Complexity of Kronecker Operations on Sparse Matrices with Applications to the Solution of Markov Models

NASA Technical Reports Server (NTRS)

Buchholz, Peter; Ciardo, Gianfranco; Donatelli, Susanna; Kemper, Peter

1997-01-01

We present a systematic discussion of algorithms to multiply a vector by a matrix expressed as the Kronecker product of sparse matrices, extending previous work in a unified notational framework. Then, we use our results to define new algorithms for the solution of large structured Markov models. In addition to a comprehensive overview of existing approaches, we give new results with respect to: (1) managing certain types of state-dependent behavior without incurring extra cost; (2) supporting both Jacobi-style and Gauss-Seidel-style methods by appropriate multiplication algorithms; (3) speeding up algorithms that consider probability vectors of size equal to the "actual" state space instead of the "potential" state space.

Inference for High-dimensional Differential Correlation Matrices.

PubMed

Cai, T Tony; Zhang, Anru

2016-01-01

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed.

Structure and stability of genetic variance-covariance matrices: A Bayesian sparse factor analysis of transcriptional variation in the three-spined stickleback.

PubMed

Siren, J; Ovaskainen, O; Merilä, J

2017-10-01

The genetic variance-covariance matrix (G) is a quantity of central importance in evolutionary biology due to its influence on the rate and direction of multivariate evolution. However, the predictive power of empirically estimated G-matrices is limited for two reasons. First, phenotypes are high-dimensional, whereas traditional statistical methods are tuned to estimate and analyse low-dimensional matrices. Second, the stability of G to environmental effects and over time remains poorly understood. Using Bayesian sparse factor analysis (BSFG) designed to estimate high-dimensional G-matrices, we analysed levels variation and covariation in 10,527 expressed genes in a large (n = 563) half-sib breeding design of three-spined sticklebacks subject to two temperature treatments. We found significant differences in the structure of G between the treatments: heritabilities and evolvabilities were higher in the warm than in the low-temperature treatment, suggesting more and faster opportunity to evolve in warm (stressful) conditions. Furthermore, comparison of G and its phenotypic equivalent P revealed the latter is a poor substitute of the former. Most strikingly, the results suggest that the expected impact of G on evolvability-as well as the similarity among G-matrices-may depend strongly on the number of traits included into analyses. In our results, the inclusion of only few traits in the analyses leads to underestimation in the differences between the G-matrices and their predicted impacts on evolution. While the results highlight the challenges involved in estimating G, they also illustrate that by enabling the estimation of large G-matrices, the BSFG method can improve predicted evolutionary responses to selection. © 2017 John Wiley & Sons Ltd.

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.

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.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

1991-01-01

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Inference for High-dimensional Differential Correlation Matrices *

PubMed Central

Cai, T. Tony; Zhang, Anru

2015-01-01

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical guarantees are given. Minimax rate of convergence is established and the proposed estimator is shown to be adaptively rate-optimal over collections of paired correlation matrices with approximately sparse differences. Simulation results show that the procedure significantly outperforms two other natural methods that are based on separate estimation of the individual correlation matrices. The procedure is also illustrated through an analysis of a breast cancer dataset, which provides evidence at the gene co-expression level that several genes, of which a subset has been previously verified, are associated with the breast cancer. Hypothesis testing on the differential correlation matrices is also considered. A test, which is particularly well suited for testing against sparse alternatives, is introduced. In addition, other related problems, including estimation of a single sparse correlation matrix, estimation of the differential covariance matrices, and estimation of the differential cross-correlation matrices, are also discussed. PMID:26500380

An algebraic equation solution process formulated in anticipation of banded linear equations.

DOT National Transportation Integrated Search

1971-01-01

A general method for the solution of large, sparsely banded, positive-definite, coefficient matrices is presented. The goal in developing the method was to produce an efficient and reliable solution process and to provide the user-programmer with a p...

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.

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

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.

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.

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.

