen, Zaidao; Hou, Zaidao; Jiao, Licheng

2017-11-01

Discriminative dictionary learning (DDL) framework has been widely used in image classification which aims to learn some class-specific feature vectors as well as a representative dictionary according to a set of labeled training samples. However, interclass similarities and intraclass variances among input samples and learned features will generally weaken the representability of dictionary and the discrimination of feature vectors so as to degrade the classification performance. Therefore, how to explicitly represent them becomes an important issue. In this paper, we present a novel DDL framework with two-level low rank and group sparse decomposition model. In the first level, we learn a class-shared and several class-specific dictionaries, where a low rank and a group sparse regularization are, respectively, imposed on the corresponding feature matrices. In the second level, the class-specific feature matrix will be further decomposed into a low rank and a sparse matrix so that intraclass variances can be separated to concentrate the corresponding feature vectors. Extensive experimental results demonstrate the effectiveness of our model. Compared with the other state-of-the-arts on several popular image databases, our model can achieve a competitive or better performance in terms of the classification accuracy.

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

NASA Technical Reports Server (NTRS)

Barnard, Stephen T.; Pothen, Alex; Simon, Horst D.

1993-01-01

The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

Low-rank matrix decomposition and spatio-temporal sparse recovery for STAP radar

DOE PAGES

Sen, Satyabrata

2015-08-04

We develop space-time adaptive processing (STAP) methods by leveraging the advantages of sparse signal processing techniques in order to detect a slowly-moving target. We observe that the inherent sparse characteristics of a STAP problem can be formulated as the low-rankness of clutter covariance matrix when compared to the total adaptive degrees-of-freedom, and also as the sparse interference spectrum on the spatio-temporal domain. By exploiting these sparse properties, we propose two approaches for estimating the interference covariance matrix. In the first approach, we consider a constrained matrix rank minimization problem (RMP) to decompose the sample covariance matrix into a low-rank positivemore » semidefinite and a diagonal matrix. The solution of RMP is obtained by applying the trace minimization technique and the singular value decomposition with matrix shrinkage operator. Our second approach deals with the atomic norm minimization problem to recover the clutter response-vector that has a sparse support on the spatio-temporal plane. We use convex relaxation based standard sparse-recovery techniques to find the solutions. With extensive numerical examples, we demonstrate the performances of proposed STAP approaches with respect to both the ideal and practical scenarios, involving Doppler-ambiguous clutter ridges, spatial and temporal decorrelation effects. As a result, the low-rank matrix decomposition based solution requires secondary measurements as many as twice the clutter rank to attain a near-ideal STAP performance; whereas the spatio-temporal sparsity based approach needs a considerably small number of secondary data.« less

AZTEC. Parallel Iterative method Software for Solving Linear Systems

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

Hutchinson, S.; Shadid, J.; Tuminaro, R.

1995-07-01

AZTEC is an interactive library that greatly simplifies the parrallelization process when solving the linear systems of equations Ax=b where A is a user supplied n X n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. AZTEC is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparse unstructured matricesmore » for parallel solutions.« less

A fast time-difference inverse solver for 3D EIT with application to lung imaging.

PubMed

Javaherian, Ashkan; Soleimani, Manuchehr; Moeller, Knut

2016-08-01

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Approximate method of variational Bayesian matrix factorization/completion with sparse prior

NASA Astrophysics Data System (ADS)

Kawasumi, Ryota; Takeda, Koujin

2018-05-01

We derive the analytical expression of a matrix factorization/completion solution by the variational Bayes method, under the assumption that the observed matrix is originally the product of low-rank, dense and sparse matrices with additive noise. We assume the prior of a sparse matrix is a Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for the derivation of a matrix factorization/completion solution. By our solution, we also numerically evaluate the performance of a sparse matrix reconstruction in matrix factorization, and completion of a missing matrix element in matrix completion.

An efficient optical architecture for sparsely connected neural networks

NASA Technical Reports Server (NTRS)

Hine, Butler P., III; Downie, John D.; Reid, Max B.

1990-01-01

An architecture for general-purpose optical neural network processor is presented in which the interconnections and weights are formed by directing coherent beams holographically, thereby making use of the space-bandwidth products of the recording medium for sparsely interconnected networks more efficiently that the commonly used vector-matrix multiplier, since all of the hologram area is in use. An investigation is made of the use of computer-generated holograms recorded on such updatable media as thermoplastic materials, in order to define the interconnections and weights of a neural network processor; attention is given to limits on interconnection densities, diffraction efficiencies, and weighing accuracies possible with such an updatable thin film holographic device.

Joint Smoothed l₀-Norm DOA Estimation Algorithm for Multiple Measurement Vectors in MIMO Radar.

PubMed

Liu, Jing; Zhou, Weidong; Juwono, Filbert H

2017-05-08

Direction-of-arrival (DOA) estimation is usually confronted with a multiple measurement vector (MMV) case. In this paper, a novel fast sparse DOA estimation algorithm, named the joint smoothed l 0 -norm algorithm, is proposed for multiple measurement vectors in multiple-input multiple-output (MIMO) radar. To eliminate the white or colored Gaussian noises, the new method first obtains a low-complexity high-order cumulants based data matrix. Then, the proposed algorithm designs a joint smoothed function tailored for the MMV case, based on which joint smoothed l 0 -norm sparse representation framework is constructed. Finally, for the MMV-based joint smoothed function, the corresponding gradient-based sparse signal reconstruction is designed, thus the DOA estimation can be achieved. The proposed method is a fast sparse representation algorithm, which can solve the MMV problem and perform well for both white and colored Gaussian noises. The proposed joint algorithm is about two orders of magnitude faster than the l 1 -norm minimization based methods, such as l 1 -SVD (singular value decomposition), RV (real-valued) l 1 -SVD and RV l 1 -SRACV (sparse representation array covariance vectors), and achieves better DOA estimation performance.

Subspace aware recovery of low rank and jointly sparse signals

PubMed Central

Biswas, Sampurna; Dasgupta, Soura; Mudumbai, Raghuraman; Jacob, Mathews

2017-01-01

We consider the recovery of a matrix X, which is simultaneously low rank and joint sparse, from few measurements of its columns using a two-step algorithm. Each column of X is measured using a combination of two measurement matrices; one which is the same for every column, while the the second measurement matrix varies from column to column. The recovery proceeds by first estimating the row subspace vectors from the measurements corresponding to the common matrix. The estimated row subspace vectors are then used to recover X from all the measurements using a convex program of joint sparsity minimization. Our main contribution is to provide sufficient conditions on the measurement matrices that guarantee the recovery of such a matrix using the above two-step algorithm. The results demonstrate quite significant savings in number of measurements when compared to the standard multiple measurement vector (MMV) scheme, which assumes same time invariant measurement pattern for all the time frames. We illustrate the impact of the sampling pattern on reconstruction quality using breath held cardiac cine MRI and cardiac perfusion MRI data, while the utility of the algorithm to accelerate the acquisition is demonstrated on MR parameter mapping. PMID:28630889

Representation-Independent Iteration of Sparse Data Arrays

NASA Technical Reports Server (NTRS)

James, Mark

2007-01-01

An approach is defined that describes a method of iterating over massively large arrays containing sparse data using an approach that is implementation independent of how the contents of the sparse arrays are laid out in memory. What is unique and important here is the decoupling of the iteration over the sparse set of array elements from how they are internally represented in memory. This enables this approach to be backward compatible with existing schemes for representing sparse arrays as well as new approaches. What is novel here is a new approach for efficiently iterating over sparse arrays that is independent of the underlying memory layout representation of the array. A functional interface is defined for implementing sparse arrays in any modern programming language with a particular focus for the Chapel programming language. Examples are provided that show the translation of a loop that computes a matrix vector product into this representation for both the distributed and not-distributed cases. This work is directly applicable to NASA and its High Productivity Computing Systems (HPCS) program that JPL and our current program are engaged in. The goal of this program is to create powerful, scalable, and economically viable high-powered computer systems suitable for use in national security and industry by 2010. This is important to NASA for its computationally intensive requirements for analyzing and understanding the volumes of science data from our returned missions.

Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.

PubMed

Okimoto, Gordon; Zeinalzadeh, Ashkan; Wenska, Tom; Loomis, Michael; Nation, James B; Fabre, Tiphaine; Tiirikainen, Maarit; Hernandez, Brenda; Chan, Owen; Wong, Linda; Kwee, Sandi

2016-01-01

Technological advances enable the cost-effective acquisition of Multi-Modal Data Sets (MMDS) composed of measurements for multiple, high-dimensional data types obtained from a common set of bio-samples. The joint analysis of the data matrices associated with the different data types of a MMDS should provide a more focused view of the biology underlying complex diseases such as cancer that would not be apparent from the analysis of a single data type alone. As multi-modal data rapidly accumulate in research laboratories and public databases such as The Cancer Genome Atlas (TCGA), the translation of such data into clinically actionable knowledge has been slowed by the lack of computational tools capable of analyzing MMDSs. Here, we describe the Joint Analysis of Many Matrices by ITeration (JAMMIT) algorithm that jointly analyzes the data matrices of a MMDS using sparse matrix approximations of rank-1. The JAMMIT algorithm jointly approximates an arbitrary number of data matrices by rank-1 outer-products composed of "sparse" left-singular vectors (eigen-arrays) that are unique to each matrix and a right-singular vector (eigen-signal) that is common to all the matrices. The non-zero coefficients of the eigen-arrays identify small subsets of variables for each data type (i.e., signatures) that in aggregate, or individually, best explain a dominant eigen-signal defined on the columns of the data matrices. The approximation is specified by a single "sparsity" parameter that is selected based on false discovery rate estimated by permutation testing. Multiple signals of interest in a given MDDS are sequentially detected and modeled by iterating JAMMIT on "residual" data matrices that result from a given sparse approximation. We show that JAMMIT outperforms other joint analysis algorithms in the detection of multiple signatures embedded in simulated MDDS. On real multimodal data for ovarian and liver cancer we show that JAMMIT identified multi-modal signatures that were clinically informative and enriched for cancer-related biology. Sparse matrix approximations of rank-1 provide a simple yet effective means of jointly reducing multiple, big data types to a small subset of variables that characterize important clinical and/or biological attributes of the bio-samples from which the data were acquired.

On the sparseness of 1-norm support vector machines.

PubMed

Zhang, Li; Zhou, Weida

2010-04-01

There is some empirical evidence available showing that 1-norm Support Vector Machines (1-norm SVMs) have good sparseness; however, both how good sparseness 1-norm SVMs can reach and whether they have a sparser representation than that of standard SVMs are not clear. In this paper we take into account the sparseness of 1-norm SVMs. Two upper bounds on the number of nonzero coefficients in the decision function of 1-norm SVMs are presented. First, the number of nonzero coefficients in 1-norm SVMs is at most equal to the number of only the exact support vectors lying on the +1 and -1 discriminating surfaces, while that in standard SVMs is equal to the number of support vectors, which implies that 1-norm SVMs have better sparseness than that of standard SVMs. Second, the number of nonzero coefficients is at most equal to the rank of the sample matrix. A brief review of the geometry of linear programming and the primal steepest edge pricing simplex method are given, which allows us to provide the proof of the two upper bounds and evaluate their tightness by experiments. Experimental results on toy data sets and the UCI data sets illustrate our analysis. Copyright 2009 Elsevier Ltd. All rights reserved.

Improved parallel data partitioning by nested dissection with applications to information retrieval.

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

Wolf, Michael M.; Chevalier, Cedric; Boman, Erik Gunnar

The computational work in many information retrieval and analysis algorithms is based on sparse linear algebra. Sparse matrix-vector multiplication is a common kernel in many of these computations. Thus, an important related combinatorial problem in parallel computing is how to distribute the matrix and the vectors among processors so as to minimize the communication cost. We focus on minimizing the total communication volume while keeping the computation balanced across processes. In [1], the first two authors presented a new 2D partitioning method, the nested dissection partitioning algorithm. In this paper, we improve on that algorithm and show that it ismore » a good option for data partitioning in information retrieval. We also show partitioning time can be substantially reduced by using the SCOTCH software, and quality improves in some cases, too.« less

FPGA implementation of sparse matrix algorithm for information retrieval

NASA Astrophysics Data System (ADS)

Bojanic, Slobodan; Jevtic, Ruzica; Nieto-Taladriz, Octavio

2005-06-01

Information text data retrieval requires a tremendous amount of processing time because of the size of the data and the complexity of information retrieval algorithms. In this paper the solution to this problem is proposed via hardware supported information retrieval algorithms. Reconfigurable computing may adopt frequent hardware modifications through its tailorable hardware and exploits parallelism for a given application through reconfigurable and flexible hardware units. The degree of the parallelism can be tuned for data. In this work we implemented standard BLAS (basic linear algebra subprogram) sparse matrix algorithm named Compressed Sparse Row (CSR) that is showed to be more efficient in terms of storage space requirement and query-processing timing over the other sparse matrix algorithms for information retrieval application. Although inverted index algorithm is treated as the de facto standard for information retrieval for years, an alternative approach to store the index of text collection in a sparse matrix structure gains more attention. This approach performs query processing using sparse matrix-vector multiplication and due to parallelization achieves a substantial efficiency over the sequential inverted index. The parallel implementations of information retrieval kernel are presented in this work targeting the Virtex II Field Programmable Gate Arrays (FPGAs) board from Xilinx. A recent development in scientific applications is the use of FPGA to achieve high performance results. Computational results are compared to implementations on other platforms. The design achieves a high level of parallelism for the overall function while retaining highly optimised hardware within processing unit.

Superresolution radar imaging based on fast inverse-free sparse Bayesian learning for multiple measurement vectors

NASA Astrophysics Data System (ADS)

He, Xingyu; Tong, Ningning; Hu, Xiaowei

2018-01-01

Compressive sensing has been successfully applied to inverse synthetic aperture radar (ISAR) imaging of moving targets. By exploiting the block sparse structure of the target image, sparse solution for multiple measurement vectors (MMV) can be applied in ISAR imaging and a substantial performance improvement can be achieved. As an effective sparse recovery method, sparse Bayesian learning (SBL) for MMV involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size. To address this problem, we develop a fast inverse-free (IF) SBL method for MMV. A relaxed evidence lower bound (ELBO), which is computationally more amiable than the traditional ELBO used by SBL, is obtained by invoking fundamental property for smooth functions. A variational expectation-maximization scheme is then employed to maximize the relaxed ELBO, and a computationally efficient IF-MSBL algorithm is proposed. Numerical results based on simulated and real data show that the proposed method can reconstruct row sparse signal accurately and obtain clear superresolution ISAR images. Moreover, the running time and computational complexity are reduced to a great extent compared with traditional SBL methods.

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

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

Yang, R; Fallone, B; Cross Cancer Institute, Edmonton, AB

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. Themore » LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).« less

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 sparse matrix algorithm on the Boolean vector machine

NASA Technical Reports Server (NTRS)

Wagner, Robert A.; Patrick, Merrell L.

1988-01-01

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

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

Performance analysis of distributed symmetric sparse matrix vector multiplication algorithm for multi-core architectures

DOE PAGES

Oryspayev, Dossay; Aktulga, Hasan Metin; Sosonkina, Masha; ...

2015-07-14

In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important featuresmore » of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.« less

Complex matrix multiplication operations with data pre-conditioning in a high performance computing architecture

DOEpatents

Eichenberger, Alexandre E; Gschwind, Michael K; Gunnels, John A

2014-02-11

Mechanisms for performing a complex matrix multiplication operation are provided. A vector load operation is performed to load a first vector operand of the complex matrix multiplication operation to a first target vector register. The first vector operand comprises a real and imaginary part of a first complex vector value. A complex load and splat operation is performed to load a second complex vector value of a second vector operand and replicate the second complex vector value within a second target vector register. The second complex vector value has a real and imaginary part. A cross multiply add operation is performed on elements of the first target vector register and elements of the second target vector register to generate a partial product of the complex matrix multiplication operation. The partial product is accumulated with other partial products and a resulting accumulated partial product is stored in a result vector register.

Matrix multiplication operations with data pre-conditioning in a high performance computing architecture

DOEpatents

Eichenberger, Alexandre E; Gschwind, Michael K; Gunnels, John A

2013-11-05

Mechanisms for performing matrix multiplication operations with data pre-conditioning in a high performance computing architecture are provided. A vector load operation is performed to load a first vector operand of the matrix multiplication operation to a first target vector register. A load and splat operation is performed to load an element of a second vector operand and replicating the element to each of a plurality of elements of a second target vector register. A multiply add operation is performed on elements of the first target vector register and elements of the second target vector register to generate a partial product of the matrix multiplication operation. The partial product of the matrix multiplication operation is accumulated with other partial products of the matrix multiplication operation.

COMPUTATION OF GLOBAL PHOTOCHEMISTRY WITH SMVGEAR II (R823186)

EPA Science Inventory

A computer model was developed to simulate global gas-phase photochemistry. The model solves chemical equations with SMVGEAR II, a sparse-matrix, vectorized Gear-type code. To obtain SMVGEAR II, the original SMVGEAR code was modified to allow computation of different sets of chem...

Optimization of sparse matrix-vector multiplication on emerging multicore platforms

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

Williams, Samuel; Oliker, Leonid; Vuduc, Richard

2007-01-01

We are witnessing a dramatic change in computer architecture due to the multicore paradigm shift, as every electronic device from cell phones to supercomputers confronts parallelism of unprecedented scale. To fully unleash the potential of these systems, the HPC community must develop multicore specific optimization methodologies for important scientific computations. In this work, we examine sparse matrix-vector multiply (SpMV) - one of the most heavily used kernels in scientific computing - across a broad spectrum of multicore designs. Our experimental platform includes the homogeneous AMD dual-core and Intel quad-core designs, the heterogeneous STI Cell, as well as the first scientificmore » study of the highly multithreaded Sun Niagara2. We present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations. Additionally, we present key insights into the architectural tradeoffs of leading multicore design strategies, in the context of demanding memory-bound numerical algorithms.« less

Multitasking the Davidson algorithm for the large, sparse eigenvalue problem

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

Umar, V.M.; Fischer, C.F.

1989-01-01

The authors report how the Davidson algorithm, developed for handling the eigenvalue problem for large and sparse matrices arising in quantum chemistry, was modified for use in atomic structure calculations. To date these calculations have used traditional eigenvalue methods, which limit the range of feasible calculations because of their excessive memory requirements and unsatisfactory performance attributed to time-consuming and costly processing of zero valued elements. The replacement of a traditional matrix eigenvalue method by the Davidson algorithm reduced these limitations. Significant speedup was found, which varied with the size of the underlying problem and its sparsity. Furthermore, the range ofmore » matrix sizes that can be manipulated efficiently was expended by more than one order or magnitude. On the CRAY X-MP the code was vectorized and the importance of gather/scatter analyzed. A parallelized version of the algorithm obtained an additional 35% reduction in execution time. Speedup due to vectorization and concurrency was also measured on the Alliant FX/8.« less

Holographic implementation of a binary associative memory for improved recognition

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Somnath; Ghosh, Ajay; Datta, Asit K.

1998-03-01

Neural network associate memory has found wide application sin pattern recognition techniques. We propose an associative memory model for binary character recognition. The interconnection strengths of the memory are binary valued. The concept of sparse coding is sued to enhance the storage efficiency of the model. The question of imposed preconditioning of pattern vectors, which is inherent in a sparsely coded conventional memory, is eliminated by using a multistep correlation technique an the ability of correct association is enhanced in a real-time application. A potential optoelectronic implementation of the proposed associative memory is also described. The learning and recall is possible by using digital optical matrix-vector multiplication, where full use of parallelism and connectivity of optics is made. A hologram is used in the experiment as a longer memory (LTM) for storing all input information. The short-term memory or the interconnection weight matrix required during the recall process is configured by retrieving the necessary information from the holographic LTM.

Aztec user`s guide. Version 1

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

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1995-10-01

Aztec is an iterative library that greatly simplifies the parallelization process when solving the linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. Aztec is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparsemore » unstructured matrices for parallel solution. Once the distributed matrix is created, computation can be performed on any of the parallel machines running Aztec: nCUBE 2, IBM SP2 and Intel Paragon, MPI platforms as well as standard serial and vector platforms. Aztec includes a number of Krylov iterative methods such as conjugate gradient (CG), generalized minimum residual (GMRES) and stabilized biconjugate gradient (BICGSTAB) to solve systems of equations. These Krylov methods are used in conjunction with various preconditioners such as polynomial or domain decomposition methods using LU or incomplete LU factorizations within subdomains. Although the matrix A can be general, the package has been designed for matrices arising from the approximation of partial differential equations (PDEs). In particular, the Aztec package is oriented toward systems arising from PDE applications.« less

Matrix multiplication operations using pair-wise load and splat operations

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

Eichenberger, Alexandre E.; Gschwind, Michael K.; Gunnels, John A.

Mechanisms for performing a matrix multiplication operation are provided. A vector load operation is performed to load a first vector operand of the matrix multiplication operation to a first target vector register. A pair-wise load and splat operation is performed to load a pair of scalar values of a second vector operand and replicate the pair of scalar values within a second target vector register. An operation is performed on elements of the first target vector register and elements of the second target vector register to generate a partial product of the matrix multiplication operation. The partial product is accumulatedmore » with other partial products and a resulting accumulated partial product is stored. This operation may be repeated for a second pair of scalar values of the second vector operand.« less

Collaborative sparse priors for multi-view ATR

NASA Astrophysics Data System (ADS)

Li, Xuelu; Monga, Vishal

2018-04-01

Recent work has seen a surge of sparse representation based classification (SRC) methods applied to automatic target recognition problems. While traditional SRC approaches used l0 or l1 norm to quantify sparsity, spike and slab priors have established themselves as the gold standard for providing general tunable sparse structures on vectors. In this work, we employ collaborative spike and slab priors that can be applied to matrices to encourage sparsity for the problem of multi-view ATR. That is, target images captured from multiple views are expanded in terms of a training dictionary multiplied with a coefficient matrix. Ideally, for a test image set comprising of multiple views of a target, coefficients corresponding to its identifying class are expected to be active, while others should be zero, i.e. the coefficient matrix is naturally sparse. We develop a new approach to solve the optimization problem that estimates the sparse coefficient matrix jointly with the sparsity inducing parameters in the collaborative prior. ATR problems are investigated on the mid-wave infrared (MWIR) database made available by the US Army Night Vision and Electronic Sensors Directorate, which has a rich collection of views. Experimental results show that the proposed joint prior and coefficient estimation method (JPCEM) can: 1.) enable improved accuracy when multiple views vs. a single one are invoked, and 2.) outperform state of the art alternatives particularly when training imagery is limited.

Portable implementation model for CFD simulations. Application to hybrid CPU/GPU supercomputers

NASA Astrophysics Data System (ADS)

Oyarzun, Guillermo; Borrell, Ricard; Gorobets, Andrey; Oliva, Assensi

2017-10-01

Nowadays, high performance computing (HPC) systems experience a disruptive moment with a variety of novel architectures and frameworks, without any clarity of which one is going to prevail. In this context, the portability of codes across different architectures is of major importance. This paper presents a portable implementation model based on an algebraic operational approach for direct numerical simulation (DNS) and large eddy simulation (LES) of incompressible turbulent flows using unstructured hybrid meshes. The strategy proposed consists in representing the whole time-integration algorithm using only three basic algebraic operations: sparse matrix-vector product, a linear combination of vectors and dot product. The main idea is based on decomposing the nonlinear operators into a concatenation of two SpMV operations. This provides high modularity and portability. An exhaustive analysis of the proposed implementation for hybrid CPU/GPU supercomputers has been conducted with tests using up to 128 GPUs. The main objective consists in understanding the challenges of implementing CFD codes on new architectures.

Multigrid Equation Solvers for Large Scale Nonlinear Finite Element Simulations

DTIC Science & Technology

1999-01-01

purpose of the second partitioning phase , on each SMP, is to minimize the communication within the SMP; even if a multi - threaded matrix vector product...8.7 Comparison of model with experimental data for send phase of matrix vector product on ne grid...140 8.4 Matrix vector product phase times : : : : : : : : : : : : : : : : : : : : : : : 145 9.1 Flat and

Combined fast multipole-QR compression technique for solving electrically small to large structures for broadband applications

NASA Technical Reports Server (NTRS)

Jandhyala, Vikram (Inventor); Chowdhury, Indranil (Inventor)

2011-01-01

An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (FMM) elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.

Computing row and column counts for sparse QR and LU factorization

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

Gilbert, John R.; Li, Xiaoye S.; Ng, Esmond G.

2001-01-01

We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and theremore » is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.« less

Optimization of Sparse Matrix-Vector Multiplication on Emerging Multicore Platforms

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

Williams, Samuel; Oliker, Leonid; Vuduc, Richard

2008-10-16

We are witnessing a dramatic change in computer architecture due to the multicore paradigm shift, as every electronic device from cell phones to supercomputers confronts parallelism of unprecedented scale. To fully unleash the potential of these systems, the HPC community must develop multicore specific-optimization methodologies for important scientific computations. In this work, we examine sparse matrix-vector multiply (SpMV) - one of the most heavily used kernels in scientific computing - across a broad spectrum of multicore designs. Our experimental platform includes the homogeneous AMD quad-core, AMD dual-core, and Intel quad-core designs, the heterogeneous STI Cell, as well as one ofmore » the first scientific studies of the highly multithreaded Sun Victoria Falls (a Niagara2 SMP). We present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations. Additionally, we present key insights into the architectural trade-offs of leading multicore design strategies, in the context of demanding memory-bound numerical algorithms.« less

Improving M-SBL for Joint Sparse Recovery Using a Subspace Penalty

NASA Astrophysics Data System (ADS)

Ye, Jong Chul; Kim, Jong Min; Bresler, Yoram

2015-12-01

The multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - M-SBL (multiple sparse Bayesian learning) and subspace-based hybrid greedy algorithms - have a very important link. More specifically, we show that replacing the $\\log\\det(\\cdot)$ term in M-SBL by a rank proxy that exploits the spark reduction property discovered in subspace-based joint sparse recovery algorithms, provides significant improvements. In particular, if we use the Schatten-$p$ quasi-norm as the corresponding rank proxy, the global minimiser of the proposed algorithm becomes identical to the true solution as $p \\rightarrow 0$. Furthermore, under the same regularity conditions, we show that the convergence to a local minimiser is guaranteed using an alternating minimization algorithm that has closed form expressions for each of the minimization steps, which are convex. Numerical simulations under a variety of scenarios in terms of SNR, and condition number of the signal amplitude matrix demonstrate that the proposed algorithm consistently outperforms M-SBL and other state-of-the art algorithms.

A Chess-Like Game for Teaching Engineering Students to Solve Large System of Simultaneous Linear Equations

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Mohammed, Ahmed Ali; Kadiam, Subhash

2010-01-01

Solving large (and sparse) system of simultaneous linear equations has been (and continues to be) a major challenging problem for many real-world engineering/science applications [1-2]. For many practical/large-scale problems, the sparse, Symmetrical and Positive Definite (SPD) system of linear equations can be conveniently represented in matrix notation as [A] {x} = {b} , where the square coefficient matrix [A] and the Right-Hand-Side (RHS) vector {b} are known. The unknown solution vector {x} can be efficiently solved by the following step-by-step procedures [1-2]: Reordering phase, Matrix Factorization phase, Forward solution phase, and Backward solution phase. In this research work, a Game-Based Learning (GBL) approach has been developed to help engineering students to understand crucial details about matrix reordering and factorization phases. A "chess-like" game has been developed and can be played by either a single player, or two players. Through this "chess-like" open-ended game, the players/learners will not only understand the key concepts involved in reordering algorithms (based on existing algorithms), but also have the opportunities to "discover new algorithms" which are better than existing algorithms. Implementing the proposed "chess-like" game for matrix reordering and factorization phases can be enhanced by FLASH [3] computer environments, where computer simulation with animated human voice, sound effects, visual/graphical/colorful displays of matrix tables, score (or monetary) awards for the best game players, etc. can all be exploited. Preliminary demonstrations of the developed GBL approach can be viewed by anyone who has access to the internet web-site [4]!

High-dimensional statistical inference: From vector to matrix

NASA Astrophysics Data System (ADS)

Zhang, Anru

Statistical inference for sparse signals or low-rank matrices in high-dimensional settings is of significant interest in a range of contemporary applications. It has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. In this thesis, we consider several problems in including sparse signal recovery (compressed sensing under restricted isometry) and low-rank matrix recovery (matrix recovery via rank-one projections and structured matrix completion). The first part of the thesis discusses compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse vectors. The technique is elementary while leads to sharp results. It is shown that, in compressed sensing, delta kA < 1/3, deltak A+ thetak,kA < 1, or deltatkA < √( t - 1)/t for any given constant t ≥ 4/3 guarantee the exact recovery of all k sparse signals in the noiseless case through the constrained ℓ1 minimization, and similarly in affine rank minimization delta rM < 1/3, deltar M + thetar, rM < 1, or deltatrM< √( t - 1)/t ensure the exact reconstruction of all matrices with rank at most r in the noiseless case via the constrained nuclear norm minimization. Moreover, for any epsilon > 0, delta kA < 1/3 + epsilon, deltak A + thetak,kA < 1 + epsilon, or deltatkA< √(t - 1) / t + epsilon are not sufficient to guarantee the exact recovery of all k-sparse signals for large k. Similar result also holds for matrix recovery. In addition, the conditions delta kA<1/3, deltak A+ thetak,kA<1, delta tkA < √(t - 1)/t and deltarM<1/3, delta rM+ thetar,rM<1, delta trM< √(t - 1)/ t are also shown to be sufficient respectively for stable recovery of approximately sparse signals and low-rank matrices in the noisy case. For the second part of the thesis, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed estimator is shown to be rate-optimal under certain conditions. The estimator is easy to implement via convex programming and performs well numerically. The techniques and main results developed in the chapter also have implications to other related statistical problems. An application to estimation of spiked covariance matrices from one-dimensional random projections is considered. The results demonstrate that it is still possible to accurately estimate the covariance matrix of a high-dimensional distribution based only on one-dimensional projections. For the third part of the thesis, we consider another setting of low-rank matrix completion. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

Comparison between sparsely distributed memory and Hopfield-type neural network models

NASA Technical Reports Server (NTRS)

Keeler, James D.

1986-01-01

The Sparsely Distributed Memory (SDM) model (Kanerva, 1984) is compared to Hopfield-type neural-network models. A mathematical framework for comparing the two is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independently of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. However, the total number of stored bits per matrix element is the same in the two models, as well as for extended models with higher order interactions. The models are also compared in their ability to store sequences of patterns. The SDM is extended to include time delays so that contextual information can be used to cover sequences. Finally, it is shown how a generalization of the SDM allows storage of correlated input pattern vectors.

Sparse kernel methods for high-dimensional survival data.

PubMed

Evers, Ludger; Messow, Claudia-Martina

2008-07-15

Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be 'kernelized'. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, depending only on a small fraction of the training data. We propose two methods. One is based on a geometric idea, where-akin to support vector classification-the margin between the failed observation and the observations currently at risk is maximised. The other approach is based on obtaining a sparse model by adding observations one after another akin to the Import Vector Machine (IVM). Data examples studied suggest that both methods can outperform competing approaches. Software is available under the GNU Public License as an R package and can be obtained from the first author's website http://www.maths.bris.ac.uk/~maxle/software.html.

GPU-accelerated algorithms for compressed signals recovery with application to astronomical imagery deblurring

NASA Astrophysics Data System (ADS)

Fiandrotti, Attilio; Fosson, Sophie M.; Ravazzi, Chiara; Magli, Enrico

2018-04-01

Compressive sensing promises to enable bandwidth-efficient on-board compression of astronomical data by lifting the encoding complexity from the source to the receiver. The signal is recovered off-line, exploiting GPUs parallel computation capabilities to speedup the reconstruction process. However, inherent GPU hardware constraints limit the size of the recoverable signal and the speedup practically achievable. In this work, we design parallel algorithms that exploit the properties of circulant matrices for efficient GPU-accelerated sparse signals recovery. Our approach reduces the memory requirements, allowing us to recover very large signals with limited memory. In addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc parallelization of matrix-vector multiplications and matrix inversions. Finally, we practically demonstrate our algorithms in a typical application of circulant matrices: deblurring a sparse astronomical image in the compressed domain.

DNA melting profiles from a matrix method.

PubMed

Poland, Douglas

2004-02-05

In this article we give a new method for the calculation of DNA melting profiles. Based on the matrix formulation of the DNA partition function, the method relies for its efficiency on the fact that the required matrices are very sparse, essentially reducing matrix multiplication to vector multiplication and thus making the computer time required to treat a DNA molecule containing N base pairs proportional to N(2). A key ingredient in the method is the result that multiplication by the inverse matrix can also be reduced to vector multiplication. The task of calculating the melting profile for the entire genome is further reduced by treating regions of the molecule between helix-plateaus, thus breaking the molecule up into independent parts that can each be treated individually. The method is easily modified to incorporate changes in the assignment of statistical weights to the different structural features of DNA. We illustrate the method using the genome of Haemophilus influenzae. Copyright 2003 Wiley Periodicals, Inc.

FPGA architecture and implementation of sparse matrix vector multiplication for the finite element method

NASA Astrophysics Data System (ADS)

Elkurdi, Yousef; Fernández, David; Souleimanov, Evgueni; Giannacopoulos, Dennis; Gross, Warren J.

2008-04-01

The Finite Element Method (FEM) is a computationally intensive scientific and engineering analysis tool that has diverse applications ranging from structural engineering to electromagnetic simulation. The trends in floating-point performance are moving in favor of Field-Programmable Gate Arrays (FPGAs), hence increasing interest has grown in the scientific community to exploit this technology. We present an architecture and implementation of an FPGA-based sparse matrix-vector multiplier (SMVM) for use in the iterative solution of large, sparse systems of equations arising from FEM applications. FEM matrices display specific sparsity patterns that can be exploited to improve the efficiency of hardware designs. Our architecture exploits FEM matrix sparsity structure to achieve a balance between performance and hardware resource requirements by relying on external SDRAM for data storage while utilizing the FPGAs computational resources in a stream-through systolic approach. The architecture is based on a pipelined linear array of processing elements (PEs) coupled with a hardware-oriented matrix striping algorithm and a partitioning scheme which enables it to process arbitrarily big matrices without changing the number of PEs in the architecture. Therefore, this architecture is only limited by the amount of external RAM available to the FPGA. The implemented SMVM-pipeline prototype contains 8 PEs and is clocked at 110 MHz obtaining a peak performance of 1.76 GFLOPS. For 8 GB/s of memory bandwidth typical of recent FPGA systems, this architecture can achieve 1.5 GFLOPS sustained performance. Using multiple instances of the pipeline, linear scaling of the peak and sustained performance can be achieved. Our stream-through architecture provides the added advantage of enabling an iterative implementation of the SMVM computation required by iterative solution techniques such as the conjugate gradient method, avoiding initialization time due to data loading and setup inside the FPGA internal memory.

Detecting double compressed MPEG videos with the same quantization matrix and synchronized group of pictures structure

NASA Astrophysics Data System (ADS)

Aghamaleki, Javad Abbasi; Behrad, Alireza

2018-01-01

Double compression detection is a crucial stage in digital image and video forensics. However, the detection of double compressed videos is challenging when the video forger uses the same quantization matrix and synchronized group of pictures (GOP) structure during the recompression history to conceal tampering effects. A passive approach is proposed for detecting double compressed MPEG videos with the same quantization matrix and synchronized GOP structure. To devise the proposed algorithm, the effects of recompression on P frames are mathematically studied. Then, based on the obtained guidelines, a feature vector is proposed to detect double compressed frames on the GOP level. Subsequently, sparse representations of the feature vectors are used for dimensionality reduction and enrich the traces of recompression. Finally, a support vector machine classifier is employed to detect and localize double compression in temporal domain. The experimental results show that the proposed algorithm achieves the accuracy of more than 95%. In addition, the comparisons of the results of the proposed method with those of other methods reveal the efficiency of the proposed algorithm.

Preliminary results in implementing a model of the world economy on the CYBER 205: A case of large sparse nonsymmetric linear equations

NASA Technical Reports Server (NTRS)

Szyld, D. B.

1984-01-01

A brief description of the Model of the World Economy implemented at the Institute for Economic Analysis is presented, together with our experience in converting the software to vector code. For each time period, the model is reduced to a linear system of over 2000 variables. The matrix of coefficients has a bordered block diagonal structure, and we show how some of the matrix operations can be carried out on all diagonal blocks at once.

Two-Dimensional DOA and Polarization Estimation for a Mixture of Uncorrelated and Coherent Sources with Sparsely-Distributed Vector Sensor Array

PubMed Central

Si, Weijian; Zhao, Pinjiao; Qu, Zhiyu

2016-01-01

This paper presents an L-shaped sparsely-distributed vector sensor (SD-VS) array with four different antenna compositions. With the proposed SD-VS array, a novel two-dimensional (2-D) direction of arrival (DOA) and polarization estimation method is proposed to handle the scenario where uncorrelated and coherent sources coexist. The uncorrelated and coherent sources are separated based on the moduli of the eigenvalues. For the uncorrelated sources, coarse estimates are acquired by extracting the DOA information embedded in the steering vectors from estimated array response matrix of the uncorrelated sources, and they serve as coarse references to disambiguate fine estimates with cyclical ambiguity obtained from the spatial phase factors. For the coherent sources, four Hankel matrices are constructed, with which the coherent sources are resolved in a similar way as for the uncorrelated sources. The proposed SD-VS array requires only two collocated antennas for each vector sensor, thus the mutual coupling effects across the collocated antennas are reduced greatly. Moreover, the inter-sensor spacings are allowed beyond a half-wavelength, which results in an extended array aperture. Simulation results demonstrate the effectiveness and favorable performance of the proposed method. PMID:27258271

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

An efficient implementation of a high-order filter for a cubed-sphere spectral element model

NASA Astrophysics Data System (ADS)

Kang, Hyun-Gyu; Cheong, Hyeong-Bin

2017-03-01

A parallel-scalable, isotropic, scale-selective spatial filter was developed for the cubed-sphere spectral element model on the sphere. The filter equation is a high-order elliptic (Helmholtz) equation based on the spherical Laplacian operator, which is transformed into cubed-sphere local coordinates. The Laplacian operator is discretized on the computational domain, i.e., on each cell, by the spectral element method with Gauss-Lobatto Lagrange interpolating polynomials (GLLIPs) as the orthogonal basis functions. On the global domain, the discrete filter equation yielded a linear system represented by a highly sparse matrix. The density of this matrix increases quadratically (linearly) with the order of GLLIP (order of the filter), and the linear system is solved in only O (Ng) operations, where Ng is the total number of grid points. The solution, obtained by a row reduction method, demonstrated the typical accuracy and convergence rate of the cubed-sphere spectral element method. To achieve computational efficiency on parallel computers, the linear system was treated by an inverse matrix method (a sparse matrix-vector multiplication). The density of the inverse matrix was lowered to only a few times of the original sparse matrix without degrading the accuracy of the solution. For better computational efficiency, a local-domain high-order filter was introduced: The filter equation is applied to multiple cells, and then the central cell was only used to reconstruct the filtered field. The parallel efficiency of applying the inverse matrix method to the global- and local-domain filter was evaluated by the scalability on a distributed-memory parallel computer. The scale-selective performance of the filter was demonstrated on Earth topography. The usefulness of the filter as a hyper-viscosity for the vorticity equation was also demonstrated.

Ontology Sparse Vector Learning Algorithm for Ontology Similarity Measuring and Ontology Mapping via ADAL Technology

NASA Astrophysics Data System (ADS)

Gao, Wei; Zhu, Linli; Wang, Kaiyun

2015-12-01

Ontology, a model of knowledge representation and storage, has had extensive applications in pharmaceutics, social science, chemistry and biology. In the age of “big data”, the constructed concepts are often represented as higher-dimensional data by scholars, and thus the sparse learning techniques are introduced into ontology algorithms. In this paper, based on the alternating direction augmented Lagrangian method, we present an ontology optimization algorithm for ontological sparse vector learning, and a fast version of such ontology technologies. The optimal sparse vector is obtained by an iterative procedure, and the ontology function is then obtained from the sparse vector. Four simulation experiments show that our ontological sparse vector learning model has a higher precision ratio on plant ontology, humanoid robotics ontology, biology ontology and physics education ontology data for similarity measuring and ontology mapping applications.

LSRN: A PARALLEL ITERATIVE SOLVER FOR STRONGLY OVER- OR UNDERDETERMINED SYSTEMS*

PubMed Central

Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.

2014-01-01

We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to minx∈ℝn ‖Ax − b‖2, where A ∈ ℝm × n with m ≫ n or m ≪ n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is involved only in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size ⌈γ min(m, n)⌉ × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results show that on a shared-memory machine, LSRN is very competitive with LAPACK’s DGELSD and a fast randomized least squares solver called Blendenpik on large dense problems, and it outperforms the least squares solver from SuiteSparseQR on sparse problems without sparsity patterns that can be exploited to reduce fill-in. Further experiments show that LSRN scales well on an Amazon Elastic Compute Cloud cluster. PMID:25419094

Lanczos eigensolution method for high-performance computers

NASA Technical Reports Server (NTRS)

Bostic, Susan W.

1991-01-01

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

NASA Astrophysics Data System (ADS)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics.

HO2 rovibrational eigenvalue studies for nonzero angular momentum

NASA Astrophysics Data System (ADS)

Wu, Xudong T.; Hayes, Edward F.

1997-08-01

An efficient parallel algorithm is reported for determining all bound rovibrational energy levels for the HO2 molecule for nonzero angular momentum values, J=1, 2, and 3. Performance tests on the CRAY T3D indicate that the algorithm scales almost linearly when up to 128 processors are used. Sustained performance levels of up to 3.8 Gflops have been achieved using 128 processors for J=3. The algorithm uses a direct product discrete variable representation (DVR) basis and the implicitly restarted Lanczos method (IRLM) of Sorensen to compute the eigenvalues of the polyatomic Hamiltonian. Since the IRLM is an iterative method, it does not require storage of the full Hamiltonian matrix—it only requires the multiplication of the Hamiltonian matrix by a vector. When the IRLM is combined with a formulation such as DVR, which produces a very sparse matrix, both memory and computation times can be reduced dramatically. This algorithm has the potential to achieve even higher performance levels for larger values of the total angular momentum.

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.

Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

NASA Technical Reports Server (NTRS)

Gupta, V. K.; Zillmer, S. D.; Allison, R. E.

1986-01-01

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix.

spammpack, Version 2013-06-18

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

2014-01-17

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

A path-oriented matrix-based knowledge representation system

NASA Technical Reports Server (NTRS)

Feyock, Stefan; Karamouzis, Stamos T.

1993-01-01

Experience has shown that designing a good representation is often the key to turning hard problems into simple ones. Most AI (Artificial Intelligence) search/representation techniques are oriented toward an infinite domain of objects and arbitrary relations among them. In reality much of what needs to be represented in AI can be expressed using a finite domain and unary or binary predicates. Well-known vector- and matrix-based representations can efficiently represent finite domains and unary/binary predicates, and allow effective extraction of path information by generalized transitive closure/path matrix computations. In order to avoid space limitations a set of abstract sparse matrix data types was developed along with a set of operations on them. This representation forms the basis of an intelligent information system for representing and manipulating relational data.

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.

A method of vehicle license plate recognition based on PCANet and compressive sensing

NASA Astrophysics Data System (ADS)

Ye, Xianyi; Min, Feng

2018-03-01

The manual feature extraction of the traditional method for vehicle license plates has no good robustness to change in diversity. And the high feature dimension that is extracted with Principal Component Analysis Network (PCANet) leads to low classification efficiency. For solving these problems, a method of vehicle license plate recognition based on PCANet and compressive sensing is proposed. First, PCANet is used to extract the feature from the images of characters. And then, the sparse measurement matrix which is a very sparse matrix and consistent with Restricted Isometry Property (RIP) condition of the compressed sensing is used to reduce the dimensions of extracted features. Finally, the Support Vector Machine (SVM) is used to train and recognize the features whose dimension has been reduced. Experimental results demonstrate that the proposed method has better performance than Convolutional Neural Network (CNN) in the recognition and time. Compared with no compression sensing, the proposed method has lower feature dimension for the increase of efficiency.

Integrated optic vector-matrix multiplier

DOEpatents

Watts, Michael R [Albuquerque, NM

2011-09-27

A vector-matrix multiplier is disclosed which uses N different wavelengths of light that are modulated with amplitudes representing elements of an N.times.1 vector and combined to form an input wavelength-division multiplexed (WDM) light stream. The input WDM light stream is split into N streamlets from which each wavelength of the light is individually coupled out and modulated for a second time using an input signal representing elements of an M.times.N matrix, and is then coupled into an output waveguide for each streamlet to form an output WDM light stream which is detected to generate a product of the vector and matrix. The vector-matrix multiplier can be formed as an integrated optical circuit using either waveguide amplitude modulators or ring resonator amplitude modulators.

Fast space-varying convolution using matrix source coding with applications to camera stray light reduction.

PubMed

Wei, Jianing; Bouman, Charles A; Allebach, Jan P

2014-05-01

Many imaging applications require the implementation of space-varying convolution for accurate restoration and reconstruction of images. Here, we use the term space-varying convolution to refer to linear operators whose impulse response has slow spatial variation. In addition, these space-varying convolution operators are often dense, so direct implementation of the convolution operator is typically computationally impractical. One such example is the problem of stray light reduction in digital cameras, which requires the implementation of a dense space-varying deconvolution operator. However, other inverse problems, such as iterative tomographic reconstruction, can also depend on the implementation of dense space-varying convolution. While space-invariant convolution can be efficiently implemented with the fast Fourier transform, this approach does not work for space-varying operators. So direct convolution is often the only option for implementing space-varying convolution. In this paper, we develop a general approach to the efficient implementation of space-varying convolution, and demonstrate its use in the application of stray light reduction. Our approach, which we call matrix source coding, is based on lossy source coding of the dense space-varying convolution matrix. Importantly, by coding the transformation matrix, we not only reduce the memory required to store it; we also dramatically reduce the computation required to implement matrix-vector products. Our algorithm is able to reduce computation by approximately factoring the dense space-varying convolution operator into a product of sparse transforms. Experimental results show that our method can dramatically reduce the computation required for stray light reduction while maintaining high accuracy.

A Fast MoM Solver (GIFFT) for Large Arrays of Microstrip and Cavity-Backed Antennas

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

Fasenfest, B J; Capolino, F; Wilton, D

2005-02-02

A straightforward numerical analysis of large arrays of arbitrary contour (and possibly missing elements) requires large memory storage and long computation times. Several techniques are currently under development to reduce this cost. One such technique is the GIFFT (Green's function interpolation and FFT) method discussed here that belongs to the class of fast solvers for large structures. This method uses a modification of the standard AIM approach [1] that takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basismore » functions, such as the RWG basis. The Green's function is then projected onto a sparse regular grid of separable interpolating polynomials. This grid can then be used in a 2D or 3D FFT to accelerate the matrix-vector product used in an iterative solver [2]. The method has been proven to greatly reduce solve time by speeding up the matrix-vector product computation. The GIFFT approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends GIFFT to layered material Green's functions and multiregion interactions via slots in ground planes. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the GIFFT method is reported in [2]; this contribution is limited to presenting new results for array antennas made of slot-excited patches and cavity-backed patch antennas.« less

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

In order to combine the initial spatial structure and features of LiDAR data for accurate classification. The LiDAR data is represented as a 4-order tensor. Sparse representation for classification(SRC) method is used for LiDAR tensor classification. It turns out SRC need only a few of training samples from each class, meanwhile can achieve good classification result. Multiple features are extracted from raw LiDAR points to generate a high-dimensional vector at each point. Then the LiDAR tensor is built by the spatial distribution and feature vectors of the point neighborhood. The entries of LiDAR tensor are accessed via four indexes. Each index is called mode: three spatial modes in direction X ,Y ,Z and one feature mode. Sparse representation for classification(SRC) method is proposed in this paper. The sparsity algorithm is to find the best represent the test sample by sparse linear combination of training samples from a dictionary. To explore the sparsity of LiDAR tensor, the tucker decomposition is used. It decomposes a tensor into a core tensor multiplied by a matrix along each mode. Those matrices could be considered as the principal components in each mode. The entries of core tensor show the level of interaction between the different components. Therefore, the LiDAR tensor can be approximately represented by a sparse tensor multiplied by a matrix selected from a dictionary along each mode. The matrices decomposed from training samples are arranged as initial elements in the dictionary. By dictionary learning, a reconstructive and discriminative structure dictionary along each mode is built. The overall structure dictionary composes of class-specified sub-dictionaries. Then the sparse core tensor is calculated by tensor OMP(Orthogonal Matching Pursuit) method based on dictionaries along each mode. It is expected that original tensor should be well recovered by sub-dictionary associated with relevant class, while entries in the sparse tensor associated with other classed should be nearly zero. Therefore, SRC use the reconstruction error associated with each class to do data classification. A section of airborne LiDAR points of Vienna city is used and classified into 6classes: ground, roofs, vegetation, covered ground, walls and other points. Only 6 training samples from each class are taken. For the final classification result, ground and covered ground are merged into one same class(ground). The classification accuracy for ground is 94.60%, roof is 95.47%, vegetation is 85.55%, wall is 76.17%, other object is 20.39%.

Sparse representation based SAR vehicle recognition along with aspect angle.

PubMed

Xing, Xiangwei; Ji, Kefeng; Zou, Huanxin; Sun, Jixiang

2014-01-01

As a method of representing the test sample with few training samples from an overcomplete dictionary, sparse representation classification (SRC) has attracted much attention in synthetic aperture radar (SAR) automatic target recognition (ATR) recently. In this paper, we develop a novel SAR vehicle recognition method based on sparse representation classification along with aspect information (SRCA), in which the correlation between the vehicle's aspect angle and the sparse representation vector is exploited. The detailed procedure presented in this paper can be summarized as follows. Initially, the sparse representation vector of a test sample is solved by sparse representation algorithm with a principle component analysis (PCA) feature-based dictionary. Then, the coefficient vector is projected onto a sparser one within a certain range of the vehicle's aspect angle. Finally, the vehicle is classified into a certain category that minimizes the reconstruction error with the novel sparse representation vector. Extensive experiments are conducted on the moving and stationary target acquisition and recognition (MSTAR) dataset and the results demonstrate that the proposed method performs robustly under the variations of depression angle and target configurations, as well as incomplete observation.

Optoelectronic Inner-Product Neural Associative Memory

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang

1993-01-01

Optoelectronic apparatus acts as artificial neural network performing associative recall of binary images. Recall process is iterative one involving optical computation of inner products between binary input vector and one or more reference binary vectors in memory. Inner-product method requires far less memory space than matrix-vector method.

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Lockard, David P.; Atkins, Harold L.

1999-01-01

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Multi-threaded Sparse Matrix Sparse Matrix Multiplication for Many-Core and GPU Architectures.

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

Deveci, Mehmet; Trott, Christian Robert; Rajamanickam, Sivasankaran

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix- matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD).

PubMed

Bermúdez Ordoñez, Juan Carlos; Arnaldo Valdés, Rosa María; Gómez Comendador, Fernando

2018-05-16

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ 1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain.

Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)

PubMed Central

Arnaldo Valdés, Rosa María; Gómez Comendador, Fernando

2018-01-01

A significant challenge in global navigation satellite system (GNSS) signal processing is a requirement for a very high sampling rate. The recently-emerging compressed sensing (CS) theory makes processing GNSS signals at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on CS and SVD theories, an algorithm for sampling GNSS signals at a rate much lower than the Nyquist rate and reconstructing the compressed signal is proposed in this research, which is validated after the output from that process still performs signal detection using the standard fast Fourier transform (FFT) parallel frequency space search acquisition. The sparse representation of the GNSS signal is the most important precondition for CS, by constructing a rectangular Toeplitz matrix (TZ) of the transmitted signal, calculating the left singular vectors using SVD from the TZ, to achieve sparse signal representation. Next, obtaining the M-dimensional observation vectors based on the left singular vectors of the SVD, which are equivalent to the sampler operator in standard compressive sensing theory, the signal can be sampled below the Nyquist rate, and can still be reconstructed via ℓ1 minimization with accuracy using convex optimization. As an added value, there is a GNSS signal acquisition enhancement effect by retaining the useful signal and filtering out noise by projecting the signal into the most significant proper orthogonal modes (PODs) which are the optimal distributions of signal power. The algorithm is validated with real recorded signals, and the results show that the proposed method is effective for sampling, reconstructing intermediate frequency (IF) GNSS signals in the time discrete domain. PMID:29772731

Online Least Squares One-Class Support Vector Machines-Based Abnormal Visual Event Detection

PubMed Central

Wang, Tian; Chen, Jie; Zhou, Yi; Snoussi, Hichem

2013-01-01

The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method. PMID:24351629

Online least squares one-class support vector machines-based abnormal visual event detection.

PubMed

Wang, Tian; Chen, Jie; Zhou, Yi; Snoussi, Hichem

2013-12-12

The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method.

Sparse Matrices in MATLAB: Design and Implementation

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Moler, Cleve; Schreiber, Robert

1992-01-01

The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Quantum algorithm for linear systems of equations.

PubMed

Harrow, Aram W; Hassidim, Avinatan; Lloyd, Seth

2009-10-09

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such that Ax(-->) = b(-->). We consider the case where one does not need to know the solution x(-->) itself, but rather an approximation of the expectation value of some operator associated with x(-->), e.g., x(-->)(dagger) Mx(-->) for some matrix M. In this case, when A is sparse, N x N and has condition number kappa, the fastest known classical algorithms can find x(-->) and estimate x(-->)(dagger) Mx(-->) in time scaling roughly as N square root(kappa). Here, we exhibit a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa. Indeed, for small values of kappa [i.e., poly log(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.

Wavelet-like bases for thin-wire integral equations in electromagnetics

NASA Astrophysics Data System (ADS)

Francomano, E.; Tortorici, A.; Toscano, E.; Ala, G.; Viola, F.

2005-03-01

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix. In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures. This leads to an efficient solution in solving the resulting sparse matrix equation. Moreover, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed. These numerical features are used in analyzing the transient behavior of a lightning protection system. In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused. The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.

Elements of the quality management in the materials' industry

NASA Astrophysics Data System (ADS)

Ioana, Adrian; Semenescu, Augustin; Costoiu, Mihnea; Marcu, Dragoş

2017-12-01

The criteria function concept consists of transforming the criteria function (CF) in a quality-economical matrix math MQE. The levels of prescribing the criteria function was obtained by using a composition algorithm for three vectors: T¯ vector - technical parameters' vector (ti); Ē vector - economical parameters' vector (ej) and P¯ vector - weight vector (p1). For each product or service, the area of the circle represents the value of its sales. The BCG Matrix thus offers a very useful map of the organization's service strengths and weaknesses, at least in terms of current profitability, as well as the likely cash flows.

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

PubMed Central

Monajemi, Hatef; Jafarpour, Sina; Gavish, Matan; Donoho, David L.; Ambikasaran, Sivaram; Bacallado, Sergio; Bharadia, Dinesh; Chen, Yuxin; Choi, Young; Chowdhury, Mainak; Chowdhury, Soham; Damle, Anil; Fithian, Will; Goetz, Georges; Grosenick, Logan; Gross, Sam; Hills, Gage; Hornstein, Michael; Lakkam, Milinda; Lee, Jason; Li, Jian; Liu, Linxi; Sing-Long, Carlos; Marx, Mike; Mittal, Akshay; Monajemi, Hatef; No, Albert; Omrani, Reza; Pekelis, Leonid; Qin, Junjie; Raines, Kevin; Ryu, Ernest; Saxe, Andrew; Shi, Dai; Siilats, Keith; Strauss, David; Tang, Gary; Wang, Chaojun; Zhou, Zoey; Zhu, Zhen

2013-01-01

In compressed sensing, one takes samples of an N-dimensional vector using an matrix A, obtaining undersampled measurements . For random matrices with independent standard Gaussian entries, it is known that, when is k-sparse, there is a precisely determined phase transition: for a certain region in the (,)-phase diagram, convex optimization typically finds the sparsest solution, whereas outside that region, it typically fails. It has been shown empirically that the same property—with the same phase transition location—holds for a wide range of non-Gaussian random matrix ensembles. We report extensive experiments showing that the Gaussian phase transition also describes numerous deterministic matrices, including Spikes and Sines, Spikes and Noiselets, Paley Frames, Delsarte-Goethals Frames, Chirp Sensing Matrices, and Grassmannian Frames. Namely, for each of these deterministic matrices in turn, for a typical k-sparse object, we observe that convex optimization is successful over a region of the phase diagram that coincides with the region known for Gaussian random matrices. Our experiments considered coefficients constrained to for four different sets , and the results establish our finding for each of the four associated phase transitions. PMID:23277588

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.

PubMed

Kim, Hyunsoo; Park, Haesun

2007-06-15

Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. The software is available as supplementary material.

SPARSKIT: A basic tool kit for sparse matrix computations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1990-01-01

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.

A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory

NASA Astrophysics Data System (ADS)

Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.

2017-09-01

In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory.

PubMed

Lee, M; Leiter, K; Eisner, C; Breuer, A; Wang, X

2017-09-21

In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

Sparse Matrix Software Catalog, Sparse Matrix Symposium 1982, Fairfield Glade, Tennessee, October 24-27, 1982,

DTIC Science & Technology

1982-10-27

are buried within * a much larger, special purpose package. We regret such omissions, but to have reached the practi- tioners in each of the diverse...sparse matrix (form PAQ ) 4. Method of solution: Distribution count sort 5. Programming language: FORTRAN g Precision: Single and double precision 7

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Heber, Gerd; Biswas, Rupak

2000-01-01

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Quantum Support Vector Machine for Big Data Classification

NASA Astrophysics Data System (ADS)

Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth

2014-09-01

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.

Solution of matrix equations using sparse techniques

NASA Technical Reports Server (NTRS)

Baddourah, Majdi

1994-01-01

The solution of large systems of matrix equations is key to the solution of a large number of scientific and engineering problems. This talk describes the sparse matrix solver developed at Langley which can routinely solve in excess of 263,000 equations in 40 seconds on one Cray C-90 processor. It appears that for large scale structural analysis applications, sparse matrix methods have a significant performance advantage over other methods.

Multi-stage classification method oriented to aerial image based on low-rank recovery and multi-feature fusion sparse representation.

PubMed

Ma, Xu; Cheng, Yongmei; Hao, Shuai

2016-12-10

Automatic classification of terrain surfaces from an aerial image is essential for an autonomous unmanned aerial vehicle (UAV) landing at an unprepared site by using vision. Diverse terrain surfaces may show similar spectral properties due to the illumination and noise that easily cause poor classification performance. To address this issue, a multi-stage classification algorithm based on low-rank recovery and multi-feature fusion sparse representation is proposed. First, color moments and Gabor texture feature are extracted from training data and stacked as column vectors of a dictionary. Then we perform low-rank matrix recovery for the dictionary by using augmented Lagrange multipliers and construct a multi-stage terrain classifier. Experimental results on an aerial map database that we prepared verify the classification accuracy and robustness of the proposed method.

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.

Compressed multi-block local binary pattern for object tracking

NASA Astrophysics Data System (ADS)

Li, Tianwen; Gao, Yun; Zhao, Lei; Zhou, Hao

2018-04-01

Both robustness and real-time are very important for the application of object tracking under a real environment. The focused trackers based on deep learning are difficult to satisfy with the real-time of tracking. Compressive sensing provided a technical support for real-time tracking. In this paper, an object can be tracked via a multi-block local binary pattern feature. The feature vector was extracted based on the multi-block local binary pattern feature, which was compressed via a sparse random Gaussian matrix as the measurement matrix. The experiments showed that the proposed tracker ran in real-time and outperformed the existed compressive trackers based on Haar-like feature on many challenging video sequences in terms of accuracy and robustness.

Multi-threaded Sparse Matrix-Matrix Multiplication for Many-Core and GPU Architectures.

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

Deveci, Mehmet; Rajamanickam, Sivasankaran; Trott, Christian Robert

Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scienti c computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we develop parallel algorithms for sparse matrix-matrix multiplication with a focus on performance portability across different high performance computing architectures. The performance of these algorithms depend on the data structures used in them. We compare different types of accumulators in these algorithms and demonstrate the performance difference between these data structures. Furthermore, we develop a meta-algorithm, kkSpGEMM, to choose the right algorithm and datamore » structure based on the characteristics of the problem. We show performance comparisons on three architectures and demonstrate the need for the community to develop two phase sparse matrix-matrix multiplication implementations for efficient reuse of the data structures involved.« less

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.

Margin based ontology sparse vector learning algorithm and applied in biology science.

PubMed

Gao, Wei; Qudair Baig, Abdul; Ali, Haidar; Sajjad, Wasim; Reza Farahani, Mohammad

2017-01-01

In biology field, the ontology application relates to a large amount of genetic information and chemical information of molecular structure, which makes knowledge of ontology concepts convey much information. Therefore, in mathematical notation, the dimension of vector which corresponds to the ontology concept is often very large, and thus improves the higher requirements of ontology algorithm. Under this background, we consider the designing of ontology sparse vector algorithm and application in biology. In this paper, using knowledge of marginal likelihood and marginal distribution, the optimized strategy of marginal based ontology sparse vector learning algorithm is presented. Finally, the new algorithm is applied to gene ontology and plant ontology to verify its efficiency.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer

NASA Astrophysics Data System (ADS)

Wang, Xiao-Gang; Carrington, Tucker

2018-02-01

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer.

PubMed

Wang, Xiao-Gang; Carrington, Tucker

2018-02-21

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Extending R packages to support 64-bit compiled code: An illustration with spam64 and GIMMS NDVI3g data

NASA Astrophysics Data System (ADS)

Gerber, Florian; Mösinger, Kaspar; Furrer, Reinhard

2017-07-01

Software packages for spatial data often implement a hybrid approach of interpreted and compiled programming languages. The compiled parts are usually written in C, C++, or Fortran, and are efficient in terms of computational speed and memory usage. Conversely, the interpreted part serves as a convenient user-interface and calls the compiled code for computationally demanding operations. The price paid for the user friendliness of the interpreted component is-besides performance-the limited access to low level and optimized code. An example of such a restriction is the 64-bit vector support of the widely used statistical language R. On the R side, users do not need to change existing code and may not even notice the extension. On the other hand, interfacing 64-bit compiled code efficiently is challenging. Since many R packages for spatial data could benefit from 64-bit vectors, we investigate strategies to efficiently pass 64-bit vectors to compiled languages. More precisely, we show how to simply extend existing R packages using the foreign function interface to seamlessly support 64-bit vectors. This extension is shown with the sparse matrix algebra R package spam. The new capabilities are illustrated with an example of GIMMS NDVI3g data featuring a parametric modeling approach for a non-stationary covariance matrix.

Sparse Matrix for ECG Identification with Two-Lead Features.

PubMed

Tseng, Kuo-Kun; Luo, Jiao; Hegarty, Robert; Wang, Wenmin; Haiting, Dong

2015-01-01

Electrocardiograph (ECG) human identification has the potential to improve biometric security. However, improvements in ECG identification and feature extraction are required. Previous work has focused on single lead ECG signals. Our work proposes a new algorithm for human identification by mapping two-lead ECG signals onto a two-dimensional matrix then employing a sparse matrix method to process the matrix. And that is the first application of sparse matrix techniques for ECG identification. Moreover, the results of our experiments demonstrate the benefits of our approach over existing methods.

Optical modular arithmetic

NASA Astrophysics Data System (ADS)

Pavlichin, Dmitri S.; Mabuchi, Hideo

2014-06-01

Nanoscale integrated photonic devices and circuits offer a path to ultra-low power computation at the few-photon level. Here we propose an optical circuit that performs a ubiquitous operation: the controlled, random-access readout of a collection of stored memory phases or, equivalently, the computation of the inner product of a vector of phases with a binary selector" vector, where the arithmetic is done modulo 2pi and the result is encoded in the phase of a coherent field. This circuit, a collection of cascaded interferometers driven by a coherent input field, demonstrates the use of coherence as a computational resource, and of the use of recently-developed mathematical tools for modeling optical circuits with many coupled parts. The construction extends in a straightforward way to the computation of matrix-vector and matrix-matrix products, and, with the inclusion of an optical feedback loop, to the computation of a weighted" readout of stored memory phases. We note some applications of these circuits for error correction and for computing tasks requiring fast vector inner products, e.g. statistical classification and some machine learning algorithms.

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. Dale, Jr.

1990-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

High-performance equation solvers and their impact on finite element analysis

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Knight, Norman F., Jr.; Davis, D. D., Jr.

1992-01-01

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Harnessing data structure for recovery of randomly missing structural vibration responses time history: Sparse representation versus low-rank structure

NASA Astrophysics Data System (ADS)

Yang, Yongchao; Nagarajaiah, Satish

2016-06-01

Randomly missing data of structural vibration responses time history often occurs in structural dynamics and health monitoring. For example, structural vibration responses are often corrupted by outliers or erroneous measurements due to sensor malfunction; in wireless sensing platforms, data loss during wireless communication is a common issue. Besides, to alleviate the wireless data sampling or communication burden, certain accounts of data are often discarded during sampling or before transmission. In these and other applications, recovery of the randomly missing structural vibration responses from the available, incomplete data, is essential for system identification and structural health monitoring; it is an ill-posed inverse problem, however. This paper explicitly harnesses the data structure itself-of the structural vibration responses-to address this (inverse) problem. What is relevant is an empirical, but often practically true, observation, that is, typically there are only few modes active in the structural vibration responses; hence a sparse representation (in frequency domain) of the single-channel data vector, or, a low-rank structure (by singular value decomposition) of the multi-channel data matrix. Exploiting such prior knowledge of data structure (intra-channel sparse or inter-channel low-rank), the new theories of ℓ1-minimization sparse recovery and nuclear-norm-minimization low-rank matrix completion enable recovery of the randomly missing or corrupted structural vibration response data. The performance of these two alternatives, in terms of recovery accuracy and computational time under different data missing rates, is investigated on a few structural vibration response data sets-the seismic responses of the super high-rise Canton Tower and the structural health monitoring accelerations of a real large-scale cable-stayed bridge. Encouraging results are obtained and the applicability and limitation of the presented methods are discussed.

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks.

PubMed

Saravanan, Chandra; Shao, Yihan; Baer, Roi; Ross, Philip N; Head-Gordon, Martin

2003-04-15

A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear-scaling methods with atom-centered basis functions. Compared to conventional element-by-element sparse matrix multiplication schemes, efficiency is gained by the use of the highly optimized basic linear algebra subroutines (BLAS). However, some sparsity is lost in the multiatom blocking scheme because these matrix blocks will in general contain negligible elements. As a result, an optimal block size that minimizes the CPU time by balancing these two effects is recovered. In calculations on linear alkanes, polyglycines, estane polymers, and water clusters the optimal block size is found to be between 40 and 100 basis functions, where about 55-75% of the machine peak performance was achieved on an IBM RS6000 workstation. In these calculations, the blocked sparse matrix multiplications can be 10 times faster than a standard element-by-element sparse matrix package. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 618-622, 2003

Massively parallel sparse matrix function calculations with NTPoly

NASA Astrophysics Data System (ADS)

Dawson, William; Nakajima, Takahito

2018-04-01

We present NTPoly, a massively parallel library for computing the functions of sparse, symmetric matrices. The theory of matrix functions is a well developed framework with a wide range of applications including differential equations, graph theory, and electronic structure calculations. One particularly important application area is diagonalization free methods in quantum chemistry. When the input and output of the matrix function are sparse, methods based on polynomial expansions can be used to compute matrix functions in linear time. We present a library based on these methods that can compute a variety of matrix functions. Distributed memory parallelization is based on a communication avoiding sparse matrix multiplication algorithm. OpenMP task parallellization is utilized to implement hybrid parallelization. We describe NTPoly's interface and show how it can be integrated with programs written in many different programming languages. We demonstrate the merits of NTPoly by performing large scale calculations on the K computer.

NoGOA: predicting noisy GO annotations using evidences and sparse representation.

PubMed

Yu, Guoxian; Lu, Chang; Wang, Jun

2017-07-21

Gene Ontology (GO) is a community effort to represent functional features of gene products. GO annotations (GOA) provide functional associations between GO terms and gene products. Due to resources limitation, only a small portion of annotations are manually checked by curators, and the others are electronically inferred. Although quality control techniques have been applied to ensure the quality of annotations, the community consistently report that there are still considerable noisy (or incorrect) annotations. Given the wide application of annotations, however, how to identify noisy annotations is an important but yet seldom studied open problem. We introduce a novel approach called NoGOA to predict noisy annotations. NoGOA applies sparse representation on the gene-term association matrix to reduce the impact of noisy annotations, and takes advantage of sparse representation coefficients to measure the semantic similarity between genes. Secondly, it preliminarily predicts noisy annotations of a gene based on aggregated votes from semantic neighborhood genes of that gene. Next, NoGOA estimates the ratio of noisy annotations for each evidence code based on direct annotations in GOA files archived on different periods, and then weights entries of the association matrix via estimated ratios and propagates weights to ancestors of direct annotations using GO hierarchy. Finally, it integrates evidence-weighted association matrix and aggregated votes to predict noisy annotations. Experiments on archived GOA files of six model species (H. sapiens, A. thaliana, S. cerevisiae, G. gallus, B. Taurus and M. musculus) demonstrate that NoGOA achieves significantly better results than other related methods and removing noisy annotations improves the performance of gene function prediction. The comparative study justifies the effectiveness of integrating evidence codes with sparse representation for predicting noisy GO annotations. Codes and datasets are available at http://mlda.swu.edu.cn/codes.php?name=NoGOA .

Recognition and defect detection of dot-matrix text via variation-model based learning

NASA Astrophysics Data System (ADS)

Ohyama, Wataru; Suzuki, Koushi; Wakabayashi, Tetsushi

2017-03-01

An algorithm for recognition and defect detection of dot-matrix text printed on products is proposed. Extraction and recognition of dot-matrix text contains several difficulties, which are not involved in standard camera-based OCR, that the appearance of dot-matrix characters is corrupted and broken by illumination, complex texture in the background and other standard characters printed on product packages. We propose a dot-matrix text extraction and recognition method which does not require any user interaction. The method employs detected location of corner points and classification score. The result of evaluation experiment using 250 images shows that recall and precision of extraction are 78.60% and 76.03%, respectively. Recognition accuracy of correctly extracted characters is 94.43%. Detecting printing defect of dot-matrix text is also important in the production scene to avoid illegal productions. We also propose a detection method for printing defect of dot-matrix characters. The method constructs a feature vector of which elements are classification scores of each character class and employs support vector machine to classify four types of printing defect. The detection accuracy of the proposed method is 96.68 %.

Disentangling giant component and finite cluster contributions in sparse random matrix spectra.

PubMed

Kühn, Reimer

2016-04-01

We describe a method for disentangling giant component and finite cluster contributions to sparse random matrix spectra, using sparse symmetric random matrices defined on Erdős-Rényi graphs as an example and test bed. Our methods apply to sparse matrices defined in terms of arbitrary graphs in the configuration model class, as long as they have finite mean degree.

On efficient randomized algorithms for finding the PageRank vector

NASA Astrophysics Data System (ADS)

Gasnikov, A. V.; Dmitriev, D. Yu.

2015-03-01

Two randomized methods are considered for finding the PageRank vector; in other words, the solution of the system p T = p T P with a stochastic n × n matrix P, where n ˜ 107-109, is sought (in the class of probability distributions) with accuracy ɛ: ɛ ≫ n -1. Thus, the possibility of brute-force multiplication of P by the column is ruled out in the case of dense objects. The first method is based on the idea of Markov chain Monte Carlo algorithms. This approach is efficient when the iterative process p {/t+1 T} = p {/t T} P quickly reaches a steady state. Additionally, it takes into account another specific feature of P, namely, the nonzero off-diagonal elements of P are equal in rows (this property is used to organize a random walk over the graph with the matrix P). Based on modern concentration-of-measure inequalities, new bounds for the running time of this method are presented that take into account the specific features of P. In the second method, the search for a ranking vector is reduced to finding the equilibrium in the antagonistic matrix game where S n (1) is a unit simplex in ℝ n and I is the identity matrix. The arising problem is solved by applying a slightly modified Grigoriadis-Khachiyan algorithm (1995). This technique, like the Nazin-Polyak method (2009), is a randomized version of Nemirovski's mirror descent method. The difference is that randomization in the Grigoriadis-Khachiyan algorithm is used when the gradient is projected onto the simplex rather than when the stochastic gradient is computed. For sparse matrices P, the method proposed yields noticeably better results.

Efficient Kriging via Fast Matrix-Vector Products

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Raykar, Vikas C.; Duraiswami, Ramani; Mount, David M.

2008-01-01

Interpolating scattered data points is a problem of wide ranging interest. Ordinary kriging is an optimal scattered data estimator, widely used in geosciences and remote sensing. A generalized version of this technique, called cokriging, can be used for image fusion of remotely sensed data. However, it is computationally very expensive for large data sets. We demonstrate the time efficiency and accuracy of approximating ordinary kriging through the use of fast matrixvector products combined with iterative methods. We used methods based on the fast Multipole methods and nearest neighbor searching techniques for implementations of the fast matrix-vector products.

Scalar products of Bethe vectors in models with {\\mathfrak{gl}}(2| 1) symmetry 1. Super-analog of Reshetikhin formula

NASA Astrophysics Data System (ADS)

Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.

2016-11-01

We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing {gl}(2| 1) symmetry. Using explicit formulas of the monodromy matrix entries’ multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with {gl}(1| 1) symmetry. Dedicated to the memory of Petr Petrovich Kulish.

Separable decompositions of bipartite mixed states

NASA Astrophysics Data System (ADS)

Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.

Crystallization of bFGF-DNA Aptamer Complexes Using a Sparse Matrix Designed for Protein-Nucleic Acid Complexes

NASA Technical Reports Server (NTRS)

Cannone, Jaime J.; Barnes, Cindy L.; Achari, Aniruddha; Kundrot, Craig E.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

The Sparse Matrix approach for obtaining lead crystallization conditions has proven to be very fruitful for the crystallization of proteins and nucleic acids. Here we report a Sparse Matrix developed specifically for the crystallization of protein-DNA complexes. This method is rapid and economical, typically requiring 2.5 mg of complex to test 48 conditions. The method was originally developed to crystallize basic fibroblast growth factor (bFGF) complexed with DNA sequences identified through in vitro selection, or SELEX, methods. Two DNA aptamers that bind with approximately nanomolar affinity and inhibit the angiogenic properties of bFGF were selected for co-crystallization. The Sparse Matrix produced lead crystallization conditions for both bFGF-DNA complexes.

High-SNR spectrum measurement based on Hadamard encoding and sparse reconstruction

NASA Astrophysics Data System (ADS)

Wang, Zhaoxin; Yue, Jiang; Han, Jing; Li, Long; Jin, Yong; Gao, Yuan; Li, Baoming

2017-12-01

The denoising capabilities of the H-matrix and cyclic S-matrix based on the sparse reconstruction, employed in the Pixel of Focal Plane Coded Visible Spectrometer for spectrum measurement are investigated, where the spectrum is sparse in a known basis. In the measurement process, the digital micromirror device plays an important role, which implements the Hadamard coding. In contrast with Hadamard transform spectrometry, based on the shift invariability, this spectrometer may have the advantage of a high efficiency. Simulations and experiments show that the nonlinear solution with a sparse reconstruction has a better signal-to-noise ratio than the linear solution and the H-matrix outperforms the cyclic S-matrix whether the reconstruction method is nonlinear or linear.

A fast indirect method to compute functions of genomic relationships concerning genotyped and ungenotyped individuals, for diversity management.

PubMed

Colleau, Jean-Jacques; Palhière, Isabelle; Rodríguez-Ramilo, Silvia T; Legarra, Andres

2017-12-01

Pedigree-based management of genetic diversity in populations, e.g., using optimal contributions, involves computation of the [Formula: see text] type yielding elements (relationships) or functions (usually averages) of relationship matrices. For pedigree-based relationships [Formula: see text], a very efficient method exists. When all the individuals of interest are genotyped, genomic management can be addressed using the genomic relationship matrix [Formula: see text]; however, to date, the computational problem of efficiently computing [Formula: see text] has not been well studied. When some individuals of interest are not genotyped, genomic management should consider the relationship matrix [Formula: see text] that combines genotyped and ungenotyped individuals; however, direct computation of [Formula: see text] is computationally very demanding, because construction of a possibly huge matrix is required. Our work presents efficient ways of computing [Formula: see text] and [Formula: see text], with applications on real data from dairy sheep and dairy goat breeding schemes. For genomic relationships, an efficient indirect computation with quadratic instead of cubic cost is [Formula: see text], where Z is a matrix relating animals to genotypes. For the relationship matrix [Formula: see text], we propose an indirect method based on the difference between vectors [Formula: see text], which involves computation of [Formula: see text] and of products such as [Formula: see text] and [Formula: see text], where [Formula: see text] is a working vector derived from [Formula: see text]. The latter computation is the most demanding but can be done using sparse Cholesky decompositions of matrix [Formula: see text], which allows handling very large genomic and pedigree data files. Studies based on simulations reported in the literature show that the trends of average relationships in [Formula: see text] and [Formula: see text] differ as genomic selection proceeds. When selection is based on genomic relationships but management is based on pedigree data, the true genetic diversity is overestimated. However, our tests on real data from sheep and goat obtained before genomic selection started do not show this. We present efficient methods to compute elements and statistics of the genomic relationships [Formula: see text] and of matrix [Formula: see text] that combines ungenotyped and genotyped individuals. These methods should be useful to monitor and handle genomic diversity.

Solving lattice QCD systems of equations using mixed precision solvers on GPUs

NASA Astrophysics Data System (ADS)

Clark, M. A.; Babich, R.; Barros, K.; Brower, R. C.; Rebbi, C.

2010-09-01

Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodynamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.

Blind compressed sensing image reconstruction based on alternating direction method

NASA Astrophysics Data System (ADS)

Liu, Qinan; Guo, Shuxu

2018-04-01

In order to solve the problem of how to reconstruct the original image under the condition of unknown sparse basis, this paper proposes an image reconstruction method based on blind compressed sensing model. In this model, the image signal is regarded as the product of a sparse coefficient matrix and a dictionary matrix. Based on the existing blind compressed sensing theory, the optimal solution is solved by the alternative minimization method. The proposed method solves the problem that the sparse basis in compressed sensing is difficult to represent, which restrains the noise and improves the quality of reconstructed image. This method ensures that the blind compressed sensing theory has a unique solution and can recover the reconstructed original image signal from a complex environment with a stronger self-adaptability. The experimental results show that the image reconstruction algorithm based on blind compressed sensing proposed in this paper can recover high quality image signals under the condition of under-sampling.

A Tensor Product Formulation of Strassen's Matrix Multiplication Algorithm with Memory Reduction

DOE PAGES

Kumar, B.; Huang, C. -H.; Sadayappan, P.; ...

1995-01-01

In this article, we present a program generation strategy of Strassen's matrix multiplication algorithm using a programming methodology based on tensor product formulas. In this methodology, block recursive programs such as the fast Fourier Transforms and Strassen's matrix multiplication algorithm are expressed as algebraic formulas involving tensor products and other matrix operations. Such formulas can be systematically translated to high-performance parallel/vector codes for various architectures. In this article, we present a nonrecursive implementation of Strassen's algorithm for shared memory vector processors such as the Cray Y-MP. A previous implementation of Strassen's algorithm synthesized from tensor product formulas required working storagemore » of size O(7 n ) for multiplying 2 n × 2 n matrices. We present a modified formulation in which the working storage requirement is reduced to O(4 n ). The modified formulation exhibits sufficient parallelism for efficient implementation on a shared memory multiprocessor. Performance results on a Cray Y-MP8/64 are presented.« less

Adenoviral transduction supports matrix expression of alginate cultured articular chondrocytes.

PubMed

Pohle, D; Kasch, R; Herlyn, P; Bader, R; Mittlmeier, T; Pützer, B M; Müller-Hilke, B

2012-09-01

The present study examines the effects of adenoviral (Ad) transduction of human primary chondrocyte on transgene expression and matrix production. Primary chondrocytes were isolated from healthy articular cartilage and from cartilage with mild osteoarthritis (OA), transduced with an Ad vector and either immediately cultured in alginate or expanded in monolayer before alginate culture. Proteoglycan production was measured using dimethylmethylene blue (DMMB) assay and matrix gene expression was quantified by real-time PCR. Viral infection of primary chondrocytes results in a stable long time transgene expression for up to 13 weeks. Ad transduction does not significantly alter gene expression and matrix production if chondrocytes are immediately embedded in alginate. However, if expanded prior to three dimension (3D) culture in alginate, chondrocytes produce not only more proteoglycans compared to non-transduced controls, but also display an increased anabolic and decreased catabolic activity compared to non-transduced controls. We therefore suggest that successful autologous chondrocyte transplantation (ACT) should combine adenoviral transduction of primary chondrocytes with expansion in monolayer followed by 3D culture. Future studies will be needed to investigate whether the subsequent matrix production can be further improved by using Ad vectors bearing genes encoding matrix proteins. Copyright © 2012 Wiley Periodicals, Inc.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.

PubMed

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L 2 -metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning

PubMed Central

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝd, and the dictionary is learned from the training data using the vector space structure of ℝd and its Euclidean L2-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis. PMID:24129583

ML 3.0 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

ML 3.1 smoothed aggregation user's guide.

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

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-10-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

Self-Taught Learning Based on Sparse Autoencoder for E-Nose in Wound Infection Detection

PubMed Central

He, Peilin; Jia, Pengfei; Qiao, Siqi; Duan, Shukai

2017-01-01

For an electronic nose (E-nose) in wound infection distinguishing, traditional learning methods have always needed large quantities of labeled wound infection samples, which are both limited and expensive; thus, we introduce self-taught learning combined with sparse autoencoder and radial basis function (RBF) into the field. Self-taught learning is a kind of transfer learning that can transfer knowledge from other fields to target fields, can solve such problems that labeled data (target fields) and unlabeled data (other fields) do not share the same class labels, even if they are from entirely different distribution. In our paper, we obtain numerous cheap unlabeled pollutant gas samples (benzene, formaldehyde, acetone and ethylalcohol); however, labeled wound infection samples are hard to gain. Thus, we pose self-taught learning to utilize these gas samples, obtaining a basis vector θ. Then, using the basis vector θ, we reconstruct the new representation of wound infection samples under sparsity constraint, which is the input of classifiers. We compare RBF with partial least squares discriminant analysis (PLSDA), and reach a conclusion that the performance of RBF is superior to others. We also change the dimension of our data set and the quantity of unlabeled data to search the input matrix that produces the highest accuracy. PMID:28991154

Sparse nonnegative matrix factorization with ℓ0-constraints

PubMed Central

Peharz, Robert; Pernkopf, Franz

2012-01-01

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. PMID:22505792

Arrowheaded enhanced multivariance products representation for matrices (AEMPRM): Specifically focusing on infinite matrices and converting arrowheadedness to tridiagonality

NASA Astrophysics Data System (ADS)

Özdemir, Gizem; Demiralp, Metin

2015-12-01

In this work, Enhanced Multivariance Products Representation (EMPR) approach which is a Demiralp-and-his- group extension to the Sobol's High Dimensional Model Representation (HDMR) has been used as the basic tool. Their discrete form have also been developed and used in practice by Demiralp and his group in addition to some other authors for the decomposition of the arrays like vectors, matrices, or multiway arrays. This work specifically focuses on the decomposition of infinite matrices involving denumerable infinitely many rows and columns. To this end the target matrix is first decomposed to the sum of certain outer products and then each outer product is treated by Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) which has been developed by Demiralp and his group. The result is a three-matrix- factor-product whose kernel (the middle factor) is an arrowheaded matrix while the pre and post factors are invertable matrices decomposed of the support vectors of TMEMPR. This new method is called as Arrowheaded Enhanced Multivariance Products Representation for Matrices. The general purpose is approximation of denumerably infinite matrices with the new method.

Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system

NASA Astrophysics Data System (ADS)

Georgakopoulos, A.; Politopoulos, K.; Georgiou, E.

2018-03-01

A new dynamic-system approach to the problem of radiative transfer inside scattering and absorbing media is presented, directly based on first-hand physical principles. This method, the Dynamic Radiative Transfer System (DRTS), employs a dynamical system formality using a global sparse matrix, which characterizes the physical, optical and geometrical properties of the material-volume of interest. The new system state is generated by the above time-independent matrix, using simple matrix-vector multiplication for each subsequent time step. DRTS is capable of calculating accurately the time evolution of photon propagation in media of complex structure and shape. The flexibility of DRTS allows the integration of time-dependent sources, boundary conditions, different media and several optical phenomena like reflection and refraction in a unified and consistent way. Various examples of DRTS simulation results are presented for ultra-fast light pulse 3-D propagation, demonstrating greatly reduced computational cost and resource requirements compared to other methods.

Project APhiD: A Lorenz-gauged A-Φ decomposition for parallelized computation of ultra-broadband electromagnetic induction in a fully heterogeneous Earth

NASA Astrophysics Data System (ADS)

Weiss, Chester J.

2013-08-01

An essential element for computational hypothesis testing, data inversion and experiment design for electromagnetic geophysics is a robust forward solver, capable of easily and quickly evaluating the electromagnetic response of arbitrary geologic structure. The usefulness of such a solver hinges on the balance among competing desires like ease of use, speed of forward calculation, scalability to large problems or compute clusters, parsimonious use of memory access, accuracy and by necessity, the ability to faithfully accommodate a broad range of geologic scenarios over extremes in length scale and frequency content. This is indeed a tall order. The present study addresses recent progress toward the development of a forward solver with these properties. Based on the Lorenz-gauged Helmholtz decomposition, a new finite volume solution over Cartesian model domains endowed with complex-valued electrical properties is shown to be stable over the frequency range 10-2-1010 Hz and range 10-3-105 m in length scale. Benchmark examples are drawn from magnetotellurics, exploration geophysics, geotechnical mapping and laboratory-scale analysis, showing excellent agreement with reference analytic solutions. Computational efficiency is achieved through use of a matrix-free implementation of the quasi-minimum-residual (QMR) iterative solver, which eliminates explicit storage of finite volume matrix elements in favor of "on the fly" computation as needed by the iterative Krylov sequence. Further efficiency is achieved through sparse coupling matrices between the vector and scalar potentials whose non-zero elements arise only in those parts of the model domain where the conductivity gradient is non-zero. Multi-thread parallelization in the QMR solver through OpenMP pragmas is used to reduce the computational cost of its most expensive step: the single matrix-vector product at each iteration. High-level MPI communicators farm independent processes to available compute nodes for simultaneous computation of multi-frequency or multi-transmitter responses.

Overcoming Challenges in Kinetic Modeling of Magnetized Plasmas and Vacuum Electronic Devices

NASA Astrophysics Data System (ADS)

Omelchenko, Yuri; Na, Dong-Yeop; Teixeira, Fernando

2017-10-01

We transform the state-of-the art of plasma modeling by taking advantage of novel computational techniques for fast and robust integration of multiscale hybrid (full particle ions, fluid electrons, no displacement current) and full-PIC models. These models are implemented in 3D HYPERS and axisymmetric full-PIC CONPIC codes. HYPERS is a massively parallel, asynchronous code. The HYPERS solver does not step fields and particles synchronously in time but instead executes local variable updates (events) at their self-adaptive rates while preserving fundamental conservation laws. The charge-conserving CONPIC code has a matrix-free explicit finite-element (FE) solver based on a sparse-approximate inverse (SPAI) algorithm. This explicit solver approximates the inverse FE system matrix (``mass'' matrix) using successive sparsity pattern orders of the original matrix. It does not reduce the set of Maxwell's equations to a vector-wave (curl-curl) equation of second order but instead utilizes the standard coupled first-order Maxwell's system. We discuss the ability of our codes to accurately and efficiently account for multiscale physical phenomena in 3D magnetized space and laboratory plasmas and axisymmetric vacuum electronic devices.

Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.

PubMed

Yang, C L; Wei, H Y; Adler, A; Soleimani, M

2013-06-01

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

Real-Valued Covariance Vector Sparsity-Inducing DOA Estimation for Monostatic MIMO Radar

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Liu, Jing

2015-01-01

In this paper, a real-valued covariance vector sparsity-inducing method for direction of arrival (DOA) estimation is proposed in monostatic multiple-input multiple-output (MIMO) radar. Exploiting the special configuration of monostatic MIMO radar, low-dimensional real-valued received data can be obtained by using the reduced-dimensional transformation and unitary transformation technique. Then, based on the Khatri–Rao product, a real-valued sparse representation framework of the covariance vector is formulated to estimate DOA. Compared to the existing sparsity-inducing DOA estimation methods, the proposed method provides better angle estimation performance and lower computational complexity. Simulation results verify the effectiveness and advantage of the proposed method. PMID:26569241

Real-Valued Covariance Vector Sparsity-Inducing DOA Estimation for Monostatic MIMO Radar.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Liu, Jing

2015-11-10

In this paper, a real-valued covariance vector sparsity-inducing method for direction of arrival (DOA) estimation is proposed in monostatic multiple-input multiple-output (MIMO) radar. Exploiting the special configuration of monostatic MIMO radar, low-dimensional real-valued received data can be obtained by using the reduced-dimensional transformation and unitary transformation technique. Then, based on the Khatri-Rao product, a real-valued sparse representation framework of the covariance vector is formulated to estimate DOA. Compared to the existing sparsity-inducing DOA estimation methods, the proposed method provides better angle estimation performance and lower computational complexity. Simulation results verify the effectiveness and advantage of the proposed method.

Language Recognition via Sparse Coding

DTIC Science & Technology

2016-09-08

a posteriori (MAP) adaptation scheme that further optimizes the discriminative quality of sparse-coded speech fea - tures. We empirically validate the...significantly improve the discriminative quality of sparse-coded speech fea - tures. In Section 4, we evaluate the proposed approaches against an i-vector

Systematic sparse matrix error control for linear scaling electronic structure calculations.

PubMed

Rubensson, Emanuel H; Sałek, Paweł

2005-11-30

Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy. Copyright 2005 Wiley Periodicals, Inc.

Parallel Preconditioning for CFD Problems on the CM-5

NASA Technical Reports Server (NTRS)

Simon, Horst D.; Kremenetsky, Mark D.; Richardson, John; Lasinski, T. A. (Technical Monitor)

1994-01-01

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition.

PubMed

Tang, Xin; Feng, Guo-Can; Li, Xiao-Xin; Cai, Jia-Xin

2015-01-01

Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases.

Learning Low-Rank Class-Specific Dictionary and Sparse Intra-Class Variant Dictionary for Face Recognition

PubMed Central

Tang, Xin; Feng, Guo-can; Li, Xiao-xin; Cai, Jia-xin

2015-01-01

Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases. PMID:26571112

Matrix product representation of the stationary state of the open zero range process

NASA Astrophysics Data System (ADS)

Bertin, Eric; Vanicat, Matthieu

2018-06-01

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

A comparison of SuperLU solvers on the intel MIC architecture

NASA Astrophysics Data System (ADS)

Tuncel, Mehmet; Duran, Ahmet; Celebi, M. Serdar; Akaydin, Bora; Topkaya, Figen O.

2016-10-01

In many science and engineering applications, problems may result in solving a sparse linear system AX=B. For example, SuperLU_MCDT, a linear solver, was used for the large penta-diagonal matrices for 2D problems and hepta-diagonal matrices for 3D problems, coming from the incompressible blood flow simulation (see [1]). It is important to test the status and potential improvements of state-of-the-art solvers on new technologies. In this work, sequential, multithreaded and distributed versions of SuperLU solvers (see [2]) are examined on the Intel Xeon Phi coprocessors using offload programming model at the EURORA cluster of CINECA in Italy. We consider a portfolio of test matrices containing patterned matrices from UFMM ([3]) and randomly located matrices. This architecture can benefit from high parallelism and large vectors. We find that the sequential SuperLU benefited up to 45 % performance improvement from the offload programming depending on the sparse matrix type and the size of transferred and processed data.

Data-driven cluster reinforcement and visualization in sparsely-matched self-organizing maps.

PubMed

Manukyan, Narine; Eppstein, Margaret J; Rizzo, Donna M

2012-05-01

A self-organizing map (SOM) is a self-organized projection of high-dimensional data onto a typically 2-dimensional (2-D) feature map, wherein vector similarity is implicitly translated into topological closeness in the 2-D projection. However, when there are more neurons than input patterns, it can be challenging to interpret the results, due to diffuse cluster boundaries and limitations of current methods for displaying interneuron distances. In this brief, we introduce a new cluster reinforcement (CR) phase for sparsely-matched SOMs. The CR phase amplifies within-cluster similarity in an unsupervised, data-driven manner. Discontinuities in the resulting map correspond to between-cluster distances and are stored in a boundary (B) matrix. We describe a new hierarchical visualization of cluster boundaries displayed directly on feature maps, which requires no further clustering beyond what was implicitly accomplished during self-organization in SOM training. We use a synthetic benchmark problem and previously published microbial community profile data to demonstrate the benefits of the proposed methods.

Assessing Fit of Item Response Models Using the Information Matrix Test

ERIC Educational Resources Information Center

Ranger, Jochen; Kuhn, Jorg-Tobias

2012-01-01

The information matrix can equivalently be determined via the expectation of the Hessian matrix or the expectation of the outer product of the score vector. The identity of these two matrices, however, is only valid in case of a correctly specified model. Therefore, differences between the two versions of the observed information matrix indicate…

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

PubMed

Fan, Jicong; Chow, Tommy W S

2017-09-01

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

General MoM Solutions for Large Arrays

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

Fasenfest, B; Capolino, F; Wilton, D R

2003-07-22

This paper focuses on a numerical procedure that addresses the difficulties of dealing with large, finite arrays while preserving the generality and robustness of full-wave methods. We present a fast method based on approximating interactions between sufficiently separated array elements via a relatively coarse interpolation of the Green's function on a uniform grid commensurate with the array's periodicity. The interaction between the basis and testing functions is reduced to a three-stage process. The first stage is a projection of standard (e.g., RWG) subdomain bases onto a set of interpolation functions that interpolate the Green's function on the array face. Thismore » projection, which is used in a matrix/vector product for each array cell in an iterative solution process, need only be carried out once for a single cell and results in a low-rank matrix. An intermediate stage matrix/vector product computation involving the uniformly sampled Green's function is of convolutional form in the lateral (transverse) directions so that a 2D FFT may be used. The final stage is a third matrix/vector product computation involving a matrix resulting from projecting testing functions onto the Green's function interpolation functions; the low-rank matrix is either identical to (using Galerkin's method) or similar to that for the bases projection. An effective MoM solution scheme is developed for large arrays using a modification of the AIM (Adaptive Integral Method) method. The method permits the analysis of arrays with arbitrary contours and nonplanar elements. Both fill and solve times within the MoM method are improved with respect to more standard MoM solvers.« less

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

Vectorial laws of refraction and reflection using the cross product and dot product.

PubMed

Tkaczyk, Eric R

2012-03-01

We demonstrate that published vectorial laws of reflection and refraction of light based solely on the cross product do not, in general, uniquely determine the direction of the reflected and refracted waves without additional information. This is because the cross product does not have a unique inverse operation, which is explained in this Letter in linear algebra terms. However, a vector is in fact uniquely determined if both the cross product (vector product) and dot product (scalar product) with a known vector are specified, which can be written as a single equation with a left-invertible matrix. It is thus possible to amend the vectorial laws of reflection and refraction to incorporate both the cross and dot products for a complete specification with unique solution. This enables highly efficient, unambiguous computation of reflected and refracted wave vectors from the incident wave and surface normal. © 2012 Optical Society of America

Technique for Solving Electrically Small to Large Structures for Broadband Applications

NASA Technical Reports Server (NTRS)

Jandhyala, Vikram; Chowdhury, Indranil

2011-01-01

Fast iterative algorithms are often used for solving Method of Moments (MoM) systems, having a large number of unknowns, to determine current distribution and other parameters. The most commonly used fast methods include the fast multipole method (FMM), the precorrected fast Fourier transform (PFFT), and low-rank QR compression methods. These methods reduce the O(N) memory and time requirements to O(N log N) by compressing the dense MoM system so as to exploit the physics of Green s Function interactions. FFT-based techniques for solving such problems are efficient for spacefilling and uniform structures, but their performance substantially degrades for non-uniformly distributed structures due to the inherent need to employ a uniform global grid. FMM or QR techniques are better suited than FFT techniques; however, neither the FMM nor the QR technique can be used at all frequencies. This method has been developed to efficiently solve for a desired parameter of a system or device that can include both electrically large FMM elements, and electrically small QR elements. The system or device is set up as an oct-tree structure that can include regions of both the FMM type and the QR type. The system is enclosed with a cube at a 0- th level, splitting the cube at the 0-th level into eight child cubes. This forms cubes at a 1st level, recursively repeating the splitting process for cubes at successive levels until a desired number of levels is created. For each cube that is thus formed, neighbor lists and interaction lists are maintained. An iterative solver is then used to determine a first matrix vector product for any electrically large elements as well as a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large and small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within the predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter. The solution for the desired parameter is then presented to a user in a tangible form; for example, on a display.