Brief announcement: Hypergraph parititioning for parallel sparse matrix-matrix multiplication

DOE PAGES

Ballard, Grey; Druinsky, Alex; Knight, Nicholas; ...

2015-01-01

The performance of parallel algorithms for sparse matrix-matrix multiplication is typically determined by the amount of interprocessor communication performed, which in turn depends on the nonzero structure of the input matrices. In this paper, we characterize the communication cost of a sparse matrix-matrix multiplication algorithm in terms of the size of a cut of an associated hypergraph that encodes the computation for a given input nonzero structure. Obtaining an optimal algorithm corresponds to solving a hypergraph partitioning problem. Furthermore, our hypergraph model generalizes several existing models for sparse matrix-vector multiplication, and we can leverage hypergraph partitioners developed for that computationmore » to improve application-specific algorithms for multiplying sparse matrices.« less

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

NASA Astrophysics Data System (ADS)

Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei

2018-04-01

We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

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.

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.

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.

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

Solving large sparse eigenvalue problems on supercomputers

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef

1988-01-01

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations 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.

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

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

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

DOE PAGES

Rouet, François-Henry; Li, Xiaoye S.; Ghysels, Pieter; ...

2016-06-30

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, reliesmore » on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.« less

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.

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.

A Shifted Block Lanczos Algorithm 1: The Block Recurrence

NASA Technical Reports Server (NTRS)

Grimes, Roger G.; Lewis, John G.; Simon, Horst D.

1990-01-01

In this paper we describe a block Lanczos algorithm that is used as the key building block of a software package for the extraction of eigenvalues and eigenvectors of large sparse symmetric generalized eigenproblems. The software package comprises: a version of the block Lanczos algorithm specialized for spectrally transformed eigenproblems; an adaptive strategy for choosing shifts, and efficient codes for factoring large sparse symmetric indefinite matrices. This paper describes the algorithmic details of our block Lanczos recurrence. This uses a novel combination of block generalizations of several features that have only been investigated independently in the past. In particular new forms of partial reorthogonalization, selective reorthogonalization and local reorthogonalization are used, as is a new algorithm for obtaining the M-orthogonal factorization of a matrix. The heuristic shifting strategy, the integration with sparse linear equation solvers and numerical experience with the code are described in a companion paper.

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

Efficient sparse matrix-matrix multiplication for computing periodic responses by shooting method on Intel Xeon Phi

NASA Astrophysics Data System (ADS)

Stoykov, S.; Atanassov, E.; Margenov, S.

2016-10-01

Many of the scientific applications involve sparse or dense matrix operations, such as solving linear systems, matrix-matrix products, eigensolvers, etc. In what concerns structural nonlinear dynamics, the computations of periodic responses and the determination of stability of the solution are of primary interest. Shooting method iswidely used for obtaining periodic responses of nonlinear systems. The method involves simultaneously operations with sparse and dense matrices. One of the computationally expensive operations in the method is multiplication of sparse by dense matrices. In the current work, a new algorithm for sparse matrix by dense matrix products is presented. The algorithm takes into account the structure of the sparse matrix, which is obtained by space discretization of the nonlinear Mindlin's plate equation of motion by the finite element method. The algorithm is developed to use the vector engine of Intel Xeon Phi coprocessors. It is compared with the standard sparse matrix by dense matrix algorithm and the one developed by Intel MKL and it is shown that by considering the properties of the sparse matrix better algorithms can be developed.

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.

Decentralized state estimation for a large-scale spatially interconnected system.

PubMed

Liu, Huabo; Yu, Haisheng

2018-03-01

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Multiprocessor sparse L/U decomposition with controlled fill-in

NASA Technical Reports Server (NTRS)

Alaghband, G.; Jordan, H. F.

1985-01-01

Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.