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Exploring Deep Learning and Sparse Matrix Format Selection

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

Zhao, Y.; Liao, C.; Shen, X.

We proposed to explore the use of Deep Neural Networks (DNN) for addressing the longstanding barriers. The recent rapid progress of DNN technology has created a large impact in many fields, which has significantly improved the prediction accuracy over traditional machine learning techniques in image classifications, speech recognitions, machine translations, and so on. To some degree, these tasks resemble the decision makings in many HPC tasks, including the aforementioned format selection for SpMV and linear solver selection. For instance, sparse matrix format selection is akin to image classification—such as, to tell whether an image contains a dog or a cat;more » in both problems, the right decisions are primarily determined by the spatial patterns of the elements in an input. For image classification, the patterns are of pixels, and for sparse matrix format selection, they are of non-zero elements. DNN could be naturally applied if we regard a sparse matrix as an image and the format selection or solver selection as classification problems.« less

MGMRES: A generalization of GMRES for solving large sparse nonsymmetric linear systems

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

Young, D.M.; Chen, J.Y.

1994-12-31

The authors are concerned with the solution of the linear system (1): Au = b, where A is a real square nonsingular matrix which is large, sparse and non-symmetric. They consider the use of Krylov subspace methods. They first choose an initial approximation u{sup (0)} to the solution {bar u} = A{sup {minus}1}B of (1). They also choose an auxiliary matrix Z which is nonsingular. For n = 1,2,{hor_ellipsis} they determine u{sup (n)} such that u{sup (n)} {minus} u{sup (0)}{epsilon}K{sub n}(r{sup (0)},A) where K{sub n}(r{sup (0)},A) is the (Krylov) subspace spanned by the Krylov vectors r{sup (0)}, Ar{sup (0)}, {hor_ellipsis},more » A{sup n{minus}1}r{sup 0} and where r{sup (0)} = b{minus}Au{sup (0)}. If ZA is SPD they also require that (u{sup (n)}{minus}{bar u}, ZA(u{sup (n)}{minus}{bar u})) be minimized. If, on the other hand, ZA is not SPD, then they require that the Galerkin condition, (Zr{sup n}, v) = 0, be satisfied for all v{epsilon}K{sub n}(r{sup (0)}, A) where r{sup n} = b{minus}Au{sup (n)}. In this paper the authors consider a generalization of GMRES. This generalized method, which they refer to as `MGMRES`, is very similar to GMRES except that they let Z = A{sup T}Y where Y is a nonsingular matrix which is symmetric by not necessarily SPD.« less

A highly efficient approach to protein interactome mapping based on collaborative filtering framework.

PubMed

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-09

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

PubMed Central

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly. PMID:25572661

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

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

Agarwal, Sapan; Quach, Tu -Thach; Parekh, Ojas

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-basedmore » architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.« less

A Highly Efficient Approach to Protein Interactome Mapping Based on Collaborative Filtering Framework

NASA Astrophysics Data System (ADS)

Luo, Xin; You, Zhuhong; Zhou, Mengchu; Li, Shuai; Leung, Hareton; Xia, Yunni; Zhu, Qingsheng

2015-01-01

The comprehensive mapping of protein-protein interactions (PPIs) is highly desired for one to gain deep insights into both fundamental cell biology processes and the pathology of diseases. Finely-set small-scale experiments are not only very expensive but also inefficient to identify numerous interactomes despite their high accuracy. High-throughput screening techniques enable efficient identification of PPIs; yet the desire to further extract useful knowledge from these data leads to the problem of binary interactome mapping. Network topology-based approaches prove to be highly efficient in addressing this problem; however, their performance deteriorates significantly on sparse putative PPI networks. Motivated by the success of collaborative filtering (CF)-based approaches to the problem of personalized-recommendation on large, sparse rating matrices, this work aims at implementing a highly efficient CF-based approach to binary interactome mapping. To achieve this, we first propose a CF framework for it. Under this framework, we model the given data into an interactome weight matrix, where the feature-vectors of involved proteins are extracted. With them, we design the rescaled cosine coefficient to model the inter-neighborhood similarity among involved proteins, for taking the mapping process. Experimental results on three large, sparse datasets demonstrate that the proposed approach outperforms several sophisticated topology-based approaches significantly.

Energy scaling advantages of resistive memory crossbar based computation and its application to sparse coding

DOE PAGES

Agarwal, Sapan; Quach, Tu -Thach; Parekh, Ojas; ...

2016-01-06

In this study, the exponential increase in data over the last decade presents a significant challenge to analytics efforts that seek to process and interpret such data for various applications. Neural-inspired computing approaches are being developed in order to leverage the computational properties of the analog, low-power data processing observed in biological systems. Analog resistive memory crossbars can perform a parallel read or a vector-matrix multiplication as well as a parallel write or a rank-1 update with high computational efficiency. For an N × N crossbar, these two kernels can be O(N) more energy efficient than a conventional digital memory-basedmore » architecture. If the read operation is noise limited, the energy to read a column can be independent of the crossbar size (O(1)). These two kernels form the basis of many neuromorphic algorithms such as image, text, and speech recognition. For instance, these kernels can be applied to a neural sparse coding algorithm to give an O(N) reduction in energy for the entire algorithm when run with finite precision. Sparse coding is a rich problem with a host of applications including computer vision, object tracking, and more generally unsupervised learning.« less

Sparse Method for Direction of Arrival Estimation Using Denoised Fourth-Order Cumulants Vector.

PubMed

Fan, Yangyu; Wang, Jianshu; Du, Rui; Lv, Guoyun

2018-06-04

Fourth-order cumulants (FOCs) vector-based direction of arrival (DOA) estimation methods of non-Gaussian sources may suffer from poor performance for limited snapshots or difficulty in setting parameters. In this paper, a novel FOCs vector-based sparse DOA estimation method is proposed. Firstly, by utilizing the concept of a fourth-order difference co-array (FODCA), an advanced FOCs vector denoising or dimension reduction procedure is presented for arbitrary array geometries. Then, a novel single measurement vector (SMV) model is established by the denoised FOCs vector, and efficiently solved by an off-grid sparse Bayesian inference (OGSBI) method. The estimation errors of FOCs are integrated in the SMV model, and are approximately estimated in a simple way. A necessary condition regarding the number of identifiable sources of our method is presented that, in order to uniquely identify all sources, the number of sources K must fulfill K ≤ ( M 4 - 2 M 3 + 7 M 2 - 6 M ) / 8 . The proposed method suits any geometry, does not need prior knowledge of the number of sources, is insensitive to associated parameters, and has maximum identifiability O ( M 4 ) , where M is the number of sensors in the array. Numerical simulations illustrate the superior performance of the proposed method.

Communication Optimal Parallel Multiplication of Sparse Random Matrices

DTIC Science & Technology

2013-02-21

Definition 2.1), and (2) the algorithm is sparsity- independent, where the computation is statically partitioned to processors independent of the sparsity...struc- ture of the input matrices (see Definition 2.5). The second assumption applies to nearly all existing al- gorithms for general sparse matrix-matrix...where A and B are n× n ER(d) matrices: Definition 2.1 An ER(d) matrix is an adjacency matrix of an Erdős-Rényi graph with parameters n and d/n. That

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

Chow, Edmond

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

Filtered gradient reconstruction algorithm for compressive spectral imaging

NASA Astrophysics Data System (ADS)

Mejia, Yuri; Arguello, Henry

2017-04-01

Compressive sensing matrices are traditionally based on random Gaussian and Bernoulli entries. Nevertheless, they are subject to physical constraints, and their structure unusually follows a dense matrix distribution, such as the case of the matrix related to compressive spectral imaging (CSI). The CSI matrix represents the integration of coded and shifted versions of the spectral bands. A spectral image can be recovered from CSI measurements by using iterative algorithms for linear inverse problems that minimize an objective function including a quadratic error term combined with a sparsity regularization term. However, current algorithms are slow because they do not exploit the structure and sparse characteristics of the CSI matrices. A gradient-based CSI reconstruction algorithm, which introduces a filtering step in each iteration of a conventional CSI reconstruction algorithm that yields improved image quality, is proposed. Motivated by the structure of the CSI matrix, Φ, this algorithm modifies the iterative solution such that it is forced to converge to a filtered version of the residual ΦTy, where y is the compressive measurement vector. We show that the filtered-based algorithm converges to better quality performance results than the unfiltered version. Simulation results highlight the relative performance gain over the existing iterative algorithms.

Fabric defect detection based on visual saliency using deep feature and low-rank recovery

NASA Astrophysics Data System (ADS)

Liu, Zhoufeng; Wang, Baorui; Li, Chunlei; Li, Bicao; Dong, Yan

2018-04-01

Fabric defect detection plays an important role in improving the quality of fabric product. In this paper, a novel fabric defect detection method based on visual saliency using deep feature and low-rank recovery was proposed. First, unsupervised training is carried out by the initial network parameters based on MNIST large datasets. The supervised fine-tuning of fabric image library based on Convolutional Neural Networks (CNNs) is implemented, and then more accurate deep neural network model is generated. Second, the fabric images are uniformly divided into the image block with the same size, then we extract their multi-layer deep features using the trained deep network. Thereafter, all the extracted features are concentrated into a feature matrix. Third, low-rank matrix recovery is adopted to divide the feature matrix into the low-rank matrix which indicates the background and the sparse matrix which indicates the salient defect. In the end, the iterative optimal threshold segmentation algorithm is utilized to segment the saliency maps generated by the sparse matrix to locate the fabric defect area. Experimental results demonstrate that the feature extracted by CNN is more suitable for characterizing the fabric texture than the traditional LBP, HOG and other hand-crafted features extraction method, and the proposed method can accurately detect the defect regions of various fabric defects, even for the image with complex texture.

Multi scales based sparse matrix spectral clustering image segmentation

NASA Astrophysics Data System (ADS)

Liu, Zhongmin; Chen, Zhicai; Li, Zhanming; Hu, Wenjin

2018-04-01

In image segmentation, spectral clustering algorithms have to adopt the appropriate scaling parameter to calculate the similarity matrix between the pixels, which may have a great impact on the clustering result. Moreover, when the number of data instance is large, computational complexity and memory use of the algorithm will greatly increase. To solve these two problems, we proposed a new spectral clustering image segmentation algorithm based on multi scales and sparse matrix. We devised a new feature extraction method at first, then extracted the features of image on different scales, at last, using the feature information to construct sparse similarity matrix which can improve the operation efficiency. Compared with traditional spectral clustering algorithm, image segmentation experimental results show our algorithm have better degree of accuracy and robustness.

A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method

NASA Astrophysics Data System (ADS)

Barbieri, Ettore; Meo, Michele

2012-05-01

Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, meshfree methods still have significant limitations that prevent their acceptance among researchers and engineers, namely the computational costs. This paper presents an in-depth analysis of computational techniques to speed-up the computation of the shape functions in the Reproducing Kernel Particle Method and Moving Least Squares, with particular focus on their bottlenecks, like the neighbour search, the inversion of the moment matrix and the assembly of the stiffness matrix. The paper presents numerous computational solutions aimed at a considerable reduction of the computational times: the use of kd-trees for the neighbour search, sparse indexing of the nodes-points connectivity and, most importantly, the explicit and vectorized inversion of the moment matrix without using loops and numerical routines.

Effective matrix-free preconditioning for the augmented immersed interface method

NASA Astrophysics Data System (ADS)

Xia, Jianlin; Li, Zhilin; Ye, Xin

2015-12-01

We present effective and efficient matrix-free preconditioning techniques for the augmented immersed interface method (AIIM). AIIM has been developed recently and is shown to be very effective for interface problems and problems on irregular domains. GMRES is often used to solve for the augmented variable(s) associated with a Schur complement A in AIIM that is defined along the interface or the irregular boundary. The efficiency of AIIM relies on how quickly the system for A can be solved. For some applications, there are substantial difficulties involved, such as the slow convergence of GMRES (particularly for free boundary and moving interface problems), and the inconvenience in finding a preconditioner (due to the situation that only the products of A and vectors are available). Here, we propose matrix-free structured preconditioning techniques for AIIM via adaptive randomized sampling, using only the products of A and vectors to construct a hierarchically semiseparable matrix approximation to A. Several improvements over existing schemes are shown so as to enhance the efficiency and also avoid potential instability. The significance of the preconditioners includes: (1) they do not require the entries of A or the multiplication of AT with vectors; (2) constructing the preconditioners needs only O (log ⁡ N) matrix-vector products and O (N) storage, where N is the size of A; (3) applying the preconditioners needs only O (N) flops; (4) they are very flexible and do not require any a priori knowledge of the structure of A. The preconditioners are observed to significantly accelerate the convergence of GMRES, with heuristical justifications of the effectiveness. Comprehensive tests on several important applications are provided, such as Navier-Stokes equations on irregular domains with traction boundary conditions, interface problems in incompressible flows, mixed boundary problems, and free boundary problems. The preconditioning techniques are also useful for several other problems and methods.

An Environmental Data Set for Vector-Borne Disease Modeling and Epidemiology

PubMed Central

Chabot-Couture, Guillaume; Nigmatulina, Karima; Eckhoff, Philip

2014-01-01

Understanding the environmental conditions of disease transmission is important in the study of vector-borne diseases. Low- and middle-income countries bear a significant portion of the disease burden; but data about weather conditions in those countries can be sparse and difficult to reconstruct. Here, we describe methods to assemble high-resolution gridded time series data sets of air temperature, relative humidity, land temperature, and rainfall for such areas; and we test these methods on the island of Madagascar. Air temperature and relative humidity were constructed using statistical interpolation of weather station measurements; the resulting median 95th percentile absolute errors were 2.75°C and 16.6%. Missing pixels from the MODIS11 remote sensing land temperature product were estimated using Fourier decomposition and time-series analysis; thus providing an alternative to the 8-day and 30-day aggregated products. The RFE 2.0 remote sensing rainfall estimator was characterized by comparing it with multiple interpolated rainfall products, and we observed significant differences in temporal and spatial heterogeneity relevant to vector-borne disease modeling. PMID:24755954

SHIP, a novel factor to ameliorate extracellular matrix accumulation via suppressing PI3K/Akt/CTGF signaling in diabetic kidney disease.

PubMed

Li, Fan; Li, Lisha; Cheng, Meijuan; Wang, Xiumin; Hao, Jun; Liu, Shuxia; Duan, Huijun

2017-01-22

Tubular interstitial extracellular matrix accumulation, which plays a key role in the pathogenesis and progression of diabetic kidney disease (DKD), is believed to be mediated by activation of PI3K/Akt signal pathway. However, it is still not clear whether SH2 domain-containing inositol 5'-phosphatase (SHIP), known as a negative regulator of PI3K/Akt pathway is also involved in extracellular matrix metabolism of diabetic kidney. In the present study, decreased SHIP and increased phospho-Akt (Ser 473, Thr 308) were found in renal tubular cells of diabetic mice accompanied by overexpression of connective tissue growth factor (CTGF) and extracellular matrix deposition versus normal mice. Again, high glucose attenuated SHIP expression in a time-dependent manner, concomitant with activation of PI3K/Akt signaling and extracellular matrix production in human renal proximal tubular epithelial cells (HK2) cultured in vitro, which was significantly prevented by transfection of M90-SHIP vector. Furthermore, in vivo delivery of rAd-INPP5D vector (SHIP expression vector) via intraperitoneal injection in diabetic mice increased SHIP expression by 3.36 times followed by 65.26%, 70.38% and 46.71% decreases of phospho-Akt (Ser 473), phospho-Akt (Thr 308) and CTGF expression versus diabetic mice receiving rAd-EGFP vector. Meanwhile, increased renal extracellular matrix accumulation of diabetic mice was also inhibited with intraperitoneal injection of rAd-INPP5D vector. These above data suggested that overexpression of SHIP might be a potent method to lessen renal extracellular matrix accumulation via inactivation of PI3K/Akt pathway and suppression of CTGF expression in DKD. Copyright © 2016 Elsevier Inc. All rights reserved.

Sparse matrix methods based on orthogonality and conjugacy

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1973-01-01

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Improved Success of Sparse Matrix Protein Crystallization Screening with Heterogeneous Nucleating Agents

PubMed Central

Thakur, Anil S.; Robin, Gautier; Guncar, Gregor; Saunders, Neil F. W.; Newman, Janet; Martin, Jennifer L.; Kobe, Bostjan

2007-01-01

Background Crystallization is a major bottleneck in the process of macromolecular structure determination by X-ray crystallography. Successful crystallization requires the formation of nuclei and their subsequent growth to crystals of suitable size. Crystal growth generally occurs spontaneously in a supersaturated solution as a result of homogenous nucleation. However, in a typical sparse matrix screening experiment, precipitant and protein concentration are not sampled extensively, and supersaturation conditions suitable for nucleation are often missed. Methodology/Principal Findings We tested the effect of nine potential heterogenous nucleating agents on crystallization of ten test proteins in a sparse matrix screen. Several nucleating agents induced crystal formation under conditions where no crystallization occurred in the absence of the nucleating agent. Four nucleating agents: dried seaweed; horse hair; cellulose and hydroxyapatite, had a considerable overall positive effect on crystallization success. This effect was further enhanced when these nucleating agents were used in combination with each other. Conclusions/Significance Our results suggest that the addition of heterogeneous nucleating agents increases the chances of crystal formation when using sparse matrix screens. PMID:17971854

A Sparse Bayesian Approach for Forward-Looking Superresolution Radar Imaging

PubMed Central

Zhang, Yin; Zhang, Yongchao; Huang, Yulin; Yang, Jianyu

2017-01-01

This paper presents a sparse superresolution approach for high cross-range resolution imaging of forward-looking scanning radar based on the Bayesian criterion. First, a novel forward-looking signal model is established as the product of the measurement matrix and the cross-range target distribution, which is more accurate than the conventional convolution model. Then, based on the Bayesian criterion, the widely-used sparse regularization is considered as the penalty term to recover the target distribution. The derivation of the cost function is described, and finally, an iterative expression for minimizing this function is presented. Alternatively, this paper discusses how to estimate the single parameter of Gaussian noise. With the advantage of a more accurate model, the proposed sparse Bayesian approach enjoys a lower model error. Meanwhile, when compared with the conventional superresolution methods, the proposed approach shows high cross-range resolution and small location error. The superresolution results for the simulated point target, scene data, and real measured data are presented to demonstrate the superior performance of the proposed approach. PMID:28604583

Dual-scale topology optoelectronic processor.

PubMed

Marsden, G C; Krishnamoorthy, A V; Esener, S C; Lee, S H

1991-12-15

The dual-scale topology optoelectronic processor (D-STOP) is a parallel optoelectronic architecture for matrix algebraic processing. The architecture can be used for matrix-vector multiplication and two types of vector outer product. The computations are performed electronically, which allows multiplication and summation concepts in linear algebra to be generalized to various nonlinear or symbolic operations. This generalization permits the application of D-STOP to many computational problems. The architecture uses a minimum number of optical transmitters, which thereby reduces fabrication requirements while maintaining area-efficient electronics. The necessary optical interconnections are space invariant, minimizing space-bandwidth requirements.

A general parallel sparse-blocked matrix multiply for linear scaling SCF theory

NASA Astrophysics Data System (ADS)

Challacombe, Matt

2000-06-01

A general approach to the parallel sparse-blocked matrix-matrix multiply is developed in the context of linear scaling self-consistent-field (SCF) theory. The data-parallel message passing method uses non-blocking communication to overlap computation and communication. The space filling curve heuristic is used to achieve data locality for sparse matrix elements that decay with “separation”. Load balance is achieved by solving the bin packing problem for blocks with variable size.With this new method as the kernel, parallel performance of the simplified density matrix minimization (SDMM) for solution of the SCF equations is investigated for RHF/6-31G ∗∗ water clusters and RHF/3-21G estane globules. Sustained rates above 5.7 GFLOPS for the SDMM have been achieved for (H 2 O) 200 with 95 Origin 2000 processors. Scalability is found to be limited by load imbalance, which increases with decreasing granularity, due primarily to the inhomogeneous distribution of variable block sizes.

A new implementation of the CMRH method for solving dense linear systems

NASA Astrophysics Data System (ADS)

Heyouni, M.; Sadok, H.

2008-04-01

The CMRH method [H. Sadok, Methodes de projections pour les systemes lineaires et non lineaires, Habilitation thesis, University of Lille1, Lille, France, 1994; H. Sadok, CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm, Numer. Algorithms 20 (1999) 303-321] is an algorithm for solving nonsymmetric linear systems in which the Arnoldi component of GMRES is replaced by the Hessenberg process, which generates Krylov basis vectors which are orthogonal to standard unit basis vectors rather than mutually orthogonal. The iterate is formed from these vectors by solving a small least squares problem involving a Hessenberg matrix. Like GMRES, this method requires one matrix-vector product per iteration. However, it can be implemented to require half as much arithmetic work and less storage. Moreover, numerical experiments show that this method performs accurately and reduces the residual about as fast as GMRES. With this new implementation, we show that the CMRH method is the only method with long-term recurrence which requires not storing at the same time the entire Krylov vectors basis and the original matrix as in the GMRES algorithmE A comparison with Gaussian elimination is provided.

High-performance sparse matrix-matrix products on Intel KNL and multicore architectures

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

Nagasaka, Y; Matsuoka, S; Azad, A

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. We firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting multi- and many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. Wemore » examine their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. A critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix.« less

Multidimensional Compressed Sensing MRI Using Tensor Decomposition-Based Sparsifying Transform

PubMed Central

Yu, Yeyang; Jin, Jin; Liu, Feng; Crozier, Stuart

2014-01-01

Compressed Sensing (CS) has been applied in dynamic Magnetic Resonance Imaging (MRI) to accelerate the data acquisition without noticeably degrading the spatial-temporal resolution. A suitable sparsity basis is one of the key components to successful CS applications. Conventionally, a multidimensional dataset in dynamic MRI is treated as a series of two-dimensional matrices, and then various matrix/vector transforms are used to explore the image sparsity. Traditional methods typically sparsify the spatial and temporal information independently. In this work, we propose a novel concept of tensor sparsity for the application of CS in dynamic MRI, and present the Higher-order Singular Value Decomposition (HOSVD) as a practical example. Applications presented in the three- and four-dimensional MRI data demonstrate that HOSVD simultaneously exploited the correlations within spatial and temporal dimensions. Validations based on cardiac datasets indicate that the proposed method achieved comparable reconstruction accuracy with the low-rank matrix recovery methods and, outperformed the conventional sparse recovery methods. PMID:24901331

AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

NASA Technical Reports Server (NTRS)

Klumpp, A. R.

1994-01-01

This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

Framework to trade optimality for local processing in large-scale wavefront reconstruction problems.

PubMed

Haber, Aleksandar; Verhaegen, Michel

2016-11-15

We show that the minimum variance wavefront estimation problems permit localized approximate solutions, in the sense that the wavefront value at a point (excluding unobservable modes, such as the piston mode) can be approximated by a linear combination of the wavefront slope measurements in the point's neighborhood. This enables us to efficiently compute a wavefront estimate by performing a single sparse matrix-vector multiplication. Moreover, our results open the possibility for the development of wavefront estimators that can be easily implemented in a decentralized/distributed manner, and in which the estimate optimality can be easily traded for computational efficiency. We numerically validate our approach on Hudgin wavefront sensor geometries, and the results can be easily generalized to Fried geometries.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

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

Spotz, William F.

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of themore » underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.« less

A multiple hold-out framework for Sparse Partial Least Squares.

PubMed

Monteiro, João M; Rao, Anil; Shawe-Taylor, John; Mourão-Miranda, Janaina

2016-09-15

Supervised classification machine learning algorithms may have limitations when studying brain diseases with heterogeneous populations, as the labels might be unreliable. More exploratory approaches, such as Sparse Partial Least Squares (SPLS), may provide insights into the brain's mechanisms by finding relationships between neuroimaging and clinical/demographic data. The identification of these relationships has the potential to improve the current understanding of disease mechanisms, refine clinical assessment tools, and stratify patients. SPLS finds multivariate associative effects in the data by computing pairs of sparse weight vectors, where each pair is used to remove its corresponding associative effect from the data by matrix deflation, before computing additional pairs. We propose a novel SPLS framework which selects the adequate number of voxels and clinical variables to describe each associative effect, and tests their reliability by fitting the model to different splits of the data. As a proof of concept, the approach was applied to find associations between grey matter probability maps and individual items of the Mini-Mental State Examination (MMSE) in a clinical sample with various degrees of dementia. The framework found two statistically significant associative effects between subsets of brain voxels and subsets of the questions/tasks. SPLS was compared with its non-sparse version (PLS). The use of projection deflation versus a classical PLS deflation was also tested in both PLS and SPLS. SPLS outperformed PLS, finding statistically significant effects and providing higher correlation values in hold-out data. Moreover, projection deflation provided better results. Copyright © 2016 The Author(s). Published by Elsevier B.V. All rights reserved.

Removal of envelope protein-free retroviral vectors by anion-exchange chromatography to improve product quality.

PubMed

Rodrigues, Teresa; Alves, Ana; Lopes, António; Carrondo, Manuel J T; Alves, Paula M; Cruz, Pedro E

2008-10-01

We have investigated the role of the retroviral lipid bilayer and envelope proteins in the adsorption of retroviral vectors (RVs) to a Fractogel DEAE matrix. Intact RVs and their degradation components (envelope protein-free vectors and solubilized vector components) were adsorbed to this matrix and eluted using a linear gradient. Envelope protein-free RVs (Env(-)) and soluble envelope proteins (gp70) eluted in a significantly lower range of conductivities than intact RVs (Env(+)) (13.7-30 mS/cm for Env(-) and gp70 proteins vs. 47-80 mS/cm for Env(+)). The zeta (zeta)-potential of Env(+) and Env(-) vectors was evaluated showing that envelope proteins define the pI of the viral particles (pI (Env(+)) < 2 versus 3 < pI (Env(-)) < 4) and that Env(+) and Env(-) vectors have similar zeta-potentials within pH 5 and 8. The results presented herein indicate that the adsorption of retroviral particles occurs through multi-point interaction of the envelope proteins with the cationic groups on the chromatographic matrix. The strength of this adsorption is thus dependent on the amount of envelope protein present in the viral lipid bilayer. In conclusion, AEXc enables the separation of gp70 proteins as well as envelope protein-free vectors constituting a significant improvement to the quality of retroviral preparations for gene therapy applications.

Fast iterative image reconstruction using sparse matrix factorization with GPU acceleration

NASA Astrophysics Data System (ADS)

Zhou, Jian; Qi, Jinyi

2011-03-01

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

Face recognition via sparse representation of SIFT feature on hexagonal-sampling image

NASA Astrophysics Data System (ADS)

Zhang, Daming; Zhang, Xueyong; Li, Lu; Liu, Huayong

2018-04-01

This paper investigates a face recognition approach based on Scale Invariant Feature Transform (SIFT) feature and sparse representation. The approach takes advantage of SIFT which is local feature other than holistic feature in classical Sparse Representation based Classification (SRC) algorithm and possesses strong robustness to expression, pose and illumination variations. Since hexagonal image has more inherit merits than square image to make recognition process more efficient, we extract SIFT keypoint in hexagonal-sampling image. Instead of matching SIFT feature, firstly the sparse representation of each SIFT keypoint is given according the constructed dictionary; secondly these sparse vectors are quantized according dictionary; finally each face image is represented by a histogram and these so-called Bag-of-Words vectors are classified by SVM. Due to use of local feature, the proposed method achieves better result even when the number of training sample is small. In the experiments, the proposed method gave higher face recognition rather than other methods in ORL and Yale B face databases; also, the effectiveness of the hexagonal-sampling in the proposed method is verified.

Land use and land cover classification for rural residential areas in China using soft-probability cascading of multifeatures

NASA Astrophysics Data System (ADS)

Zhang, Bin; Liu, Yueyan; Zhang, Zuyu; Shen, Yonglin

2017-10-01

A multifeature soft-probability cascading scheme to solve the problem of land use and land cover (LULC) classification using high-spatial-resolution images to map rural residential areas in China is proposed. The proposed method is used to build midlevel LULC features. Local features are frequently considered as low-level feature descriptors in a midlevel feature learning method. However, spectral and textural features, which are very effective low-level features, are neglected. The acquisition of the dictionary of sparse coding is unsupervised, and this phenomenon reduces the discriminative power of the midlevel feature. Thus, we propose to learn supervised features based on sparse coding, a support vector machine (SVM) classifier, and a conditional random field (CRF) model to utilize the different effective low-level features and improve the discriminability of midlevel feature descriptors. First, three kinds of typical low-level features, namely, dense scale-invariant feature transform, gray-level co-occurrence matrix, and spectral features, are extracted separately. Second, combined with sparse coding and the SVM classifier, the probabilities of the different LULC classes are inferred to build supervised feature descriptors. Finally, the CRF model, which consists of two parts: unary potential and pairwise potential, is employed to construct an LULC classification map. Experimental results show that the proposed classification scheme can achieve impressive performance when the total accuracy reached about 87%.

An Efficient Scheme for Updating Sparse Cholesky Factors

NASA Technical Reports Server (NTRS)

Raghavan, Padma

2002-01-01

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Cost Study of Educational Media Systems and Their Equipment Components. Volume II, Technical Report. Final Report.

ERIC Educational Resources Information Center

General Learning Corp., Washington, DC.

A common instructional task and a set of educational environments are hypothesized for analysis of media cost data. The analytic structure may be conceptulized as a three-dimensional matrix: the first vector separates costs into production, distribution, and reception; the second vector delineates capital (initial) and operating (annual) costs;…

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure.

PubMed

Mozrzymas, Anna

2011-12-14

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant. Copyright © 2011 Elsevier Ltd. All rights reserved.

An adaptive sparse deconvolution method for distinguishing the overlapping echoes of ultrasonic guided waves for pipeline crack inspection

NASA Astrophysics Data System (ADS)

Chang, Yong; Zi, Yanyang; Zhao, Jiyuan; Yang, Zhe; He, Wangpeng; Sun, Hailiang

2017-03-01

In guided wave pipeline inspection, echoes reflected from closely spaced reflectors generally overlap, meaning useful information is lost. To solve the overlapping problem, sparse deconvolution methods have been developed in the past decade. However, conventional sparse deconvolution methods have limitations in handling guided wave signals, because the input signal is directly used as the prototype of the convolution matrix, without considering the waveform change caused by the dispersion properties of the guided wave. In this paper, an adaptive sparse deconvolution (ASD) method is proposed to overcome these limitations. First, the Gaussian echo model is employed to adaptively estimate the column prototype of the convolution matrix instead of directly using the input signal as the prototype. Then, the convolution matrix is constructed upon the estimated results. Third, the split augmented Lagrangian shrinkage (SALSA) algorithm is introduced to solve the deconvolution problem with high computational efficiency. To verify the effectiveness of the proposed method, guided wave signals obtained from pipeline inspection are investigated numerically and experimentally. Compared to conventional sparse deconvolution methods, e.g. the {{l}1} -norm deconvolution method, the proposed method shows better performance in handling the echo overlap problem in the guided wave signal.

Robust extraction of basis functions for simultaneous and proportional myoelectric control via sparse non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Lin, Chuang; Wang, Binghui; Jiang, Ning; Farina, Dario

2018-04-01

Objective. This paper proposes a novel simultaneous and proportional multiple degree of freedom (DOF) myoelectric control method for active prostheses. Approach. The approach is based on non-negative matrix factorization (NMF) of surface EMG signals with the inclusion of sparseness constraints. By applying a sparseness constraint to the control signal matrix, it is possible to extract the basis information from arbitrary movements (quasi-unsupervised approach) for multiple DOFs concurrently. Main Results. In online testing based on target hitting, able-bodied subjects reached a greater throughput (TP) when using sparse NMF (SNMF) than with classic NMF or with linear regression (LR). Accordingly, the completion time (CT) was shorter for SNMF than NMF or LR. The same observations were made in two patients with unilateral limb deficiencies. Significance. The addition of sparseness constraints to NMF allows for a quasi-unsupervised approach to myoelectric control with superior results with respect to previous methods for the simultaneous and proportional control of multi-DOF. The proposed factorization algorithm allows robust simultaneous and proportional control, is superior to previous supervised algorithms, and, because of minimal supervision, paves the way to online adaptation in myoelectric control.

Sparse PCA with Oracle Property.

PubMed

Gu, Quanquan; Wang, Zhaoran; Liu, Han

In this paper, we study the estimation of the k -dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank- k , and attains a [Formula: see text] statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

Sparse PCA with Oracle Property

PubMed Central

Gu, Quanquan; Wang, Zhaoran; Liu, Han

2014-01-01

In this paper, we study the estimation of the k-dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-k, and attains a s/n statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets. PMID:25684971

Effects of partitioning and scheduling sparse matrix factorization on communication and load balance

NASA Technical Reports Server (NTRS)

Venugopal, Sesh; Naik, Vijay K.

1991-01-01

A block based, automatic partitioning and scheduling methodology is presented for sparse matrix factorization on distributed memory systems. Using experimental results, this technique is analyzed for communication and load imbalance overhead. To study the performance effects, these overheads were compared with those obtained from a straightforward 'wrap mapped' column assignment scheme. All experimental results were obtained using test sparse matrices from the Harwell-Boeing data set. The results show that there is a communication and load balance tradeoff. The block based method results in lower communication cost whereas the wrap mapped scheme gives better load balance.

Some Correlation Functions in Matrix Product Ground States of One-Dimensional Two-State Chains

NASA Astrophysics Data System (ADS)

Shariati, Ahmad; Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad

2014-04-01

Consider one-dimensional chains with nearest neighbour interactions, for which to each site correspond two independent states (say up and down), and the ground state is a matrix product state. It has been shown [23] that for such systems, the ground states are linear combinations of specific vectors which are essentially direct products of specific numbers of ups and downs, symmetrized in a generalized manner. By a generalized manner, it is meant that the coefficient corresponding to the interchange of states of two sites, in not necessarily plus one or minus one, but a phase which depends on the Hamiltonian and the position of the two sites. Such vectors are characterized by a phase χ, the N-th power of which is one (where N is the number of sites), and an integer. Corresponding to χ, there is another integer M which is the smallest positive integer that χM is one. Two classes of correlation functions for such systems (basically correlation functions for such vectors) are calculated. The first class consists of correlation functions of tensor products of one-site diagonal observables; the second class consists of correlation functions of tensor products of less than M one-site observables (but not necessarily diagonal).

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory.

PubMed

Coriani, Sonia; Høst, Stinne; Jansík, Branislav; Thøgersen, Lea; Olsen, Jeppe; Jørgensen, Poul; Reine, Simen; Pawłowski, Filip; Helgaker, Trygve; Sałek, Paweł

2007-04-21

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

Numerical Modeling of Nanoelectronic Devices

NASA Technical Reports Server (NTRS)

Klimeck, Gerhard; Oyafuso, Fabiano; Bowen, R. Chris; Boykin, Timothy

2003-01-01

Nanoelectronic Modeling 3-D (NEMO 3-D) is a computer program for numerical modeling of the electronic structure properties of a semiconductor device that is embodied in a crystal containing as many as 16 million atoms in an arbitrary configuration and that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantummechanical behavior of the device resolved to the atomistic level of granularity. The system of electrons in the device is represented by a sparse Hamiltonian matrix that contains hundreds of millions of terms. NEMO 3-D solves the matrix equation on a Beowulf-class cluster computer, by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. In a recent update of NEMO 3-D, a new strain treatment, parameterized for bulk material properties of GaAs and InAs, was developed for two tight-binding submodels. The utility of the NEMO 3-D was demonstrated in an atomistic analysis of the effects of disorder in alloys and, in particular, in bulk In(x)Ga(l-x)As and in In0.6Ga0.4As quantum dots.

FoSSI: the family of simplified solver interfaces for the rapid development of parallel numerical atmosphere and ocean models

NASA Astrophysics Data System (ADS)

Frickenhaus, Stephan; Hiller, Wolfgang; Best, Meike

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fast solver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under the name ScOPES: the Scalable Open Parallel sparse linear Equations Solver.

Finding a Hadamard matrix by simulated annealing of spin vectors

NASA Astrophysics Data System (ADS)

Bayu Suksmono, Andriyan

2017-05-01

Reformulation of a combinatorial problem into optimization of a statistical-mechanics system enables finding a better solution using heuristics derived from a physical process, such as by the simulated annealing (SA). In this paper, we present a Hadamard matrix (H-matrix) searching method based on the SA on an Ising model. By equivalence, an H-matrix can be converted into a seminormalized Hadamard (SH) matrix, whose first column is unit vector and the rest ones are vectors with equal number of -1 and +1 called SH-vectors. We define SH spin vectors as representation of the SH vectors, which play a similar role as the spins on Ising model. The topology of the lattice is generalized into a graph, whose edges represent orthogonality relationship among the SH spin vectors. Starting from a randomly generated quasi H-matrix Q, which is a matrix similar to the SH-matrix without imposing orthogonality, we perform the SA. The transitions of Q are conducted by random exchange of {+, -} spin-pair within the SH-spin vectors that follow the Metropolis update rule. Upon transition toward zeroth energy, the Q-matrix is evolved following a Markov chain toward an orthogonal matrix, at which the H-matrix is said to be found. We demonstrate the capability of the proposed method to find some low-order H-matrices, including the ones that cannot trivially be constructed by the Sylvester method.

Full-reference quality assessment of stereoscopic images by learning binocular receptive field properties.

PubMed

Shao, Feng; Li, Kemeng; Lin, Weisi; Jiang, Gangyi; Yu, Mei; Dai, Qionghai

2015-10-01

Quality assessment of 3D images encounters more challenges than its 2D counterparts. Directly applying 2D image quality metrics is not the solution. In this paper, we propose a new full-reference quality assessment for stereoscopic images by learning binocular receptive field properties to be more in line with human visual perception. To be more specific, in the training phase, we learn a multiscale dictionary from the training database, so that the latent structure of images can be represented as a set of basis vectors. In the quality estimation phase, we compute sparse feature similarity index based on the estimated sparse coefficient vectors by considering their phase difference and amplitude difference, and compute global luminance similarity index by considering luminance changes. The final quality score is obtained by incorporating binocular combination based on sparse energy and sparse complexity. Experimental results on five public 3D image quality assessment databases demonstrate that in comparison with the most related existing methods, the devised algorithm achieves high consistency with subjective assessment.

Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships

USGS Publications Warehouse

Archer, A.W.; Maples, C.G.

1989-01-01

Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.

Sparse representation of whole-brain fMRI signals for identification of functional networks.

PubMed

Lv, Jinglei; Jiang, Xi; Li, Xiang; Zhu, Dajiang; Chen, Hanbo; Zhang, Tuo; Zhang, Shu; Hu, Xintao; Han, Junwei; Huang, Heng; Zhang, Jing; Guo, Lei; Liu, Tianming

2015-02-01

There have been several recent studies that used sparse representation for fMRI signal analysis and activation detection based on the assumption that each voxel's fMRI signal is linearly composed of sparse components. Previous studies have employed sparse coding to model functional networks in various modalities and scales. These prior contributions inspired the exploration of whether/how sparse representation can be used to identify functional networks in a voxel-wise way and on the whole brain scale. This paper presents a novel, alternative methodology of identifying multiple functional networks via sparse representation of whole-brain task-based fMRI signals. Our basic idea is that all fMRI signals within the whole brain of one subject are aggregated into a big data matrix, which is then factorized into an over-complete dictionary basis matrix and a reference weight matrix via an effective online dictionary learning algorithm. Our extensive experimental results have shown that this novel methodology can uncover multiple functional networks that can be well characterized and interpreted in spatial, temporal and frequency domains based on current brain science knowledge. Importantly, these well-characterized functional network components are quite reproducible in different brains. In general, our methods offer a novel, effective and unified solution to multiple fMRI data analysis tasks including activation detection, de-activation detection, and functional network identification. Copyright © 2014 Elsevier B.V. All rights reserved.

Solution of nonlinear time-dependent PDEs through componentwise approximation of matrix functions

NASA Astrophysics Data System (ADS)

Cibotarica, Alexandru; Lambers, James V.; Palchak, Elisabeth M.

2016-09-01

Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODEs, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this paper, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. Numerical experiments demonstrate that this modification causes the number of Krylov projection steps to become bounded independently of the grid size, thus dramatically improving efficiency and scalability. As a result, for each test problem featured, as the total number of grid points increases, the growth in computation time is just below linear, while other methods achieved this only on selected test problems or not at all.

An alternative design for a sparse distributed memory

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1989-01-01

A new design for a Sparse Distributed Memory, called the selected-coordinate design, is described. As in the original design, there are a large number of memory locations, each of which may be activated by many different addresses (binary vectors) in a very large address space. Each memory location is defined by specifying ten selected coordinates (bit positions in the address vectors) and a set of corresponding assigned values, consisting of one bit for each selected coordinate. A memory location is activated by an address if, for all ten of the locations's selected coordinates, the corresponding bits in the address vector match the respective assigned value bits, regardless of the other bits in the address vector. Some comparative memory capacity and signal-to-noise ratio estimates for the both the new and original designs are given. A few possible hardware embodiments of the new design are described.

Salient Object Detection via Structured Matrix Decomposition.

PubMed

Peng, Houwen; Li, Bing; Ling, Haibin; Hu, Weiming; Xiong, Weihua; Maybank, Stephen J

2016-05-04

Low-rank recovery models have shown potential for salient object detection, where a matrix is decomposed into a low-rank matrix representing image background and a sparse matrix identifying salient objects. Two deficiencies, however, still exist. First, previous work typically assumes the elements in the sparse matrix are mutually independent, ignoring the spatial and pattern relations of image regions. Second, when the low-rank and sparse matrices are relatively coherent, e.g., when there are similarities between the salient objects and background or when the background is complicated, it is difficult for previous models to disentangle them. To address these problems, we propose a novel structured matrix decomposition model with two structural regularizations: (1) a tree-structured sparsity-inducing regularization that captures the image structure and enforces patches from the same object to have similar saliency values, and (2) a Laplacian regularization that enlarges the gaps between salient objects and the background in feature space. Furthermore, high-level priors are integrated to guide the matrix decomposition and boost the detection. We evaluate our model for salient object detection on five challenging datasets including single object, multiple objects and complex scene images, and show competitive results as compared with 24 state-of-the-art methods in terms of seven performance metrics.

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, W. R.; Nguyen, D. T.; Reddy, C. J.; Vatsa, V. N.; Tang, W. H.

2001-01-01

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Visual Tracking Based on Extreme Learning Machine and Sparse Representation

PubMed Central

Wang, Baoxian; Tang, Linbo; Yang, Jinglin; Zhao, Baojun; Wang, Shuigen

2015-01-01

The existing sparse representation-based visual trackers mostly suffer from both being time consuming and having poor robustness problems. To address these issues, a novel tracking method is presented via combining sparse representation and an emerging learning technique, namely extreme learning machine (ELM). Specifically, visual tracking can be divided into two consecutive processes. Firstly, ELM is utilized to find the optimal separate hyperplane between the target observations and background ones. Thus, the trained ELM classification function is able to remove most of the candidate samples related to background contents efficiently, thereby reducing the total computational cost of the following sparse representation. Secondly, to further combine ELM and sparse representation, the resultant confidence values (i.e., probabilities to be a target) of samples on the ELM classification function are used to construct a new manifold learning constraint term of the sparse representation framework, which tends to achieve robuster results. Moreover, the accelerated proximal gradient method is used for deriving the optimal solution (in matrix form) of the constrained sparse tracking model. Additionally, the matrix form solution allows the candidate samples to be calculated in parallel, thereby leading to a higher efficiency. Experiments demonstrate the effectiveness of the proposed tracker. PMID:26506359

An Improved Compressive Sensing and Received Signal Strength-Based Target Localization Algorithm with Unknown Target Population for Wireless Local Area Networks.

PubMed

Yan, Jun; Yu, Kegen; Chen, Ruizhi; Chen, Liang

2017-05-30

In this paper a two-phase compressive sensing (CS) and received signal strength (RSS)-based target localization approach is proposed to improve position accuracy by dealing with the unknown target population and the effect of grid dimensions on position error. In the coarse localization phase, by formulating target localization as a sparse signal recovery problem, grids with recovery vector components greater than a threshold are chosen as the candidate target grids. In the fine localization phase, by partitioning each candidate grid, the target position in a grid is iteratively refined by using the minimum residual error rule and the least-squares technique. When all the candidate target grids are iteratively partitioned and the measurement matrix is updated, the recovery vector is re-estimated. Threshold-based detection is employed again to determine the target grids and hence the target population. As a consequence, both the target population and the position estimation accuracy can be significantly improved. Simulation results demonstrate that the proposed approach achieves the best accuracy among all the algorithms compared.

Automatic segmentation of right ventricle on ultrasound images using sparse matrix transform and level set

NASA Astrophysics Data System (ADS)

Qin, Xulei; Cong, Zhibin; Halig, Luma V.; Fei, Baowei

2013-03-01

An automatic framework is proposed to segment right ventricle on ultrasound images. This method can automatically segment both epicardial and endocardial boundaries from a continuous echocardiography series by combining sparse matrix transform (SMT), a training model, and a localized region based level set. First, the sparse matrix transform extracts main motion regions of myocardium as eigenimages by analyzing statistical information of these images. Second, a training model of right ventricle is registered to the extracted eigenimages in order to automatically detect the main location of the right ventricle and the corresponding transform relationship between the training model and the SMT-extracted results in the series. Third, the training model is then adjusted as an adapted initialization for the segmentation of each image in the series. Finally, based on the adapted initializations, a localized region based level set algorithm is applied to segment both epicardial and endocardial boundaries of the right ventricle from the whole series. Experimental results from real subject data validated the performance of the proposed framework in segmenting right ventricle from echocardiography. The mean Dice scores for both epicardial and endocardial boundaries are 89.1%+/-2.3% and 83.6+/-7.3%, respectively. The automatic segmentation method based on sparse matrix transform and level set can provide a useful tool for quantitative cardiac imaging.

Robust Principal Component Analysis Regularized by Truncated Nuclear Norm for Identifying Differentially Expressed Genes.

PubMed

Wang, Ya-Xuan; Gao, Ying-Lian; Liu, Jin-Xing; Kong, Xiang-Zhen; Li, Hai-Jun

2017-09-01

Identifying differentially expressed genes from the thousands of genes is a challenging task. Robust principal component analysis (RPCA) is an efficient method in the identification of differentially expressed genes. RPCA method uses nuclear norm to approximate the rank function. However, theoretical studies showed that the nuclear norm minimizes all singular values, so it may not be the best solution to approximate the rank function. The truncated nuclear norm is defined as the sum of some smaller singular values, which may achieve a better approximation of the rank function than nuclear norm. In this paper, a novel method is proposed by replacing nuclear norm of RPCA with the truncated nuclear norm, which is named robust principal component analysis regularized by truncated nuclear norm (TRPCA). The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Thus, the differentially expressed genes can be identified according to the sparse matrix. The experimental results on The Cancer Genome Atlas data illustrate that the TRPCA method outperforms other state-of-the-art methods in the identification of differentially expressed genes.