Partitioning Rectangular and Structurally Nonsymmetric Sparse Matrices for Parallel Processing

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

B. Hendrickson; T.G. Kolda

1998-09-01

A common operation in scientific computing is the multiplication of a sparse, rectangular or structurally nonsymmetric matrix and a vector. In many applications the matrix- transpose-vector product is also required. This paper addresses the efficient parallelization of these operations. We show that the problem can be expressed in terms of partitioning bipartite graphs. We then introduce several algorithms for this partitioning problem and compare their performance on a set of test matrices.

Condition number estimation of preconditioned matrices.

PubMed

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.

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

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).

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 development of efficient algorithms for three dimensional fluid flow

NASA Technical Reports Server (NTRS)

Maccormack, R. W.

1988-01-01

The difficulties of constructing efficient algorithms for three-dimensional flow are discussed. Reasonable candidates are analyzed and tested, and most are found to have obvious shortcomings. Yet, there is promise that an efficient class of algorithms exist between the severely time-step sized-limited explicit or approximately factored algorithms and the computationally intensive direct inversion of large sparse matrices by Gaussian elimination.

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.

Condition Number Estimation of Preconditioned Matrices

PubMed Central

Kushida, Noriyuki

2015-01-01

The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager’s method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei’s matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei’s matrix, and matrices generated with the finite element method. PMID:25816331

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets.

PubMed

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O; Gelfand, Alan E

2016-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

PubMed Central

Datta, Abhirup; Banerjee, Sudipto; Finley, Andrew O.; Gelfand, Alan E.

2018-01-01

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This article develops a class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive U.S. Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods. Supplementary materials for this article are available online. PMID:29720777

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.

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

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

TESTING HIGH-DIMENSIONAL COVARIANCE MATRICES, WITH APPLICATION TO DETECTING SCHIZOPHRENIA RISK GENES

PubMed Central

Zhu, Lingxue; Lei, Jing; Devlin, Bernie; Roeder, Kathryn

2017-01-01

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene “relationship” matrices that are of practical interest, such as the weighted adjacency matrices. PMID:29081874

TESTING HIGH-DIMENSIONAL COVARIANCE MATRICES, WITH APPLICATION TO DETECTING SCHIZOPHRENIA RISK GENES.

PubMed

Zhu, Lingxue; Lei, Jing; Devlin, Bernie; Roeder, Kathryn

2017-09-01

Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.

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

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

DOE PAGES

Ghysels, Pieter; Li, Xiaoye S.; Rouet, Francois -Henry; ...

2016-10-27

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite.more » The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.« less

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

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

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

Sequential Designs Based on Bayesian Uncertainty Quantification in Sparse Representation Surrogate Modeling

DOE PAGES

Chen, Ray -Bing; Wang, Weichung; Jeff Wu, C. F.

2017-04-12

A numerical method, called OBSM, was recently proposed which employs overcomplete basis functions to achieve sparse representations. While the method can handle non-stationary response without the need of inverting large covariance matrices, it lacks the capability to quantify uncertainty in predictions. We address this issue by proposing a Bayesian approach which first imposes a normal prior on the large space of linear coefficients, then applies the MCMC algorithm to generate posterior samples for predictions. From these samples, Bayesian credible intervals can then be obtained to assess prediction uncertainty. A key application for the proposed method is the efficient construction ofmore » sequential designs. Several sequential design procedures with different infill criteria are proposed based on the generated posterior samples. As a result, numerical studies show that the proposed schemes are capable of solving problems of positive point identification, optimization, and surrogate fitting.« less

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

Accelerating Full Configuration Interaction Calculations for Nuclear Structure

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

Yang, Chao; Sternberg, Philip; Maris, Pieter

2008-04-14

One of the emerging computational approaches in nuclear physics is the full configuration interaction (FCI) method for solving the many-body nuclear Hamiltonian in a sufficiently large single-particle basis space to obtain exact answers - either directly or by extrapolation. The lowest eigenvalues and correspondingeigenvectors for very large, sparse and unstructured nuclear Hamiltonian matrices are obtained and used to evaluate additional experimental quantities. These matrices pose a significant challenge to the design and implementation of efficient and scalable algorithms for obtaining solutions on massively parallel computer systems. In this paper, we describe the computational strategies employed in a state-of-the-art FCI codemore » MFDn (Many Fermion Dynamics - nuclear) as well as techniques we recently developed to enhance the computational efficiency of MFDn. We will demonstrate the current capability of MFDn and report the latest performance improvement we have achieved. We will also outline our future research directions.« less

Insights from Classifying Visual Concepts with Multiple Kernel Learning

PubMed Central

Binder, Alexander; Nakajima, Shinichi; Kloft, Marius; Müller, Christina; Samek, Wojciech; Brefeld, Ulf; Müller, Klaus-Robert; Kawanabe, Motoaki

2012-01-01

Combining information from various image features has become a standard technique in concept recognition tasks. However, the optimal way of fusing the resulting kernel functions is usually unknown in practical applications. Multiple kernel learning (MKL) techniques allow to determine an optimal linear combination of such similarity matrices. Classical approaches to MKL promote sparse mixtures. Unfortunately, 1-norm regularized MKL variants are often observed to be outperformed by an unweighted sum kernel. The main contributions of this paper are the following: we apply a recently developed non-sparse MKL variant to state-of-the-art concept recognition tasks from the application domain of computer vision. We provide insights on benefits and limits of non-sparse MKL and compare it against its direct competitors, the sum-kernel SVM and sparse MKL. We report empirical results for the PASCAL VOC 2009 Classification and ImageCLEF2010 Photo Annotation challenge data sets. Data sets (kernel matrices) as well as further information are available at http://doc.ml.tu-berlin.de/image_mkl/(Accessed 2012 Jun 25). PMID:22936970

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.

beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types

PubMed Central

Pagès, Hervé

2018-01-01

Biological experiments involving genomics or other high-throughput assays typically yield a data matrix that can be explored and analyzed using the R programming language with packages from the Bioconductor project. Improvements in the throughput of these assays have resulted in an explosion of data even from routine experiments, which poses a challenge to the existing computational infrastructure for statistical data analysis. For example, single-cell RNA sequencing (scRNA-seq) experiments frequently generate large matrices containing expression values for each gene in each cell, requiring sparse or file-backed representations for memory-efficient manipulation in R. These alternative representations are not easily compatible with high-performance C++ code used for computationally intensive tasks in existing R/Bioconductor packages. Here, we describe a C++ interface named beachmat, which enables agnostic data access from various matrix representations. This allows package developers to write efficient C++ code that is interoperable with dense, sparse and file-backed matrices, amongst others. We evaluated the performance of beachmat for accessing data from each matrix representation using both simulated and real scRNA-seq data, and defined a clear memory/speed trade-off to motivate the choice of an appropriate representation. We also demonstrate how beachmat can be incorporated into the code of other packages to drive analyses of a very large scRNA-seq data set. PMID:29723188

beachmat: A Bioconductor C++ API for accessing high-throughput biological data from a variety of R matrix types.

PubMed

Lun, Aaron T L; Pagès, Hervé; Smith, Mike L

2018-05-01

Biological experiments involving genomics or other high-throughput assays typically yield a data matrix that can be explored and analyzed using the R programming language with packages from the Bioconductor project. Improvements in the throughput of these assays have resulted in an explosion of data even from routine experiments, which poses a challenge to the existing computational infrastructure for statistical data analysis. For example, single-cell RNA sequencing (scRNA-seq) experiments frequently generate large matrices containing expression values for each gene in each cell, requiring sparse or file-backed representations for memory-efficient manipulation in R. These alternative representations are not easily compatible with high-performance C++ code used for computationally intensive tasks in existing R/Bioconductor packages. Here, we describe a C++ interface named beachmat, which enables agnostic data access from various matrix representations. This allows package developers to write efficient C++ code that is interoperable with dense, sparse and file-backed matrices, amongst others. We evaluated the performance of beachmat for accessing data from each matrix representation using both simulated and real scRNA-seq data, and defined a clear memory/speed trade-off to motivate the choice of an appropriate representation. We also demonstrate how beachmat can be incorporated into the code of other packages to drive analyses of a very large scRNA-seq data set.