Speckle noise reduction for optical coherence tomography based on adaptive 2D dictionary

NASA Astrophysics Data System (ADS)

Lv, Hongli; Fu, Shujun; Zhang, Caiming; Zhai, Lin

2018-05-01

As a high-resolution biomedical imaging modality, optical coherence tomography (OCT) is widely used in medical sciences. However, OCT images often suffer from speckle noise, which can mask some important image information, and thus reduce the accuracy of clinical diagnosis. Taking full advantage of nonlocal self-similarity and adaptive 2D-dictionary-based sparse representation, in this work, a speckle noise reduction algorithm is proposed for despeckling OCT images. To reduce speckle noise while preserving local image features, similar nonlocal patches are first extracted from the noisy image and put into groups using a gamma- distribution-based block matching method. An adaptive 2D dictionary is then learned for each patch group. Unlike traditional vector-based sparse coding, we express each image patch by the linear combination of a few matrices. This image-to-matrix method can exploit the local correlation between pixels. Since each image patch might belong to several groups, the despeckled OCT image is finally obtained by aggregating all filtered image patches. The experimental results demonstrate the superior performance of the proposed method over other state-of-the-art despeckling methods, in terms of objective metrics and visual inspection.

Sparse Regression as a Sparse Eigenvalue Problem

NASA Technical Reports Server (NTRS)

Moghaddam, Baback; Gruber, Amit; Weiss, Yair; Avidan, Shai

2008-01-01

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

HYPOTHESIS TESTING FOR HIGH-DIMENSIONAL SPARSE BINARY REGRESSION

PubMed Central

Mukherjee, Rajarshi; Pillai, Natesh S.; Lin, Xihong

2015-01-01

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection boundary as a function of two components: a design matrix sparsity index and signal strength, each of which is a function of the sparsity of the alternative. For any alternative, if the design matrix sparsity index is too high, any test is asymptotically powerless irrespective of the magnitude of signal strength. For binary design matrices with the sparsity index that is not too high, our results are parallel to those in the Gaussian case. In this context, we derive detection boundaries for both dense and sparse regimes. For the dense regime, we show that the generalized likelihood ratio is rate optimal; for the sparse regime, we propose an extended Higher Criticism Test and show it is rate optimal and sharp. We illustrate the finite sample properties of the theoretical results using simulation studies. PMID:26246645

Sparse regularization for force identification using dictionaries

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Wang, Chenxi; Zhang, Hang; Chen, Xuefeng

2016-04-01

The classical function expansion method based on minimizing l2-norm of the response residual employs various basis functions to represent the unknown force. Its difficulty lies in determining the optimum number of basis functions. Considering the sparsity of force in the time domain or in other basis space, we develop a general sparse regularization method based on minimizing l1-norm of the coefficient vector of basis functions. The number of basis functions is adaptively determined by minimizing the number of nonzero components in the coefficient vector during the sparse regularization process. First, according to the profile of the unknown force, the dictionary composed of basis functions is determined. Second, a sparsity convex optimization model for force identification is constructed. Third, given the transfer function and the operational response, Sparse reconstruction by separable approximation (SpaRSA) is developed to solve the sparse regularization problem of force identification. Finally, experiments including identification of impact and harmonic forces are conducted on a cantilever thin plate structure to illustrate the effectiveness and applicability of SpaRSA. Besides the Dirac dictionary, other three sparse dictionaries including Db6 wavelets, Sym4 wavelets and cubic B-spline functions can also accurately identify both the single and double impact forces from highly noisy responses in a sparse representation frame. The discrete cosine functions can also successfully reconstruct the harmonic forces including the sinusoidal, square and triangular forces. Conversely, the traditional Tikhonov regularization method with the L-curve criterion fails to identify both the impact and harmonic forces in these cases.

A cross-species bi-clustering approach to identifying conserved co-regulated genes.

PubMed

Sun, Jiangwen; Jiang, Zongliang; Tian, Xiuchun; Bi, Jinbo

2016-06-15

A growing number of studies have explored the process of pre-implantation embryonic development of multiple mammalian species. However, the conservation and variation among different species in their developmental programming are poorly defined due to the lack of effective computational methods for detecting co-regularized genes that are conserved across species. The most sophisticated method to date for identifying conserved co-regulated genes is a two-step approach. This approach first identifies gene clusters for each species by a cluster analysis of gene expression data, and subsequently computes the overlaps of clusters identified from different species to reveal common subgroups. This approach is ineffective to deal with the noise in the expression data introduced by the complicated procedures in quantifying gene expression. Furthermore, due to the sequential nature of the approach, the gene clusters identified in the first step may have little overlap among different species in the second step, thus difficult to detect conserved co-regulated genes. We propose a cross-species bi-clustering approach which first denoises the gene expression data of each species into a data matrix. The rows of the data matrices of different species represent the same set of genes that are characterized by their expression patterns over the developmental stages of each species as columns. A novel bi-clustering method is then developed to cluster genes into subgroups by a joint sparse rank-one factorization of all the data matrices. This method decomposes a data matrix into a product of a column vector and a row vector where the column vector is a consistent indicator across the matrices (species) to identify the same gene cluster and the row vector specifies for each species the developmental stages that the clustered genes co-regulate. Efficient optimization algorithm has been developed with convergence analysis. This approach was first validated on synthetic data and compared to the two-step method and several recent joint clustering methods. We then applied this approach to two real world datasets of gene expression during the pre-implantation embryonic development of the human and mouse. Co-regulated genes consistent between the human and mouse were identified, offering insights into conserved functions, as well as similarities and differences in genome activation timing between the human and mouse embryos. The R package containing the implementation of the proposed method in C ++ is available at: https://github.com/JavonSun/mvbc.git and also at the R platform https://www.r-project.org/ jinbo@engr.uconn.edu. © The Author 2016. Published by Oxford University Press.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

PubMed

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

Characterizing and differentiating task-based and resting state fMRI signals via two-stage sparse representations.

PubMed

Zhang, Shu; Li, Xiang; Lv, Jinglei; Jiang, Xi; Guo, Lei; Liu, Tianming

2016-03-01

A relatively underexplored question in fMRI is whether there are intrinsic differences in terms of signal composition patterns that can effectively characterize and differentiate task-based or resting state fMRI (tfMRI or rsfMRI) signals. In this paper, we propose a novel two-stage sparse representation framework to examine the fundamental difference between tfMRI and rsfMRI signals. Specifically, in the first stage, the whole-brain tfMRI or rsfMRI signals of each subject were composed into a big data matrix, which was then factorized into a subject-specific dictionary matrix and a weight coefficient matrix for sparse representation. In the second stage, all of the dictionary matrices from both tfMRI/rsfMRI data across multiple subjects were composed into another big data-matrix, which was further sparsely represented by a cross-subjects common dictionary and a weight matrix. This framework has been applied on the recently publicly released Human Connectome Project (HCP) fMRI data and experimental results revealed that there are distinctive and descriptive atoms in the cross-subjects common dictionary that can effectively characterize and differentiate tfMRI and rsfMRI signals, achieving 100% classification accuracy. Moreover, our methods and results can be meaningfully interpreted, e.g., the well-known default mode network (DMN) activities can be recovered from the very noisy and heterogeneous aggregated big-data of tfMRI and rsfMRI signals across all subjects in HCP Q1 release.

Computing sparse derivatives and consecutive zeros problem

NASA Astrophysics Data System (ADS)

Chandra, B. V. Ravi; Hossain, Shahadat

2013-02-01

We describe a substitution based sparse Jacobian matrix determination method using algorithmic differentiation. Utilizing the a priori known sparsity pattern, a compression scheme is determined using graph coloring. The "compressed pattern" of the Jacobian matrix is then reordered into a form suitable for computation by substitution. We show that the column reordering of the compressed pattern matrix (so as to align the zero entries into consecutive locations in each row) can be viewed as a variant of traveling salesman problem. Preliminary computational results show that on the test problems the performance of nearest-neighbor type heuristic algorithms is highly encouraging.

Sparse coded image super-resolution using K-SVD trained dictionary based on regularized orthogonal matching pursuit.

PubMed

Sajjad, Muhammad; Mehmood, Irfan; Baik, Sung Wook

2015-01-01

Image super-resolution (SR) plays a vital role in medical imaging that allows a more efficient and effective diagnosis process. Usually, diagnosing is difficult and inaccurate from low-resolution (LR) and noisy images. Resolution enhancement through conventional interpolation methods strongly affects the precision of consequent processing steps, such as segmentation and registration. Therefore, we propose an efficient sparse coded image SR reconstruction technique using a trained dictionary. We apply a simple and efficient regularized version of orthogonal matching pursuit (ROMP) to seek the coefficients of sparse representation. ROMP has the transparency and greediness of OMP and the robustness of the L1-minization that enhance the dictionary learning process to capture feature descriptors such as oriented edges and contours from complex images like brain MRIs. The sparse coding part of the K-SVD dictionary training procedure is modified by substituting OMP with ROMP. The dictionary update stage allows simultaneously updating an arbitrary number of atoms and vectors of sparse coefficients. In SR reconstruction, ROMP is used to determine the vector of sparse coefficients for the underlying patch. The recovered representations are then applied to the trained dictionary, and finally, an optimization leads to high-resolution output of high-quality. Experimental results demonstrate that the super-resolution reconstruction quality of the proposed scheme is comparatively better than other state-of-the-art schemes.

A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra

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

Avila, Gustavo, E-mail: Gustavo-Avila@telefonica.net; Carrington, Tucker, E-mail: Tucker.Carrington@queensu.ca

In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinatemore » dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates.« less

Sparse matrix methods research using the CSM testbed software system

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, J. Alan

1989-01-01

Research is described on sparse matrix techniques for the Computational Structural Mechanics (CSM) Testbed. The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the CSM Testbed. Thus, one of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A suite of subroutines to extract from the data base the relevant structural and numerical information about the matrix equations was written, and all the demonstration problems distributed with the testbed were successfully solved. These codes were documented, and performance studies comparing the SPARSPAK technology to the methods currently in the testbed were completed. In addition, some preliminary studies were done comparing some recently developed out-of-core techniques with the performance of the testbed processor INV.

Face recognition using tridiagonal matrix enhanced multivariance products representation

NASA Astrophysics Data System (ADS)

Ã-zay, Evrim Korkmaz

2017-01-01

This study aims to retrieve face images from a database according to a target face image. For this purpose, Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) is taken into consideration. TMEMPR is a recursive algorithm based on Enhanced Multivariance Products Representation (EMPR). TMEMPR decomposes a matrix into three components which are a matrix of left support terms, a tridiagonal matrix of weight parameters for each recursion, and a matrix of right support terms, respectively. In this sense, there is an analogy between Singular Value Decomposition (SVD) and TMEMPR. However TMEMPR is a more flexible algorithm since its initial support terms (or vectors) can be chosen as desired. Low computational complexity is another advantage of TMEMPR because the algorithm has been constructed with recursions of certain arithmetic operations without requiring any iteration. The algorithm has been trained and tested with ORL face image database with 400 different grayscale images of 40 different people. TMEMPR's performance has been compared with SVD's performance as a result.

A tight and explicit representation of Q in sparse QR factorization

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

Ng, E.G.; Peyton, B.W.

1992-05-01

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be themore » matrix consisting of the first n columns of Q. Using results from, we show that the data structures for H and U resulting from our characterizations are tight when A is a strong Hall matrix. We also show that H and the lower trapezoidal part of U have the same sparsity characterization when A is strong Hall. We then show that this characterization can be extended to any weak Hall matrix that has been permuted into block upper triangular form. Finally, we show that permuting to block triangular form never increases the fill incurred during the factorization.« less

Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

PubMed

Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Xu, Richard Yi Da; Luo, Xiangfeng

2018-05-01

Sparse nonnegative matrix factorization (SNMF) aims to factorize a data matrix into two optimized nonnegative sparse factor matrices, which could benefit many tasks, such as document-word co-clustering. However, the traditional SNMF typically assumes the number of latent factors (i.e., dimensionality of the factor matrices) to be fixed. This assumption makes it inflexible in practice. In this paper, we propose a doubly sparse nonparametric NMF framework to mitigate this issue by using dependent Indian buffet processes (dIBP). We apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by IBP. As a consequence, the generation of two factor matrices will be columnwise correlated. Under this framework, two classes of correlation function are proposed: 1) using bivariate Beta distribution and 2) using Copula function. Compared with the single IBP-based NMF, this paper jointly makes two factor matrices nonparametric and sparse, which could be applied to broader scenarios, such as co-clustering. This paper is seen to be much more flexible than Gaussian process-based and hierarchial Beta process-based dIBPs in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries. Our experiments on synthetic data show the merits of this paper compared with the state-of-the-art models in respect of factorization efficiency, sparsity, and flexibility. Experiments on real-world data sets demonstrate the efficiency of this paper in document-word co-clustering tasks.

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

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented. PMID:24348088

Large Covariance Estimation by Thresholding Principal Orthogonal Complements.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2013-09-01

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented.

Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method.

PubMed

Acevedo, Ramiro; Lombardini, Richard; Turner, Matthew A; Kinsey, James L; Johnson, Bruce R

2008-02-14

The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schrodinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schrodinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly, the expansion coefficients are the same for each uniform time step, a fact that is only spoiled by basis incompleteness and finite precision. This is true for the Krylov basis and, with further investigation, is also found to be true for the Lanczos basis, important for efficient orthogonal projection-based algorithms. The CSL method errors roughly track those of the short iterative Lanczos method while requiring fewer matrix-vector products than the Chebyshev method. With the CSL method, only a few vectors need to be stored at a time, there is no need to estimate the Hamiltonian spectral range, and only matrix-vector and vector-vector products are required. Applications using localized wavelet bases are made to harmonic oscillator and anharmonic Morse oscillator systems as well as electrodynamic pulse propagation using the Hamiltonian form of Maxwell's equations. For gold with a Drude dielectric function, the latter is non-Hermitian, requiring consideration of corrections to the CSL algorithm.

Seismic data interpolation and denoising by learning a tensor tight frame

NASA Astrophysics Data System (ADS)

Liu, Lina; Plonka, Gerlind; Ma, Jianwei

2017-10-01

Seismic data interpolation and denoising plays a key role in seismic data processing. These problems can be understood as sparse inverse problems, where the desired data are assumed to be sparsely representable within a suitable dictionary. In this paper, we present a new method based on a data-driven tight frame (DDTF) of Kronecker type (KronTF) that avoids the vectorization step and considers the multidimensional structure of data in a tensor-product way. It takes advantage of the structure contained in all different modes (dimensions) simultaneously. In order to overcome the limitations of a usual tensor-product approach we also incorporate data-driven directionality. The complete method is formulated as a sparsity-promoting minimization problem. It includes two main steps. In the first step, a hard thresholding algorithm is used to update the frame coefficients of the data in the dictionary; in the second step, an iterative alternating method is used to update the tight frame (dictionary) in each different mode. The dictionary that is learned in this way contains the principal components in each mode. Furthermore, we apply the proposed KronTF to seismic interpolation and denoising. Examples with synthetic and real seismic data show that the proposed method achieves better results than the traditional projection onto convex sets method based on the Fourier transform and the previous vectorized DDTF methods. In particular, the simple structure of the new frame construction makes it essentially more efficient.

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

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

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Deflation as a method of variance reduction for estimating the trace of a matrix inverse

DOE PAGES

Gambhir, Arjun Singh; Stathopoulos, Andreas; Orginos, Kostas

2017-04-06

Many fields require computing the trace of the inverse of a large, sparse matrix. The typical method used for such computations is the Hutchinson method which is a Monte Carlo (MC) averaging over matrix quadratures. To improve its convergence, several variance reductions techniques have been proposed. In this paper, we study the effects of deflating the near null singular value space. We make two main contributions. First, we analyze the variance of the Hutchinson method as a function of the deflated singular values and vectors. Although this provides good intuition in general, by assuming additionally that the singular vectors aremore » random unitary matrices, we arrive at concise formulas for the deflated variance that include only the variance and mean of the singular values. We make the remarkable observation that deflation may increase variance for Hermitian matrices but not for non-Hermitian ones. This is a rare, if not unique, property where non-Hermitian matrices outperform Hermitian ones. The theory can be used as a model for predicting the benefits of deflation. Second, we use deflation in the context of a large scale application of "disconnected diagrams" in Lattice QCD. On lattices, Hierarchical Probing (HP) has previously provided an order of magnitude of variance reduction over MC by removing "error" from neighboring nodes of increasing distance in the lattice. Although deflation used directly on MC yields a limited improvement of 30% in our problem, when combined with HP they reduce variance by a factor of over 150 compared to MC. For this, we pre-computated 1000 smallest singular values of an ill-conditioned matrix of size 25 million. Furthermore, using PRIMME and a domain-specific Algebraic Multigrid preconditioner, we perform one of the largest eigenvalue computations in Lattice QCD at a fraction of the cost of our trace computation.« less

Rational approximations from power series of vector-valued meromorphic functions

NASA Technical Reports Server (NTRS)

Sidi, Avram

1992-01-01

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

Optical implementation of systolic array processing

NASA Technical Reports Server (NTRS)

Caulfield, H. J.; Rhodes, W. T.; Foster, M. J.; Horvitz, S.

1981-01-01

Algorithms for matrix vector multiplication are implemented using acousto-optic cells for multiplication and input data transfer and using charge coupled devices detector arrays for accumulation and output of the results. No two dimensional matrix mask is required; matrix changes are implemented electronically. A system for multiplying a 50 component nonnegative real vector by a 50 by 50 nonnegative real matrix is described. Modifications for bipolar real and complex valued processing are possible, as are extensions to matrix-matrix multiplication and multiplication of a vector by multiple matrices.

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.

Subject-based discriminative sparse representation model for detection of concealed information.

PubMed

Akhavan, Amir; Moradi, Mohammad Hassan; Vand, Safa Rafiei

2017-05-01

The use of machine learning approaches in concealed information test (CIT) plays a key role in the progress of this neurophysiological field. In this paper, we presented a new machine learning method for CIT in which each subject is considered independent of the others. The main goal of this study is to adapt the discriminative sparse models to be applicable for subject-based concealed information test. In order to provide sufficient discriminability between guilty and innocent subjects, we introduced a novel discriminative sparse representation model and its appropriate learning methods. For evaluation of the method forty-four subjects participated in a mock crime scenario and their EEG data were recorded. As the model input, in this study the recurrence plot features were extracted from single trial data of different stimuli. Then the extracted feature vectors were reduced using statistical dependency method. The reduced feature vector went through the proposed subject-based sparse model in which the discrimination power of sparse code and reconstruction error were applied simultaneously. Experimental results showed that the proposed approach achieved better performance than other competing discriminative sparse models. The classification accuracy, sensitivity and specificity of the presented sparsity-based method were about 93%, 91% and 95% respectively. Using the EEG data of a single subject in response to different stimuli types and with the aid of the proposed discriminative sparse representation model, one can distinguish guilty subjects from innocent ones. Indeed, this property eliminates the necessity of several subject EEG data in model learning and decision making for a specific subject. Copyright © 2017 Elsevier B.V. All rights reserved.

A Bayesian method for detecting pairwise associations in compositional data

PubMed Central

Ventz, Steffen; Huttenhower, Curtis

2017-01-01

Compositional data consist of vectors of proportions normalized to a constant sum from a basis of unobserved counts. The sum constraint makes inference on correlations between unconstrained features challenging due to the information loss from normalization. However, such correlations are of long-standing interest in fields including ecology. We propose a novel Bayesian framework (BAnOCC: Bayesian Analysis of Compositional Covariance) to estimate a sparse precision matrix through a LASSO prior. The resulting posterior, generated by MCMC sampling, allows uncertainty quantification of any function of the precision matrix, including the correlation matrix. We also use a first-order Taylor expansion to approximate the transformation from the unobserved counts to the composition in order to investigate what characteristics of the unobserved counts can make the correlations more or less difficult to infer. On simulated datasets, we show that BAnOCC infers the true network as well as previous methods while offering the advantage of posterior inference. Larger and more realistic simulated datasets further showed that BAnOCC performs well as measured by type I and type II error rates. Finally, we apply BAnOCC to a microbial ecology dataset from the Human Microbiome Project, which in addition to reproducing established ecological results revealed unique, competition-based roles for Proteobacteria in multiple distinct habitats. PMID:29140991

Sparsistency and Rates of Convergence in Large Covariance Matrix Estimation.

PubMed

Lam, Clifford; Fan, Jianqing

2009-01-01

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration problems under a unified framework with a general penalty function. We show that the rates of convergence for these problems under the Frobenius norm are of order (s(n) log p(n)/n)(1/2), where s(n) is the number of nonzero elements, p(n) is the size of the covariance matrix and n is the sample size. This explicitly spells out the contribution of high-dimensionality is merely of a logarithmic factor. The conditions on the rate with which the tuning parameter λ(n) goes to 0 have been made explicit and compared under different penalties. As a result, for the L(1)-penalty, to guarantee the sparsistency and optimal rate of convergence, the number of nonzero elements should be small: sn'=O(pn) at most, among O(pn2) parameters, for estimating sparse covariance or correlation matrix, sparse precision or inverse correlation matrix or sparse Cholesky factor, where sn' is the number of the nonzero elements on the off-diagonal entries. On the other hand, using the SCAD or hard-thresholding penalty functions, there is no such a restriction.

Immunohistochemical evidence of rapid extracellular matrix remodeling after iron-particle irradiation of mouse mammary gland

NASA Technical Reports Server (NTRS)

Ehrhart, E. J.; Gillette, E. L.; Barcellos-Hoff, M. H.; Chaterjee, A. (Principal Investigator)

1996-01-01

High-LET radiation has unique physical and biological properties compared to sparsely ionizing radiation. Recent studies demonstrate that sparsely ionizing radiation rapidly alters the pattern of extracellular matrix expression in several tissues, but little is known about the effect of heavy-ion radiation. This study investigates densely ionizing radiation-induced changes in extracellular matrix localization in the mammary glands of adult female BALB/c mice after whole-body irradiation with 0.8 Gy 600 MeV iron particles. The basement membrane and interstitial extracellular matrix proteins of the mammary gland stroma were mapped with respect to time postirradiation using immunofluorescence. Collagen III was induced in the adipose stroma within 1 day, continued to increase through day 9 and was resolved by day 14. Immunoreactive tenascin was induced in the epithelium by day 1, was evident at the epithelial-stromal interface by day 5-9 and persisted as a condensed layer beneath the basement membrane through day 14. These findings parallel similar changes induced by gamma irradiation but demonstrate different onset and chronicity. In contrast, the integrity of epithelial basement membrane, which was unaffected by sparsely ionizing radiation, was disrupted by iron-particle irradiation. Laminin immunoreactivity was mildly irregular at 1 h postirradiation and showed discontinuities and thickening from days 1 to 9. Continuity was restored by day 14. Thus high-LET radiation, like sparsely ionizing radiation, induces rapid-remodeling of the stromal extracellular matrix but also appears to alter the integrity of the epithelial basement membrane, which is an important regulator of epithelial cell proliferation and differentiation.

An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms

PubMed Central

Thomas, Phillip S.

2017-01-01

We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (C2H4O) and cyclopentadiene (C5H6), with 7 and 11 atoms, respectively. PMID:28571348

An intertwined method for making low-rank, sum-of-product basis functions that makes it possible to compute vibrational spectra of molecules with more than 10 atoms.

PubMed

Thomas, Phillip S; Carrington, Tucker

2017-05-28

We propose a method for solving the vibrational Schrödinger equation with which one can compute spectra for molecules with more than ten atoms. It uses sum-of-product (SOP) basis functions stored in a canonical polyadic tensor format and generated by evaluating matrix-vector products. By doing a sequence of partial optimizations, in each of which the factors in a SOP basis function for a single coordinate are optimized, the rank of the basis functions is reduced as matrix-vector products are computed. This is better than using an alternating least squares method to reduce the rank, as is done in the reduced-rank block power method. Partial optimization is better because it speeds up the calculation by about an order of magnitude and allows one to significantly reduce the memory cost. We demonstrate the effectiveness of the new method by computing vibrational spectra of two molecules, ethylene oxide (C 2 H 4 O) and cyclopentadiene (C 5 H 6 ), with 7 and 11 atoms, respectively.

Ellipsoidal fuzzy learning for smart car platoons

NASA Astrophysics Data System (ADS)

Dickerson, Julie A.; Kosko, Bart

1993-12-01

A neural-fuzzy system combined supervised and unsupervised learning to find and tune the fuzzy-rules. An additive fuzzy system approximates a function by covering its graph with fuzzy rules. A fuzzy rule patch can take the form of an ellipsoid in the input-output space. Unsupervised competitive learning found the statistics of data clusters. The covariance matrix of each synaptic quantization vector defined on ellipsoid centered at the centroid of the data cluster. Tightly clustered data gave smaller ellipsoids or more certain rules. Sparse data gave larger ellipsoids or less certain rules. Supervised learning tuned the ellipsoids to improve the approximation. The supervised neural system used gradient descent to find the ellipsoidal fuzzy patches. It locally minimized the mean-squared error of the fuzzy approximation. Hybrid ellipsoidal learning estimated the control surface for a smart car controller.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

Pure endmember extraction using robust kernel archetypoid analysis for hyperspectral imagery

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Yang, Gang; Wu, Ke; Li, Weiyue; Zhang, Dianfa

2017-09-01

A robust kernel archetypoid analysis (RKADA) method is proposed to extract pure endmembers from hyperspectral imagery (HSI). The RKADA assumes that each pixel is a sparse linear mixture of all endmembers and each endmember corresponds to a real pixel in the image scene. First, it improves the re8gular archetypal analysis with a new binary sparse constraint, and the adoption of the kernel function constructs the principal convex hull in an infinite Hilbert space and enlarges the divergences between pairwise pixels. Second, the RKADA transfers the pure endmember extraction problem into an optimization problem by minimizing residual errors with the Huber loss function. The Huber loss function reduces the effects from big noises and outliers in the convergence procedure of RKADA and enhances the robustness of the optimization function. Third, the random kernel sinks for fast kernel matrix approximation and the two-stage algorithm for optimizing initial pure endmembers are utilized to improve its computational efficiency in realistic implementations of RKADA, respectively. The optimization equation of RKADA is solved by using the block coordinate descend scheme and the desired pure endmembers are finally obtained. Six state-of-the-art pure endmember extraction methods are employed to make comparisons with the RKADA on both synthetic and real Cuprite HSI datasets, including three geometrical algorithms vertex component analysis (VCA), alternative volume maximization (AVMAX) and orthogonal subspace projection (OSP), and three matrix factorization algorithms the preconditioning for successive projection algorithm (PreSPA), hierarchical clustering based on rank-two nonnegative matrix factorization (H2NMF) and self-dictionary multiple measurement vector (SDMMV). Experimental results show that the RKADA outperforms all the six methods in terms of spectral angle distance (SAD) and root-mean-square-error (RMSE). Moreover, the RKADA has short computational times in offline operations and shows significant improvement in identifying pure endmembers for ground objects with smaller spectrum differences. Therefore, the RKADA could be an alternative for pure endmember extraction from hyperspectral images.

Solving large tomographic linear systems: size reduction and error estimation

NASA Astrophysics Data System (ADS)

Voronin, Sergey; Mikesell, Dylan; Slezak, Inna; Nolet, Guust

2014-10-01

We present a new approach to reduce a sparse, linear system of equations associated with tomographic inverse problems. We begin by making a modification to the commonly used compressed sparse-row format, whereby our format is tailored to the sparse structure of finite-frequency (volume) sensitivity kernels in seismic tomography. Next, we cluster the sparse matrix rows to divide a large matrix into smaller subsets representing ray paths that are geographically close. Singular value decomposition of each subset allows us to project the data onto a subspace associated with the largest eigenvalues of the subset. After projection we reject those data that have a signal-to-noise ratio (SNR) below a chosen threshold. Clustering in this way assures that the sparse nature of the system is minimally affected by the projection. Moreover, our approach allows for a precise estimation of the noise affecting the data while also giving us the ability to identify outliers. We illustrate the method by reducing large matrices computed for global tomographic systems with cross-correlation body wave delays, as well as with surface wave phase velocity anomalies. For a massive matrix computed for 3.7 million Rayleigh wave phase velocity measurements, imposing a threshold of 1 for the SNR, we condensed the matrix size from 1103 to 63 Gbyte. For a global data set of multiple-frequency P wave delays from 60 well-distributed deep earthquakes we obtain a reduction to 5.9 per cent. This type of reduction allows one to avoid loss of information due to underparametrizing models. Alternatively, if data have to be rejected to fit the system into computer memory, it assures that the most important data are preserved.

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).

Nonleachable Imidazolium-Incorporated Composite for Disruption of Bacterial Clustering, Exopolysaccharide-Matrix Assembly, and Enhanced Biofilm Removal.

PubMed

Hwang, Geelsu; Koltisko, Bernard; Jin, Xiaoming; Koo, Hyun

2017-11-08

Surface-grown bacteria and production of an extracellular polymeric matrix modulate the assembly of highly cohesive and firmly attached biofilms, making them difficult to remove from solid surfaces. Inhibition of cell growth and inactivation of matrix-producing bacteria can impair biofilm formation and facilitate removal. Here, we developed a novel nonleachable antibacterial composite with potent antibiofilm activity by directly incorporating polymerizable imidazolium-containing resin (antibacterial resin with carbonate linkage; ABR-C) into a methacrylate-based scaffold (ABR-modified composite; ABR-MC) using an efficient yet simplified chemistry. Low-dose inclusion of imidazolium moiety (∼2 wt %) resulted in bioactivity with minimal cytotoxicity without compromising mechanical integrity of the restorative material. The antibiofilm properties of ABR-MC were assessed using an exopolysaccharide-matrix-producing (EPS-matrix-producing) oral pathogen (Streptococcus mutans) in an experimental biofilm model. Using high-resolution confocal fluorescence imaging and biophysical methods, we observed remarkable disruption of bacterial accumulation and defective 3D matrix structure on the surface of ABR-MC. Specifically, the antibacterial composite impaired the ability of S. mutans to form organized bacterial clusters on the surface, resulting in altered biofilm architecture with sparse cell accumulation and reduced amounts of EPS matrix (versus control composite). Biofilm topology analyses on the control composite revealed a highly organized and weblike EPS structure that tethers the bacterial clusters to each other and to the surface, forming a highly cohesive unit. In contrast, such a structured matrix was absent on the surface of ABR-MC with mostly sparse and amorphous EPS, indicating disruption in the biofilm physical stability. Consistent with lack of structural organization, the defective biofilm on the surface of ABR-MC was readily detached when subjected to low shear stress, while most of the biofilm biomass remained on the control surface. Altogether, we demonstrate a new nonleachable antibacterial composite with excellent antibiofilm activity without affecting its mechanical properties, which may serve as a platform for development of alternative antifouling biomaterials.

Photon and vector meson exchanges in the production of light meson pairs and elementary atoms

NASA Astrophysics Data System (ADS)

Gevorkyan, S. R.; Kuraev, E. A.; Volkov, M. K.

2013-01-01

The production of pseudoscalar and scalar meson pairs ππ, ηη, η‧η‧, σσ as well as bound states in high energy γγ collisions are considered. The exchange by a vector particle in the binary process γ + γ → ha + hb with hadronic states ha, hb in fragmentation regions of the initial particle leads to nondecreasing cross sections with increasing energy, that is a priority of peripheral kinematics. Unlike the photon exchange the vector meson exchange needs a reggeization leading to fall with energy growth. Nevertheless, due to the peripheral kinematics beyond very forward production angles the vector meson exchanges dominate over all possible exchanges. The proposed approach allows one to express the matrix elements of the considered processes through impacting factors, which can be calculated in perturbation models like chiral perturbation theory (ChPT) or the Nambu-Jona-Lasinio (NJL) model. In particular cases the impact factors can be determined from relevant γγ sub-processes or the vector meson radiative decay width. The pionium atom production in the collisions of high energy electrons and pions with protons is considered and the relevant cross sections have been estimated.

Discriminative Transfer Subspace Learning via Low-Rank and Sparse Representation.

PubMed

Xu, Yong; Fang, Xiaozhao; Wu, Jian; Li, Xuelong; Zhang, David

2016-02-01

In this paper, we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain. We use a transformation matrix to transfer both the source and target data to a common subspace, where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced. In this way, the discrepancy of the source and target domains is reduced. By imposing joint low-rank and sparse constraints on the reconstruction coefficient matrix, the global and local structures of data can be preserved. To enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy, a flexible linear classifier (projection) is obtained by learning a non-negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix. Our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and, thus, is more robust to different types of noise. We formulate our problem as a constrained low-rankness and sparsity minimization problem and solve it by the inexact augmented Lagrange multiplier method. Extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state-of-the art methods. The MATLAB code of our method will be publicly available at http://www.yongxu.org/lunwen.html.

Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

PubMed Central

Liu, Weidong; Luo, Xi

2014-01-01

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset. PMID:25750463

Rotations with Rodrigues' Vector

ERIC Educational Resources Information Center

Pina, E.

2011-01-01

The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears…

Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM).

PubMed

Gao, Hao; Yu, Hengyong; Osher, Stanley; Wang, Ge

2011-11-01

We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column dimension in energy), where the low-rank matrix corresponds to the stationary background over energy that has a low matrix rank, and the sparse matrix represents the rest of distinct spectral features that are often sparse. Distinct from previous methods, the PRISM utilizes the generalized rank, e.g., the matrix rank of tight-frame transform of a multi-energy image, which offers a way to characterize the multi-level and multi-filtered image coherence across the energy spectrum. Besides, the energy-dependent intensity information can be incorporated into the PRISM in terms of the spectral curves for base materials, with which the restoration of the multi-energy image becomes the reconstruction of the energy-independent material composition matrix. In other words, the PRISM utilizes prior knowledge on the generalized rank and sparsity of a multi-energy image, and intensity/spectral characteristics of base materials. Furthermore, we develop an accurate and fast split Bregman method for the PRISM and demonstrate the superior performance of the PRISM relative to several competing methods in simulations.

Energy Dissipation of Rayleigh Waves due to Absorption Along the Path by the Use of Finite Element Method

DTIC Science & Technology

1979-07-31

3 x 3 t Strain vector a ij,j Space derivative of the stress tensor Fi Force vector per unit volume o Density x CHAPTER III F Total force K Stiffness...matrix 6Vector displacements M Mass matrix B Space operating matrix DO Matrix moduli 2 x 3 DZ Operating matrix in Z direction N Matrix of shape...dissipating medium the deformation of a solid is a function of time, temperature and space . Creep phenomenon is a deformation process in which there is

Detection of Protein Complexes Based on Penalized Matrix Decomposition in a Sparse Protein⁻Protein Interaction Network.

PubMed

Cao, Buwen; Deng, Shuguang; Qin, Hua; Ding, Pingjian; Chen, Shaopeng; Li, Guanghui

2018-06-15

High-throughput technology has generated large-scale protein interaction data, which is crucial in our understanding of biological organisms. Many complex identification algorithms have been developed to determine protein complexes. However, these methods are only suitable for dense protein interaction networks, because their capabilities decrease rapidly when applied to sparse protein⁻protein interaction (PPI) networks. In this study, based on penalized matrix decomposition ( PMD ), a novel method of penalized matrix decomposition for the identification of protein complexes (i.e., PMD pc ) was developed to detect protein complexes in the human protein interaction network. This method mainly consists of three steps. First, the adjacent matrix of the protein interaction network is normalized. Second, the normalized matrix is decomposed into three factor matrices. The PMD pc method can detect protein complexes in sparse PPI networks by imposing appropriate constraints on factor matrices. Finally, the results of our method are compared with those of other methods in human PPI network. Experimental results show that our method can not only outperform classical algorithms, such as CFinder, ClusterONE, RRW, HC-PIN, and PCE-FR, but can also achieve an ideal overall performance in terms of a composite score consisting of F-measure, accuracy (ACC), and the maximum matching ratio (MMR).

Target detection in GPR data using joint low-rank and sparsity constraints

NASA Astrophysics Data System (ADS)

Bouzerdoum, Abdesselam; Tivive, Fok Hing Chi; Abeynayake, Canicious

2016-05-01

In ground penetrating radars, background clutter, which comprises the signals backscattered from the rough, uneven ground surface and the background noise, impairs the visualization of buried objects and subsurface inspections. In this paper, a clutter mitigation method is proposed for target detection. The removal of background clutter is formulated as a constrained optimization problem to obtain a low-rank matrix and a sparse matrix. The low-rank matrix captures the ground surface reflections and the background noise, whereas the sparse matrix contains the target reflections. An optimization method based on split-Bregman algorithm is developed to estimate these two matrices from the input GPR data. Evaluated on real radar data, the proposed method achieves promising results in removing the background clutter and enhancing the target signature.

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

Gebis, Joseph; Oliker, Leonid; Shalf, John

The disparity between microprocessor clock frequencies and memory latency is a primary reason why many demanding applications run well below peak achievable performance. Software controlled scratchpad memories, such as the Cell local store, attempt to ameliorate this discrepancy by enabling precise control over memory movement; however, scratchpad technology confronts the programmer and compiler with an unfamiliar and difficult programming model. In this work, we present the Virtual Vector Architecture (ViVA), which combines the memory semantics of vector computers with a software-controlled scratchpad memory in order to provide a more effective and practical approach to latency hiding. ViVA requires minimal changesmore » to the core design and could thus be easily integrated with conventional processor cores. To validate our approach, we implemented ViVA on the Mambo cycle-accurate full system simulator, which was carefully calibrated to match the performance on our underlying PowerPC Apple G5 architecture. Results show that ViVA is able to deliver significant performance benefits over scalar techniques for a variety of memory access patterns as well as two important memory-bound compact kernels, corner turn and sparse matrix-vector multiplication -- achieving 2x-13x improvement compared the scalar version. Overall, our preliminary ViVA exploration points to a promising approach for improving application performance on leading microprocessors with minimal design and complexity costs, in a power efficient manner.« less

Emotional textile image classification based on cross-domain convolutional sparse autoencoders with feature selection

NASA Astrophysics Data System (ADS)

Li, Zuhe; Fan, Yangyu; Liu, Weihua; Yu, Zeqi; Wang, Fengqin

2017-01-01

We aim to apply sparse autoencoder-based unsupervised feature learning to emotional semantic analysis for textile images. To tackle the problem of limited training data, we present a cross-domain feature learning scheme for emotional textile image classification using convolutional autoencoders. We further propose a correlation-analysis-based feature selection method for the weights learned by sparse autoencoders to reduce the number of features extracted from large size images. First, we randomly collect image patches on an unlabeled image dataset in the source domain and learn local features with a sparse autoencoder. We then conduct feature selection according to the correlation between different weight vectors corresponding to the autoencoder's hidden units. We finally adopt a convolutional neural network including a pooling layer to obtain global feature activations of textile images in the target domain and send these global feature vectors into logistic regression models for emotional image classification. The cross-domain unsupervised feature learning method achieves 65% to 78% average accuracy in the cross-validation experiments corresponding to eight emotional categories and performs better than conventional methods. Feature selection can reduce the computational cost of global feature extraction by about 50% while improving classification performance.

A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors.

PubMed

Sawamura, Jitsuki; Morishita, Shigeru; Ishigooka, Jun

2016-02-09

Previously, we applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). To gain a more concrete comprehension, we here apply the concept of matrix representation, which was not explicitly exploited in our previous work. Starting with a set of orthonormal vectors, called the basis, an operator Rj (an N-tuple patient disease state at the j-th session) was expressed as a set of stratified vectors representing plural operations on individual components, so as to satisfy the group matrix representation. The stratified vectors containing individual unit operations were combined into one-dimensional square matrices [Rj]s. The [Rj]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of [Rj]s. The method is demonstrated on simple examples. Despite the incompleteness of our model, the group matrix representation of stratified vectors offers a formal mathematical approach to clinical medicine, aligning it with other branches of natural science.

Sparse image reconstruction for molecular imaging.

PubMed

Ting, Michael; Raich, Raviv; Hero, Alfred O

2009-06-01

The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy (MRFM), an emerging technology where imaging of an individual tobacco mosaic virus was recently demonstrated with nanometer resolution. We also consider additive white Gaussian noise (AWGN) in the measurements. Many prior works of sparse estimators have focused on the case when H has low coherence; however, the system matrix H in our application is the convolution matrix for the system psf. A typical convolution matrix has high coherence. This paper, therefore, does not assume a low coherence H. A discrete-continuous form of the Laplacian and atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and two sparse estimators derived by maximizing the joint p.d.f. of the observation and image conditioned on the hyperparameters. A thresholding rule that generalizes the hard and soft thresholding rule appears in the course of the derivation. This so-called hybrid thresholding rule, when used in the iterative thresholding framework, gives rise to the hybrid estimator, a generalization of the lasso. Estimates of the hyperparameters for the lasso and hybrid estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical study with a Gaussian psf and two sparse images shows that the hybrid estimator outperforms the lasso.

A Preliminary Shape Model of 27 Euterpe

NASA Astrophysics Data System (ADS)

Stephens, R.; Warner, B. D.; Megna, R.; Coley, D.

2011-10-01

We obtained dense rotational lightcurves for the Main-Belt asteroid (27) Euterpe during three apparitions in 2000, 2009 and 2010 with planned observations in the summer of 2011. These were combined with sparse lightcurve data from the USNO to determine a preliminary spin vector and model shape (see Durech et al. [2] for a discussion regarding the differences between dense and sparse data sets). The analysis suggests that Euterpe has albedo features making the determination of an unambiguous spin vector and model shape difficult. So far, Euterpe's near spherical shape, low inclination, pole within 30 degrees of the plane of the solar system, and possible albedo features cause multiple pole and shape solutions to be present.

Total variation-based method for radar coincidence imaging with model mismatch for extended target

NASA Astrophysics Data System (ADS)

Cao, Kaicheng; Zhou, Xiaoli; Cheng, Yongqiang; Fan, Bo; Qin, Yuliang

2017-11-01

Originating from traditional optical coincidence imaging, radar coincidence imaging (RCI) is a staring/forward-looking imaging technique. In RCI, the reference matrix must be computed precisely to reconstruct the image as preferred; unfortunately, such precision is almost impossible due to the existence of model mismatch in practical applications. Although some conventional sparse recovery algorithms are proposed to solve the model-mismatch problem, they are inapplicable to nonsparse targets. We therefore sought to derive the signal model of RCI with model mismatch by replacing the sparsity constraint item with total variation (TV) regularization in the sparse total least squares optimization problem; in this manner, we obtain the objective function of RCI with model mismatch for an extended target. A more robust and efficient algorithm called TV-TLS is proposed, in which the objective function is divided into two parts and the perturbation matrix and scattering coefficients are updated alternately. Moreover, due to the ability of TV regularization to recover sparse signal or image with sparse gradient, TV-TLS method is also applicable to sparse recovering. Results of numerical experiments demonstrate that, for uniform extended targets, sparse targets, and real extended targets, the algorithm can achieve preferred imaging performance both in suppressing noise and in adapting to model mismatch.

Fault detection, isolation, and diagnosis of self-validating multifunctional sensors.

PubMed

Yang, Jing-Li; Chen, Yin-Sheng; Zhang, Li-Li; Sun, Zhen

2016-06-01

A novel fault detection, isolation, and diagnosis (FDID) strategy for self-validating multifunctional sensors is presented in this paper. The sparse non-negative matrix factorization-based method can effectively detect faults by using the squared prediction error (SPE) statistic, and the variables contribution plots based on SPE statistic can help to locate and isolate the faulty sensitive units. The complete ensemble empirical mode decomposition is employed to decompose the fault signals to a series of intrinsic mode functions (IMFs) and a residual. The sample entropy (SampEn)-weighted energy values of each IMFs and the residual are estimated to represent the characteristics of the fault signals. Multi-class support vector machine is introduced to identify the fault mode with the purpose of diagnosing status of the faulty sensitive units. The performance of the proposed strategy is compared with other fault detection strategies such as principal component analysis, independent component analysis, and fault diagnosis strategies such as empirical mode decomposition coupled with support vector machine. The proposed strategy is fully evaluated in a real self-validating multifunctional sensors experimental system, and the experimental results demonstrate that the proposed strategy provides an excellent solution to the FDID research topic of self-validating multifunctional sensors.

Randomized subspace-based robust principal component analysis for hyperspectral anomaly detection

NASA Astrophysics Data System (ADS)

Sun, Weiwei; Yang, Gang; Li, Jialin; Zhang, Dianfa

2018-01-01

A randomized subspace-based robust principal component analysis (RSRPCA) method for anomaly detection in hyperspectral imagery (HSI) is proposed. The RSRPCA combines advantages of randomized column subspace and robust principal component analysis (RPCA). It assumes that the background has low-rank properties, and the anomalies are sparse and do not lie in the column subspace of the background. First, RSRPCA implements random sampling to sketch the original HSI dataset from columns and to construct a randomized column subspace of the background. Structured random projections are also adopted to sketch the HSI dataset from rows. Sketching from columns and rows could greatly reduce the computational requirements of RSRPCA. Second, the RSRPCA adopts the columnwise RPCA (CWRPCA) to eliminate negative effects of sampled anomaly pixels and that purifies the previous randomized column subspace by removing sampled anomaly columns. The CWRPCA decomposes the submatrix of the HSI data into a low-rank matrix (i.e., background component), a noisy matrix (i.e., noise component), and a sparse anomaly matrix (i.e., anomaly component) with only a small proportion of nonzero columns. The algorithm of inexact augmented Lagrange multiplier is utilized to optimize the CWRPCA problem and estimate the sparse matrix. Nonzero columns of the sparse anomaly matrix point to sampled anomaly columns in the submatrix. Third, all the pixels are projected onto the complemental subspace of the purified randomized column subspace of the background and the anomaly pixels in the original HSI data are finally exactly located. Several experiments on three real hyperspectral images are carefully designed to investigate the detection performance of RSRPCA, and the results are compared with four state-of-the-art methods. Experimental results show that the proposed RSRPCA outperforms four comparison methods both in detection performance and in computational time.

High precision computing with charge domain devices and a pseudo-spectral method therefor

NASA Technical Reports Server (NTRS)

Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor); Fijany, Amir (Inventor); Zak, Michail (Inventor)

1997-01-01

The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Amino acid "little Big Bang": representing amino acid substitution matrices as dot products of Euclidian vectors.

PubMed

Zimmermann, Karel; Gibrat, Jean-François

2010-01-04

Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices. We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices. This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.

Highly parallel sparse Cholesky factorization

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Schreiber, Robert

1990-01-01

Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

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

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

Application of the Backward-Smoothing Extended Kalman Filter to Attitude Estimation and Prediction using Radar Observations

DTIC Science & Technology

2009-06-01

projection, the measurement matrix is of rank 3. This is known as the rank theorem and enables the matrix Y to be factored into the product of two...Interface 270 6.5.5. Bistatic Radar Measurements 271 6.5.6. Computer Aided Image-Model Matching 273 8 6.5.7. Tomasi-Kanade Factorization Method...the vectors of an orthonormal basis satisfy the following scalar- product relations (2 p. 239): = i. ir = n (2.1) i-j = i-k j-k 0 i-i= j • j = k-k

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS.

PubMed

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2011-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Evaluation of the transport matrix method for simulation of ocean biogeochemical tracers

NASA Astrophysics Data System (ADS)

Kvale, Karin F.; Khatiwala, Samar; Dietze, Heiner; Kriest, Iris; Oschlies, Andreas

2017-06-01

Conventional integration of Earth system and ocean models can accrue considerable computational expenses, particularly for marine biogeochemical applications. Offline numerical schemes in which only the biogeochemical tracers are time stepped and transported using a pre-computed circulation field can substantially reduce the burden and are thus an attractive alternative. One such scheme is the transport matrix method (TMM), which represents tracer transport as a sequence of sparse matrix-vector products that can be performed efficiently on distributed-memory computers. While the TMM has been used for a variety of geochemical and biogeochemical studies, to date the resulting solutions have not been comprehensively assessed against their online counterparts. Here, we present a detailed comparison of the two. It is based on simulations of the state-of-the-art biogeochemical sub-model embedded within the widely used coarse-resolution University of Victoria Earth System Climate Model (UVic ESCM). The default, non-linear advection scheme was first replaced with a linear, third-order upwind-biased advection scheme to satisfy the linearity requirement of the TMM. Transport matrices were extracted from an equilibrium run of the physical model and subsequently used to integrate the biogeochemical model offline to equilibrium. The identical biogeochemical model was also run online. Our simulations show that offline integration introduces some bias to biogeochemical quantities through the omission of the polar filtering used in UVic ESCM and in the offline application of time-dependent forcing fields, with high latitudes showing the largest differences with respect to the online model. Differences in other regions and in the seasonality of nutrients and phytoplankton distributions are found to be relatively minor, giving confidence that the TMM is a reliable tool for offline integration of complex biogeochemical models. Moreover, while UVic ESCM is a serial code, the TMM can be run on a parallel machine with no change to the underlying biogeochemical code, thus providing orders of magnitude speed-up over the online model.