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.

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

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1991-01-01

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

Assessing the effects of cocaine dependence and pathological gambling using group-wise sparse representation of natural stimulus FMRI data.

PubMed

Ren, Yudan; Fang, Jun; Lv, Jinglei; Hu, Xintao; Guo, Cong Christine; Guo, Lei; Xu, Jiansong; Potenza, Marc N; Liu, Tianming

2017-08-01

Assessing functional brain activation patterns in neuropsychiatric disorders such as cocaine dependence (CD) or pathological gambling (PG) under naturalistic stimuli has received rising interest in recent years. In this paper, we propose and apply a novel group-wise sparse representation framework to assess differences in neural responses to naturalistic stimuli across multiple groups of participants (healthy control, cocaine dependence, pathological gambling). Specifically, natural stimulus fMRI (N-fMRI) signals from all three groups of subjects are aggregated into a big data matrix, which is then decomposed into a common signal basis dictionary and associated weight coefficient matrices via an effective online dictionary learning and sparse coding method. The coefficient matrices associated with each common dictionary atom are statistically assessed for each group separately. With the inter-group comparisons based on the group-wise correspondence established by the common dictionary, our experimental results demonstrated that the group-wise sparse coding and representation strategy can effectively and specifically detect brain networks/regions affected by different pathological conditions of the brain under naturalistic stimuli.

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

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

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

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.

Stability and stabilisation of a class of networked dynamic systems

NASA Astrophysics Data System (ADS)

Liu, H. B.; Wang, D. Q.

2018-04-01

We investigate the stability and stabilisation of a linear time invariant networked heterogeneous system with arbitrarily connected subsystems. A new linear matrix inequality based sufficient and necessary condition for the stability is derived, based on which the stabilisation is provided. The obtained conditions efficiently utilise the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, a sufficient condition only dependent on each individual subsystem is also presented for the stabilisation of the networked systems with a large scale. Numerical simulations show that these conditions are computationally valid in the analysis and synthesis of a large-scale networked system.

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

Improved Estimation and Interpretation of Correlations in Neural Circuits

PubMed Central

Yatsenko, Dimitri; Josić, Krešimir; Ecker, Alexander S.; Froudarakis, Emmanouil; Cotton, R. James; Tolias, Andreas S.

2015-01-01

Ambitious projects aim to record the activity of ever larger and denser neuronal populations in vivo. Correlations in neural activity measured in such recordings can reveal important aspects of neural circuit organization. However, estimating and interpreting large correlation matrices is statistically challenging. Estimation can be improved by regularization, i.e. by imposing a structure on the estimate. The amount of improvement depends on how closely the assumed structure represents dependencies in the data. Therefore, the selection of the most efficient correlation matrix estimator for a given neural circuit must be determined empirically. Importantly, the identity and structure of the most efficient estimator informs about the types of dominant dependencies governing the system. We sought statistically efficient estimators of neural correlation matrices in recordings from large, dense groups of cortical neurons. Using fast 3D random-access laser scanning microscopy of calcium signals, we recorded the activity of nearly every neuron in volumes 200 μm wide and 100 μm deep (150–350 cells) in mouse visual cortex. We hypothesized that in these densely sampled recordings, the correlation matrix should be best modeled as the combination of a sparse graph of pairwise partial correlations representing local interactions and a low-rank component representing common fluctuations and external inputs. Indeed, in cross-validation tests, the covariance matrix estimator with this structure consistently outperformed other regularized estimators. The sparse component of the estimate defined a graph of interactions. These interactions reflected the physical distances and orientation tuning properties of cells: The density of positive ‘excitatory’ interactions decreased rapidly with geometric distances and with differences in orientation preference whereas negative ‘inhibitory’ interactions were less selective. Because of its superior performance, this ‘sparse+latent’ estimator likely provides a more physiologically relevant representation of the functional connectivity in densely sampled recordings than the sample correlation matrix. PMID:25826696

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

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

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.

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.; Tungkahotara, Siroj; Watson, Willie R.; Rajan, Subramaniam D.

2005-01-01

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

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.

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.

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'.

Fast Solution in Sparse LDA for Binary Classification

NASA Technical Reports Server (NTRS)

Moghaddam, Baback

2010-01-01

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

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

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need formore » matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

Sparse and incomplete factorial matrices to screen membrane protein 2D crystallization

PubMed Central

Lasala, R.; Coudray, N.; Abdine, A.; Zhang, Z.; Lopez-Redondo, M.; Kirshenbaum, R.; Alexopoulos, J.; Zolnai, Z.; Stokes, D.L.; Ubarretxena-Belandia, I.

2014-01-01

Electron crystallography is well suited for studying the structure of membrane proteins in their native lipid bilayer environment. This technique relies on electron cryomicroscopy of two-dimensional (2D) crystals, grown generally by reconstitution of purified membrane proteins into proteoliposomes under conditions favoring the formation of well-ordered lattices. Growing these crystals presents one of the major hurdles in the application of this technique. To identify conditions favoring crystallization a wide range of factors that can lead to a vast matrix of possible reagent combinations must be screened. However, in 2D crystallization these factors have traditionally been surveyed in a relatively limited fashion. To address this problem we carried out a detailed analysis of published 2D crystallization conditions for 12 β-barrel and 138 α-helical membrane proteins. From this analysis we identified the most successful conditions and applied them in the design of new sparse and incomplete factorial matrices to screen membrane protein 2D crystallization. Using these matrices we have run 19 crystallization screens for 16 different membrane proteins totaling over 1,300 individual crystallization conditions. Six membrane proteins have yielded diffracting 2D crystals suitable for structure determination, indicating that these new matrices show promise to accelerate the success rate of membrane protein 2D crystallization. PMID:25478971

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

Magnus integrators on multicore CPUs and GPUs

NASA Astrophysics Data System (ADS)

Auer, N.; Einkemmer, L.; Kandolf, P.; Ostermann, A.

2018-07-01

In the present paper we consider numerical methods to solve the discrete Schrödinger equation with a time dependent Hamiltonian (motivated by problems encountered in the study of spin systems). We will consider both short-range interactions, which lead to evolution equations involving sparse matrices, and long-range interactions, which lead to dense matrices. Both of these settings show very different computational characteristics. We use Magnus integrators for time integration and employ a framework based on Leja interpolation to compute the resulting action of the matrix exponential. We consider both traditional Magnus integrators (which are extensively used for these types of problems in the literature) as well as the recently developed commutator-free Magnus integrators and implement them on modern CPU and GPU (graphics processing unit) based systems. We find that GPUs can yield a significant speed-up (up to a factor of 10 in the dense case) for these types of problems. In the sparse case GPUs are only advantageous for large problem sizes and the achieved speed-ups are more modest. In most cases the commutator-free variant is superior but especially on the GPU this advantage is rather small. In fact, none of the advantage of commutator-free methods on GPUs (and on multi-core CPUs) is due to the elimination of commutators. This has important consequences for the design of more efficient numerical methods.

Sparse graph regularization for robust crop mapping using hyperspectral remotely sensed imagery with very few in situ data

NASA Astrophysics Data System (ADS)