A Sparse Reconstruction Approach for Identifying Gene Regulatory Networks Using Steady-State Experiment Data

PubMed Central

Zhang, Wanhong; Zhou, Tong

2015-01-01

Motivation Identifying gene regulatory networks (GRNs) which consist of a large number of interacting units has become a problem of paramount importance in systems biology. Situations exist extensively in which causal interacting relationships among these units are required to be reconstructed from measured expression data and other a priori information. Though numerous classical methods have been developed to unravel the interactions of GRNs, these methods either have higher computing complexities or have lower estimation accuracies. Note that great similarities exist between identification of genes that directly regulate a specific gene and a sparse vector reconstruction, which often relates to the determination of the number, location and magnitude of nonzero entries of an unknown vector by solving an underdetermined system of linear equations y = Φx. Based on these similarities, we propose a novel framework of sparse reconstruction to identify the structure of a GRN, so as to increase accuracy of causal regulation estimations, as well as to reduce their computational complexity. Results In this paper, a sparse reconstruction framework is proposed on basis of steady-state experiment data to identify GRN structure. Different from traditional methods, this approach is adopted which is well suitable for a large-scale underdetermined problem in inferring a sparse vector. We investigate how to combine the noisy steady-state experiment data and a sparse reconstruction algorithm to identify causal relationships. Efficiency of this method is tested by an artificial linear network, a mitogen-activated protein kinase (MAPK) pathway network and the in silico networks of the DREAM challenges. The performance of the suggested approach is compared with two state-of-the-art algorithms, the widely adopted total least-squares (TLS) method and those available results on the DREAM project. Actual results show that, with a lower computational cost, the proposed method can significantly enhance estimation accuracy and greatly reduce false positive and negative errors. Furthermore, numerical calculations demonstrate that the proposed algorithm may have faster convergence speed and smaller fluctuation than other methods when either estimate error or estimate bias is considered. PMID:26207991

Sparse electrocardiogram signals recovery based on solving a row echelon-like form of system.

PubMed

Cai, Pingmei; Wang, Guinan; Yu, Shiwei; Zhang, Hongjuan; Ding, Shuxue; Wu, Zikai

2016-02-01

The study of biology and medicine in a noise environment is an evolving direction in biological data analysis. Among these studies, analysis of electrocardiogram (ECG) signals in a noise environment is a challenging direction in personalized medicine. Due to its periodic characteristic, ECG signal can be roughly regarded as sparse biomedical signals. This study proposes a two-stage recovery algorithm for sparse biomedical signals in time domain. In the first stage, the concentration subspaces are found in advance. Then by exploiting these subspaces, the mixing matrix is estimated accurately. In the second stage, based on the number of active sources at each time point, the time points are divided into different layers. Next, by constructing some transformation matrices, these time points form a row echelon-like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. It is noting that all these operations are conducted under a weak sparse condition that the number of active sources is less than the number of observations. Experimental results show that the proposed method has a better performance for sparse ECG signal recovery problem.

Hypergraph partitioning implementation for parallelizing matrix-vector multiplication using CUDA GPU-based parallel computing

NASA Astrophysics Data System (ADS)

Murni, Bustamam, A.; Ernastuti, Handhika, T.; Kerami, D.

2017-07-01

Calculation of the matrix-vector multiplication in the real-world problems often involves large matrix with arbitrary size. Therefore, parallelization is needed to speed up the calculation process that usually takes a long time. Graph partitioning techniques that have been discussed in the previous studies cannot be used to complete the parallelized calculation of matrix-vector multiplication with arbitrary size. This is due to the assumption of graph partitioning techniques that can only solve the square and symmetric matrix. Hypergraph partitioning techniques will overcome the shortcomings of the graph partitioning technique. This paper addresses the efficient parallelization of matrix-vector multiplication through hypergraph partitioning techniques using CUDA GPU-based parallel computing. CUDA (compute unified device architecture) is a parallel computing platform and programming model that was created by NVIDIA and implemented by the GPU (graphics processing unit).

Fast super-resolution estimation of DOA and DOD in bistatic MIMO Radar with off-grid targets

NASA Astrophysics Data System (ADS)

Zhang, Dong; Zhang, Yongshun; Zheng, Guimei; Feng, Cunqian; Tang, Jun

2018-05-01

In this paper, we focus on the problem of joint DOA and DOD estimation in Bistatic MIMO Radar using sparse reconstruction method. In traditional ways, we usually convert the 2D parameter estimation problem into 1D parameter estimation problem by Kronecker product which will enlarge the scale of the parameter estimation problem and bring more computational burden. Furthermore, it requires that the targets must fall on the predefined grids. In this paper, a 2D-off-grid model is built which can solve the grid mismatch problem of 2D parameters estimation. Then in order to solve the joint 2D sparse reconstruction problem directly and efficiently, three kinds of fast joint sparse matrix reconstruction methods are proposed which are Joint-2D-OMP algorithm, Joint-2D-SL0 algorithm and Joint-2D-SOONE algorithm. Simulation results demonstrate that our methods not only can improve the 2D parameter estimation accuracy but also reduce the computational complexity compared with the traditional Kronecker Compressed Sensing method.

Remote sensing image stitch using modified structure deformation

NASA Astrophysics Data System (ADS)

Pan, Ke-cheng; Chen, Jin-wei; Chen, Yueting; Feng, Huajun

2012-10-01

To stitch remote sensing images seamlessly without producing visual artifact which is caused by severe intensity discrepancy and structure misalignment, we modify the original structure deformation based stitching algorithm which have two main problems: Firstly, using Poisson equation to propagate deformation vectors leads to the change of the topological relationship between the key points and their surrounding pixels, which may bring in wrong image characteristics. Secondly, the diffusion area of the sparse matrix is too limited to rectify the global intensity discrepancy. To solve the first problem, we adopt Spring-Mass model and bring in external force to keep the topological relationship between key points and their surrounding pixels. We also apply tensor voting algorithm to achieve the global intensity corresponding curve of the two images to solve the second problem. Both simulated and experimental results show that our algorithm is faster and can reach better result than the original algorithm.

GPU Accelerated Chemical Similarity Calculation for Compound Library Comparison

PubMed Central

Ma, Chao; Wang, Lirong; Xie, Xiang-Qun

2012-01-01

Chemical similarity calculation plays an important role in compound library design, virtual screening, and “lead” optimization. In this manuscript, we present a novel GPU-accelerated algorithm for all-vs-all Tanimoto matrix calculation and nearest neighbor search. By taking advantage of multi-core GPU architecture and CUDA parallel programming technology, the algorithm is up to 39 times superior to the existing commercial software that runs on CPUs. Because of the utilization of intrinsic GPU instructions, this approach is nearly 10 times faster than existing GPU-accelerated sparse vector algorithm, when Unity fingerprints are used for Tanimoto calculation. The GPU program that implements this new method takes about 20 minutes to complete the calculation of Tanimoto coefficients between 32M PubChem compounds and 10K Active Probes compounds, i.e., 324G Tanimoto coefficients, on a 128-CUDA-core GPU. PMID:21692447

Site-percolation threshold of carbon nanotube fibers-Fast inspection of percolation with Markov stochastic theory

NASA Astrophysics Data System (ADS)

Xu, Fangbo; Xu, Zhiping; Yakobson, Boris I.

2014-08-01

We present a site-percolation model based on a modified FCC lattice, as well as an efficient algorithm of inspecting percolation which takes advantage of the Markov stochastic theory, in order to study the percolation threshold of carbon nanotube (CNT) fibers. Our Markov-chain based algorithm carries out the inspection of percolation by performing repeated sparse matrix-vector multiplications, which allows parallelized computation to accelerate the inspection for a given configuration. With this approach, we determine that the site-percolation transition of CNT fibers occurs at pc=0.1533±0.0013, and analyze the dependence of the effective percolation threshold (corresponding to 0.5 percolation probability) on the length and the aspect ratio of a CNT fiber on a finite-size-scaling basis. We also discuss the aspect ratio dependence of percolation probability with various values of p (not restricted to pc).

An iterative technique to stabilize a linear time invariant multivariable system with output feedback

NASA Technical Reports Server (NTRS)

Sankaran, V.

1974-01-01

An iterative procedure for determining the constant gain matrix that will stabilize a linear constant multivariable system using output feedback is described. The use of this procedure avoids the transformation of variables which is required in other procedures. For the case in which the product of the output and input vector dimensions is greater than the number of states of the plant, general solution is given. In the case in which the states exceed the product of input and output vector dimensions, a least square solution which may not be stable in all cases is presented. The results are illustrated with examples.

A physiologically motivated sparse, compact, and smooth (SCS) approach to EEG source localization.

PubMed

Cao, Cheng; Akalin Acar, Zeynep; Kreutz-Delgado, Kenneth; Makeig, Scott

2012-01-01

Here, we introduce a novel approach to the EEG inverse problem based on the assumption that principal cortical sources of multi-channel EEG recordings may be assumed to be spatially sparse, compact, and smooth (SCS). To enforce these characteristics of solutions to the EEG inverse problem, we propose a correlation-variance model which factors a cortical source space covariance matrix into the multiplication of a pre-given correlation coefficient matrix and the square root of the diagonal variance matrix learned from the data under a Bayesian learning framework. We tested the SCS method using simulated EEG data with various SNR and applied it to a real ECOG data set. We compare the results of SCS to those of an established SBL algorithm.

A performance study of sparse Cholesky factorization on INTEL iPSC/860

NASA Technical Reports Server (NTRS)

Zubair, M.; Ghose, M.

1992-01-01

The problem of Cholesky factorization of a sparse matrix has been very well investigated on sequential machines. A number of efficient codes exist for factorizing large unstructured sparse matrices. However, there is a lack of such efficient codes on parallel machines in general, and distributed machines in particular. Some of the issues that are critical to the implementation of sparse Cholesky factorization on a distributed memory parallel machine are ordering, partitioning and mapping, load balancing, and ordering of various tasks within a processor. Here, we focus on the effect of various partitioning schemes on the performance of sparse Cholesky factorization on the Intel iPSC/860. Also, a new partitioning heuristic for structured as well as unstructured sparse matrices is proposed, and its performance is compared with other schemes.

Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Alaghband, Gita; Jordan, Harry F.

1989-01-01

It is shown that in sparse matrices arising from electronic circuits, it is possible to do computations on many diagonal elements simultaneously. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A novel heuristic algorithm is presented that combines the idea of an order-compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set for reducing the matrix is generated and selected on the basis of a minimum Markowitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Thus, it is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices using the HEP multiprocessor (Kowalik, 1985) are presented and analyzed.

Geometry of matrix product states: Metric, parallel transport, and curvature

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

Haegeman, Jutho, E-mail: jutho.haegeman@gmail.com; Verstraete, Frank; Faculty of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, 9000 Gent

2014-02-15

We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold,more » which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.« less

Securing image information using double random phase encoding and parallel compressive sensing with updated sampling processes

NASA Astrophysics Data System (ADS)

Hu, Guiqiang; Xiao, Di; Wang, Yong; Xiang, Tao; Zhou, Qing

2017-11-01

Recently, a new kind of image encryption approach using compressive sensing (CS) and double random phase encoding has received much attention due to the advantages such as compressibility and robustness. However, this approach is found to be vulnerable to chosen plaintext attack (CPA) if the CS measurement matrix is re-used. Therefore, designing an efficient measurement matrix updating mechanism that ensures resistance to CPA is of practical significance. In this paper, we provide a novel solution to update the CS measurement matrix by altering the secret sparse basis with the help of counter mode operation. Particularly, the secret sparse basis is implemented by a reality-preserving fractional cosine transform matrix. Compared with the conventional CS-based cryptosystem that totally generates all the random entries of measurement matrix, our scheme owns efficiency superiority while guaranteeing resistance to CPA. Experimental and analysis results show that the proposed scheme has a good security performance and has robustness against noise and occlusion.

Sparse Modeling of Human Actions from Motion Imagery

DTIC Science & Technology

2011-09-02

is here developed. Spatio-temporal features that char- acterize local changes in the image are rst extracted. This is followed by the learning of a...video comes from the optimal sparse linear com- bination of the learned basis vectors (action primitives) representing the actions. A low...computational cost deep-layer model learning the inter- class correlations of the data is added for increasing discriminative power. In spite of its simplicity

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

DOE PAGES

Azad, Ariful; Ballard, Grey; Buluc, Aydin; ...

2016-11-08

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdös-Rényi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first implementation of the 3D SpGEMM formulation that exploits multiple (intranode and internode) levels of parallelism, achievingmore » significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research.« less

HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

PubMed Central

Fan, Jianqing; Liao, Yuan; Mincheva, Martina

2012-01-01

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied. PMID:22661790

Discovering mutated driver genes through a robust and sparse co-regularized matrix factorization framework with prior information from mRNA expression patterns and interaction network.

PubMed

Xi, Jianing; Wang, Minghui; Li, Ao

2018-06-05

Discovery of mutated driver genes is one of the primary objective for studying tumorigenesis. To discover some relatively low frequently mutated driver genes from somatic mutation data, many existing methods incorporate interaction network as prior information. However, the prior information of mRNA expression patterns are not exploited by these existing network-based methods, which is also proven to be highly informative of cancer progressions. To incorporate prior information from both interaction network and mRNA expressions, we propose a robust and sparse co-regularized nonnegative matrix factorization to discover driver genes from mutation data. Furthermore, our framework also conducts Frobenius norm regularization to overcome overfitting issue. Sparsity-inducing penalty is employed to obtain sparse scores in gene representations, of which the top scored genes are selected as driver candidates. Evaluation experiments by known benchmarking genes indicate that the performance of our method benefits from the two type of prior information. Our method also outperforms the existing network-based methods, and detect some driver genes that are not predicted by the competing methods. In summary, our proposed method can improve the performance of driver gene discovery by effectively incorporating prior information from interaction network and mRNA expression patterns into a robust and sparse co-regularized matrix factorization framework.

Dynamic Textures Modeling via Joint Video Dictionary Learning.

PubMed

Wei, Xian; Li, Yuanxiang; Shen, Hao; Chen, Fang; Kleinsteuber, Martin; Wang, Zhongfeng

2017-04-06

Video representation is an important and challenging task in the computer vision community. In this paper, we consider the problem of modeling and classifying video sequences of dynamic scenes which could be modeled in a dynamic textures (DT) framework. At first, we assume that image frames of a moving scene can be modeled as a Markov random process. We propose a sparse coding framework, named joint video dictionary learning (JVDL), to model a video adaptively. By treating the sparse coefficients of image frames over a learned dictionary as the underlying "states", we learn an efficient and robust linear transition matrix between two adjacent frames of sparse events in time series. Hence, a dynamic scene sequence is represented by an appropriate transition matrix associated with a dictionary. In order to ensure the stability of JVDL, we impose several constraints on such transition matrix and dictionary. The developed framework is able to capture the dynamics of a moving scene by exploring both sparse properties and the temporal correlations of consecutive video frames. Moreover, such learned JVDL parameters can be used for various DT applications, such as DT synthesis and recognition. Experimental results demonstrate the strong competitiveness of the proposed JVDL approach in comparison with state-of-the-art video representation methods. Especially, it performs significantly better in dealing with DT synthesis and recognition on heavily corrupted data.

Intersection of Three Planes Revisited--An Algebraic Approach

ERIC Educational Resources Information Center

Trenkler, Götz; Trenkler, Dietrich

2017-01-01

Given three planes in space, a complete characterization of their intersection is provided. Special attention is paid to the case when the intersection set does not exist of one point only. Besides the vector cross product, the tool of generalized inverse of a matrix is used extensively.

A Sparse Matrix Approach for Simultaneous Quantification of Nystagmus and Saccade

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Stone, Lee; Boyle, Richard D.

2012-01-01

The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

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

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

ViSBARD: Visual System for Browsing, Analysis and Retrieval of Data

NASA Astrophysics Data System (ADS)

Roberts, D. Aaron; Boller, Ryan; Rezapkin, V.; Coleman, J.; McGuire, R.; Goldstein, M.; Kalb, V.; Kulkarni, R.; Luckyanova, M.; Byrnes, J.; Kerbel, U.; Candey, R.; Holmes, C.; Chimiak, R.; Harris, B.

2018-04-01

ViSBARD interactively visualizes and analyzes space physics data. It provides an interactive integrated 3-D and 2-D environment to determine correlations between measurements across many spacecraft. It supports a variety of spacecraft data products and MHD models and is easily extensible to others. ViSBARD provides a way of visualizing multiple vector and scalar quantities as measured by many spacecraft at once. The data are displayed three-dimesionally along the orbits which may be displayed either as connected lines or as points. The data display allows the rapid determination of vector configurations, correlations between many measurements at multiple points, and global relationships. With the addition of magnetohydrodynamic (MHD) model data, this environment can also be used to validate simulation results with observed data, use simulated data to provide a global context for sparse observed data, and apply feature detection techniques to the simulated data.

On-Chip Neural Data Compression Based On Compressed Sensing With Sparse Sensing Matrices.

PubMed

Zhao, Wenfeng; Sun, Biao; Wu, Tong; Yang, Zhi

2018-02-01

On-chip neural data compression is an enabling technique for wireless neural interfaces that suffer from insufficient bandwidth and power budgets to transmit the raw data. The data compression algorithm and its implementation should be power and area efficient and functionally reliable over different datasets. Compressed sensing is an emerging technique that has been applied to compress various neurophysiological data. However, the state-of-the-art compressed sensing (CS) encoders leverage random but dense binary measurement matrices, which incur substantial implementation costs on both power and area that could offset the benefits from the reduced wireless data rate. In this paper, we propose two CS encoder designs based on sparse measurement matrices that could lead to efficient hardware implementation. Specifically, two different approaches for the construction of sparse measurement matrices, i.e., the deterministic quasi-cyclic array code (QCAC) matrix and -sparse random binary matrix [-SRBM] are exploited. We demonstrate that the proposed CS encoders lead to comparable recovery performance. And efficient VLSI architecture designs are proposed for QCAC-CS and -SRBM encoders with reduced area and total power consumption.

Smoothed low rank and sparse matrix recovery by iteratively reweighted least squares minimization.

PubMed

Lu, Canyi; Lin, Zhouchen; Yan, Shuicheng

2015-02-01

This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten-p norm and l2,q-norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q ≥ 1). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten-p norm and l2,q-norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient.

BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks

PubMed Central

Shen, Hong-Bin

2011-01-01

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/. PMID:22140454

Two alternate proofs of Wang's lune formula for sparse distributed memory and an integral approximation

NASA Technical Reports Server (NTRS)

Jaeckel, Louis A.

1988-01-01

In Kanerva's Sparse Distributed Memory, writing to and reading from the memory are done in relation to spheres in an n-dimensional binary vector space. Thus it is important to know how many points are in the intersection of two spheres in this space. Two proofs are given of Wang's formula for spheres of unequal radii, and an integral approximation for the intersection in this case.

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Removing flicker based on sparse color correspondences in old film restoration

NASA Astrophysics Data System (ADS)

Huang, Xi; Ding, Youdong; Yu, Bing; Xia, Tianran

2018-04-01

In the long history of human civilization, archived film is an indispensable part of it, and using digital method to repair damaged film is also a mainstream trend nowadays. In this paper, we propose a sparse color correspondences based technique to remove fading flicker for old films. Our model, combined with multi frame images to establish a simple correction model, includes three key steps. Firstly, we recover sparse color correspondences in the input frames to build a matrix with many missing entries. Secondly, we present a low-rank matrix factorization approach to estimate the unknown parameters of this model. Finally, we adopt a two-step strategy that divide the estimated parameters into reference frame parameters for color recovery correction and other frame parameters for color consistency correction to remove flicker. Our method combined multi-frames takes continuity of the input sequence into account, and the experimental results show the method can remove fading flicker efficiently.

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

NASA Astrophysics Data System (ADS)

Gillis, Nicolas; Luce, Robert

2018-01-01

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust methods to identify these conic basis columns are based on nonnegative sparse regression and self dictionaries, and require the solution of large-scale convex optimization problems. In this paper we study a particular nonnegative sparse regression model with self dictionary. As opposed to previously proposed models, this model yields a smooth optimization problem where the sparsity is enforced through linear constraints. We show that the Euclidean projection on the polyhedron defined by these constraints can be computed efficiently, and propose a fast gradient method to solve our model. We compare our algorithm with several state-of-the-art methods on synthetic data sets and real-world hyperspectral images.

Sparse Covariance Matrix Estimation by DCA-Based Algorithms.

PubMed

Phan, Duy Nhat; Le Thi, Hoai An; Dinh, Tao Pham

2017-11-01

This letter proposes a novel approach using the [Formula: see text]-norm regularization for the sparse covariance matrix estimation (SCME) problem. The objective function of SCME problem is composed of a nonconvex part and the [Formula: see text] term, which is discontinuous and difficult to tackle. Appropriate DC (difference of convex functions) approximations of [Formula: see text]-norm are used that result in approximation SCME problems that are still nonconvex. DC programming and DCA (DC algorithm), powerful tools in nonconvex programming framework, are investigated. Two DC formulations are proposed and corresponding DCA schemes developed. Two applications of the SCME problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization. A careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms. Numerical results showed their efficiency and their superiority compared with seven state-of-the-art methods.

Closed-form integrator for the quaternion (euler angle) kinematics equations

NASA Technical Reports Server (NTRS)

Whitmore, Stephen A. (Inventor)

2000-01-01

The invention is embodied in a method of integrating kinematics equations for updating a set of vehicle attitude angles of a vehicle using 3-dimensional angular velocities of the vehicle, which includes computing an integrating factor matrix from quantities corresponding to the 3-dimensional angular velocities, computing a total integrated angular rate from the quantities corresponding to a 3-dimensional angular velocities, computing a state transition matrix as a sum of (a) a first complementary function of the total integrated angular rate and (b) the integrating factor matrix multiplied by a second complementary function of the total integrated angular rate, and updating the set of vehicle attitude angles using the state transition matrix. Preferably, the method further includes computing a quanternion vector from the quantities corresponding to the 3-dimensional angular velocities, in which case the updating of the set of vehicle attitude angles using the state transition matrix is carried out by (a) updating the quanternion vector by multiplying the quanternion vector by the state transition matrix to produce an updated quanternion vector and (b) computing an updated set of vehicle attitude angles from the updated quanternion vector. The first and second trigonometric functions are complementary, such as a sine and a cosine. The quantities corresponding to the 3-dimensional angular velocities include respective averages of the 3-dimensional angular velocities over plural time frames. The updating of the quanternion vector preserves the norm of the vector, whereby the updated set of vehicle attitude angles are virtually error-free.

Automatic segmentation of right ventricular ultrasound images using sparse matrix transform and a level set

NASA Astrophysics Data System (ADS)

Qin, Xulei; Cong, Zhibin; Fei, Baowei

2013-11-01

An automatic segmentation framework is proposed to segment the right ventricle (RV) in echocardiographic images. The method can automatically segment both epicardial and endocardial boundaries from a continuous echocardiography series by combining sparse matrix transform, a training model, and a localized region-based level set. First, the sparse matrix transform extracts main motion regions of the myocardium as eigen-images by analyzing the statistical information of the images. Second, an RV training model is registered to the eigen-images in order to locate the position of the RV. Third, the training model is adjusted and then serves as an optimized initialization for the segmentation of each image. Finally, based on the initializations, a localized, region-based level set algorithm is applied to segment both epicardial and endocardial boundaries in each echocardiograph. Three evaluation methods were used to validate the performance of the segmentation framework. The Dice coefficient measures the overall agreement between the manual and automatic segmentation. The absolute distance and the Hausdorff distance between the boundaries from manual and automatic segmentation were used to measure the accuracy of the segmentation. Ultrasound images of human subjects were used for validation. For the epicardial and endocardial boundaries, the Dice coefficients were 90.8 ± 1.7% and 87.3 ± 1.9%, the absolute distances were 2.0 ± 0.42 mm and 1.79 ± 0.45 mm, and the Hausdorff distances were 6.86 ± 1.71 mm and 7.02 ± 1.17 mm, respectively. The automatic segmentation method based on a sparse matrix transform and level set can provide a useful tool for quantitative cardiac imaging.

Decoding and optimized implementation of SECDED codes over GF(q)

DOEpatents

Ward, H. Lee; Ganti, Anand; Resnick, David R

2013-10-22

A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.

Design, decoding and optimized implementation of SECDED codes over GF(q)

DOEpatents

Ward, H Lee; Ganti, Anand; Resnick, David R

2014-06-17

A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.

Decoding and optimized implementation of SECDED codes over GF(q)

DOEpatents

Ward, H Lee; Ganti, Anand; Resnick, David R

2014-11-18

A plurality of columns for a check matrix that implements a distance d linear error correcting code are populated by providing a set of vectors from which to populate the columns, and applying to the set of vectors a filter operation that reduces the set by eliminating therefrom all vectors that would, if used to populate the columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes. One of the vectors from the reduced set may then be selected to populate one of the columns. The filtering and selecting repeats iteratively until either all of the columns are populated or the number of currently unpopulated columns exceeds the number of vectors in the reduced set. Columns for the check matrix may be processed to reduce the amount of logic needed to implement the check matrix in circuit logic.

Compressive sensing using optimized sensing matrix for face verification

NASA Astrophysics Data System (ADS)

Oey, Endra; Jeffry; Wongso, Kelvin; Tommy

2017-12-01

Biometric appears as one of the solutions which is capable in solving problems that occurred in the usage of password in terms of data access, for example there is possibility in forgetting password and hard to recall various different passwords. With biometrics, physical characteristics of a person can be captured and used in the identification process. In this research, facial biometric is used in the verification process to determine whether the user has the authority to access the data or not. Facial biometric is chosen as its low cost implementation and generate quite accurate result for user identification. Face verification system which is adopted in this research is Compressive Sensing (CS) technique, in which aims to reduce dimension size as well as encrypt data in form of facial test image where the image is represented in sparse signals. Encrypted data can be reconstructed using Sparse Coding algorithm. Two types of Sparse Coding namely Orthogonal Matching Pursuit (OMP) and Iteratively Reweighted Least Squares -ℓp (IRLS-ℓp) will be used for comparison face verification system research. Reconstruction results of sparse signals are then used to find Euclidean norm with the sparse signal of user that has been previously saved in system to determine the validity of the facial test image. Results of system accuracy obtained in this research are 99% in IRLS with time response of face verification for 4.917 seconds and 96.33% in OMP with time response of face verification for 0.4046 seconds with non-optimized sensing matrix, while 99% in IRLS with time response of face verification for 13.4791 seconds and 98.33% for OMP with time response of face verification for 3.1571 seconds with optimized sensing matrix.

A transversal approach to predict gene product networks from ontology-based similarity

PubMed Central

Chabalier, Julie; Mosser, Jean; Burgun, Anita

2007-01-01

Background Interpretation of transcriptomic data is usually made through a "standard" approach which consists in clustering the genes according to their expression patterns and exploiting Gene Ontology (GO) annotations within each expression cluster. This approach makes it difficult to underline functional relationships between gene products that belong to different expression clusters. To address this issue, we propose a transversal analysis that aims to predict functional networks based on a combination of GO processes and data expression. Results The transversal approach presented in this paper consists in computing the semantic similarity between gene products in a Vector Space Model. Through a weighting scheme over the annotations, we take into account the representativity of the terms that annotate a gene product. Comparing annotation vectors results in a matrix of gene product similarities. Combined with expression data, the matrix is displayed as a set of functional gene networks. The transversal approach was applied to 186 genes related to the enterocyte differentiation stages. This approach resulted in 18 functional networks proved to be biologically relevant. These results were compared with those obtained through a standard approach and with an approach based on information content similarity. Conclusion Complementary to the standard approach, the transversal approach offers new insight into the cellular mechanisms and reveals new research hypotheses by combining gene product networks based on semantic similarity, and data expression. PMID:17605807

Analysis of structural response data using discrete modal filters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Freudinger, Lawrence C.

1991-01-01

The application of reciprocal modal vectors to the analysis of structural response data is described. Reciprocal modal vectors are constructed using an existing experimental modal model and an existing frequency response matrix of a structure, and can be assembled into a matrix that effectively transforms the data from the physical space to a modal space within a particular frequency range. In other words, the weighting matrix necessary for modal vector orthogonality (typically the mass matrix) is contained within the reciprocal model matrix. The underlying goal of this work is mostly directed toward observing the modal state responses in the presence of unknown, possibly closed loop forcing functions, thus having an impact on both operating data analysis techniques and independent modal space control techniques. This study investigates the behavior of reciprocol modal vectors as modal filters with respect to certain calculation parameters and their performance with perturbed system frequency response data.

Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state

NASA Astrophysics Data System (ADS)