Xue, Zhaohui; Du, Peijun; Li, Jun; Su, Hongjun

2017-02-01

The generally limited availability of training data relative to the usually high data dimension pose a great challenge to accurate classification of hyperspectral imagery, especially for identifying crops characterized with highly correlated spectra. However, traditional parametric classification models are problematic due to the need of non-singular class-specific covariance matrices. In this research, a novel sparse graph regularization (SGR) method is presented, aiming at robust crop mapping using hyperspectral imagery with very few in situ data. The core of SGR lies in propagating labels from known data to unknown, which is triggered by: (1) the fraction matrix generated for the large unknown data by using an effective sparse representation algorithm with respect to the few training data serving as the dictionary; (2) the prediction function estimated for the few training data by formulating a regularization model based on sparse graph. Then, the labels of large unknown data can be obtained by maximizing the posterior probability distribution based on the two ingredients. SGR is more discriminative, data-adaptive, robust to noise, and efficient, which is unique with regard to previously proposed approaches and has high potentials in discriminating crops, especially when facing insufficient training data and high-dimensional spectral space. The study area is located at Zhangye basin in the middle reaches of Heihe watershed, Gansu, China, where eight crop types were mapped with Compact Airborne Spectrographic Imager (CASI) and Shortwave Infrared Airborne Spectrogrpahic Imager (SASI) hyperspectral data. Experimental results demonstrate that the proposed method significantly outperforms other traditional and state-of-the-art methods.

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.

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.

An exact formulation of the time-ordered exponential using path-sums

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

Giscard, P.-L., E-mail: p.giscard1@physics.ox.ac.uk; Lui, K.; Thwaite, S. J.

2015-05-15

We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitudemore » of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.« less

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

PubMed

Ghosh, A

1988-08-01

Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.

On Fluctuations of Eigenvalues of Random Band Matrices

NASA Astrophysics Data System (ADS)

Shcherbina, M.

2015-10-01

We consider the fluctuations of linear eigenvalue statistics of random band matrices whose entries have the form with i.i.d. possessing the th moment, where the function u has a finite support , so that M has only nonzero diagonals. The parameter b (called the bandwidth) is assumed to grow with n in a way such that . Without any additional assumptions on the growth of b we prove CLT for linear eigenvalue statistics for a rather wide class of test functions. Thus we improve and generalize the results of the previous papers (Jana et al., arXiv:1412.2445; Li et al. Random Matrices 2:04, 2013), where CLT was proven under the assumption . Moreover, we develop a method which allows to prove automatically the CLT for linear eigenvalue statistics of the smooth test functions for almost all classical models of random matrix theory: deformed Wigner and sample covariance matrices, sparse matrices, diluted random matrices, matrices with heavy tales etc.

Exploiting Data Sparsity in Parallel Matrix Powers Computations

DTIC Science & Technology

2013-05-03

2013 Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour...matrices of the form A = D+USV H, where D is sparse and USV H has low rank but may be dense. Matrices of this form arise in many practical applications...methods numerical partial di erential equation solvers, and preconditioned iterative methods. If A has this form , our algorithm enables a communication

Mismatch and resolution in compressive imaging

NASA Astrophysics Data System (ADS)

Fannjiang, Albert; Liao, Wenjing

2011-09-01

Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as sparsifying operators. Algorithms (BOMP, BLOOMP) based on techniques of band exclusion and local optimization are proposed to enhance Orthogonal Matching Pursuit (OMP) and deal with such coherent sensing matrices. BOMP and BLOOMP have provably performance guarantee of reconstructing sparse, widely separated objects independent of the redundancy and have a sparsity constraint and computational cost similar to OMP's. Numerical study demonstrates the effectiveness of BLOOMP for compressed sensing with highly coherent, redundant sensing matrices.

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

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

Parallel iterative methods for sparse linear and nonlinear equations

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Scalability improvements to NRLMOL for DFT calculations of large molecules

NASA Astrophysics Data System (ADS)

Diaz, Carlos Manuel

Advances in high performance computing (HPC) have provided a way to treat large, computationally demanding tasks using thousands of processors. With the development of more powerful HPC architectures, the need to create efficient and scalable code has grown more important. Electronic structure calculations are valuable in understanding experimental observations and are routinely used for new materials predictions. For the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for these calculations scale as N2, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure code hinder their efficient usage of these platforms. This thesis will present some developments to overcome these bottlenecks in order to study large systems. These developments, which are implemented in the NRLMOL electronic structure code, involve the use of sparse matrix storage formats and the use of linear algebra using sparse and distributed matrices. These developments along with other related development now allow ground state density functional calculations using up to 25,000 basis functions and the excited state calculations using up to 17,000 basis functions while utilizing all cores on a node. An example on a light-harvesting triad molecule is described. Finally, future plans to further improve the scalability will be presented.