Sirunyan, A. M.; Tumasyan, A.; Adam, W.; Ambrogi, F.; Asilar, E.; Bergauer, T.; Brandstetter, J.; Brondolin, E.; Dragicevic, M.; Erö, J.; Flechl, M.; Friedl, M.; Frühwirth, R.; Ghete, V. M.; Grossmann, J.; Hrubec, J.; Jeitler, M.; König, A.; Krammer, N.; Krätschmer, I.; Liko, D.; Madlener, T.; Mikulec, I.; Pree, E.; Rabady, D.; Rad, N.; Rohringer, H.; Schieck, J.; Schöfbeck, R.; Spanring, M.; Spitzbart, D.; Waltenberger, W.; Wittmann, J.; Wulz, C.-E.; Zarucki, M.; Chekhovsky, V.; Mossolov, V.; Suarez Gonzalez, J.; De Wolf, E. A.; Di Croce, D.; Janssen, X.; Lauwers, J.; Van Haevermaet, H.; Van Mechelen, P.; Van Remortel, N.; Abu Zeid, S.; Blekman, F.; D'Hondt, J.; De Bruyn, I.; De Clercq, J.; Deroover, K.; Flouris, G.; Lontkovskyi, D.; Lowette, S.; Moortgat, S.; Moreels, L.; Python, Q.; Skovpen, K.; Tavernier, S.; Van Doninck, W.; Van Mulders, P.; Van Parijs, I.; Brun, H.; Clerbaux, B.; De Lentdecker, G.; Delannoy, H.; Fasanella, G.; Favart, L.; Goldouzian, R.; Grebenyuk, A.; Karapostoli, G.; Lenzi, T.; Luetic, J.; Maerschalk, T.; Marinov, A.; Randle-conde, A.; Vander Velde, C.; Vanlaer, P.; Vannerom, D.; Yonamine, R.; Zenoni, F.; Zhang, F.; Cimmino, A.; Cornelis, T.; Dobur, D.; Fagot, A.; Gul, M.; Khvastunov, I.; Poyraz, D.; Roskas, C.; Salva, S.; Tytgat, M.; Verbeke, W.; Zaganidis, N.; Bakhshiansohi, H.; Bondu, O.; Brochet, S.; Bruno, G.; Caputo, C.; Caudron, A.; De Visscher, S.; Delaere, C.; Delcourt, M.; Francois, B.; Giammanco, A.; Jafari, A.; Komm, M.; Krintiras, G.; Lemaitre, V.; Magitteri, A.; Mertens, A.; Musich, M.; Piotrzkowski, K.; Quertenmont, L.; Vidal Marono, M.; Wertz, S.; Beliy, N.; Aldá Júnior, W. L.; Alves, F. L.; Alves, G. A.; Brito, L.; Correa Martins Junior, M.; Hensel, C.; Moraes, A.; Pol, M. E.; Rebello Teles, P.; Belchior Batista Das Chagas, E.; Carvalho, W.; Chinellato, J.; Custódio, A.; Da Costa, E. M.; Da Silveira, G. G.; De Jesus Damiao, D.; Fonseca De Souza, S.; Huertas Guativa, L. M.; Malbouisson, H.; Melo De Almeida, M.; Mora Herrera, C.; Mundim, L.; Nogima, H.; Santoro, A.; Sznajder, A.; Tonelli Manganote, E. J.; Torres Da Silva De Araujo, F.; Vilela Pereira, A.; Ahuja, S.; Bernardes, C. A.; Fernandez Perez Tomei, T. R.; Gregores, E. M.; Mercadante, P. G.; Novaes, S. F.; Padula, Sandra S.; Romero Abad, D.; Ruiz Vargas, J. C.; Aleksandrov, A.; Hadjiiska, R.; Iaydjiev, P.; Misheva, M.; Rodozov, M.; Shopova, M.; Stoykova, S.; Sultanov, G.; Dimitrov, A.; Glushkov, I.; Litov, L.; Pavlov, B.; Petkov, P.; Fang, W.; Gao, X.; Ahmad, M.; Bian, J. G.; Chen, G. M.; Chen, H. S.; Chen, M.; Chen, Y.; Jiang, C. H.; Leggat, D.; Liao, H.; Liu, Z.; Romeo, F.; Shaheen, S. M.; Spiezia, A.; Tao, J.; Wang, C.; Wang, Z.; Yazgan, E.; Zhang, H.; Zhang, S.; Zhao, J.; Ban, Y.; Chen, G.; Li, Q.; Liu, S.; Mao, Y.; Qian, S. J.; Wang, D.; Xu, Z.; Avila, C.; Cabrera, A.; Chaparro Sierra, L. F.; Florez, C.; González Hernández, C. F.; Ruiz Alvarez, J. D.; Courbon, B.; Godinovic, N.; Lelas, D.; Puljak, I.; Ribeiro Cipriano, P. M.; Sculac, T.; Antunovic, Z.; Kovac, M.; Brigljevic, V.; Ferencek, D.; Kadija, K.; Mesic, B.; Starodumov, A.; Susa, T.; Ather, M. W.; Attikis, A.; Mavromanolakis, G.; Mousa, J.; Nicolaou, C.; Ptochos, F.; Razis, P. A.; Rykaczewski, H.; Finger, M.; Finger, M.; Carrera Jarrin, E.; Assran, Y.; Elgammal, S.; Mahrous, A.; Dewanjee, R. K.; Kadastik, M.; Perrini, L.; Raidal, M.; Tiko, A.; Veelken, C.; Eerola, P.; Pekkanen, J.; Voutilainen, M.; Härkönen, J.; Järvinen, T.; Karimäki, V.; Kinnunen, R.; Lampén, T.; Lassila-Perini, K.; Lehti, S.; Lindén, T.; Luukka, P.; Tuominen, E.; Tuominiemi, J.; Tuovinen, E.; Talvitie, J.; Tuuva, T.; Besancon, M.; Couderc, F.; Dejardin, M.; Denegri, D.; Faure, J. L.; Ferri, F.; Ganjour, S.; Ghosh, S.; Givernaud, A.; Gras, P.; Hamel de Monchenault, G.; Jarry, P.; Kucher, I.; Locci, E.; Machet, M.; Malcles, J.; Negro, G.; Rander, J.; Rosowsky, A.; Sahin, M. Ö.; Titov, M.; Abdulsalam, A.; Antropov, I.; Baffioni, S.; Beaudette, F.; Busson, P.; Cadamuro, L.; Charlot, C.; Granier de Cassagnac, R.; Jo, M.; Lisniak, S.; Lobanov, A.; Martin Blanco, J.; Nguyen, M.; Ochando, C.; Ortona, G.; Paganini, P.; Pigard, P.; Regnard, S.; Salerno, R.; Sauvan, J. B.; Sirois, Y.; Stahl Leiton, A. G.; Strebler, T.; Yilmaz, Y.; Zabi, A.; Zghiche, A.; Agram, J.-L.; Andrea, J.; Bloch, D.; Brom, J.-M.; Buttignol, M.; Chabert, E. C.; Chanon, N.; Collard, C.; Conte, E.; Coubez, X.; Fontaine, J.-C.; Gelé, D.; Goerlach, U.; Jansová, M.; Le Bihan, A.-C.; Tonon, N.; Van Hove, P.; Gadrat, S.; Beauceron, S.; Bernet, C.; Boudoul, G.; Chierici, R.; Contardo, D.; Depasse, P.; El Mamouni, H.; Fay, J.; Finco, L.; Gascon, S.; Gouzevitch, M.; Grenier, G.; Ille, B.; Lagarde, F.; Laktineh, I. B.; Lethuillier, M.; Mirabito, L.; Pequegnot, A. L.; Perries, S.; Popov, A.; Sordini, V.; Vander Donckt, M.; Viret, S.; Khvedelidze, A.; Tsamalaidze, Z.; Autermann, C.; Beranek, S.; Feld, L.; Kiesel, M. K.; Klein, K.; Lipinski, M.; Preuten, M.; Schomakers, C.; Schulz, J.; Verlage, T.; Albert, A.; Dietz-Laursonn, E.; Duchardt, D.; Endres, M.; Erdmann, M.; Erdweg, S.; Esch, T.; Fischer, R.; Güth, A.; Hamer, M.; Hebbeker, T.; Heidemann, C.; Hoepfner, K.; Knutzen, S.; Merschmeyer, M.; Meyer, A.; Millet, P.; Mukherjee, S.; Olschewski, M.; Padeken, K.; Pook, T.; Radziej, M.; Reithler, H.; Rieger, M.; Scheuch, F.; Teyssier, D.; Thüer, S.; Flügge, G.; Kargoll, B.; Kress, T.; Künsken, A.; Lingemann, J.; Müller, T.; Nehrkorn, A.; Nowack, A.; Pistone, C.; Pooth, O.; Stahl, A.; Aldaya Martin, M.; Arndt, T.; Asawatangtrakuldee, C.; Beernaert, K.; Behnke, O.; Behrens, U.; Bermúdez Martínez, A.; Bin Anuar, A. A.; Borras, K.; Botta, V.; Campbell, A.; Connor, P.; Contreras-Campana, C.; Costanza, F.; Diez Pardos, C.; Eckerlin, G.; Eckstein, D.; Eichhorn, T.; Eren, E.; Gallo, E.; Garay Garcia, J.; Geiser, A.; Gizhko, A.; Grados Luyando, J. M.; Grohsjean, A.; Gunnellini, P.; Guthoff, M.; Harb, A.; Hauk, J.; Hempel, M.; Jung, H.; Kalogeropoulos, A.; Kasemann, M.; Keaveney, J.; Kleinwort, C.; Korol, I.; Krücker, D.; Lange, W.; Lelek, A.; Lenz, T.; Leonard, J.; Lipka, K.; Lohmann, W.; Mankel, R.; Melzer-Pellmann, I.-A.; Meyer, A. B.; Mittag, G.; Mnich, J.; Mussgiller, A.; Ntomari, E.; Pitzl, D.; Raspereza, A.; Roland, B.; Savitskyi, M.; Saxena, P.; Shevchenko, R.; Spannagel, S.; Stefaniuk, N.; Van Onsem, G. P.; Walsh, R.; Wen, Y.; Wichmann, K.; Wissing, C.; Zenaiev, O.; Bein, S.; Blobel, V.; Centis Vignali, M.; Dreyer, T.; Garutti, E.; Gonzalez, D.; Haller, J.; Hinzmann, A.; Hoffmann, M.; Karavdina, A.; Klanner, R.; Kogler, R.; Kovalchuk, N.; Kurz, S.; Lapsien, T.; Marchesini, I.; Marconi, D.; Meyer, M.; Niedziela, M.; Nowatschin, D.; Pantaleo, F.; Peiffer, T.; Perieanu, A.; Scharf, C.; Schleper, P.; Schmidt, A.; Schumann, S.; Schwandt, J.; Sonneveld, J.; Stadie, H.; Steinbrück, G.; Stober, F. M.; Stöver, M.; Tholen, H.; Troendle, D.; Usai, E.; Vanelderen, L.; Vanhoefer, A.; Vormwald, B.; Akbiyik, M.; Barth, C.; Baur, S.; Butz, E.; Caspart, R.; Chwalek, T.; Colombo, F.; De Boer, W.; Dierlamm, A.; Freund, B.; Friese, R.; Giffels, M.; Gilbert, A.; Haitz, D.; Hartmann, F.; Heindl, S. M.; Husemann, U.; Kassel, F.; Kudella, S.; Mildner, H.; Mozer, M. U.; Müller, Th.; Plagge, M.; Quast, G.; Rabbertz, K.; Schröder, M.; Shvetsov, I.; Sieber, G.; Simonis, H. J.; Ulrich, R.; Wayand, S.; Weber, M.; Weiler, T.; Williamson, S.; Wöhrmann, C.; Wolf, R.; Anagnostou, G.; Daskalakis, G.; Geralis, T.; Giakoumopoulou, V. A.; Kyriakis, A.; Loukas, D.; Topsis-Giotis, I.; Karathanasis, G.; Kesisoglou, S.; Panagiotou, A.; Saoulidou, N.; Kousouris, K.; Evangelou, I.; Foudas, C.; Kokkas, P.; Mallios, S.; Manthos, N.; Papadopoulos, I.; Paradas, E.; Strologas, J.; Triantis, F. A.; Csanad, M.; Filipovic, N.; Pasztor, G.; Veres, G. I.; Bencze, G.; Hajdu, C.; Horvath, D.; Hunyadi, Á.; Sikler, F.; Veszpremi, V.; Zsigmond, A. J.; Beni, N.; Czellar, S.; Karancsi, J.; Makovec, A.; Molnar, J.; Szillasi, Z.; Bartók, M.; Raics, P.; Trocsanyi, Z. L.; Ujvari, B.; Choudhury, S.; Komaragiri, J. R.; Bahinipati, S.; Bhowmik, S.; Mal, P.; Mandal, K.; Nayak, A.; Sahoo, D. K.; Sahoo, N.; Swain, S. K.; Bansal, S.; Beri, S. B.; Bhatnagar, V.; Chawla, R.; Dhingra, N.; Kalsi, A. K.; Kaur, A.; Kaur, M.; Kumar, R.; Kumari, P.; Mehta, A.; Singh, J. B.; Walia, G.; Kumar, Ashok; Aashaq, Shah; Bhardwaj, A.; Chauhan, S.; Choudhary, B. C.; Garg, R. B.; Keshri, S.; Kumar, A.; Malhotra, S.; Naimuddin, M.; Ranjan, K.; Sharma, R.; Bhardwaj, R.; Bhattacharya, R.; Bhattacharya, S.; Bhawandeep, U.; Dey, S.; Dutt, S.; Dutta, S.; Ghosh, S.; Majumdar, N.; Modak, A.; Mondal, K.; Mukhopadhyay, S.; Nandan, S.; Purohit, A.; Roy, A.; Roy, D.; Roy Chowdhury, S.; Sarkar, S.; Sharan, M.; Thakur, S.; Behera, P. K.; Chudasama, R.; Dutta, D.; Jha, V.; Kumar, V.; Mohanty, A. K.; Netrakanti, P. K.; Pant, L. M.; Shukla, P.; Topkar, A.; Aziz, T.; Dugad, S.; Mahakud, B.; Mitra, S.; Mohanty, G. B.; Sur, N.; Sutar, B.; Banerjee, S.; Bhattacharya, S.; Chatterjee, S.; Das, P.; Guchait, M.; Jain, Sa.; Kumar, S.; Maity, M.; Majumder, G.; Mazumdar, K.; Sarkar, T.; Wickramage, N.; Chauhan, S.; Dube, S.; Hegde, V.; Kapoor, A.; Kothekar, K.; Pandey, S.; Rane, A.; Sharma, S.; Chenarani, S.; Eskandari Tadavani, E.; Etesami, S. M.; Khakzad, M.; Mohammadi Najafabadi, M.; Naseri, M.; Paktinat Mehdiabadi, S.; Rezaei Hosseinabadi, F.; Safarzadeh, B.; Zeinali, M.; Felcini, M.; Grunewald, M.; Abbrescia, M.; Calabria, C.; Colaleo, A.; Creanza, D.; Cristella, L.; De Filippis, N.; De Palma, M.; Errico, F.; Fiore, L.; Iaselli, G.; Lezki, S.; Maggi, G.; Maggi, M.; Miniello, G.; My, S.; Nuzzo, S.; Pompili, A.; Pugliese, G.; Radogna, R.; Ranieri, A.; Selvaggi, G.; Sharma, A.; Silvestris, L.; Venditti, R.; Verwilligen, P.; Abbiendi, G.; Battilana, C.; Bonacorsi, D.; Braibant-Giacomelli, S.; Campanini, R.; Capiluppi, P.; Castro, A.; Cavallo, F. R.; Chhibra, S. S.; Codispoti, G.; Cuffiani, M.; Dallavalle, G. M.; Fabbri, F.; Fanfani, A.; Fasanella, D.; Giacomelli, P.; Grandi, C.; Guiducci, L.; Marcellini, S.; Masetti, G.; Montanari, A.; Navarria, F. L.; Perrotta, A.; Rossi, A. M.; Rovelli, T.; Siroli, G. P.; Tosi, N.; Albergo, S.; Costa, S.; Di Mattia, A.; Giordano, F.; Potenza, R.; Tricomi, A.; Tuve, C.; Barbagli, G.; Chatterjee, K.; Ciulli, V.; Civinini, C.; D'Alessandro, R.; Focardi, E.; Lenzi, P.; Meschini, M.; Paoletti, S.; Russo, L.; Sguazzoni, G.; Strom, D.; Viliani, L.; Benussi, L.; Bianco, S.; Fabbri, F.; Piccolo, D.; Primavera, F.; Calvelli, V.; Ferro, F.; Robutti, E.; Tosi, S.; Benaglia, A.; Brianza, L.; Brivio, F.; Ciriolo, V.; Dinardo, M. E.; Fiorendi, S.; Gennai, S.; Ghezzi, A.; Govoni, P.; Malberti, M.; Malvezzi, S.; Manzoni, R. A.; Menasce, D.; Moroni, L.; Paganoni, M.; Pauwels, K.; Pedrini, D.; Pigazzini, S.; Ragazzi, S.; Tabarelli de Fatis, T.; Buontempo, S.; Cavallo, N.; Di Guida, S.; Fabozzi, F.; Fienga, F.; Iorio, A. O. M.; Khan, W. A.; Lista, L.; Meola, S.; Paolucci, P.; Sciacca, C.; Thyssen, F.; Azzi, P.; Bacchetta, N.; Benato, L.; Bisello, D.; Boletti, A.; Carlin, R.; Carvalho Antunes De Oliveira, A.; Checchia, P.; Dall'Osso, M.; De Castro Manzano, P.; Dorigo, T.; Gasparini, F.; Gasparini, U.; Gozzelino, A.; Lacaprara, S.; Lujan, P.; Margoni, M.; Meneguzzo, A. T.; Pozzobon, N.; Ronchese, P.; Rossin, R.; Simonetto, F.; Torassa, E.; Zanetti, M.; Zotto, P.; Zumerle, G.; Braghieri, A.; Magnani, A.; Montagna, P.; Ratti, S. P.; Re, V.; Ressegotti, M.; Riccardi, C.; Salvini, P.; Vai, I.; Vitulo, P.; Alunni Solestizi, L.; Biasini, M.; Bilei, G. M.; Cecchi, C.; Ciangottini, D.; Fanò, L.; Lariccia, P.; Leonardi, R.; Manoni, E.; Mantovani, G.; Mariani, V.; Menichelli, M.; Rossi, A.; Santocchia, A.; Spiga, D.; Androsov, K.; Azzurri, P.; Bagliesi, G.; Bernardini, J.; Boccali, T.; Borrello, L.; Castaldi, R.; Ciocci, M. A.; Dell'Orso, R.; Fedi, G.; Giannini, L.; Giassi, A.; Grippo, M. T.; Ligabue, F.; Lomtadze, T.; Manca, E.; Mandorli, G.; Martini, L.; Messineo, A.; Palla, F.; Rizzi, A.; Savoy-Navarro, A.; Spagnolo, P.; Tenchini, R.; Tonelli, G.; Venturi, A.; Verdini, P. G.; Barone, L.; Cavallari, F.; Cipriani, M.; Del Re, D.; Di Marco, E.; Diemoz, M.; Gelli, S.; Longo, E.; Margaroli, F.; Marzocchi, B.; Meridiani, P.; Organtini, G.; Paramatti, R.; Preiato, F.; Rahatlou, S.; Rovelli, C.; Santanastasio, F.; Amapane, N.; Arcidiacono, R.; Argiro, S.; Arneodo, M.; Bartosik, N.; Bellan, R.; Biino, C.; Cartiglia, N.; Cenna, F.; Costa, M.; Covarelli, R.; Degano, A.; Demaria, N.; Kiani, B.; Mariotti, C.; Maselli, S.; Migliore, E.; Monaco, V.; Monteil, E.; Monteno, M.; Obertino, M. M.; Pacher, L.; Pastrone, N.; Pelliccioni, M.; Pinna Angioni, G. L.; Ravera, F.; Romero, A.; Ruspa, M.; Sacchi, R.; Shchelina, K.; Sola, V.; Solano, A.; Staiano, A.; Traczyk, P.; Belforte, S.; Casarsa, M.; Cossutti, F.; Della Ricca, G.; Zanetti, A.; Kim, D. H.; Kim, G. N.; Kim, M. S.; Lee, J.; Lee, S.; Lee, S. W.; Moon, C. S.; Oh, Y. D.; Sekmen, S.; Son, D. C.; Yang, Y. C.; Lee, A.; Kim, H.; Moon, D. H.; Oh, G.; Brochero Cifuentes, J. A.; Goh, J.; Kim, T. J.; Cho, S.; Choi, S.; Go, Y.; Gyun, D.; Ha, S.; Hong, B.; Jo, Y.; Kim, Y.; Lee, K.; Lee, K. S.; Lee, S.; Lim, J.; Park, S. K.; Roh, Y.; Almond, J.; Kim, J.; Kim, J. S.; Lee, H.; Lee, K.; Nam, K.; Oh, S. B.; Radburn-Smith, B. C.; Seo, S. h.; Yang, U. K.; Yoo, H. D.; Yu, G. B.; Choi, M.; Kim, H.; Kim, J. H.; Lee, J. S. H.; Park, I. C.; Choi, Y.; Hwang, C.; Lee, J.; Yu, I.; Dudenas, V.; Juodagalvis, A.; Vaitkus, J.; Ahmed, I.; Ibrahim, Z. A.; Md Ali, M. A. B.; Mohamad Idris, F.; Wan Abdullah, W. A. T.; Yusli, M. N.; Zolkapli, Z.; Reyes-Almanza, R.; Ramirez-Sanchez, G.; Duran-Osuna, M. C.; Castilla-Valdez, H.; De La Cruz-Burelo, E.; Heredia-De La Cruz, I.; Rabadan-Trejo, R. I.; Lopez-Fernandez, R.; Mejia Guisao, J.; Sanchez-Hernandez, A.; Carrillo Moreno, S.; Oropeza Barrera, C.; Vazquez Valencia, F.; Pedraza, I.; Salazar Ibarguen, H. A.; Uribe Estrada, C.; Morelos Pineda, A.; Krofcheck, D.; Butler, P. H.; Ahmad, A.; Ahmad, M.; Hassan, Q.; Hoorani, H. R.; Saddique, A.; Shah, M. A.; Shoaib, M.; Waqas, M.; Bialkowska, H.; Bluj, M.; Boimska, B.; Frueboes, T.; Górski, M.; Kazana, M.; Nawrocki, K.; Szleper, M.; Zalewski, P.; Bunkowski, K.; Byszuk, A.; Doroba, K.; Kalinowski, A.; Konecki, M.; Krolikowski, J.; Misiura, M.; Olszewski, M.; Pyskir, A.; Walczak, M.; Bargassa, P.; Beirão Da Cruz E Silva, C.; Di Francesco, A.; Faccioli, P.; Galinhas, B.; Gallinaro, M.; Hollar, J.; Leonardo, N.; Lloret Iglesias, L.; Nemallapudi, M. V.; Seixas, J.; Strong, G.; Toldaiev, O.; Vadruccio, D.; Varela, J.; Afanasiev, S.; Bunin, P.; Gavrilenko, M.; Golutvin, I.; Gorbunov, I.; Kamenev, A.; Karjavin, V.; Lanev, A.; Malakhov, A.; Matveev, V.; Palichik, V.; Perelygin, V.; Shmatov, S.; Shulha, S.; Skatchkov, N.; Smirnov, V.; Voytishin, N.; Zarubin, A.; Ivanov, Y.; Kim, V.; Kuznetsova, E.; Levchenko, P.; Murzin, V.; Oreshkin, V.; Smirnov, I.; Sulimov, V.; Uvarov, L.; Vavilov, S.; Vorobyev, A.; Andreev, Yu.; Dermenev, A.; Gninenko, S.; Golubev, N.; Karneyeu, A.; Kirsanov, M.; Krasnikov, N.; Pashenkov, A.; Tlisov, D.; Toropin, A.; Epshteyn, V.; Gavrilov, V.; Lychkovskaya, N.; Popov, V.; Pozdnyakov, I.; Safronov, G.; Spiridonov, A.; Stepennov, A.; Toms, M.; Vlasov, E.; Zhokin, A.; Aushev, T.; Bylinkin, A.; Chadeeva, M.; Markin, O.; Parygin, P.; Philippov, D.; Polikarpov, S.; Rusinov, V.; Andreev, V.; Azarkin, M.; Dremin, I.; Kirakosyan, M.; Terkulov, A.; Baskakov, A.; Belyaev, A.; Boos, E.; Bunichev, V.; Dubinin, M.; Dudko, L.; Ershov, A.; Gribushin, A.; Klyukhin, V.; Kodolova, O.; Lokhtin, I.; Miagkov, I.; Obraztsov, S.; Petrushanko, S.; Savrin, V.; Blinov, V.; Skovpen, Y.; Shtol, D.; Azhgirey, I.; Bayshev, I.; Bitioukov, S.; Elumakhov, D.; Kachanov, V.; Kalinin, A.; Konstantinov, D.; Krychkine, V.; Petrov, V.; Ryutin, R.; Sobol, A.; Troshin, S.; Tyurin, N.; Uzunian, A.; Volkov, A.; Adzic, P.; Cirkovic, P.; Devetak, D.; Dordevic, M.; Milosevic, J.; Rekovic, V.; Alcaraz Maestre, J.; Barrio Luna, M.; Cerrada, M.; Colino, N.; De La Cruz, B.; Delgado Peris, A.; Escalante Del Valle, A.; Fernandez Bedoya, C.; Fernández Ramos, J. P.; Flix, J.; Fouz, M. C.; Garcia-Abia, P.; Gonzalez Lopez, O.; Goy Lopez, S.; Hernandez, J. M.; Josa, M. I.; Pérez-Calero Yzquierdo, A.; Puerta Pelayo, J.; Quintario Olmeda, A.; Redondo, I.; Romero, L.; Soares, M. S.; Álvarez Fernández, A.; de Trocóniz, J. F.; Missiroli, M.; Moran, D.; Cuevas, J.; Erice, C.; Fernandez Menendez, J.; Gonzalez Caballero, I.; González Fernández, J. R.; Palencia Cortezon, E.; Sanchez Cruz, S.; Suárez Andrés, I.; Vischia, P.; Vizan Garcia, J. M.; Cabrillo, I. J.; Calderon, A.; Chazin Quero, B.; Curras, E.; Duarte Campderros, J.; Fernandez, M.; Garcia-Ferrero, J.; Gomez, G.; Lopez Virto, A.; Marco, J.; Martinez Rivero, C.; Martinez Ruiz del Arbol, P.; Matorras, F.; Piedra Gomez, J.; Rodrigo, T.; Ruiz-Jimeno, A.; Scodellaro, L.; Trevisani, N.; Vila, I.; Vilar Cortabitarte, R.; Abbaneo, D.; Auffray, E.; Baillon, P.; Ball, A. H.; Barney, D.; Bianco, M.; Bloch, P.; Bocci, A.; Botta, C.; Camporesi, T.; Castello, R.; Cepeda, M.; Cerminara, G.; Chapon, E.; Chen, Y.; d'Enterria, D.; Dabrowski, A.; Daponte, V.; David, A.; De Gruttola, M.; De Roeck, A.; Dobson, M.; Dorney, B.; du Pree, T.; Dünser, M.; Dupont, N.; Elliott-Peisert, A.; Everaerts, P.; Fallavollita, F.; Franzoni, G.; Fulcher, J.; Funk, W.; Gigi, D.; Gill, K.; Glege, F.; Gulhan, D.; Harris, P.; Hegeman, J.; Innocente, V.; Janot, P.; Karacheban, O.; Kieseler, J.; Kirschenmann, H.; Knünz, V.; Kornmayer, A.; Kortelainen, M. J.; Lange, C.; Lecoq, P.; Lourenço, C.; Lucchini, M. T.; Malgeri, L.; Mannelli, M.; Martelli, A.; Meijers, F.; Merlin, J. A.; Mersi, S.; Meschi, E.; Milenovic, P.; Moortgat, F.; Mulders, M.; Neugebauer, H.; Orfanelli, S.; Orsini, L.; Pape, L.; Perez, E.; Peruzzi, M.; Petrilli, A.; Petrucciani, G.; Pfeiffer, A.; Pierini, M.; Racz, A.; Reis, T.; Rolandi, G.; Rovere, M.; Sakulin, H.; Schäfer, C.; Schwick, C.; Seidel, M.; Selvaggi, M.; Sharma, A.; Silva, P.; Sphicas, P.; Stakia, A.; Steggemann, J.; Stoye, M.; Tosi, M.; Treille, D.; Triossi, A.; Tsirou, A.; Veckalns, V.; Verweij, M.; Zeuner, W. D.; Bertl, W.; Caminada, L.; Deiters, K.; Erdmann, W.; Horisberger, R.; Ingram, Q.; Kaestli, H. C.; Kotlinski, D.; Langenegger, U.; Rohe, T.; Wiederkehr, S. A.; Bachmair, F.; Bäni, L.; Berger, P.; Bianchini, L.; Casal, B.; Dissertori, G.; Dittmar, M.; Donegà, M.; Grab, C.; Heidegger, C.; Hits, D.; Hoss, J.; Kasieczka, G.; Klijnsma, T.; Lustermann, W.; Mangano, B.; Marionneau, M.; Meinhard, M. T.; Meister, D.; Micheli, F.; Musella, P.; Nessi-Tedaldi, F.; Pandolfi, F.; Pata, J.; Pauss, F.; Perrin, G.; Perrozzi, L.; Quittnat, M.; Reichmann, M.; Schönenberger, M.; Shchutska, L.; Tavolaro, V. R.; Theofilatos, K.; Vesterbacka Olsson, M. L.; Wallny, R.; Zhu, D. H.; Aarrestad, T. K.; Amsler, C.; Canelli, M. F.; De Cosa, A.; Del Burgo, R.; Donato, S.; Galloni, C.; Hreus, T.; Kilminster, B.; Ngadiuba, J.; Pinna, D.; Rauco, G.; Robmann, P.; Salerno, D.; Seitz, C.; Takahashi, Y.; Zucchetta, A.; Candelise, V.; Doan, T. H.; Jain, Sh.; Khurana, R.; Kuo, C. M.; Lin, W.; Pozdnyakov, A.; Yu, S. S.; Kumar, Arun; Chang, P.; Chao, Y.; Chen, K. F.; Chen, P. H.; Fiori, F.; Hou, W.-S.; Hsiung, Y.; Liu, Y. F.; Lu, R.-S.; Paganis, E.; Psallidas, A.; Steen, A.; Tsai, J. f.; Asavapibhop, B.; Kovitanggoon, K.; Singh, G.; Srimanobhas, N.; Boran, F.; Cerci, S.; Damarseckin, S.; Demiroglu, Z. S.; Dozen, C.; Dumanoglu, I.; Girgis, S.; Gokbulut, G.; Guler, Y.; Hos, I.; Kangal, E. E.; Kara, O.; Kayis Topaksu, A.; Kiminsu, U.; Oglakci, M.; Onengut, G.; Ozdemir, K.; Sunar Cerci, D.; Tali, B.; Turkcapar, S.; Zorbakir, I. S.; Zorbilmez, C.; Bilin, B.; Karapinar, G.; Ocalan, K.; Yalvac, M.; Zeyrek, M.; Gülmez, E.; Kaya, M.; Kaya, O.; Tekten, S.; Yetkin, E. A.; Agaras, M. N.; Atay, S.; Cakir, A.; Cankocak, K.; Grynyov, B.; Levchuk, L.; Sorokin, P.; Aggleton, R.; Ball, F.; Beck, L.; Brooke, J. J.; Burns, D.; Clement, E.; Cussans, D.; Davignon, O.; Flacher, H.; Goldstein, J.; Grimes, M.; Heath, G. P.; Heath, H. F.; Jacob, J.; Kreczko, L.; Lucas, C.; Newbold, D. M.; Paramesvaran, S.; Poll, A.; Sakuma, T.; Seif El Nasr-storey, S.; Smith, D.; Smith, V. J.; Bell, K. W.; Belyaev, A.; Brew, C.; Brown, R. M.; Calligaris, L.; Cieri, D.; Cockerill, D. J. A.; Coughlan, J. A.; Harder, K.; Harper, S.; Olaiya, E.; Petyt, D.; Shepherd-Themistocleous, C. H.; Thea, A.; Tomalin, I. R.; Williams, T.; Auzinger, G.; Bainbridge, R.; Breeze, S.; Buchmuller, O.; Bundock, A.; Casasso, S.; Citron, M.; Colling, D.; Corpe, L.; Dauncey, P.; Davies, G.; De Wit, A.; Della Negra, M.; Di Maria, R.; Elwood, A.; Haddad, Y.; Hall, G.; Iles, G.; James, T.; Lane, R.; Laner, C.; Lyons, L.; Magnan, A.-M.; Malik, S.; Mastrolorenzo, L.; Matsushita, T.; Nash, J.; Nikitenko, A.; Palladino, V.; Pesaresi, M.; Raymond, D. M.; Richards, A.; Rose, A.; Scott, E.; Seez, C.; Shtipliyski, A.; Summers, S.; Tapper, A.; Uchida, K.; Vazquez Acosta, M.; Virdee, T.; Wardle, N.; Winterbottom, D.; Wright, J.; Zenz, S. C.; Cole, J. E.; Hobson, P. R.; Khan, A.; Kyberd, P.; Reid, I. D.; Symonds, P.; Teodorescu, L.; Turner, M.; Borzou, A.; Call, K.; Dittmann, J.; Hatakeyama, K.; Liu, H.; Pastika, N.; Smith, C.; Bartek, R.; Dominguez, A.; Buccilli, A.; Cooper, S. I.; Henderson, C.; Rumerio, P.; West, C.; Arcaro, D.; Avetisyan, A.; Bose, T.; Gastler, D.; Rankin, D.; Richardson, C.; Rohlf, J.; Sulak, L.; Zou, D.; Benelli, G.; Cutts, D.; Garabedian, A.; Hakala, J.; Heintz, U.; Hogan, J. M.; Kwok, K. H. M.; Laird, E.; Landsberg, G.; Mao, Z.; Narain, M.; Pazzini, J.; Piperov, S.; Sagir, S.; Syarif, R.; Yu, D.; Band, R.; Brainerd, C.; Burns, D.; Calderon De La Barca Sanchez, M.; Chertok, M.; Conway, J.; Conway, R.; Cox, P. T.; Erbacher, R.; Flores, C.; Funk, G.; Gardner, M.; Ko, W.; Lander, R.; Mclean, C.; Mulhearn, M.; Pellett, D.; Pilot, J.; Shalhout, S.; Shi, M.; Smith, J.; Squires, M.; Stolp, D.; Tos, K.; Tripathi, M.; Wang, Z.; Bachtis, M.; Bravo, C.; Cousins, R.; Dasgupta, A.; Florent, A.; Hauser, J.; Ignatenko, M.; Mccoll, N.; Saltzberg, D.; Schnaible, C.; Valuev, V.; Bouvier, E.; Burt, K.; Clare, R.; Ellison, J.; Gary, J. W.; Ghiasi Shirazi, S. M. A.; Hanson, G.; Heilman, J.; Jandir, P.; Kennedy, E.; Lacroix, F.; Long, O. R.; Olmedo Negrete, M.; Paneva, M. I.; Shrinivas, A.; Si, W.; Wang, L.; Wei, H.; Wimpenny, S.; Yates, B. R.; Branson, J. G.; Cittolin, S.; Derdzinski, M.; Hashemi, B.; Holzner, A.; Klein, D.; Kole, G.; Krutelyov, V.; Letts, J.; Macneill, I.; Masciovecchio, M.; Olivito, D.; Padhi, S.; Pieri, M.; Sani, M.; Sharma, V.; Simon, S.; Tadel, M.; Vartak, A.; Wasserbaech, S.; Wood, J.; Würthwein, F.; Yagil, A.; Zevi Della Porta, G.; Amin, N.; Bhandari, R.; Bradmiller-Feld, J.; Campagnari, C.; Dishaw, A.; Dutta, V.; Franco Sevilla, M.; George, C.; Golf, F.; Gouskos, L.; Gran, J.; Heller, R.; Incandela, J.; Mullin, S. D.; Ovcharova, A.; Qu, H.; Richman, J.; Stuart, D.; Suarez, I.; Yoo, J.; Anderson, D.; Bendavid, J.; Bornheim, A.; Lawhorn, J. M.; Newman, H. B.; Nguyen, T.; Pena, C.; Spiropulu, M.; Vlimant, J. R.; Xie, S.; Zhang, Z.; Zhu, R. Y.; Andrews, M. B.; Ferguson, T.; Mudholkar, T.; Paulini, M.; Russ, J.; Sun, M.; Vogel, H.; Vorobiev, I.; Weinberg, M.; Cumalat, J. P.; Ford, W. T.; Jensen, F.; Johnson, A.; Krohn, M.; Leontsinis, S.; Mulholland, T.; Stenson, K.; Wagner, S. R.; Alexander, J.; Chaves, J.; Chu, J.; Dittmer, S.; Mcdermott, K.; Mirman, N.; Patterson, J. R.; Rinkevicius, A.; Ryd, A.; Skinnari, L.; Soffi, L.; Tan, S. M.; Tao, Z.; Thom, J.; Tucker, J.; Wittich, P.; Zientek, M.; Abdullin, S.; Albrow, M.; Apollinari, G.; Apresyan, A.; Apyan, A.; Banerjee, S.; Bauerdick, L. A. T.; Beretvas, A.; Berryhill, J.; Bhat, P. C.; Bolla, G.; Burkett, K.; Butler, J. N.; Canepa, A.; Cerati, G. B.; Cheung, H. W. K.; Chlebana, F.; Cremonesi, M.; Duarte, J.; Elvira, V. D.; Freeman, J.; Gecse, Z.; Gottschalk, E.; Gray, L.; Green, D.; Grünendahl, S.; Gutsche, O.; Harris, R. M.; Hasegawa, S.; Hirschauer, J.; Hu, Z.; Jayatilaka, B.; Jindariani, S.; Johnson, M.; Joshi, U.; Klima, B.; Kreis, B.; Lammel, S.; Lincoln, D.; Lipton, R.; Liu, M.; Liu, T.; Lopes De Sá, R.; Lykken, J.; Maeshima, K.; Magini, N.; Marraffino, J. M.; Maruyama, S.; Mason, D.; McBride, P.; Merkel, P.; Mrenna, S.; Nahn, S.; O'Dell, V.; Pedro, K.; Prokofyev, O.; Rakness, G.; Ristori, L.; Schneider, B.; Sexton-Kennedy, E.; Soha, A.; Spalding, W. J.; Spiegel, L.; Stoynev, S.; Strait, J.; Strobbe, N.; Taylor, L.; Tkaczyk, S.; Tran, N. V.; Uplegger, L.; Vaandering, E. W.; Vernieri, C.; Verzocchi, M.; Vidal, R.; Wang, M.; Weber, H. A.; Whitbeck, A.; Acosta, D.; Avery, P.; Bortignon, P.; Bourilkov, D.; Brinkerhoff, A.; Carnes, A.; Carver, M.; Curry, D.; Field, R. D.; Furic, I. K.; Konigsberg, J.; Korytov, A.; Kotov, K.; Ma, P.; Matchev, K.; Mei, H.; Mitselmakher, G.; Rank, D.; Sperka, D.; Terentyev, N.; Thomas, L.; Wang, J.; Wang, S.; Yelton, J.; Joshi, Y. R.; Linn, S.; Markowitz, P.; Rodriguez, J. L.; Ackert, A.; Adams, T.; Askew, A.; Hagopian, S.; Hagopian, V.; Johnson, K. F.; Kolberg, T.; Martinez, G.; Perry, T.; Prosper, H.; Saha, A.; Santra, A.; Sharma, V.; Yohay, R.; Baarmand, M. M.; Bhopatkar, V.; Colafranceschi, S.; Hohlmann, M.; Noonan, D.; Roy, T.; Yumiceva, F.; Adams, M. R.; Apanasevich, L.; Berry, D.; Betts, R. R.; Cavanaugh, R.; Chen, X.; Evdokimov, O.; Gerber, C. E.; Hangal, D. A.; Hofman, D. J.; Jung, K.; Kamin, J.; Sandoval Gonzalez, I. D.; Tonjes, M. B.; Trauger, H.; Varelas, N.; Wang, H.; Wu, Z.; Zhang, J.; Bilki, B.; Clarida, W.; Dilsiz, K.; Durgut, S.; Gandrajula, R. P.; Haytmyradov, M.; Khristenko, V.; Merlo, J.-P.; Mermerkaya, H.; Mestvirishvili, A.; Moeller, A.; Nachtman, J.; Ogul, H.; Onel, Y.; Ozok, F.; Penzo, A.; Snyder, C.; Tiras, E.; Wetzel, J.; Yi, K.; Blumenfeld, B.; Cocoros, A.; Eminizer, N.; Fehling, D.; Feng, L.; Gritsan, A. V.; Maksimovic, P.; Roskes, J.; Sarica, U.; Swartz, M.; Xiao, M.; You, C.; Al-bataineh, A.; Baringer, P.; Bean, A.; Boren, S.; Bowen, J.; Castle, J.; Khalil, S.; Kropivnitskaya, A.; Majumder, D.; Mcbrayer, W.; Murray, M.; Royon, C.; Sanders, S.; Schmitz, E.; Stringer, R.; Tapia Takaki, J. D.; Wang, Q.; Ivanov, A.; Kaadze, K.; Maravin, Y.; Mohammadi, A.; Saini, L. K.; Skhirtladze, N.; Toda, S.; Rebassoo, F.; Wright, D.; Anelli, C.; Baden, A.; Baron, O.; Belloni, A.; Calvert, B.; Eno, S. C.; Ferraioli, C.; Hadley, N. J.; Jabeen, S.; Jeng, G. Y.; Kellogg, R. G.; Kunkle, J.; Mignerey, A. C.; Ricci-Tam, F.; Shin, Y. H.; Skuja, A.; Tonwar, S. C.; Abercrombie, D.; Allen, B.; Azzolini, V.; Barbieri, R.; Baty, A.; Bi, R.; Brandt, S.; Busza, W.; Cali, I. A.; D'Alfonso, M.; Demiragli, Z.; Gomez Ceballos, G.; Goncharov, M.; Hsu, D.; Iiyama, Y.; Innocenti, G. M.; Klute, M.; Kovalskyi, D.; Lai, Y. S.; Lee, Y.-J.; Levin, A.; Luckey, P. D.; Maier, B.; Marini, A. C.; Mcginn, C.; Mironov, C.; Narayanan, S.; Niu, X.; Paus, C.; Roland, C.; Roland, G.; Salfeld-Nebgen, J.; Stephans, G. S. F.; Tatar, K.; Velicanu, D.; Wang, J.; Wang, T. W.; Wyslouch, B.; Benvenuti, A. C.; Chatterjee, R. M.; Evans, A.; Hansen, P.; Kalafut, S.; Kubota, Y.; Lesko, Z.; Mans, J.; Nourbakhsh, S.; Ruckstuhl, N.; Rusack, R.; Turkewitz, J.; Acosta, J. G.; Oliveros, S.; Avdeeva, E.; Bloom, K.; Claes, D. R.; Fangmeier, C.; Gonzalez Suarez, R.; Kamalieddin, R.; Kravchenko, I.; Monroy, J.; Siado, J. E.; Snow, G. R.; Stieger, B.; Alyari, M.; Dolen, J.; Godshalk, A.; Harrington, C.; Iashvili, I.; Nguyen, D.; Parker, A.; Rappoccio, S.; Roozbahani, B.; Alverson, G.; Barberis, E.; Hortiangtham, A.; Massironi, A.; Morse, D. M.; Nash, D.; Orimoto, T.; Teixeira De Lima, R.; Trocino, D.; Wood, D.; Bhattacharya, S.; Charaf, O.; Hahn, K. A.; Mucia, N.; Odell, N.; Pollack, B.; Schmitt, M. H.; Sung, K.; Trovato, M.; Velasco, M.; Dev, N.; Hildreth, M.; Hurtado Anampa, K.; Jessop, C.; Karmgard, D. J.; Kellams, N.; Lannon, K.; Loukas, N.; Marinelli, N.; Meng, F.; Mueller, C.; Musienko, Y.; Planer, M.; Reinsvold, A.; Ruchti, R.; Smith, G.; Taroni, S.; Wayne, M.; Wolf, M.; Woodard, A.; Alimena, J.; Antonelli, L.; Bylsma, B.; Durkin, L. S.; Flowers, S.; Francis, B.; Hart, A.; Hill, C.; Ji, W.; Liu, B.; Luo, W.; Puigh, D.; Winer, B. L.; Wulsin, H. W.; Cooperstein, S.; Driga, O.; Elmer, P.; Hardenbrook, J.; Hebda, P.; Higginbotham, S.; Lange, D.; Luo, J.; Marlow, D.; Mei, K.; Ojalvo, I.; Olsen, J.; Palmer, C.; Piroué, P.; Stickland, D.; Tully, C.; Malik, S.; Norberg, S.; Barker, A.; Barnes, V. E.; Das, S.; Folgueras, S.; Gutay, L.; Jha, M. K.; Jones, M.; Jung, A. W.; Khatiwada, A.; Miller, D. H.; Neumeister, N.; Peng, C. C.; Schulte, J. F.; Sun, J.; Wang, F.; Xie, W.; Cheng, T.; Parashar, N.; Stupak, J.; Adair, A.; Akgun, B.; Chen, Z.; Ecklund, K. M.; Geurts, F. J. M.; Guilbaud, M.; Li, W.; Michlin, B.; Northup, M.; Padley, B. P.; Roberts, J.; Rorie, J.; Tu, Z.; Zabel, J.; Bodek, A.; de Barbaro, P.; Demina, R.; Duh, Y. t.; Ferbel, T.; Galanti, M.; Garcia-Bellido, A.; Han, J.; Hindrichs, O.; Khukhunaishvili, A.; Lo, K. H.; Tan, P.; Verzetti, M.; Ciesielski, R.; Goulianos, K.; Mesropian, C.; Agapitos, A.; Chou, J. P.; Gershtein, Y.; Gómez Espinosa, T. A.; Halkiadakis, E.; Heindl, M.; Hughes, E.; Kaplan, S.; Kunnawalkam Elayavalli, R.; Kyriacou, S.; Lath, A.; Montalvo, R.; Nash, K.; Osherson, M.; Saka, H.; Salur, S.; Schnetzer, S.; Sheffield, D.; Somalwar, S.; Stone, R.; Thomas, S.; Thomassen, P.; Walker, M.; Delannoy, A. G.; Foerster, M.; Heideman, J.; Riley, G.; Rose, K.; Spanier, S.; Thapa, K.; Bouhali, O.; Castaneda Hernandez, A.; Celik, A.; Dalchenko, M.; De Mattia, M.; Delgado, A.; Dildick, S.; Eusebi, R.; Gilmore, J.; Huang, T.; Kamon, T.; Mueller, R.; Pakhotin, Y.; Patel, R.; Perloff, A.; Perniè, L.; Rathjens, D.; Safonov, A.; Tatarinov, A.; Ulmer, K. A.; Akchurin, N.; Damgov, J.; De Guio, F.; Dudero, P. R.; Faulkner, J.; Gurpinar, E.; Kunori, S.; Lamichhane, K.; Lee, S. W.; Libeiro, T.; Peltola, T.; Undleeb, S.; Volobouev, I.; Wang, Z.; Greene, S.; Gurrola, A.; Janjam, R.; Johns, W.; Maguire, C.; Melo, A.; Ni, H.; Sheldon, P.; Tuo, S.; Velkovska, J.; Xu, Q.; Arenton, M. W.; Barria, P.; Cox, B.; Hirosky, R.; Ledovskoy, A.; Li, H.; Neu, C.; Sinthuprasith, T.; Wang, Y.; Wolfe, E.; Xia, F.; Harr, R.; Karchin, P. E.; Sturdy, J.; Zaleski, S.; Brodski, M.; Buchanan, J.; Caillol, C.; Dasu, S.; Dodd, L.; Duric, S.; Gomber, B.; Grothe, M.; Herndon, M.; Hervé, A.; Hussain, U.; Klabbers, P.; Lanaro, A.; Levine, A.; Long, K.; Loveless, R.; Pierro, G. A.; Polese, G.; Ruggles, T.; Savin, A.; Smith, N.; Smith, W. H.; Taylor, D.; Woods, N.; CMS Collaboration

2017-12-01

A search is performed for anomalous interactions of the recently discovered Higgs boson using matrix element techniques with the information from its decay to four leptons and from associated Higgs boson production with two quark jets in either vector boson fusion or associated production with a vector boson. The data were recorded by the CMS experiment at the LHC at a center-of-mass energy of 13TeV and correspond to an integrated luminosity of 38.6fb-1. They are combined with the data collected at center-of-mass energies of 7 and 8TeV, corresponding to integrated luminosities of 5.1 and 19.7fb-1, respectively. All observations are consistent with the expectations for the standard model Higgs boson.

Parallel computation safety analysis irradiation targets fission product molybdenum in neutronic aspect using the successive over-relaxation algorithm

NASA Astrophysics Data System (ADS)

Susmikanti, Mike; Dewayatna, Winter; Sulistyo, Yos

2014-09-01

One of the research activities in support of commercial radioisotope production program is a safety research on target FPM (Fission Product Molybdenum) irradiation. FPM targets form a tube made of stainless steel which contains nuclear-grade high-enrichment uranium. The FPM irradiation tube is intended to obtain fission products. Fission materials such as Mo99 used widely the form of kits in the medical world. The neutronics problem is solved using first-order perturbation theory derived from the diffusion equation for four groups. In contrast, Mo isotopes have longer half-lives, about 3 days (66 hours), so the delivery of radioisotopes to consumer centers and storage is possible though still limited. The production of this isotope potentially gives significant economic value. The criticality and flux in multigroup diffusion model was calculated for various irradiation positions and uranium contents. This model involves complex computation, with large and sparse matrix system. Several parallel algorithms have been developed for the sparse and large matrix solution. In this paper, a successive over-relaxation (SOR) algorithm was implemented for the calculation of reactivity coefficients which can be done in parallel. Previous works performed reactivity calculations serially with Gauss-Seidel iteratives. The parallel method can be used to solve multigroup diffusion equation system and calculate the criticality and reactivity coefficients. In this research a computer code was developed to exploit parallel processing to perform reactivity calculations which were to be used in safety analysis. The parallel processing in the multicore computer system allows the calculation to be performed more quickly. This code was applied for the safety limits calculation of irradiated FPM targets containing highly enriched uranium. The results of calculations neutron show that for uranium contents of 1.7676 g and 6.1866 g (× 106 cm-1) in a tube, their delta reactivities are the still within safety limits; however, for 7.9542 g and 8.838 g (× 106 cm-1) the limits were exceeded.

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

2017-12-01

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

[Orthogonal Vector Projection Algorithm for Spectral Unmixing].

PubMed

Song, Mei-ping; Xu, Xing-wei; Chang, Chein-I; An, Ju-bai; Yao, Li

2015-12-01

Spectrum unmixing is an important part of hyperspectral technologies, which is essential for material quantity analysis in hyperspectral imagery. Most linear unmixing algorithms require computations of matrix multiplication and matrix inversion or matrix determination. These are difficult for programming, especially hard for realization on hardware. At the same time, the computation costs of the algorithms increase significantly as the number of endmembers grows. Here, based on the traditional algorithm Orthogonal Subspace Projection, a new method called. Orthogonal Vector Projection is prompted using orthogonal principle. It simplifies this process by avoiding matrix multiplication and inversion. It firstly computes the final orthogonal vector via Gram-Schmidt process for each endmember spectrum. And then, these orthogonal vectors are used as projection vector for the pixel signature. The unconstrained abundance can be obtained directly by projecting the signature to the projection vectors, and computing the ratio of projected vector length and orthogonal vector length. Compared to the Orthogonal Subspace Projection and Least Squares Error algorithms, this method does not need matrix inversion, which is much computation costing and hard to implement on hardware. It just completes the orthogonalization process by repeated vector operations, easy for application on both parallel computation and hardware. The reasonability of the algorithm is proved by its relationship with Orthogonal Sub-space Projection and Least Squares Error algorithms. And its computational complexity is also compared with the other two algorithms', which is the lowest one. At last, the experimental results on synthetic image and real image are also provided, giving another evidence for effectiveness of the method.

3-D Magnetotelluric Forward Modeling And Inversion Incorporating Topography By Using Vector Finite-Element Method Combined With Divergence Corrections Based On The Magnetic Field (VFEH++)

NASA Astrophysics Data System (ADS)

Shi, X.; Utada, H.; Jiaying, W.

2009-12-01

The vector finite-element method combined with divergence corrections based on the magnetic field H, referred to as VFEH++ method, is developed to simulate the magnetotelluric (MT) responses of 3-D conductivity models. The advantages of the new VFEH++ method are the use of edge-elements to eliminate the vector parasites and the divergence corrections to explicitly guarantee the divergence-free conditions in the whole modeling domain. 3-D MT topographic responses are modeling using the new VFEH++ method, and are compared with those calculated by other numerical methods. The results show that MT responses can be modeled highly accurate using the VFEH+ +method. The VFEH++ algorithm is also employed for the 3-D MT data inversion incorporating topography. The 3-D MT inverse problem is formulated as a minimization problem of the regularized misfit function. In order to avoid the huge memory requirement and very long time for computing the Jacobian sensitivity matrix for Gauss-Newton method, we employ the conjugate gradient (CG) approach to solve the inversion equation. In each iteration of CG algorithm, the cost computation is the product of the Jacobian sensitivity matrix with a model vector x or its transpose with a data vector y, which can be transformed into two pseudo-forwarding modeling. This avoids the full explicitly Jacobian matrix calculation and storage which leads to considerable savings in the memory required by the inversion program in PC computer. The performance of CG algorithm will be illustrated by several typical 3-D models with horizontal earth surface and topographic surfaces. The results show that the VFEH++ and CG algorithms can be effectively employed to 3-D MT field data inversion.

Finite-time scaling at the Anderson transition for vibrations in solids

NASA Astrophysics Data System (ADS)

Beltukov, Y. M.; Skipetrov, S. E.

2017-11-01

A model in which a three-dimensional elastic medium is represented by a network of identical masses connected by springs of random strengths and allowed to vibrate only along a selected axis of the reference frame exhibits an Anderson localization transition. To study this transition, we assume that the dynamical matrix of the network is given by a product of a sparse random matrix with real, independent, Gaussian-distributed nonzero entries and its transpose. A finite-time scaling analysis of the system's response to an initial excitation allows us to estimate the critical parameters of the localization transition. The critical exponent is found to be ν =1.57 ±0.02 , in agreement with previous studies of the Anderson transition belonging to the three-dimensional orthogonal universality class.

Partitioning sparse matrices with eigenvectors of graphs

NASA Technical Reports Server (NTRS)

Pothen, Alex; Simon, Horst D.; Liou, Kang-Pu

1990-01-01

The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.

Direction of Arrival Estimation for MIMO Radar via Unitary Nuclear Norm Minimization

PubMed Central

Wang, Xianpeng; Huang, Mengxing; Wu, Xiaoqin; Bi, Guoan

2017-01-01

In this paper, we consider the direction of arrival (DOA) estimation issue of noncircular (NC) source in multiple-input multiple-output (MIMO) radar and propose a novel unitary nuclear norm minimization (UNNM) algorithm. In the proposed method, the noncircular properties of signals are used to double the virtual array aperture, and the real-valued data are obtained by utilizing unitary transformation. Then a real-valued block sparse model is established based on a novel over-complete dictionary, and a UNNM algorithm is formulated for recovering the block-sparse matrix. In addition, the real-valued NC-MUSIC spectrum is used to design a weight matrix for reweighting the nuclear norm minimization to achieve the enhanced sparsity of solutions. Finally, the DOA is estimated by searching the non-zero blocks of the recovered matrix. Because of using the noncircular properties of signals to extend the virtual array aperture and an additional real structure to suppress the noise, the proposed method provides better performance compared with the conventional sparse recovery based algorithms. Furthermore, the proposed method can handle the case of underdetermined DOA estimation. Simulation results show the effectiveness and advantages of the proposed method. PMID:28441770

A Two-Layer Least Squares Support Vector Machine Approach to Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Liu, Jingli; Li, Jianping; Xu, Weixuan; Shi, Yong

Least squares support vector machine (LS-SVM) is a revised version of support vector machine (SVM) and has been proved to be a useful tool for pattern recognition. LS-SVM had excellent generalization performance and low computational cost. In this paper, we propose a new method called two-layer least squares support vector machine which combines kernel principle component analysis (KPCA) and linear programming form of least square support vector machine. With this method sparseness and robustness is obtained while solving large dimensional and large scale database. A U.S. commercial credit card database is used to test the efficiency of our method and the result proved to be a satisfactory one.

How Well Does Fracture Set Characterization Reduce Uncertainty in Capture Zone Size for Wells Situated in Sedimentary Bedrock Aquifers?

NASA Astrophysics Data System (ADS)

West, A. C.; Novakowski, K. S.

2005-12-01

Regional groundwater flow models are rife with uncertainty. The three-dimensional flux vector fields must generally be inferred using inverse modelling from sparse measurements of hydraulic head, from measurements of hydraulic parameters at a scale that is miniscule in comparison to that of the domain, and from none to a very few measurements of recharge or discharge rate. Despite the inherent uncertainty in these models they are routinely used to delineate steady-state or time-of-travel capture zones for the purpose of wellhead protection. The latter are defined as the volume of the aquifer within which released particles will arrive at the well within the specified time and their delineation requires the additional step of dividing the magnitudes of the flux vectors by the assumed porosity to arrive at the ``average linear groundwater velocity'' vector field. Since the porosity is usually assumed constant over the domain one could be forgiven for thinking that the uncertainty introduced at this step is minor in comparison to the flow model calibration step. We consider this question when the porosity in question is fracture porosity in flat-lying sedimentary bedrock. We also consider whether or not the diffusive uptake of solute into the rock matrix which lies between the source and the production well reduces or enhances the uncertainty. To evaluate the uncertainty an aquifer cross section is conceptualized as an array of horizontal, randomly-spaced, parallel-plate fractures of random aperture, with adjacent horizontal fractures connected by vertical fractures again of random spacing and aperture. The source is assumed to be a continuous concentration (i.e. a dirichlet boundary condition) representing a leaking tank or a DNAPL pool, and the receptor is a fully pentrating well located in the down-gradient direction. In this context the time-of-travel capture zone is defined as the separation distance required such that the source does not contaminate the well beyond a threshold concentration within the specified time. Aquifers are simulated by drawing the random spacings and apertures from specified distributions. Predictions are made of capture zone size assuming various degrees of knowledge of these distributions, with the parameters of the horizontal fractures being estimated using simulated hydraulic tests and a maximum likelihood estimator. The uncertainty is evaluated by calculating the variance in the capture zone size estimated in multiple realizations. The results show that despite good strategies to estimate the parameters of the horizontal fractures the uncertainty in capture zone size is enormous, mostly due to the lack of available information on vertical fractures. Also, at realistic distances (less than ten kilometers) and using realistic transmissivity distributions for the horizontal fractures the uptake of solute from fractures into matrix cannot be relied upon to protect the production well from contamination.

MATLAB Simulation of Gradient-Based Neural Network for Online Matrix Inversion

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Chen, Ke; Ma, Weimu; Li, Xiao-Dong

This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Tensor Dictionary Learning for Positive Definite Matrices.

PubMed

Sivalingam, Ravishankar; Boley, Daniel; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2015-11-01

Sparse models have proven to be extremely successful in image processing and computer vision. However, a majority of the effort has been focused on sparse representation of vectors and low-rank models for general matrices. The success of sparse modeling, along with popularity of region covariances, has inspired the development of sparse coding approaches for these positive definite descriptors. While in earlier work, the dictionary was formed from all, or a random subset of, the training signals, it is clearly advantageous to learn a concise dictionary from the entire training set. In this paper, we propose a novel approach for dictionary learning over positive definite matrices. The dictionary is learned by alternating minimization between sparse coding and dictionary update stages, and different atom update methods are described. A discriminative version of the dictionary learning approach is also proposed, which simultaneously learns dictionaries for different classes in classification or clustering. Experimental results demonstrate the advantage of learning dictionaries from data both from reconstruction and classification viewpoints. Finally, a software library is presented comprising C++ binaries for all the positive definite sparse coding and dictionary learning approaches presented here.

Sparse Matrix Motivated Reconstruction of Far-Field Radiation Patterns

DTIC Science & Technology

2015-03-01

method for base - station antenna radiation patterns. IEEE Antennas Propagation Magazine. 2001;43(2):132. 4. Vasiliadis TG, Dimitriou D, Sergiadis JD...algorithm based on sparse representations of radiation patterns using the inverse Discrete Fourier Transform (DFT) and the inverse Discrete Cosine...patterns using a Model- Based Parameter Estimation (MBPE) technique that reduces the computational time required to model radiation patterns. Another

Task Parallel Incomplete Cholesky Factorization using 2D Partitioned-Block Layout

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

Kim, Kyungjoo; Rajamanickam, Sivasankaran; Stelle, George Widgery

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block layout. The algorithm-byblocks approach induces a task graph for the factorization. These tasks are inter-related to each other through their data dependences in the factorization algorithm. To process the tasks on various manycore architectures in a portable manner, we also present a portable tasking API that incorporates different tasking backends and device-specific features using an open-source framework for manycore platforms i.e., Kokkos. A performance evaluation is presented onmore » both Intel Sandybridge and Xeon Phi platforms for matrices from the University of Florida sparse matrix collection to illustrate merits of the proposed task-based factorization. Experimental results demonstrate that our task-parallel implementation delivers about 26.6x speedup (geometric mean) over single-threaded incomplete Choleskyby- blocks and 19.2x speedup over serial Cholesky performance which does not carry tasking overhead using 56 threads on the Intel Xeon Phi processor for sparse matrices arising from various application problems.« less

Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction

NASA Astrophysics Data System (ADS)

Niu, Shanzhou; Yu, Gaohang; Ma, Jianhua; Wang, Jing

2018-02-01

Spectral computed tomography (CT) has been a promising technique in research and clinics because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of the different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifact suppression and resolution preservation.

An Alternative Method for Computing Mean and Covariance Matrix of Some Multivariate Distributions

ERIC Educational Resources Information Center

Radhakrishnan, R.; Choudhury, Askar

2009-01-01

Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…

Polar decomposition for attitude determination from vector observations

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.

1993-01-01

This work treats the problem of weighted least squares fitting of a 3D Euclidean-coordinate transformation matrix to a set of unit vectors measured in the reference and transformed coordinates. A closed-form analytic solution to the problem is re-derived. The fact that the solution is the closest orthogonal matrix to some matrix defined on the measured vectors and their weights is clearly demonstrated. Several known algorithms for computing the analytic closed form solution are considered. An algorithm is discussed which is based on the polar decomposition of matrices into the closest unitary matrix to the decomposed matrix and a Hermitian matrix. A somewhat longer improved algorithm is suggested too. A comparison of several algorithms is carried out using simulated data as well as real data from the Upper Atmosphere Research Satellite. The comparison is based on accuracy and time consumption. It is concluded that the algorithms based on polar decomposition yield a simple although somewhat less accurate solution. The precision of the latter algorithms increase with the number of the measured vectors and with the accuracy of their measurement.

Simple modification of Oja rule limits L1-norm of weight vector and leads to sparse connectivity.

PubMed

Aparin, Vladimir

2012-03-01

This letter describes a simple modification of the Oja learning rule, which asymptotically constrains the L1-norm of an input weight vector instead of the L2-norm as in the original rule. This constraining is local as opposed to commonly used instant normalizations, which require the knowledge of all input weights of a neuron to update each one of them individually. The proposed rule converges to a weight vector that is sparser (has more zero weights) than the vector learned by the original Oja rule with or without the zero bound, which could explain the developmental synaptic pruning.

Greedy Algorithms for Nonnegativity-Constrained Simultaneous Sparse Recovery

PubMed Central

Kim, Daeun; Haldar, Justin P.

2016-01-01

This work proposes a family of greedy algorithms to jointly reconstruct a set of vectors that are (i) nonnegative and (ii) simultaneously sparse with a shared support set. The proposed algorithms generalize previous approaches that were designed to impose these constraints individually. Similar to previous greedy algorithms for sparse recovery, the proposed algorithms iteratively identify promising support indices. In contrast to previous approaches, the support index selection procedure has been adapted to prioritize indices that are consistent with both the nonnegativity and shared support constraints. Empirical results demonstrate for the first time that the combined use of simultaneous sparsity and nonnegativity constraints can substantially improve recovery performance relative to existing greedy algorithms that impose less signal structure. PMID:26973368

Analysis of programming properties and the row-column generation method for 1-norm support vector machines.

PubMed

Zhang, Li; Zhou, WeiDa

2013-12-01

This paper deals with fast methods for training a 1-norm support vector machine (SVM). First, we define a specific class of linear programming with many sparse constraints, i.e., row-column sparse constraint linear programming (RCSC-LP). In nature, the 1-norm SVM is a sort of RCSC-LP. In order to construct subproblems for RCSC-LP and solve them, a family of row-column generation (RCG) methods is introduced. RCG methods belong to a category of decomposition techniques, and perform row and column generations in a parallel fashion. Specially, for the 1-norm SVM, the maximum size of subproblems of RCG is identical with the number of Support Vectors (SVs). We also introduce a semi-deleting rule for RCG methods and prove the convergence of RCG methods when using the semi-deleting rule. Experimental results on toy data and real-world datasets illustrate that it is efficient to use RCG to train the 1-norm SVM, especially in the case of small SVs. Copyright © 2013 Elsevier Ltd. All rights reserved.

Acoustooptic linear algebra processors - Architectures, algorithms, and applications

NASA Technical Reports Server (NTRS)

Casasent, D.

1984-01-01

Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.

Matrix-Inversion-Free Compressed Sensing With Variable Orthogonal Multi-Matching Pursuit Based on Prior Information for ECG Signals.

PubMed

Cheng, Yih-Chun; Tsai, Pei-Yun; Huang, Ming-Hao

2016-05-19

Low-complexity compressed sensing (CS) techniques for monitoring electrocardiogram (ECG) signals in wireless body sensor network (WBSN) are presented. The prior probability of ECG sparsity in the wavelet domain is first exploited. Then, variable orthogonal multi-matching pursuit (vOMMP) algorithm that consists of two phases is proposed. In the first phase, orthogonal matching pursuit (OMP) algorithm is adopted to effectively augment the support set with reliable indices and in the second phase, the orthogonal multi-matching pursuit (OMMP) is employed to rescue the missing indices. The reconstruction performance is thus enhanced with the prior information and the vOMMP algorithm. Furthermore, the computation-intensive pseudo-inverse operation is simplified by the matrix-inversion-free (MIF) technique based on QR decomposition. The vOMMP-MIF CS decoder is then implemented in 90 nm CMOS technology. The QR decomposition is accomplished by two systolic arrays working in parallel. The implementation supports three settings for obtaining 40, 44, and 48 coefficients in the sparse vector. From the measurement result, the power consumption is 11.7 mW at 0.9 V and 12 MHz. Compared to prior chip implementations, our design shows good hardware efficiency and is suitable for low-energy applications.

Solving periodic block tridiagonal systems using the Sherman-Morrison-Woodbury formula

NASA Technical Reports Server (NTRS)

Yarrow, Maurice

1989-01-01

Many algorithms for solving the Navier-Stokes equations require the solution of periodic block tridiagonal systems of equations. By applying a splitting to the matrix representing this system of equations, it may first be reduced to a block tridiagonal matrix plus an outer product of two block vectors. The Sherman-Morrison-Woodbury formula is then applied. The algorithm thus reduces a periodic banded system to a non-periodic banded system with additional right-hand sides and is of higher efficiency than standard Thomas algorithm/LU decompositions.

Slope angle estimation method based on sparse subspace clustering for probe safe landing

NASA Astrophysics Data System (ADS)

Li, Haibo; Cao, Yunfeng; Ding, Meng; Zhuang, Likui

2018-06-01

To avoid planetary probes landing on steep slopes where they may slip or tip over, a new method of slope angle estimation based on sparse subspace clustering is proposed to improve accuracy. First, a coordinate system is defined and established to describe the measured data of light detection and ranging (LIDAR). Second, this data is processed and expressed with a sparse representation. Third, on this basis, the data is made to cluster to determine which subspace it belongs to. Fourth, eliminating outliers in subspace, the correct data points are used for the fitting planes. Finally, the vectors normal to the planes are obtained using the plane model, and the angle between the normal vectors is obtained through calculation. Based on the geometric relationship, this angle is equal in value to the slope angle. The proposed method was tested in a series of experiments. The experimental results show that this method can effectively estimate the slope angle, can overcome the influence of noise and obtain an exact slope angle. Compared with other methods, this method can minimize the measuring errors and further improve the estimation accuracy of the slope angle.

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

PubMed Central

Bajaj, Chandrajit; Ihm, Insung; Min, Jungki; Oh, Jinsang

2009-01-01

The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of ȳ = Ax̄ + b̄, where A is a matrix, and x̄, ȳ and b̄ are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. PMID:19946569

Eigensolver for a Sparse, Large Hermitian Matrix

NASA Technical Reports Server (NTRS)

Tisdale, E. Robert; Oyafuso, Fabiano; Klimeck, Gerhard; Brown, R. Chris

2003-01-01

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Sparse distributed memory and related models

NASA Technical Reports Server (NTRS)

Kanerva, Pentti

1992-01-01

Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.

Newmark-Beta-FDTD method for super-resolution analysis of time reversal waves

NASA Astrophysics Data System (ADS)

Shi, Sheng-Bing; Shao, Wei; Ma, Jing; Jin, Congjun; Wang, Xiao-Hua

2017-09-01

In this work, a new unconditionally stable finite-difference time-domain (FDTD) method with the split-field perfectly matched layer (PML) is proposed for the analysis of time reversal (TR) waves. The proposed method is very suitable for multiscale problems involving microstructures. The spatial and temporal derivatives in this method are discretized by the central difference technique and Newmark-Beta algorithm, respectively, and the derivation results in the calculation of a banded-sparse matrix equation. Since the coefficient matrix keeps unchanged during the whole simulation process, the lower-upper (LU) decomposition of the matrix needs to be performed only once at the beginning of the calculation. Moreover, the reverse Cuthill-Mckee (RCM) technique, an effective preprocessing technique in bandwidth compression of sparse matrices, is used to improve computational efficiency. The super-resolution focusing of TR wave propagation in two- and three-dimensional spaces is included to validate the accuracy and efficiency of the proposed method.

Split Octonion Reformulation for Electromagnetic Chiral Media of Massive Dyons

NASA Astrophysics Data System (ADS)

Chanyal, B. C.

2017-12-01

In an explicit, unified, and covariant formulation of an octonion algebra, we study and generalize the electromagnetic chiral fields equations of massive dyons with the split octonionic representation. Starting with 2×2 Zorn’s vector matrix realization of split-octonion and its dual Euclidean spaces, we represent the unified structure of split octonionic electric and magnetic induction vectors for chiral media. As such, in present paper, we describe the chiral parameter and pairing constants in terms of split octonionic matrix representation of Drude-Born-Fedorov constitutive relations. We have expressed a split octonionic electromagnetic field vector for chiral media, which exhibits the unified field structure of electric and magnetic chiral fields of dyons. The beauty of split octonionic representation of Zorn vector matrix realization is that, the every scalar and vector components have its own meaning in the generalized chiral electromagnetism of dyons. Correspondingly, we obtained the alternative form of generalized Proca-Maxwell’s equations of massive dyons in chiral media. Furthermore, the continuity equations, Poynting theorem and wave propagation for generalized electromagnetic fields of chiral media of massive dyons are established by split octonionic form of Zorn vector matrix algebra.

Rank-Optimized Logistic Matrix Regression toward Improved Matrix Data Classification.

PubMed

Zhang, Jianguang; Jiang, Jianmin

2018-02-01

While existing logistic regression suffers from overfitting and often fails in considering structural information, we propose a novel matrix-based logistic regression to overcome the weakness. In the proposed method, 2D matrices are directly used to learn two groups of parameter vectors along each dimension without vectorization, which allows the proposed method to fully exploit the underlying structural information embedded inside the 2D matrices. Further, we add a joint [Formula: see text]-norm on two parameter matrices, which are organized by aligning each group of parameter vectors in columns. This added co-regularization term has two roles-enhancing the effect of regularization and optimizing the rank during the learning process. With our proposed fast iterative solution, we carried out extensive experiments. The results show that in comparison to both the traditional tensor-based methods and the vector-based regression methods, our proposed solution achieves better performance for matrix data classifications.

Embedded sparse representation of fMRI data via group-wise dictionary optimization

NASA Astrophysics Data System (ADS)

Zhu, Dajiang; Lin, Binbin; Faskowitz, Joshua; Ye, Jieping; Thompson, Paul M.

2016-03-01

Sparse learning enables dimension reduction and efficient modeling of high dimensional signals and images, but it may need to be tailored to best suit specific applications and datasets. Here we used sparse learning to efficiently represent functional magnetic resonance imaging (fMRI) data from the human brain. We propose a novel embedded sparse representation (ESR), to identify the most consistent dictionary atoms across different brain datasets via an iterative group-wise dictionary optimization procedure. In this framework, we introduced additional criteria to make the learned dictionary atoms more consistent across different subjects. We successfully identified four common dictionary atoms that follow the external task stimuli with very high accuracy. After projecting the corresponding coefficient vectors back into the 3-D brain volume space, the spatial patterns are also consistent with traditional fMRI analysis results. Our framework reveals common features of brain activation in a population, as a new, efficient fMRI analysis method.

Communication requirements of sparse Cholesky factorization with nested dissection ordering

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1989-01-01

Load distribution schemes for minimizing the communication requirements of the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems are presented. The total data traffic in factoring an n x n sparse symmetric positive definite matrix representing an n-vertex regular two-dimensional grid graph using n exp alpha, alpha not greater than 1, processors are shown to be O(n exp 1 + alpha/2). It is O(n), when n exp alpha, alpha not smaller than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal.

GPU-accelerated element-free reverse-time migration with Gauss points partition

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Jia, Xiaofeng; Qiang, Xiaodong

2018-06-01

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration (RTM). Compared with the finite difference method and the finite element method, the EFM has unique advantages: (1) independence of grids in computation and (2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and RTM for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition and utilise the graphics processing unit to improve the computational efficiency. We employ the compressed sparse row format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

Single-Sided Noinvasive Inspection of Multielement Sample Using Fan-Beam Multiplexed Compton Scatter Tomography

DTIC Science & Technology

2000-05-01

a vector , ρ "# represents the set of voxel densities sorted into a vector , and ( )A ρ $# "# represents a 8 mapping of the voxel densities to...density vector in equation (4) suggests that solving for ρ "# by direct inversion is not possible, calling for an iterative technique beginning with...the vector of measured spectra, and D is the diagonal matrix of the inverse of the variances. The diagonal matrix provides weighting terms, which

Alphavirus Replicon DNA Vectors Expressing Ebola GP and VP40 Antigens Induce Humoral and Cellular Immune Responses in Mice

PubMed Central

Ren, Shoufeng; Wei, Qimei; Cai, Liya; Yang, Xuejing; Xing, Cuicui; Tan, Feng; Leavenworth, Jianmei W.; Liang, Shaohui; Liu, Wenquan

2018-01-01

Ebola virus (EBOV) causes severe hemorrhagic fevers in humans, and no approved therapeutics or vaccine is currently available. Glycoprotein (GP) is the major protective antigen of EBOV, and can generate virus-like particles (VLPs) by co-expression with matrix protein (VP40). In this study, we constructed a recombinant Alphavirus Semliki Forest virus (SFV) replicon vector DREP to express EBOV GP and matrix viral protein (VP40). EBOV VLPs were successfully generated and achieved budding from 293 cells after co-transfection with DREP-based GP and VP40 vectors (DREP-GP+DREP-VP40). Vaccination of BALB/c mice with DREP-GP, DREP-VP40, or DREP-GP+DREP-VP40 vectors, followed by immediate electroporation resulted in a mixed IgG subclass production, which recognized EBOV GP and/or VP40 proteins. This vaccination regimen also led to the generation of both Th1 and Th2 cellular immune responses in mice. Notably, vaccination with DREP-GP and DREP-VP40, which produces both GP and VP40 antigens, induced a significantly higher level of anti-GP IgG2a antibody and increased IFN-γ secreting CD8+ T-cell responses relative to vaccination with DREP-GP or DREP-VP40 vector alone. Our study indicates that co-expression of GP and VP40 antigens based on the SFV replicon vector generates EBOV VLPs in vitro, and vaccination with recombinant DREP vectors containing GP and VP40 antigens induces Ebola antigen-specific humoral and cellular immune responses in mice. This novel approach provides a simple and efficient vaccine platform for Ebola disease prevention. PMID:29375526

Determining conduction patterns on a sparse electrode grid: Implications for the analysis of clinical arrhythmias

NASA Astrophysics Data System (ADS)

Vidmar, David; Narayan, Sanjiv M.; Krummen, David E.; Rappel, Wouter-Jan

2016-11-01

We present a general method of utilizing bioelectric recordings from a spatially sparse electrode grid to compute a dynamic vector field describing the underlying propagation of electrical activity. This vector field, termed the wave-front flow field, permits quantitative analysis of the magnitude of rotational activity (vorticity) and focal activity (divergence) at each spatial point. We apply this method to signals recorded during arrhythmias in human atria and ventricles using a multipolar contact catheter and show that the flow fields correlate with corresponding activation maps. Further, regions of elevated vorticity and divergence correspond to sites identified as clinically significant rotors and focal sources where therapeutic intervention can be effective. These flow fields can provide quantitative insights into the dynamics of normal and abnormal conduction in humans and could potentially be used to enhance therapies for cardiac arrhythmias.

Sparse Reconstruction of Regional Gravity Signal Based on Stabilized Orthogonal Matching Pursuit (SOMP)

NASA Astrophysics Data System (ADS)

Saadat, S. A.; Safari, A.; Needell, D.

2016-06-01

The main role of gravity field recovery is the study of dynamic processes in the interior of the Earth especially in exploration geophysics. In this paper, the Stabilized Orthogonal Matching Pursuit (SOMP) algorithm is introduced for sparse reconstruction of regional gravity signals of the Earth. In practical applications, ill-posed problems may be encountered regarding unknown parameters that are sensitive to the data perturbations. Therefore, an appropriate regularization method needs to be applied to find a stabilized solution. The SOMP algorithm aims to regularize the norm of the solution vector, while also minimizing the norm of the corresponding residual vector. In this procedure, a convergence point of the algorithm that specifies optimal sparsity-level of the problem is determined. The results show that the SOMP algorithm finds the stabilized solution for the ill-posed problem at the optimal sparsity-level, improving upon existing sparsity based approaches.

Incremental Transductive Learning Approaches to Schistosomiasis Vector Classification

NASA Astrophysics Data System (ADS)

Fusco, Terence; Bi, Yaxin; Wang, Haiying; Browne, Fiona

2016-08-01

The key issues pertaining to collection of epidemic disease data for our analysis purposes are that it is a labour intensive, time consuming and expensive process resulting in availability of sparse sample data which we use to develop prediction models. To address this sparse data issue, we present the novel Incremental Transductive methods to circumvent the data collection process by applying previously acquired data to provide consistent, confidence-based labelling alternatives to field survey research. We investigated various reasoning approaches for semi-supervised machine learning including Bayesian models for labelling data. The results show that using the proposed methods, we can label instances of data with a class of vector density at a high level of confidence. By applying the Liberal and Strict Training Approaches, we provide a labelling and classification alternative to standalone algorithms. The methods in this paper are components in the process of reducing the proliferation of the Schistosomiasis disease and its effects.

Attitude determination using vector observations: A fast optimal matrix algorithm

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1993-01-01

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function.

Color normalization of histology slides using graph regularized sparse NMF

NASA Astrophysics Data System (ADS)

Sha, Lingdao; Schonfeld, Dan; Sethi, Amit

2017-03-01

Computer based automatic medical image processing and quantification are becoming popular in digital pathology. However, preparation of histology slides can vary widely due to differences in staining equipment, procedures and reagents, which can reduce the accuracy of algorithms that analyze their color and texture information. To re- duce the unwanted color variations, various supervised and unsupervised color normalization methods have been proposed. Compared with supervised color normalization methods, unsupervised color normalization methods have advantages of time and cost efficient and universal applicability. Most of the unsupervised color normaliza- tion methods for histology are based on stain separation. Based on the fact that stain concentration cannot be negative and different parts of the tissue absorb different stains, nonnegative matrix factorization (NMF), and particular its sparse version (SNMF), are good candidates for stain separation. However, most of the existing unsupervised color normalization method like PCA, ICA, NMF and SNMF fail to consider important information about sparse manifolds that its pixels occupy, which could potentially result in loss of texture information during color normalization. Manifold learning methods like Graph Laplacian have proven to be very effective in interpreting high-dimensional data. In this paper, we propose a novel unsupervised stain separation method called graph regularized sparse nonnegative matrix factorization (GSNMF). By considering the sparse prior of stain concentration together with manifold information from high-dimensional image data, our method shows better performance in stain color deconvolution than existing unsupervised color deconvolution methods, especially in keeping connected texture information. To utilized the texture information, we construct a nearest neighbor graph between pixels within a spatial area of an image based on their distances using heat kernal in lαβ space. The representation of a pixel in the stain density space is constrained to follow the feature distance of the pixel to pixels in the neighborhood graph. Utilizing color matrix transfer method with the stain concentrations found using our GSNMF method, the color normalization performance was also better than existing methods.

Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.

PubMed

Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N

2015-10-13

We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.

Efficient Basis Formulation for (1 +1 )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States

NASA Astrophysics Data System (ADS)

Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio; Jansen, Karl; Kühn, Stefan

2017-10-01

We propose an explicit formulation of the physical subspace for a (1 +1 )-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.

Bit error rate tester using fast parallel generation of linear recurring sequences

DOEpatents

Pierson, Lyndon G.; Witzke, Edward L.; Maestas, Joseph H.

2003-05-06

A fast method for generating linear recurring sequences by parallel linear recurring sequence generators (LRSGs) with a feedback circuit optimized to balance minimum propagation delay against maximal sequence period. Parallel generation of linear recurring sequences requires decimating the sequence (creating small contiguous sections of the sequence in each LRSG). A companion matrix form is selected depending on whether the LFSR is right-shifting or left-shifting. The companion matrix is completed by selecting a primitive irreducible polynomial with 1's most closely grouped in a corner of the companion matrix. A decimation matrix is created by raising the companion matrix to the (n*k).sup.th power, where k is the number of parallel LRSGs and n is the number of bits to be generated at a time by each LRSG. Companion matrices with 1's closely grouped in a corner will yield sparse decimation matrices. A feedback circuit comprised of XOR logic gates implements the decimation matrix in hardware. Sparse decimation matrices can be implemented with minimum number of XOR gates, and therefore a minimum propagation delay through the feedback circuit. The LRSG of the invention is particularly well suited to use as a bit error rate tester on high speed communication lines because it permits the receiver to synchronize to the transmitted pattern within 2n bits.

An efficient parallel algorithm for matrix-vector multiplication

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

Hendrickson, B.; Leland, R.; Plimpton, S.

The multiplication of a vector by a matrix is the kernel computation of many algorithms in scientific computation. A fast parallel algorithm for this calculation is therefore necessary if one is to make full use of the new generation of parallel supercomputers. This paper presents a high performance, parallel matrix-vector multiplication algorithm that is particularly well suited to hypercube multiprocessors. For an n x n matrix on p processors, the communication cost of this algorithm is O(n/[radical]p + log(p)), independent of the matrix sparsity pattern. The performance of the algorithm is demonstrated by employing it as the kernel in themore » well-known NAS conjugate gradient benchmark, where a run time of 6.09 seconds was observed. This is the best published performance on this benchmark achieved to date using a massively parallel supercomputer.« less

The covariance matrix for the solution vector of an equality-constrained least-squares problem

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1976-01-01

Methods are given for computing the covariance matrix for the solution vector of an equality-constrained least squares problem. The methods are matched to the solution algorithms given in the book, 'Solving Least Squares Problems.'

Improvement of Disease Prediction and Modeling through the Use of Meteorological Ensembles: Human Plague in Uganda

PubMed Central

Moore, Sean M.; Monaghan, Andrew; Griffith, Kevin S.; Apangu, Titus; Mead, Paul S.; Eisen, Rebecca J.

2012-01-01

Climate and weather influence the occurrence, distribution, and incidence of infectious diseases, particularly those caused by vector-borne or zoonotic pathogens. Thus, models based on meteorological data have helped predict when and where human cases are most likely to occur. Such knowledge aids in targeting limited prevention and control resources and may ultimately reduce the burden of diseases. Paradoxically, localities where such models could yield the greatest benefits, such as tropical regions where morbidity and mortality caused by vector-borne diseases is greatest, often lack high-quality in situ local meteorological data. Satellite- and model-based gridded climate datasets can be used to approximate local meteorological conditions in data-sparse regions, however their accuracy varies. Here we investigate how the selection of a particular dataset can influence the outcomes of disease forecasting models. Our model system focuses on plague (Yersinia pestis infection) in the West Nile region of Uganda. The majority of recent human cases have been reported from East Africa and Madagascar, where meteorological observations are sparse and topography yields complex weather patterns. Using an ensemble of meteorological datasets and model-averaging techniques we find that the number of suspected cases in the West Nile region was negatively associated with dry season rainfall (December-February) and positively with rainfall prior to the plague season. We demonstrate that ensembles of available meteorological datasets can be used to quantify climatic uncertainty and minimize its impacts on infectious disease models. These methods are particularly valuable in regions with sparse observational networks and high morbidity and mortality from vector-borne diseases. PMID:23024750

Sparse approximation problem: how rapid simulated annealing succeeds and fails

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Kabashima, Yoshiyuki

2016-03-01

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.

SPAR reference manual

NASA Technical Reports Server (NTRS)

Whetstone, W. D.

1976-01-01

The functions and operating rules of the SPAR system, which is a group of computer programs used primarily to perform stress, buckling, and vibrational analyses of linear finite element systems, were given. The following subject areas were discussed: basic information, structure definition, format system matrix processors, utility programs, static solutions, stresses, sparse matrix eigensolver, dynamic response, graphics, and substructure processors.

Matrix Recipes for Hard Thresholding Methods

DTIC Science & Technology

2012-11-07

have been proposed to approximate the solution. In [11], Donoho et al . demonstrate that, in the sparse approximation problem, under basic incoherence...inducing convex surrogate ‖ · ‖1 with provable guarantees for unique signal recovery. In the ARM problem, Fazel et al . [12] identified the nuclear norm...sparse recovery for all. Technical report, EPFL, 2011 . [25] N. Halko , P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: Probabilistic

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

PubMed

Mohr, Stephan; Dawson, William; Wagner, Michael; Caliste, Damien; Nakajima, Takahito; Genovese, Luigi

2017-10-10

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.

Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state

DOE PAGES

Sirunyan, A. M.; Tumasyan, A.; Adam, W.; ...

2017-10-16

A search is performed for anomalous interactions of the recently discovered Higgs boson using matrix element techniques with the information from its decay to four leptons and from associated Higgs boson production with two quark jets in either vector boson fusion or associated production with a vector boson. The data were recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 38.6 fb –1. These data are combined with the data collected at center-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7more » fb –1, respectively. As a result, all observations are consistent with the expectations for the standard model Higgs boson.« less

Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state

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

Sirunyan, A. M.; Tumasyan, A.; Adam, W.

A search is performed for anomalous interactions of the recently discovered Higgs boson using matrix element techniques with the information from its decay to four leptons and from associated Higgs boson production with two quark jets in either vector boson fusion or associated production with a vector boson. The data were recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 38.6 fb –1. These data are combined with the data collected at center-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7more » fb –1, respectively. As a result, all observations are consistent with the expectations for the standard model Higgs boson.« less

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

NASA Technical Reports Server (NTRS)

Tsang, Leung; Chan, Chi Hou; Kong, Jin AU; Joseph, James

1992-01-01

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Heading-vector navigation based on head-direction cells and path integration.

PubMed

Kubie, John L; Fenton, André A

2009-05-01

Insect navigation is guided by heading vectors that are computed by path integration. Mammalian navigation models, on the other hand, are typically based on map-like place representations provided by hippocampal place cells. Such models compute optimal routes as a continuous series of locations that connect the current location to a goal. We propose a "heading-vector" model in which head-direction cells or their derivatives serve both as key elements in constructing the optimal route and as the straight-line guidance during route execution. The model is based on a memory structure termed the "shortcut matrix," which is constructed during the initial exploration of an environment when a set of shortcut vectors between sequential pairs of visited waypoint locations is stored. A mechanism is proposed for calculating and storing these vectors that relies on a hypothesized cell type termed an "accumulating head-direction cell." Following exploration, shortcut vectors connecting all pairs of waypoint locations are computed by vector arithmetic and stored in the shortcut matrix. On re-entry, when local view or place representations query the shortcut matrix with a current waypoint and goal, a shortcut trajectory is retrieved. Since the trajectory direction is in head-direction compass coordinates, navigation is accomplished by tracking the firing of head-direction cells that are tuned to the heading angle. Section 1 of the manuscript describes the properties of accumulating head-direction cells. It then shows how accumulating head-direction cells can store local vectors and perform vector arithmetic to perform path-integration-based homing. Section 2 describes the construction and use of the shortcut matrix for computing direct paths between any pair of locations that have been registered in the shortcut matrix. In the discussion, we analyze the advantages of heading-based navigation over map-based navigation. Finally, we survey behavioral evidence that nonhippocampal, heading-based navigation is used in small mammals and humans. Copyright 2008 Wiley-Liss, Inc.

Exploring and Making Sense of Large Graphs

DTIC Science & Technology

2015-08-01

and bold) are n × n ; vectors (lower-case bold) are n × 1 column vectors, and scalars (in lower-case plain font) typically correspond to strength of...graph is often denoted as |V| or n . Edges or Links: A finite set E of lines between objects in a graph. The edges represent relationships between the...Adjacency matrix of a simple, unweighted and undirected graph. Adjacency matrix: The adjacency matrix of a graph G is an n × n matrix A, whose element aij

The application of a sparse, distributed memory to the detection, identification and manipulation of physical objects

NASA Technical Reports Server (NTRS)

Kanerva, P.

1986-01-01

To determine the relation of the sparse, distributed memory to other architectures, a broad review of the literature was made. The memory is called a pattern memory because they work with large patterns of features (high-dimensional vectors). A pattern is stored in a pattern memory by distributing it over a large number of storage elements and by superimposing it over other stored patterns. A pattern is retrieved by mathematical or statistical reconstruction from the distributed elements. Three pattern memories are discussed.

Application of Krylov exponential propagation to fluid dynamics equations

NASA Technical Reports Server (NTRS)

Saad, Youcef; Semeraro, David

1991-01-01

An application of matrix exponentiation via Krylov subspace projection to the solution of fluid dynamics problems is presented. The main idea is to approximate the operation exp(A)v by means of a projection-like process onto a krylov subspace. This results in a computation of an exponential matrix vector product similar to the one above but of a much smaller size. Time integration schemes can then be devised to exploit this basic computational kernel. The motivation of this approach is to provide time-integration schemes that are essentially of an explicit nature but which have good stability properties.

Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

Rotman Lens Sidewall Design and Optimization with Hybrid Hardware/Software Based Programming

DTIC Science & Technology

2015-01-09

conventional MoM and stored in memory. The components of Zfar are computed as needed through a fast matrix vector multiplication ( MVM ), which...V vector. Iterative methods, e.g. BiCGSTAB, are employed for solving the linear equation. The matrix-vector multiplications ( MVMs ), which dominate...most of the computation in the solving phase, consists of calculating near and far MVMs . The far MVM comprises aggregation, translation, and

Variational Iterative Methods for Nonsymmetric Systems of Linear Equations.

DTIC Science & Technology

1981-08-01

With a third matrix-vector product, b(i) can be computed as i j ( ATAr i+l’pj)/ApjpApj), and the previous (Apj) need not be saved. Page 8 I OCR I Orthomin... Economics and Mathematical Systems, Volume 134, Springer-Verlag, Berlin, 1976. [51 Paul Concus, Gene H. Golub, and Dianne P. O’Leary. A generalized

Energy Efficient Sparse Connectivity from Imbalanced Synaptic Plasticity Rules

PubMed Central

Sacramento, João; Wichert, Andreas; van Rossum, Mark C. W.

2015-01-01

It is believed that energy efficiency is an important constraint in brain evolution. As synaptic transmission dominates energy consumption, energy can be saved by ensuring that only a few synapses are active. It is therefore likely that the formation of sparse codes and sparse connectivity are fundamental objectives of synaptic plasticity. In this work we study how sparse connectivity can result from a synaptic learning rule of excitatory synapses. Information is maximised when potentiation and depression are balanced according to the mean presynaptic activity level and the resulting fraction of zero-weight synapses is around 50%. However, an imbalance towards depression increases the fraction of zero-weight synapses without significantly affecting performance. We show that imbalanced plasticity corresponds to imposing a regularising constraint on the L 1-norm of the synaptic weight vector, a procedure that is well-known to induce sparseness. Imbalanced plasticity is biophysically plausible and leads to more efficient synaptic configurations than a previously suggested approach that prunes synapses after learning. Our framework gives a novel interpretation to the high fraction of silent synapses found in brain regions like the cerebellum. PMID:26046817

An efficient classification method based on principal component and sparse representation.

PubMed

Zhai, Lin; Fu, Shujun; Zhang, Caiming; Liu, Yunxian; Wang, Lu; Liu, Guohua; Yang, Mingqiang

2016-01-01

As an important application in optical imaging, palmprint recognition is interfered by many unfavorable factors. An effective fusion of blockwise bi-directional two-dimensional principal component analysis and grouping sparse classification is presented. The dimension reduction and normalizing are implemented by the blockwise bi-directional two-dimensional principal component analysis for palmprint images to extract feature matrixes, which are assembled into an overcomplete dictionary in sparse classification. A subspace orthogonal matching pursuit algorithm is designed to solve the grouping sparse representation. Finally, the classification result is gained by comparing the residual between testing and reconstructed images. Experiments are carried out on a palmprint database, and the results show that this method has better robustness against position and illumination changes of palmprint images, and can get higher rate of palmprint recognition.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem.

PubMed

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-21

Quantum mechanical calculations of ro-vibrational energies of CH 4 , CHD 3 , CH 3 D, and CH 3 F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH 3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH 3 . Euler angles specifying the orientation of a frame attached to CH 3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH 4 , CHD 3 , and CH 3 D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH 3 F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem

NASA Astrophysics Data System (ADS)

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H.; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-01

Quantum mechanical calculations of ro-vibrational energies of CH4, CHD3, CH3D, and CH3F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH3. Euler angles specifying the orientation of a frame attached to CH3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH3F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions.

PubMed

Harris, Frank E

2016-05-28

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance rij. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.

Adaptive OFDM Waveform Design for Spatio-Temporal-Sparsity Exploited STAP Radar

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

Sen, Satyabrata

In this chapter, we describe a sparsity-based space-time adaptive processing (STAP) algorithm to detect a slowly moving target using an orthogonal frequency division multiplexing (OFDM) radar. The motivation of employing an OFDM signal is that it improves the target-detectability from the interfering signals by increasing the frequency diversity of the system. However, due to the addition of one extra dimension in terms of frequency, the adaptive degrees-of-freedom in an OFDM-STAP also increases. Therefore, to avoid the construction a fully adaptive OFDM-STAP, we develop a sparsity-based STAP algorithm. We observe that the interference spectrum is inherently sparse in the spatio-temporal domain,more » as the clutter responses occupy only a diagonal ridge on the spatio-temporal plane and the jammer signals interfere only from a few spatial directions. Hence, we exploit that sparsity to develop an efficient STAP technique that utilizes considerably lesser number of secondary data compared to the other existing STAP techniques, and produces nearly optimum STAP performance. In addition to designing the STAP filter, we optimally design the transmit OFDM signals by maximizing the output signal-to-interference-plus-noise ratio (SINR) in order to improve the STAP performance. The computation of output SINR depends on the estimated value of the interference covariance matrix, which we obtain by applying the sparse recovery algorithm. Therefore, we analytically assess the effects of the synthesized OFDM coefficients on the sparse recovery of the interference covariance matrix by computing the coherence measure of the sparse measurement matrix. Our numerical examples demonstrate the achieved STAP-performance due to sparsity-based technique and adaptive waveform design.« less

Hypergraph-Based Combinatorial Optimization of Matrix-Vector Multiplication

ERIC Educational Resources Information Center

Wolf, Michael Maclean

2009-01-01

Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrix-vector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific…

Design and experimental verification for optical module of optical vector-matrix multiplier.

PubMed

Zhu, Weiwei; Zhang, Lei; Lu, Yangyang; Zhou, Ping; Yang, Lin

2013-06-20

Optical computing is a new method to implement signal processing functions. The multiplication between a vector and a matrix is an important arithmetic algorithm in the signal processing domain. The optical vector-matrix multiplier (OVMM) is an optoelectronic system to carry out this operation, which consists of an electronic module and an optical module. In this paper, we propose an optical module for OVMM. To eliminate the cross talk and make full use of the optical elements, an elaborately designed structure that involves spherical lenses and cylindrical lenses is utilized in this optical system. The optical design software package ZEMAX is used to optimize the parameters and simulate the whole system. Finally, experimental data is obtained through experiments to evaluate the overall performance of the system. The results of both simulation and experiment indicate that the system constructed can implement the multiplication between a matrix with dimensions of 16 by 16 and a vector with a dimension of 16 successfully.

Distributed Matrix Completion: Application to Cooperative Positioning in Noisy Environments

DTIC Science & Technology

2013-12-11

positioning, and a gossip version of low-rank approximation were developed. A convex relaxation for positioning in the presence of noise was shown to...of a large data matrix through gossip algorithms. A new algorithm is proposed that amounts to iteratively multiplying a vector by independent random...sparsification of the original matrix and averaging the resulting normalized vectors. This can be viewed as a generalization of gossip algorithms for

A Perron-Frobenius theory for block matrices associated to a multiplex network

NASA Astrophysics Data System (ADS)

Romance, Miguel; Solá, Luis; Flores, Julio; García, Esther; García del Amo, Alejandro; Criado, Regino

2015-03-01

The uniqueness of the Perron vector of a nonnegative block matrix associated to a multiplex network is discussed. The conclusions come from the relationships between the irreducibility of some nonnegative block matrix associated to a multiplex network and the irreducibility of the corresponding matrices to each layer as well as the irreducibility of the adjacency matrix of the projection network. In addition the computation of that Perron vector in terms of the Perron vectors of the blocks is also addressed. Finally we present the precise relations that allow to express the Perron eigenvector of the multiplex network in terms of the Perron eigenvectors of its layers.

Parallel-vector unsymmetric Eigen-Solver on high performance computers

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Jiangning, Qin

1993-01-01

The popular QR algorithm for solving all eigenvalues of an unsymmetric matrix is reviewed. Among the basic components in the QR algorithm, it was concluded from this study, that the reduction of an unsymmetric matrix to a Hessenberg form (before applying the QR algorithm itself) can be done effectively by exploiting the vector speed and multiple processors offered by modern high-performance computers. Numerical examples of several test cases have indicated that the proposed parallel-vector algorithm for converting a given unsymmetric matrix to a Hessenberg form offers computational advantages over the existing algorithm. The time saving obtained by the proposed methods is increased as the problem size increased.

Optical computing and image processing using photorefractive gallium arsenide

NASA Technical Reports Server (NTRS)

Cheng, Li-Jen; Liu, Duncan T. H.

1990-01-01

Recent experimental results on matrix-vector multiplication and multiple four-wave mixing using GaAs are presented. Attention is given to a simple concept of using two overlapping holograms in GaAs to do two matrix-vector multiplication processes operating in parallel with a common input vector. This concept can be used to construct high-speed, high-capacity, reconfigurable interconnection and multiplexing modules, important for optical computing and neural-network applications.

Dynamic Forms. Part 1: Functions

NASA Technical Reports Server (NTRS)

Meyer, George; Smith, G. Allan

1993-01-01

The formalism of dynamic forms is developed as a means for organizing and systematizing the design control systems. The formalism allows the designer to easily compute derivatives to various orders of large composite functions that occur in flight-control design. Such functions involve many function-of-a-function calls that may be nested to many levels. The component functions may be multiaxis, nonlinear, and they may include rotation transformations. A dynamic form is defined as a variable together with its time derivatives up to some fixed but arbitrary order. The variable may be a scalar, a vector, a matrix, a direction cosine matrix, Euler angles, or Euler parameters. Algorithms for standard elementary functions and operations of scalar dynamic forms are developed first. Then vector and matrix operations and transformations between parameterization of rotations are developed in the next level in the hierarchy. Commonly occurring algorithms in control-system design, including inversion of pure feedback systems, are developed in the third level. A large-angle, three-axis attitude servo and other examples are included to illustrate the effectiveness of the developed formalism. All algorithms were implemented in FORTRAN code. Practical experience shows that the proposed formalism may significantly improve the productivity of the design and coding process.

A novel aliasing-free subband information fusion approach for wideband sparse spectral estimation

NASA Astrophysics Data System (ADS)

Luo, Ji-An; Zhang, Xiao-Ping; Wang, Zhi

2017-12-01

Wideband sparse spectral estimation is generally formulated as a multi-dictionary/multi-measurement (MD/MM) problem which can be solved by using group sparsity techniques. In this paper, the MD/MM problem is reformulated as a single sparse indicative vector (SIV) recovery problem at the cost of introducing an additional system error. Thus, the number of unknowns is reduced greatly. We show that the system error can be neglected under certain conditions. We then present a new subband information fusion (SIF) method to estimate the SIV by jointly utilizing all the frequency bins. With orthogonal matching pursuit (OMP) leveraging the binary property of SIV's components, we develop a SIF-OMP algorithm to reconstruct the SIV. The numerical simulations demonstrate the performance of the proposed method.

Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications

PubMed Central

Papalexakis, Evangelos E.; Faloutsos, Christos; Mitchell, Tom M.; Talukdar, Partha Pratim; Sidiropoulos, Nicholas D.; Murphy, Brian

2016-01-01

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like ’edible’, ’fits in hand’)? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, ’friends’, wall-postings); there, Turbo-SMT spots spammer-like anomalies. PMID:27672406

Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications

PubMed Central

Chaibub Neto, Elias

2015-01-01

In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a resampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson’s sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying sample sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/moderate sample sizes. The same results were observed in the comparison with the straightforward implementation, except for large sample sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling. PMID:26125965

Research on the application of a decoupling algorithm for structure analysis

NASA Technical Reports Server (NTRS)

Denman, E. D.

1980-01-01

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent vectors as a subset. The spectral decomposition of a matrix and the application to differential equations is given.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION.

PubMed

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-06-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Zou, Hui

2014-01-01

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, i.e., sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression. PMID:25598560

Matrix computations in MACSYMA

NASA Technical Reports Server (NTRS)

Wang, P. S.

1977-01-01

Facilities built into MACSYMA for manipulating matrices with numeric or symbolic entries are described. Computations will be done exactly, keeping symbols as symbols. Topics discussed include how to form a matrix and create other matrices by transforming existing matrices within MACSYMA; arithmetic and other computation with matrices; and user control of computational processes through the use of optional variables. Two algorithms designed for sparse matrices are given. The computing times of several different ways to compute the determinant of a matrix are compared.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

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

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

DOE PAGES

Negre, Christian F. A; Mniszewski, Susan M.; Cawkwell, Marc Jon; ...

2016-06-06

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance ismore » obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.« less

Predicting the past: a simple reverse stand table projection method

Treesearch

Quang V. Cao; Shanna M. McCarty

2006-01-01

A stand table gives number of trees in each diameter class. Future stand tables can be predicted from current stand tables using a stand table projection method. In the simplest form of this method, a future stand table can be expressed as the product of a matrix of transitional proportions (based on diameter growth rates) and a vector of the current stand table. There...

Factorization in large-scale many-body calculations

DOE PAGES

Johnson, Calvin W.; Ormand, W. Erich; Krastev, Plamen G.

2013-08-07

One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmetrized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm recreates the many-body matrix elementsmore » on the fly and can reduce the storage requirements by an order of magnitude or more. Here, we discuss factorization in general and introduce a novel, generalized factorization method, essentially a ‘double-factorization’ which speeds up basis generation and set-up of required arrays. Although we emphasize techniques, we also place factorization in the context of a specific (unpublished) configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines, and discuss the savings in memory due to factorization.« less

Sparse Coding for N-Gram Feature Extraction and Training for File Fragment Classification

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

Wang, Felix; Quach, Tu-Thach; Wheeler, Jason

File fragment classification is an important step in the task of file carving in digital forensics. In file carving, files must be reconstructed based on their content as a result of their fragmented storage on disk or in memory. Existing methods for classification of file fragments typically use hand-engineered features such as byte histograms or entropy measures. In this paper, we propose an approach using sparse coding that enables automated feature extraction. Sparse coding, or sparse dictionary learning, is an unsupervised learning algorithm, and is capable of extracting features based simply on how well those features can be used tomore » reconstruct the original data. With respect to file fragments, we learn sparse dictionaries for n-grams, continuous sequences of bytes, of different sizes. These dictionaries may then be used to estimate n-gram frequencies for a given file fragment, but for significantly larger n-gram sizes than are typically found in existing methods which suffer from combinatorial explosion. To demonstrate the capability of our sparse coding approach, we used the resulting features to train standard classifiers such as support vector machines (SVMs) over multiple file types. Experimentally, we achieved significantly better classification results with respect to existing methods, especially when the features were used in supplement to existing hand-engineered features.« less

Sparse Coding for N-Gram Feature Extraction and Training for File Fragment Classification

DOE PAGES

Wang, Felix; Quach, Tu-Thach; Wheeler, Jason; ...

2018-04-05

File fragment classification is an important step in the task of file carving in digital forensics. In file carving, files must be reconstructed based on their content as a result of their fragmented storage on disk or in memory. Existing methods for classification of file fragments typically use hand-engineered features such as byte histograms or entropy measures. In this paper, we propose an approach using sparse coding that enables automated feature extraction. Sparse coding, or sparse dictionary learning, is an unsupervised learning algorithm, and is capable of extracting features based simply on how well those features can be used tomore » reconstruct the original data. With respect to file fragments, we learn sparse dictionaries for n-grams, continuous sequences of bytes, of different sizes. These dictionaries may then be used to estimate n-gram frequencies for a given file fragment, but for significantly larger n-gram sizes than are typically found in existing methods which suffer from combinatorial explosion. To demonstrate the capability of our sparse coding approach, we used the resulting features to train standard classifiers such as support vector machines (SVMs) over multiple file types. Experimentally, we achieved significantly better classification results with respect to existing methods, especially when the features were used in supplement to existing hand-engineered features.« less

Label consistent K-SVD: learning a discriminative dictionary for recognition.

PubMed

Jiang, Zhuolin; Lin, Zhe; Davis, Larry S

2013-11-01

A label consistent K-SVD (LC-KSVD) algorithm to learn a discriminative dictionary for sparse coding is presented. In addition to using class labels of training data, we also associate label information with each dictionary item (columns of the dictionary matrix) to enforce discriminability in sparse codes during the dictionary learning process. More specifically, we introduce a new label consistency constraint called "discriminative sparse-code error" and combine it with the reconstruction error and the classification error to form a unified objective function. The optimal solution is efficiently obtained using the K-SVD algorithm. Our algorithm learns a single overcomplete dictionary and an optimal linear classifier jointly. The incremental dictionary learning algorithm is presented for the situation of limited memory resources. It yields dictionaries so that feature points with the same class labels have similar sparse codes. Experimental results demonstrate that our algorithm outperforms many recently proposed sparse-coding techniques for face, action, scene, and object category recognition under the same learning conditions.

Convergence Speed of a Dynamical System for Sparse Recovery

NASA Astrophysics Data System (ADS)

Balavoine, Aurele; Rozell, Christopher J.; Romberg, Justin

2013-09-01

This paper studies the convergence rate of a continuous-time dynamical system for L1-minimization, known as the Locally Competitive Algorithm (LCA). Solving L1-minimization} problems efficiently and rapidly is of great interest to the signal processing community, as these programs have been shown to recover sparse solutions to underdetermined systems of linear equations and come with strong performance guarantees. The LCA under study differs from the typical L1 solver in that it operates in continuous time: instead of being specified by discrete iterations, it evolves according to a system of nonlinear ordinary differential equations. The LCA is constructed from simple components, giving it the potential to be implemented as a large-scale analog circuit. The goal of this paper is to give guarantees on the convergence time of the LCA system. To do so, we analyze how the LCA evolves as it is recovering a sparse signal from underdetermined measurements. We show that under appropriate conditions on the measurement matrix and the problem parameters, the path the LCA follows can be described as a sequence of linear differential equations, each with a small number of active variables. This allows us to relate the convergence time of the system to the restricted isometry constant of the matrix. Interesting parallels to sparse-recovery digital solvers emerge from this study. Our analysis covers both the noisy and noiseless settings and is supported by simulation results.

Fast Eigensolver for Computing 3D Earth's Normal Modes

NASA Astrophysics Data System (ADS)

Shi, J.; De Hoop, M. V.; Li, R.; Xi, Y.; Saad, Y.

2017-12-01

We present a novel parallel computational approach to compute Earth's normal modes. We discretize Earth via an unstructured tetrahedral mesh and apply the continuous Galerkin finite element method to the elasto-gravitational system. To resolve the eigenvalue pollution issue, following the analysis separating the seismic point spectrum, we utilize explicitly a representation of the displacement for describing the oscillations of the non-seismic modes in the fluid outer core. Effectively, we separate out the essential spectrum which is naturally related to the Brunt-Väisälä frequency. We introduce two Lanczos approaches with polynomial and rational filtering for solving this generalized eigenvalue problem in prescribed intervals. The polynomial filtering technique only accesses the matrix pair through matrix-vector products and is an ideal candidate for solving three-dimensional large-scale eigenvalue problems. The matrix-free scheme allows us to deal with fluid separation and self-gravitation in an efficient way, while the standard shift-and-invert method typically needs an explicit shifted matrix and its factorization. The rational filtering method converges much faster than the standard shift-and-invert procedure when computing all the eigenvalues inside an interval. Both two Lanczos approaches solve for the internal eigenvalues extremely accurately, comparing with the standard eigensolver. In our computational experiments, we compare our results with the radial earth model benchmark, and visualize the normal modes using vector plots to illustrate the properties of the displacements in different modes.

Accelerating scientific computations with mixed precision algorithms

NASA Astrophysics Data System (ADS)

Baboulin, Marc; Buttari, Alfredo; Dongarra, Jack; Kurzak, Jakub; Langou, Julie; Langou, Julien; Luszczek, Piotr; Tomov, Stanimire

2009-12-01

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. The approach presented here can apply not only to conventional processors but also to other technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the STI Cell BE processor. Results on modern processor architectures and the STI Cell BE are presented. Program summaryProgram title: ITER-REF Catalogue identifier: AECO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7211 No. of bytes in distributed program, including test data, etc.: 41 862 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: desktop, server Operating system: Unix/Linux RAM: 512 Mbytes Classification: 4.8 External routines: BLAS (optional) Nature of problem: On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. Solution method: Mixed precision algorithms stem from the observation that, in many cases, a single precision solution of a problem can be refined to the point where double precision accuracy is achieved. A common approach to the solution of linear systems, either dense or sparse, is to perform the LU factorization of the coefficient matrix using Gaussian elimination. First, the coefficient matrix A is factored into the product of a lower triangular matrix L and an upper triangular matrix U. Partial row pivoting is in general used to improve numerical stability resulting in a factorization PA=LU, where P is a permutation matrix. The solution for the system is achieved by first solving Ly=Pb (forward substitution) and then solving Ux=y (backward substitution). Due to round-off errors, the computed solution, x, carries a numerical error magnified by the condition number of the coefficient matrix A. In order to improve the computed solution, an iterative process can be applied, which produces a correction to the computed solution at each iteration, which then yields the method that is commonly known as the iterative refinement algorithm. Provided that the system is not too ill-conditioned, the algorithm produces a solution correct to the working precision. Running time: seconds/minutes

Angle-resolved spin wave band diagrams of square antidot lattices studied by Brillouin light scattering

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

Gubbiotti, G.; Tacchi, S.; Montoncello, F.

2015-06-29

The Brillouin light scattering technique has been exploited to study the angle-resolved spin wave band diagrams of squared Permalloy antidot lattice. Frequency dispersion of spin waves has been measured for a set of fixed wave vector magnitudes, while varying the wave vector in-plane orientation with respect to the applied magnetic field. The magnonic band gap between the two most dispersive modes exhibits a minimum value at an angular position, which exclusively depends on the product between the selected wave vector magnitude and the lattice constant of the array. The experimental data are in very good agreement with predictions obtained bymore » dynamical matrix method calculations. The presented results are relevant for magnonic devices where the antidot lattice, acting as a diffraction grating, is exploited to achieve multidirectional spin wave emission.« less

A fast, preconditioned conjugate gradient Toeplitz solver

NASA Technical Reports Server (NTRS)

Pan, Victor; Schrieber, Robert

1989-01-01

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

New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1998-01-01

Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

PubMed Central

Ong, Frank; Lustig, Michael

2016-01-01

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information. PMID:28450978

Visualization of x-ray computer tomography using computer-generated holography

NASA Astrophysics Data System (ADS)

Daibo, Masahiro; Tayama, Norio

1998-09-01

The theory converted from x-ray projection data to the hologram directly by combining the computer tomography (CT) with the computer generated hologram (CGH), is proposed. The purpose of this study is to offer the theory for realizing the all- electronic and high-speed seeing through 3D visualization system, which is for the application to medical diagnosis and non- destructive testing. First, the CT is expressed using the pseudo- inverse matrix which is obtained by the singular value decomposition. CGH is expressed in the matrix style. Next, `projection to hologram conversion' (PTHC) matrix is calculated by the multiplication of phase matrix of CGH with pseudo-inverse matrix of the CT. Finally, the projection vector is converted to the hologram vector directly, by multiplication of the PTHC matrix with the projection vector. Incorporating holographic analog computation into CT reconstruction, it becomes possible that the calculation amount is drastically reduced. We demonstrate the CT cross section which is reconstituted by He-Ne laser in the 3D space from the real x-ray projection data acquired by x-ray television equipment, using our direct conversion technique.

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions

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

Harris, Frank E., E-mail: harris@qtp.ufl.edu

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance r{sub ij}. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validatedmore » by showing that they yield correct results for a large number of integrals published by other investigators.« less

Refractive index inversion based on Mueller matrix method

NASA Astrophysics Data System (ADS)

Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao

2016-03-01

Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

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

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrixmore » is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.« less

Signal processing applications of massively parallel charge domain computing devices

NASA Technical Reports Server (NTRS)

Fijany, Amir (Inventor); Barhen, Jacob (Inventor); Toomarian, Nikzad (Inventor)

1999-01-01

The present invention is embodied in a charge coupled device (CCD)/charge injection device (CID) architecture capable of performing a Fourier transform by simultaneous matrix vector multiplication (MVM) operations in respective plural CCD/CID arrays in parallel in O(1) steps. For example, in one embodiment, a first CCD/CID array stores charge packets representing a first matrix operator based upon permutations of a Hartley transform and computes the Fourier transform of an incoming vector. A second CCD/CID array stores charge packets representing a second matrix operator based upon different permutations of a Hartley transform and computes the Fourier transform of an incoming vector. The incoming vector is applied to the inputs of the two CCD/CID arrays simultaneously, and the real and imaginary parts of the Fourier transform are produced simultaneously in the time required to perform a single MVM operation in a CCD/CID array.

PERI - Auto-tuning Memory Intensive Kernels for Multicore

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

Bailey, David H; Williams, Samuel; Datta, Kaushik

2008-06-24

We present an auto-tuning approach to optimize application performance on emerging multicore architectures. The methodology extends the idea of search-based performance optimizations, popular in linear algebra and FFT libraries, to application-specific computational kernels. Our work applies this strategy to Sparse Matrix Vector Multiplication (SpMV), the explicit heat equation PDE on a regular grid (Stencil), and a lattice Boltzmann application (LBMHD). We explore one of the broadest sets of multicore architectures in the HPC literature, including the Intel Xeon Clovertown, AMD Opteron Barcelona, Sun Victoria Falls, and the Sony-Toshiba-IBM (STI) Cell. Rather than hand-tuning each kernel for each system, we developmore » a code generator for each kernel that allows us to identify a highly optimized version for each platform, while amortizing the human programming effort. Results show that our auto-tuned kernel applications often achieve a better than 4X improvement compared with the original code. Additionally, we analyze a Roofline performance model for each platform to reveal hardware bottlenecks and software challenges for future multicore systems and applications.« less

Implementation and Assessment of Advanced Analog Vector-Matrix Processor

NASA Technical Reports Server (NTRS)

Gary, Charles K.; Bualat, Maria G.; Lum, Henry, Jr. (Technical Monitor)

1994-01-01

This paper discusses the design and implementation of an analog optical vecto-rmatrix coprocessor with a throughput of 128 Mops for a personal computer. Vector matrix calculations are inherently parallel, providing a promising domain for the use of optical calculators. However, to date, digital optical systems have proven too cumbersome to replace electronics, and analog processors have not demonstrated sufficient accuracy in large scale systems. The goal of the work described in this paper is to demonstrate a viable optical coprocessor for linear operations. The analog optical processor presented has been integrated with a personal computer to provide full functionality and is the first demonstration of an optical linear algebra processor with a throughput greater than 100 Mops. The optical vector matrix processor consists of a laser diode source, an acoustooptical modulator array to input the vector information, a liquid crystal spatial light modulator to input the matrix information, an avalanche photodiode array to read out the result vector of the vector matrix multiplication, as well as transport optics and the electronics necessary to drive the optical modulators and interface to the computer. The intent of this research is to provide a low cost, highly energy efficient coprocessor for linear operations. Measurements of the analog accuracy of the processor performing 128 Mops are presented along with an assessment of the implications for future systems. A range of noise sources, including cross-talk, source amplitude fluctuations, shot noise at the detector, and non-linearities of the optoelectronic components are measured and compared to determine the most significant source of error. The possibilities for reducing these sources of error are discussed. Also, the total error is compared with that expected from a statistical analysis of the individual components and their relation to the vector-matrix operation. The sufficiency of the measured accuracy of the processor is compared with that required for a range of typical problems. Calculations resolving alloy concentrations from spectral plume data of rocket engines are implemented on the optical processor, demonstrating its sufficiency for this problem. We also show how this technology can be easily extended to a 100 x 100 10 MHz (200 Cops) processor.

A study of multi-jet production in association with an electroweak vector boson

DOE PAGES

Frederix, R.; Frixione, S.; Papaefstathiou, A.; ...

2016-02-19

Here, we consider the production of a single Z or W boson in association with jets at the LHC. We compute the corresponding cross sections by matching NLO QCD predictions with the Herwig++ and Pythia8 parton showers, and by merging all of the underlying matrix elements with up to two light partons at the Born level. We compare our results with several 7-TeV measurements by the ATLAS and CMS collaborations, and overall we find a good agreement between theory and data.

Proceedings of Workshop on Atmospheric Density and Aerodynamic Drag Models for Air Force Operations Held at Air Force Geophysics Laboratory on 20-22 October 1987. Volume 1

DTIC Science & Technology

1990-02-13

considered with these production processes in a simple photochemical equilibrium calculation , we are able to determine the contribution each makes to the...Hessian matrix of second derivatives (which is required in the Newton-Raphson procedure) by the vector product of the gradient (VJ) and its transpose...was focused on the altitude region 80-250 Km. Papers were presented in the folowing areas: Air Force requirements , physics of density and drag

Current status of Plasmodium knowlesi vectors: a public health concern?

PubMed

Vythilingam, I; Wong, M L; Wan-Yussof, W S

2018-01-01

Plasmodium knowlesi a simian malaria parasite is currently affecting humans in Southeast Asia. Malaysia has reported the most number of cases and P. knowlesi is the predominant species occurring in humans. The vectors of P. knowlesi belong to the Leucosphyrus group of Anopheles mosquitoes. These are generally described as forest-dwelling mosquitoes. With deforestation and changes in land-use, some species have become predominant in farms and villages. However, knowledge on the distribution of these vectors in the country is sparse. From a public health point of view it is important to know the vectors, so that risk factors towards knowlesi malaria can be identified and control measures instituted where possible. Here, we review what is known about the knowlesi malaria vectors and ascertain the gaps in knowledge, so that future studies could concentrate on this paucity of data in-order to address this zoonotic problem.

Computational Methods for Sparse Solution of Linear Inverse Problems

DTIC Science & Technology

2009-03-01

this approach is that the algorithms take advantage of fast matrix–vector multiplications. An implementation is available as pdco and SolveBP in the...M. A. Saunders, “ PDCO : primal-dual interior-point method for con- vex objectives,” Systems Optimization Laboratory, Stanford University, Tech. Rep

Research and simulation of the decoupling transformation in AC motor vector control

NASA Astrophysics Data System (ADS)

He, Jiaojiao; Zhao, Zhongjie; Liu, Ken; Zhang, Yongping; Yao, Tuozhong

2018-04-01

Permanent magnet synchronous motor (PMSM) is a nonlinear, strong coupling, multivariable complex object, and transformation decoupling can solve the coupling problem of permanent magnet synchronous motor. This paper gives a permanent magnet synchronous motor (PMSM) mathematical model, introduces the permanent magnet synchronous motor vector control coordinate transformation in the process of modal matrix inductance matrix transform through the matrix related knowledge of different coordinates of diagonalization, which makes the coupling between the independent, realize the control of motor current and excitation the torque current coupling separation, and derived the coordinate transformation matrix, the thought to solve the coupling problem of AC motor. Finally, in the Matlab/Simulink environment, through the establishment and combination between the PMSM ontology, coordinate conversion module, built the simulation model of permanent magnet synchronous motor vector control, introduces the model of each part, and analyzed the simulation results.

Compressed sensing for high-resolution nonlipid suppressed 1 H FID MRSI of the human brain at 9.4T.

PubMed

Nassirpour, Sahar; Chang, Paul; Avdievitch, Nikolai; Henning, Anke

2018-04-29

The aim of this study was to apply compressed sensing to accelerate the acquisition of high resolution metabolite maps of the human brain using a nonlipid suppressed ultra-short TR and TE 1 H FID MRSI sequence at 9.4T. X-t sparse compressed sensing reconstruction was optimized for nonlipid suppressed 1 H FID MRSI data. Coil-by-coil x-t sparse reconstruction was compared with SENSE x-t sparse and low rank reconstruction. The effect of matrix size and spatial resolution on the achievable acceleration factor was studied. Finally, in vivo metabolite maps with different acceleration factors of 2, 4, 5, and 10 were acquired and compared. Coil-by-coil x-t sparse compressed sensing reconstruction was not able to reliably recover the nonlipid suppressed data, rather a combination of parallel and sparse reconstruction was necessary (SENSE x-t sparse). For acceleration factors of up to 5, both the low-rank and the compressed sensing methods were able to reconstruct the data comparably well (root mean squared errors [RMSEs] ≤ 10.5% for Cre). However, the reconstruction time of the low rank algorithm was drastically longer than compressed sensing. Using the optimized compressed sensing reconstruction, acceleration factors of 4 or 5 could be reached for the MRSI data with a matrix size of 64 × 64. For lower spatial resolutions, an acceleration factor of up to R∼4 was successfully achieved. By tailoring the reconstruction scheme to the nonlipid suppressed data through parameter optimization and performance evaluation, we present high resolution (97 µL voxel size) accelerated in vivo metabolite maps of the human brain acquired at 9.4T within scan times of 3 to 3.75 min. © 2018 International Society for Magnetic Resonance in Medicine.

Preconditioned MoM Solutions for Complex Planar Arrays

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

Fasenfest, B J; Jackson, D; Champagne, N

2004-01-23

The numerical analysis of large arrays is a complex problem. There are several techniques currently under development in this area. One such technique is the FAIM (Faster Adaptive Integral Method). This method uses a modification of the standard AIM approach which takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basis functions, such as the RWG basis. These bases are then projected onto a regular grid of interpolating polynomials. This grid can then be used in a 2D ormore » 3D FFT to accelerate the matrix-vector product used in an iterative solver. The method has been proven to greatly reduce solve time by speeding the matrix-vector product computation. The FAIM approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends FAIM by modifying it to allow for layered material Green's Functions and dielectrics. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the FAIM method is reported in; this contribution is limited to presenting new results.« less

Estimation of the chemical rank for the three-way data: a principal norm vector orthogonal projection approach.

PubMed

Hong-Ping, Xie; Jian-Hui, Jiang; Guo-Li, Shen; Ru-Qin, Yu

2002-01-01

A new approach for estimating the chemical rank of the three-way array called the principal norm vector orthogonal projection method has been proposed. The method is based on the fact that the chemical rank of the three-way data array is equal to one of the column space of the unfolded matrix along the spectral or chromatographic mode. A vector with maximum Frobenius norm is selected among all the column vectors of the unfolded matrix as the principal norm vector (PNV). A transformation is conducted for the column vectors with an orthogonal projection matrix formulated by PNV. The mathematical rank of the column space of the residual matrix thus obtained should decrease by one. Such orthogonal projection is carried out repeatedly till the contribution of chemical species to the signal data is all deleted. At this time the decrease of the mathematical rank would equal that of the chemical rank, and the remaining residual subspace would entirely be due to the noise contribution. The chemical rank can be estimated easily by using an F-test. The method has been used successfully to the simulated HPLC-DAD type three-way data array and two real excitation-emission fluorescence data sets of amino acid mixtures and dye mixtures. The simulation with added relatively high level noise shows that the method is robust in resisting the heteroscedastic noise. The proposed algorithm is simple and easy to program with quite light computational burden.

Simultaneous analysis of large INTEGRAL/SPI1 datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

NASA Astrophysics Data System (ADS)

Bouchet, L.; Amestoy, P.; Buttari, A.; Rouet, F.-H.; Chauvin, M.

2013-02-01

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/γ-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all. Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage. Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy. We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances. In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

Algorithms and software for solving finite element equations on serial and parallel architectures

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, Alan

1988-01-01

The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the Computational Structural Mechanics (MSC) testbed. One of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A brief overview of the CSM Testbed software and its usage is presented. An overview of the sparse matrix research for the Testbed currently employed in the CSM Testbed is given. An interface which was designed and implemented as a research tool for installing and appraising new matrix processors in the CSM Testbed is described. The results of numerical experiments performed in solving a set of testbed demonstration problems using the processor SPK and other experimental processors are contained.

Supercomputing on massively parallel bit-serial architectures

NASA Technical Reports Server (NTRS)

Iobst, Ken

1985-01-01

Research on the Goodyear Massively Parallel Processor (MPP) suggests that high-level parallel languages are practical and can be designed with powerful new semantics that allow algorithms to be efficiently mapped to the real machines. For the MPP these semantics include parallel/associative array selection for both dense and sparse matrices, variable precision arithmetic to trade accuracy for speed, micro-pipelined train broadcast, and conditional branching at the processing element (PE) control unit level. The preliminary design of a FORTRAN-like parallel language for the MPP has been completed and is being used to write programs to perform sparse matrix array selection, min/max search, matrix multiplication, Gaussian elimination on single bit arrays and other generic algorithms. A description is given of the MPP design. Features of the system and its operation are illustrated in the form of charts and diagrams.

Activation product transport in fusion reactors. [RAPTOR

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

Klein, A.C.

1983-01-01

Activated corrosion and neutron sputtering products will enter the coolant and/or tritium breeding material of fusion reactor power plants and experiments and cause personnel access problems. Radiation levels around plant components due to these products will cause difficulties with maintenance and repair operations throughout the plant. Similar problems are experienced around fission reactor systems. The determination of the transport of radioactive corrosion and neutron sputtering products through the system is achieved using the computer code RAPTOR. This code calculates the mass transfer of a number of activation products based on the corrosion and sputtering rates through the system, the depositionmore » and release characteristics of various plant components, the neturon flux spectrum, as well as other plant parameters. RAPTOR assembles a system of first order linear differential equations into a matrix equation based upon the reactor system parameters. Included in the transfer matrix are the deposition and erosion coefficients, and the decay and activation data for the various plant nodes and radioactive isotopes. A source vector supplies the corrosion and neutron sputtering source rates. This matrix equation is then solved using a matrix operator technique to give the specific activity distribution of each radioactive species throughout the plant. Once the amount of mass transfer is determined, the photon transport due to the radioactive corrosion and sputtering product sources can be evaluated, and dose rates around the plant components of interest as a function of time can be determined. This method has been used to estimate the radiation hazards around a number of fusion reactor system designs.« less

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

NASA Technical Reports Server (NTRS)

Gedney, Stephen D.; Lansing, Faiza

1993-01-01

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Understanding Singular Vectors

ERIC Educational Resources Information Center

James, David; Botteron, Cynthia

2013-01-01

matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so…

Implementation of biological tissue Mueller matrix for polarization-sensitive optical coherence tomography based on LabVIEW

NASA Astrophysics Data System (ADS)

Lin, Yongping; Zhang, Xiyang; He, Youwu; Cai, Jianyong; Li, Hui

2018-02-01

The Jones matrix and the Mueller matrix are main tools to study polarization devices. The Mueller matrix can also be used for biological tissue research to get complete tissue properties, while the commercial optical coherence tomography system does not give relevant analysis function. Based on the LabVIEW, a near real time display method of Mueller matrix image of biological tissue is developed and it gives the corresponding phase retardant image simultaneously. A quarter-wave plate was placed at 45 in the sample arm. Experimental results of the two orthogonal channels show that the phase retardance based on incident light vector fixed mode and the Mueller matrix based on incident light vector dynamic mode can provide an effective analysis method of the existing system.

A Semiparametric Approach to Simultaneous Covariance Estimation for Bivariate Sparse Longitudinal Data

PubMed Central

Das, Kiranmoy; Daniels, Michael J.

2014-01-01

Summary Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium and low) at baseline. PMID:24400941

Compressed sensing for energy-efficient wireless telemonitoring of noninvasive fetal ECG via block sparse Bayesian learning.

PubMed

Zhang, Zhilin; Jung, Tzyy-Ping; Makeig, Scott; Rao, Bhaskar D

2013-02-01

Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with low energy consumption. However, due to some specific characteristics of raw FECG recordings such as nonsparsity and strong noise contamination, current CS algorithms generally fail in this application. This paper proposes to use the block sparse Bayesian learning framework to compress/reconstruct nonsparse raw FECG recordings. Experimental results show that the framework can reconstruct the raw recordings with high quality. Especially, the reconstruction does not destroy the interdependence relation among the multichannel recordings. This ensures that the independent component analysis decomposition of the reconstructed recordings has high fidelity. Furthermore, the framework allows the use of a sparse binary sensing matrix with much fewer nonzero entries to compress recordings. Particularly, each column of the matrix can contain only two nonzero entries. This shows that the framework, compared to other algorithms such as current CS algorithms and wavelet algorithms, can greatly reduce code execution in CPU in the data compression stage.

Technical note: an R package for fitting sparse neural networks with application in animal breeding.

PubMed

Wang, Yangfan; Mi, Xue; Rosa, Guilherme J M; Chen, Zhihui; Lin, Ping; Wang, Shi; Bao, Zhenmin

2018-05-04

Neural networks (NNs) have emerged as a new tool for genomic selection (GS) in animal breeding. However, the properties of NN used in GS for the prediction of phenotypic outcomes are not well characterized due to the problem of over-parameterization of NN and difficulties in using whole-genome marker sets as high-dimensional NN input. In this note, we have developed an R package called snnR that finds an optimal sparse structure of a NN by minimizing the square error subject to a penalty on the L1-norm of the parameters (weights and biases), therefore solving the problem of over-parameterization in NN. We have also tested some models fitted in the snnR package to demonstrate their feasibility and effectiveness to be used in several cases as examples. In comparison of snnR to the R package brnn (the Bayesian regularized single layer NNs), with both using the entries of a genotype matrix or a genomic relationship matrix as inputs, snnR has greatly improved the computational efficiency and the prediction ability for the GS in animal breeding because snnR implements a sparse NN with many hidden layers.

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

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

Himmetoglu, Burak; Peloso, Marco; Contaldi, Carlo R.

2009-12-15

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), andmore » (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.« less

Automatic Overset Grid Generation with Heuristic Feedback Control

NASA Technical Reports Server (NTRS)

Robinson, Peter I.

2001-01-01

An advancing front grid generation system for structured Overset grids is presented which automatically modifies Overset structured surface grids and control lines until user-specified grid qualities are achieved. The system is demonstrated on two examples: the first refines a space shuttle fuselage control line until global truncation error is achieved; the second advances, from control lines, the space shuttle orbiter fuselage top and fuselage side surface grids until proper overlap is achieved. Surface grids are generated in minutes for complex geometries. The system is implemented as a heuristic feedback control (HFC) expert system which iteratively modifies the input specifications for Overset control line and surface grids. It is developed as an extension of modern control theory, production rules systems and subsumption architectures. The methodology provides benefits over the full knowledge lifecycle of an expert system for knowledge acquisition, knowledge representation, and knowledge execution. The vector/matrix framework of modern control theory systematically acquires and represents expert system knowledge. Missing matrix elements imply missing expert knowledge. The execution of the expert system knowledge is performed through symbolic execution of the matrix algebra equations of modern control theory. The dot product operation of matrix algebra is generalized for heuristic symbolic terms. Constant time execution is guaranteed.

Angular-Rate Estimation Using Delayed Quaternion Measurements

NASA Technical Reports Server (NTRS)

Azor, R.; Bar-Itzhack, I. Y.; Harman, R. R.

1999-01-01

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared one that uses differentiated quaternion measurements to yield coarse rate measurements, which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear part of the rotas rotational dynamics equation of a body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This non unique decomposition, enables the treatment of the nonlinear spacecraft (SC) dynamics model as a linear one and, thus, the application of a PseudoLinear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the gain matrix and thus eliminates the need to compute recursively the filter covariance matrix. The replacement of the rotational dynamics by a simple Markov model is also examined. In this paper special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results are presented.

Systematic Constraint Selection Strategy for Rate-Controlled Constrained-Equilibrium Modeling of Complex Nonequilibrium Chemical Kinetics

NASA Astrophysics Data System (ADS)

Beretta, Gian Paolo; Rivadossi, Luca; Janbozorgi, Mohammad

2018-04-01

Rate-Controlled Constrained-Equilibrium (RCCE) modeling of complex chemical kinetics provides acceptable accuracies with much fewer differential equations than for the fully Detailed Kinetic Model (DKM). Since its introduction by James C. Keck, a drawback of the RCCE scheme has been the absence of an automatable, systematic procedure to identify the constraints that most effectively warrant a desired level of approximation for a given range of initial, boundary, and thermodynamic conditions. An optimal constraint identification has been recently proposed. Given a DKM with S species, E elements, and R reactions, the procedure starts by running a probe DKM simulation to compute an S-vector that we call overall degree of disequilibrium (ODoD) because its scalar product with the S-vector formed by the stoichiometric coefficients of any reaction yields its degree of disequilibrium (DoD). The ODoD vector evolves in the same (S-E)-dimensional stoichiometric subspace spanned by the R stoichiometric S-vectors. Next we construct the rank-(S-E) matrix of ODoD traces obtained from the probe DKM numerical simulation and compute its singular value decomposition (SVD). By retaining only the first C largest singular values of the SVD and setting to zero all the others we obtain the best rank-C approximation of the matrix of ODoD traces whereby its columns span a C-dimensional subspace of the stoichiometric subspace. This in turn yields the best approximation of the evolution of the ODoD vector in terms of only C parameters that we call the constraint potentials. The resulting order-C RCCE approximate model reduces the number of independent differential equations related to species, mass, and energy balances from S+2 to C+E+2, with substantial computational savings when C ≪ S-E.

A simple procedure for construction of the orthonormal basis vectors of irreducible representations of O(5) in the OT (3) ⊗ON (2) basis

NASA Astrophysics Data System (ADS)

Pan, Feng; Ding, Xiaoxue; Launey, Kristina D.; Draayer, J. P.

2018-06-01

A simple and effective algebraic isospin projection procedure for constructing orthonormal basis vectors of irreducible representations of O (5) ⊃OT (3) ⊗ON (2) from those in the canonical O (5) ⊃ SUΛ (2) ⊗ SUI (2) basis is outlined. The expansion coefficients are components of null space vectors of the projection matrix with four nonzero elements in each row in general. Explicit formulae for evaluating OT (3)-reduced matrix elements of O (5) generators are derived.

Distance learning in discriminative vector quantization.

PubMed

Schneider, Petra; Biehl, Michael; Hammer, Barbara

2009-10-01

Discriminative vector quantization schemes such as learning vector quantization (LVQ) and extensions thereof offer efficient and intuitive classifiers based on the representation of classes by prototypes. The original methods, however, rely on the Euclidean distance corresponding to the assumption that the data can be represented by isotropic clusters. For this reason, extensions of the methods to more general metric structures have been proposed, such as relevance adaptation in generalized LVQ (GLVQ) and matrix learning in GLVQ. In these approaches, metric parameters are learned based on the given classification task such that a data-driven distance measure is found. In this letter, we consider full matrix adaptation in advanced LVQ schemes. In particular, we introduce matrix learning to a recent statistical formalization of LVQ, robust soft LVQ, and we compare the results on several artificial and real-life data sets to matrix learning in GLVQ, a derivation of LVQ-like learning based on a (heuristic) cost function. In all cases, matrix adaptation allows a significant improvement of the classification accuracy. Interestingly, however, the principled behavior of the models with respect to prototype locations and extracted matrix dimensions shows several characteristic differences depending on the data sets.

Acoustic 3D modeling by the method of integral equations

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2018-02-01

This paper presents a parallel algorithm for frequency-domain acoustic modeling by the method of integral equations (IE). The algorithm is applied to seismic simulation. The IE method reduces the size of the problem but leads to a dense system matrix. A tolerable memory consumption and numerical complexity were achieved by applying an iterative solver, accompanied by an effective matrix-vector multiplication operation, based on the fast Fourier transform (FFT). We demonstrate that, the IE system matrix is better conditioned than that of the finite-difference (FD) method, and discuss its relation to a specially preconditioned FD matrix. We considered several methods of matrix-vector multiplication for the free-space and layered host models. The developed algorithm and computer code were benchmarked against the FD time-domain solution. It was demonstrated that, the method could accurately calculate the seismic field for the models with sharp material boundaries and a point source and receiver located close to the free surface. We used OpenMP to speed up the matrix-vector multiplication, while MPI was used to speed up the solution of the system equations, and also for parallelizing across multiple sources. The practical examples and efficiency tests are presented as well.

Comparison of two matrix data structures for advanced CSM testbed applications

NASA Technical Reports Server (NTRS)

Regelbrugge, M. E.; Brogan, F. A.; Nour-Omid, B.; Rankin, C. C.; Wright, M. A.

1989-01-01

The first section describes data storage schemes presently used by the Computational Structural Mechanics (CSM) testbed sparse matrix facilities and similar skyline (profile) matrix facilities. The second section contains a discussion of certain features required for the implementation of particular advanced CSM algorithms, and how these features might be incorporated into the data storage schemes described previously. The third section presents recommendations, based on the discussions of the prior sections, for directing future CSM testbed development to provide necessary matrix facilities for advanced algorithm implementation and use. The objective is to lend insight into the matrix structures discussed and to help explain the process of evaluating alternative matrix data structures and utilities for subsequent use in the CSM testbed.

Data-driven probability concentration and sampling on manifold

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

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2016-09-15

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation methodmore » for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.« less

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

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

Clark, M. A.; Strelchenko, Alexei; Vaquero, Alejandro

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

Equiangular tight frames and unistochastic matrices

NASA Astrophysics Data System (ADS)

Goyeneche, Dardo; Turek, Ondřej

2017-06-01

We demonstrate that a complex equiangular tight frame composed of N vectors in dimension d, denoted ETF (d, N), exists if and only if a certain bistochastic matrix, univocally determined by N and d, belongs to a special class of unistochastic matrices. This connection allows us to find new complex ETFs in infinitely many dimensions and to derive a method to introduce non-trivial free parameters in ETFs. We present an explicit six-parametric family of complex ETF(6,16), which defines a family of symmetric POVMs. Minimal and maximal possible average entanglement of the vectors within this qubit-qutrit family are described. Furthermore, we propose an efficient numerical procedure to compute the unitary matrix underlying a unistochastic matrix, which we apply to find all existing classes of complex ETFs containing up to 20 vectors.

Efficient solution of parabolic equations by Krylov approximation methods

NASA Technical Reports Server (NTRS)

Gallopoulos, E.; Saad, Y.

1990-01-01

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

Rapid determination of biogenic amines in cooked beef using hyperspectral imaging with sparse representation algorithm

NASA Astrophysics Data System (ADS)

Yang, Dong; Lu, Anxiang; Ren, Dong; Wang, Jihua

2017-11-01

This study explored the feasibility of rapid detection of biogenic amines (BAs) in cooked beef during the storage process using hyperspectral imaging technique combined with sparse representation (SR) algorithm. The hyperspectral images of samples were collected in the two spectral ranges of 400-1000 nm and 1000-1800 nm, separately. The spectral data were reduced dimensionality by SR and principal component analysis (PCA) algorithms, and then integrated the least square support vector machine (LS-SVM) to build the SR-LS-SVM and PC-LS-SVM models for the prediction of BAs values in cooked beef. The results showed that the SR-LS-SVM model exhibited the best predictive ability with determination coefficients (RP2) of 0.943 and root mean square errors (RMSEP) of 1.206 in the range of 400-1000 nm of prediction set. The SR and PCA algorithms were further combined to establish the best SR-PC-LS-SVM model for BAs prediction, which had high RP2of 0.969 and low RMSEP of 1.039 in the region of 400-1000 nm. The visual map of the BAs was generated using the best SR-PC-LS-SVM model with imaging process algorithms, which could be used to observe the changes of BAs in cooked beef more intuitively. The study demonstrated that hyperspectral imaging technique combined with sparse representation were able to detect effectively the BAs values in cooked beef during storage and the built SR-PC-LS-SVM model had a potential for rapid and accurate determination of freshness indexes in other meat and meat products.

Dense and Sparse Matrix Operations on the Cell Processor

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

Williams, Samuel W.; Shalf, John; Oliker, Leonid

2005-05-01

The slowing pace of commodity microprocessor performance improvements combined with ever-increasing chip power demands has become of utmost concern to computational scientists. Therefore, the high performance computing community is examining alternative architectures that address the limitations of modern superscalar designs. In this work, we examine STI's forthcoming Cell processor: a novel, low-power architecture that combines a PowerPC core with eight independent SIMD processing units coupled with a software-controlled memory to offer high FLOP/s/Watt. Since neither Cell hardware nor cycle-accurate simulators are currently publicly available, we develop an analytic framework to predict Cell performance on dense and sparse matrix operations, usingmore » a variety of algorithmic approaches. Results demonstrate Cell's potential to deliver more than an order of magnitude better GFLOP/s per watt performance, when compared with the Intel Itanium2 and Cray X1 processors.« less

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Research on sparse feature matching of improved RANSAC algorithm

NASA Astrophysics Data System (ADS)

Kong, Xiangsi; Zhao, Xian

2018-04-01

In this paper, a sparse feature matching method based on modified RANSAC algorithm is proposed to improve the precision and speed. Firstly, the feature points of the images are extracted using the SIFT algorithm. Then, the image pair is matched roughly by generating SIFT feature descriptor. At last, the precision of image matching is optimized by the modified RANSAC algorithm,. The RANSAC algorithm is improved from three aspects: instead of the homography matrix, this paper uses the fundamental matrix generated by the 8 point algorithm as the model; the sample is selected by a random block selecting method, which ensures the uniform distribution and the accuracy; adds sequential probability ratio test(SPRT) on the basis of standard RANSAC, which cut down the overall running time of the algorithm. The experimental results show that this method can not only get higher matching accuracy, but also greatly reduce the computation and improve the matching speed.

3D Reconstruction of human bones based on dictionary learning.

PubMed

Zhang, Binkai; Wang, Xiang; Liang, Xiao; Zheng, Jinjin

2017-11-01

An effective method for reconstructing a 3D model of human bones from computed tomography (CT) image data based on dictionary learning is proposed. In this study, the dictionary comprises the vertices of triangular meshes, and the sparse coefficient matrix indicates the connectivity information. For better reconstruction performance, we proposed a balance coefficient between the approximation and regularisation terms and a method for optimisation. Moreover, we applied a local updating strategy and a mesh-optimisation method to update the dictionary and the sparse matrix, respectively. The two updating steps are iterated alternately until the objective function converges. Thus, a reconstructed mesh could be obtained with high accuracy and regularisation. The experimental results show that the proposed method has the potential to obtain high precision and high-quality triangular meshes for rapid prototyping, medical diagnosis, and tissue engineering. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

Arbitrary norm support vector machines.

PubMed

Huang, Kaizhu; Zheng, Danian; King, Irwin; Lyu, Michael R

2009-02-01

Support vector machines (SVM) are state-of-the-art classifiers. Typically L2-norm or L1-norm is adopted as a regularization term in SVMs, while other norm-based SVMs, for example, the L0-norm SVM or even the L(infinity)-norm SVM, are rarely seen in the literature. The major reason is that L0-norm describes a discontinuous and nonconvex term, leading to a combinatorially NP-hard optimization problem. In this letter, motivated by Bayesian learning, we propose a novel framework that can implement arbitrary norm-based SVMs in polynomial time. One significant feature of this framework is that only a sequence of sequential minimal optimization problems needs to be solved, thus making it practical in many real applications. The proposed framework is important in the sense that Bayesian priors can be efficiently plugged into most learning methods without knowing the explicit form. Hence, this builds a connection between Bayesian learning and the kernel machines. We derive the theoretical framework, demonstrate how our approach works on the L0-norm SVM as a typical example, and perform a series of experiments to validate its advantages. Experimental results on nine benchmark data sets are very encouraging. The implemented L0-norm is competitive with or even better than the standard L2-norm SVM in terms of accuracy but with a reduced number of support vectors, -9.46% of the number on average. When compared with another sparse model, the relevance vector machine, our proposed algorithm also demonstrates better sparse properties with a training speed over seven times faster.

AITRAC: Augmented Interactive Transient Radiation Analysis by Computer. User's information manual

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

Not Available

1977-10-01

AITRAC is a program designed for on-line, interactive, DC, and transient analysis of electronic circuits. The program solves linear and nonlinear simultaneous equations which characterize the mathematical models used to predict circuit response. The program features 100 external node--200 branch capability; conversional, free-format input language; built-in junction, FET, MOS, and switch models; sparse matrix algorithm with extended-precision H matrix and T vector calculations, for fast and accurate execution; linear transconductances: beta, GM, MU, ZM; accurate and fast radiation effects analysis; special interface for user-defined equations; selective control of multiple outputs; graphical outputs in wide and narrow formats; and on-line parametermore » modification capability. The user describes the problem by entering the circuit topology and part parameters. The program then automatically generates and solves the circuit equations, providing the user with printed or plotted output. The circuit topology and/or part values may then be changed by the user, and a new analysis, requested. Circuit descriptions may be saved on disk files for storage and later use. The program contains built-in standard models for resistors, voltage and current sources, capacitors, inductors including mutual couplings, switches, junction diodes and transistors, FETS, and MOS devices. Nonstandard models may be constructed from standard models or by using the special equations interface. Time functions may be described by straight-line segments or by sine, damped sine, and exponential functions. 42 figures, 1 table. (RWR)« less

Application of a sparse representation method using K-SVD to data compression of experimental ambient vibration data for SHM

NASA Astrophysics Data System (ADS)

Noh, Hae Young; Kiremidjian, Anne S.

2011-04-01

This paper introduces a data compression method using the K-SVD algorithm and its application to experimental ambient vibration data for structural health monitoring purposes. Because many damage diagnosis algorithms that use system identification require vibration measurements of multiple locations, it is necessary to transmit long threads of data. In wireless sensor networks for structural health monitoring, however, data transmission is often a major source of battery consumption. Therefore, reducing the amount of data to transmit can significantly lengthen the battery life and reduce maintenance cost. The K-SVD algorithm was originally developed in information theory for sparse signal representation. This algorithm creates an optimal over-complete set of bases, referred to as a dictionary, using singular value decomposition (SVD) and represents the data as sparse linear combinations of these bases using the orthogonal matching pursuit (OMP) algorithm. Since ambient vibration data are stationary, we can segment them and represent each segment sparsely. Then only the dictionary and the sparse vectors of the coefficients need to be transmitted wirelessly for restoration of the original data. We applied this method to ambient vibration data measured from a four-story steel moment resisting frame. The results show that the method can compress the data efficiently and restore the data with very little error.

Bayes linear covariance matrix adjustment

NASA Astrophysics Data System (ADS)

Wilkinson, Darren J.

1995-12-01

In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of random matrices is motivated and constructed. The inner-product on this space captures aspects of our beliefs about the relationship between covariance matrices of interest to us, providing a structure rich enough for us to adjust beliefs about unknown matrices in the light of data such as sample covariance matrices, exploiting second-order exchangeability and related specifications to obtain representations allowing analysis. Adjustment is associated with orthogonal projection, and illustrated with examples of adjustments for some common problems. The problem of adjusting the covariance matrices underlying exchangeable random vectors is tackled and discussed. Learning about the covariance matrices associated with multivariate time series dynamic linear models is shown to be amenable to a similar approach. Diagnostics for matrix adjustments are also discussed.

Parallel pivoting combined with parallel reduction

NASA Technical Reports Server (NTRS)

Alaghband, Gita

1987-01-01

Parallel algorithms for triangularization of large, sparse, and unsymmetric matrices are presented. The method combines the parallel reduction with a new parallel pivoting technique, control over generations of fill-ins and a check for numerical stability, all done in parallel with the work being distributed over the active processes. The parallel technique uses the compatibility relation between pivots to identify parallel pivot candidates and uses the Markowitz number of pivots to minimize fill-in. This technique is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds.

Temporally-Constrained Group Sparse Learning for Longitudinal Data Analysis in Alzheimer’s Disease

PubMed Central

Jie, Biao; Liu, Mingxia; Liu, Jun

2016-01-01

Sparse learning has been widely investigated for analysis of brain images to assist the diagnosis of Alzheimer’s disease (AD) and its prodromal stage, i.e., mild cognitive impairment (MCI). However, most existing sparse learning-based studies only adopt cross-sectional analysis methods, where the sparse model is learned using data from a single time-point. Actually, multiple time-points of data are often available in brain imaging applications, which can be used in some longitudinal analysis methods to better uncover the disease progression patterns. Accordingly, in this paper we propose a novel temporally-constrained group sparse learning method aiming for longitudinal analysis with multiple time-points of data. Specifically, we learn a sparse linear regression model by using the imaging data from multiple time-points, where a group regularization term is first employed to group the weights for the same brain region across different time-points together. Furthermore, to reflect the smooth changes between data derived from adjacent time-points, we incorporate two smoothness regularization terms into the objective function, i.e., one fused smoothness term which requires that the differences between two successive weight vectors from adjacent time-points should be small, and another output smoothness term which requires the differences between outputs of two successive models from adjacent time-points should also be small. We develop an efficient optimization algorithm to solve the proposed objective function. Experimental results on ADNI database demonstrate that, compared with conventional sparse learning-based methods, our proposed method can achieve improved regression performance and also help in discovering disease-related biomarkers. PMID:27093313

ℓ0 -based sparse hyperspectral unmixing using spectral information and a multi-objectives formulation

NASA Astrophysics Data System (ADS)

Xu, Xia; Shi, Zhenwei; Pan, Bin

2018-07-01

Sparse unmixing aims at recovering pure materials from hyperpspectral images and estimating their abundance fractions. Sparse unmixing is actually ℓ0 problem which is NP-h ard, and a relaxation is often used. In this paper, we attempt to deal with ℓ0 problem directly via a multi-objective based method, which is a non-convex manner. The characteristics of hyperspectral images are integrated into the proposed method, which leads to a new spectra and multi-objective based sparse unmixing method (SMoSU). In order to solve the ℓ0 norm optimization problem, the spectral library is encoded in a binary vector, and a bit-wise flipping strategy is used to generate new individuals in the evolution process. However, a multi-objective method usually produces a number of non-dominated solutions, while sparse unmixing requires a single solution. How to make the final decision for sparse unmixing is challenging. To handle this problem, we integrate the spectral characteristic of hyperspectral images into SMoSU. By considering the spectral correlation in hyperspectral data, we improve the Tchebycheff decomposition function in SMoSU via a new regularization item. This regularization item is able to enforce the individual divergence in the evolution process of SMoSU. In this way, the diversity and convergence of population is further balanced, which is beneficial to the concentration of individuals. In the experiments part, three synthetic datasets and one real-world data are used to analyse the effectiveness of SMoSU, and several state-of-art sparse unmixing algorithms are compared.

Comparison of l₁-Norm SVR and Sparse Coding Algorithms for Linear Regression.

PubMed

Zhang, Qingtian; Hu, Xiaolin; Zhang, Bo

2015-08-01

Support vector regression (SVR) is a popular function estimation technique based on Vapnik's concept of support vector machine. Among many variants, the l1-norm SVR is known to be good at selecting useful features when the features are redundant. Sparse coding (SC) is a technique widely used in many areas and a number of efficient algorithms are available. Both l1-norm SVR and SC can be used for linear regression. In this brief, the close connection between the l1-norm SVR and SC is revealed and some typical algorithms are compared for linear regression. The results show that the SC algorithms outperform the Newton linear programming algorithm, an efficient l1-norm SVR algorithm, in efficiency. The algorithms are then used to design the radial basis function (RBF) neural networks. Experiments on some benchmark data sets demonstrate the high efficiency of the SC algorithms. In particular, one of the SC algorithms, the orthogonal matching pursuit is two orders of magnitude faster than a well-known RBF network designing algorithm, the orthogonal least squares algorithm.

On Schrödinger's bridge problem

NASA Astrophysics Data System (ADS)

Friedland, S.

2017-11-01

In the first part of this paper we generalize Georgiou-Pavon's result that a positive square matrix can be scaled uniquely to a column stochastic matrix which maps a given positive probability vector to another given positive probability vector. In the second part we prove that a positive quantum channel can be scaled to another positive quantum channel which maps a given positive definite density matrix to another given positive definite density matrix using Brouwer's fixed point theorem. This result proves the Georgiou-Pavon conjecture for two positive definite density matrices, made in their recent paper. We show that the fixed points are unique for certain pairs of positive definite density matrices. Bibliography: 15 titles.

A T Matrix Method Based upon Scalar Basis Functions

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Kahnert, F. M.; Mishchenko, Michael I.

2013-01-01

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

pySAPC, a python package for sparse affinity propagation clustering: Application to odontogenesis whole genome time series gene-expression data.

PubMed

Cao, Huojun; Amendt, Brad A

2016-11-01

Developmental dental anomalies are common forms of congenital defects. The molecular mechanisms of dental anomalies are poorly understood. Systematic approaches such as clustering genes based on similar expression patterns could identify novel genes involved in dental anomalies and provide a framework for understanding molecular regulatory mechanisms of these genes during tooth development (odontogenesis). A python package (pySAPC) of sparse affinity propagation clustering algorithm for large datasets was developed. Whole genome pair-wise similarity was calculated based on expression pattern similarity based on 45 microarrays of several stages during odontogenesis. pySAPC identified 743 gene clusters based on expression pattern similarity during mouse tooth development. Three clusters are significantly enriched for genes associated with dental anomalies (with FDR <0.1). The three clusters of genes have distinct expression patterns during odontogenesis. Clustering genes based on similar expression profiles recovered several known regulatory relationships for genes involved in odontogenesis, as well as many novel genes that may be involved with the same genetic pathways as genes that have already been shown to contribute to dental defects. By using sparse similarity matrix, pySAPC use much less memory and CPU time compared with the original affinity propagation program that uses a full similarity matrix. This python package will be useful for many applications where dataset(s) are too large to use full similarity matrix. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang. Copyright © 2016. Published by Elsevier B.V.

A Semi-Vectorization Algorithm to Synthesis of Gravitational Anomaly Quantities on the Earth

NASA Astrophysics Data System (ADS)

Abdollahzadeh, M.; Eshagh, M.; Najafi Alamdari, M.

2009-04-01

The Earth's gravitational potential can be expressed by the well-known spherical harmonic expansion. The computational time of summing up this expansion is an important practical issue which can be reduced by an efficient numerical algorithm. This paper proposes such a method for block-wise synthesizing the anomaly quantities on the Earth surface using vectorization. Fully-vectorization means transformation of the summations to the simple matrix and vector products. It is not a practical for the matrices with large dimensions. Here a semi-vectorization algorithm is proposed to avoid working with large vectors and matrices. It speeds up the computations by using one loop for the summation either on degrees or on orders. The former is a good option to synthesize the anomaly quantities on the Earth surface considering a digital elevation model (DEM). This approach is more efficient than the two-step method which computes the quantities on the reference ellipsoid and continues them upward to the Earth surface. The algorithm has been coded in MATLAB which synthesizes a global grid of 5′Ã- 5′ (corresponding 9 million points) of gravity anomaly or geoid height using a geopotential model to degree 360 in 10000 seconds by an ordinary computer with 2G RAM.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

Expression in Escherichia coli, refolding and crystallization of Aspergillus niger feruloyl esterase A using a serial factorial approach.

PubMed

Benoit, Isabelle; Coutard, Bruno; Oubelaid, Rachid; Asther, Marcel; Bignon, Christophe

2007-09-01

Hydrolysis of plant biomass is achieved by the combined action of enzymes secreted by microorganisms and directed against the backbone and the side chains of plant cell wall polysaccharides. Among side chains degrading enzymes, the feruloyl esterase A (FAEA) specifically removes feruloyl residues. Thus, FAEA has potential applications in a wide range of industrial processes such as paper bleaching or bio-ethanol production. To gain insight into FAEA hydrolysis activity, we solved its crystal structure. In this paper, we report how the use of four consecutive factorial approaches (two incomplete factorials, one sparse matrix, and one full factorial) allowed expressing in Escherichia coli, refolding and then crystallizing Aspergillus niger FAEA in 6 weeks. Culture conditions providing the highest expression level were determined using an incomplete factorial approach made of 12 combinations of four E. coli strains, three culture media and three temperatures (full factorial: 36 combinations). Aspergillus niger FAEA was expressed in the form of inclusion bodies. These were dissolved using a chaotropic agent, and the protein was purified by affinity chromatography on Ni column under denaturing conditions. A suitable buffer for refolding the protein eluted from the Ni column was found using a second incomplete factorial approach made of 96 buffers (full factorial: 3840 combinations). After refolding, the enzyme was further purified by gel filtration, and then crystallized following a standard protocol: initial crystallization conditions were found using commercial crystallization screens based on a sparse matrix. Crystals were then optimized using a full factorial screen.

A Performance Comparison of the Parallel Preconditioners for Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations on Structured Grids

NASA Astrophysics Data System (ADS)

Ma, Sangback

In this paper we compare various parallel preconditioners such as Point-SSOR (Symmetric Successive OverRelaxation), ILU(0) (Incomplete LU) in the Wavefront ordering, ILU(0) in the Multi-color ordering, Multi-Color Block SOR (Successive OverRelaxation), SPAI (SParse Approximate Inverse) and pARMS (Parallel Algebraic Recursive Multilevel Solver) for solving large sparse linear systems arising from two-dimensional PDE (Partial Differential Equation)s on structured grids. Point-SSOR is well-known, and ILU(0) is one of the most popular preconditioner, but it is inherently serial. ILU(0) in the Wavefront ordering maximizes the parallelism in the natural order, but the lengths of the wave-fronts are often nonuniform. ILU(0) in the Multi-color ordering is a simple way of achieving a parallelism of the order N, where N is the order of the matrix, but its convergence rate often deteriorates as compared to that of natural ordering. We have chosen the Multi-Color Block SOR preconditioner combined with direct sparse matrix solver, since for the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with the Multi-Color ordering. By using block version we expect to minimize the interprocessor communications. SPAI computes the sparse approximate inverse directly by least squares method. Finally, ARMS is a preconditioner recursively exploiting the concept of independent sets and pARMS is the parallel version of ARMS. Experiments were conducted for the Finite Difference and Finite Element discretizations of five two-dimensional PDEs with large meshsizes up to a million on an IBM p595 machine with distributed memory. Our matrices are real positive, i. e., their real parts of the eigenvalues are positive. We have used GMRES(m) as our outer iterative method, so that the convergence of GMRES(m) for our test matrices are mathematically guaranteed. Interprocessor communications were done using MPI (Message Passing Interface) primitives. The results show that in general ILU(0) in the Multi-Color ordering ahd ILU(0) in the Wavefront ordering outperform the other methods but for symmetric and nearly symmetric 5-point matrices Multi-Color Block SOR gives the best performance, except for a few cases with a small number of processors.

Error Analysis of Deep Sequencing of Phage Libraries: Peptides Censored in Sequencing

PubMed Central

Matochko, Wadim L.; Derda, Ratmir

2013-01-01

Next-generation sequencing techniques empower selection of ligands from phage-display libraries because they can detect low abundant clones and quantify changes in the copy numbers of clones without excessive selection rounds. Identification of errors in deep sequencing data is the most critical step in this process because these techniques have error rates >1%. Mechanisms that yield errors in Illumina and other techniques have been proposed, but no reports to date describe error analysis in phage libraries. Our paper focuses on error analysis of 7-mer peptide libraries sequenced by Illumina method. Low theoretical complexity of this phage library, as compared to complexity of long genetic reads and genomes, allowed us to describe this library using convenient linear vector and operator framework. We describe a phage library as N × 1 frequency vector n = ||ni||, where ni is the copy number of the ith sequence and N is the theoretical diversity, that is, the total number of all possible sequences. Any manipulation to the library is an operator acting on n. Selection, amplification, or sequencing could be described as a product of a N × N matrix and a stochastic sampling operator (S a). The latter is a random diagonal matrix that describes sampling of a library. In this paper, we focus on the properties of S a and use them to define the sequencing operator (S e q). Sequencing without any bias and errors is S e q = S a IN, where IN is a N × N unity matrix. Any bias in sequencing changes IN to a nonunity matrix. We identified a diagonal censorship matrix (C E N), which describes elimination or statistically significant downsampling, of specific reads during the sequencing process. PMID:24416071

Biclustering sparse binary genomic data.

PubMed

van Uitert, Miranda; Meuleman, Wouter; Wessels, Lodewyk

2008-12-01

Genomic datasets often consist of large, binary, sparse data matrices. In such a dataset, one is often interested in finding contiguous blocks that (mostly) contain ones. This is a biclustering problem, and while many algorithms have been proposed to deal with gene expression data, only two algorithms have been proposed that specifically deal with binary matrices. None of the gene expression biclustering algorithms can handle the large number of zeros in sparse binary matrices. The two proposed binary algorithms failed to produce meaningful results. In this article, we present a new algorithm that is able to extract biclusters from sparse, binary datasets. A powerful feature is that biclusters with different numbers of rows and columns can be detected, varying from many rows to few columns and few rows to many columns. It allows the user to guide the search towards biclusters of specific dimensions. When applying our algorithm to an input matrix derived from TRANSFAC, we find transcription factors with distinctly dissimilar binding motifs, but a clear set of common targets that are significantly enriched for GO categories.