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.

Recursive inverse factorization.

PubMed

Rubensson, Emanuel H; Bock, Nicolas; Holmström, Erik; Niklasson, Anders M N

2008-03-14

A recursive algorithm for the inverse factorization S(-1)=ZZ(*) of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.

lme4qtl: linear mixed models with flexible covariance structure for genetic studies of related individuals.

PubMed

Ziyatdinov, Andrey; Vázquez-Santiago, Miquel; Brunel, Helena; Martinez-Perez, Angel; Aschard, Hugues; Soria, Jose Manuel

2018-02-27

Quantitative trait locus (QTL) mapping in genetic data often involves analysis of correlated observations, which need to be accounted for to avoid false association signals. This is commonly performed by modeling such correlations as random effects in linear mixed models (LMMs). The R package lme4 is a well-established tool that implements major LMM features using sparse matrix methods; however, it is not fully adapted for QTL mapping association and linkage studies. In particular, two LMM features are lacking in the base version of lme4: the definition of random effects by custom covariance matrices; and parameter constraints, which are essential in advanced QTL models. Apart from applications in linkage studies of related individuals, such functionalities are of high interest for association studies in situations where multiple covariance matrices need to be modeled, a scenario not covered by many genome-wide association study (GWAS) software. To address the aforementioned limitations, we developed a new R package lme4qtl as an extension of lme4. First, lme4qtl contributes new models for genetic studies within a single tool integrated with lme4 and its companion packages. Second, lme4qtl offers a flexible framework for scenarios with multiple levels of relatedness and becomes efficient when covariance matrices are sparse. We showed the value of our package using real family-based data in the Genetic Analysis of Idiopathic Thrombophilia 2 (GAIT2) project. Our software lme4qtl enables QTL mapping models with a versatile structure of random effects and efficient computation for sparse covariances. lme4qtl is available at https://github.com/variani/lme4qtl .

Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.

PubMed

Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli

2016-05-01

Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.

A new scheduling algorithm for parallel sparse LU factorization with static pivoting

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

Grigori, Laura; Li, Xiaoye S.

2002-08-20

In this paper we present a static scheduling algorithm for parallel sparse LU factorization with static pivoting. The algorithm is divided into mapping and scheduling phases, using the symmetric pruned graphs of L' and U to represent dependencies. The scheduling algorithm is designed for driving the parallel execution of the factorization on a distributed-memory architecture. Experimental results and comparisons with SuperLU{_}DIST are reported after applying this algorithm on real world application matrices on an IBM SP RS/6000 distributed memory machine.

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.

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.

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

NASA Technical Reports Server (NTRS)

Freund, Roland W.; Nachtigal, Noel M.

1990-01-01

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

Iterative-method performance evaluation for multiple vectors associated with a large-scale sparse matrix

NASA Astrophysics Data System (ADS)

Imamura, Seigo; Ono, Kenji; Yokokawa, Mitsuo

2016-07-01

Ensemble computing, which is an instance of capacity computing, is an effective computing scenario for exascale parallel supercomputers. In ensemble computing, there are multiple linear systems associated with a common coefficient matrix. We improve the performance of iterative solvers for multiple vectors by solving them at the same time, that is, by solving for the product of the matrices. We implemented several iterative methods and compared their performance. The maximum performance on Sparc VIIIfx was 7.6 times higher than that of a naïve implementation. Finally, to deal with the different convergence processes of linear systems, we introduced a control method to eliminate the calculation of already converged vectors.

Fast RBF OGr for solving PDEs on arbitrary surfaces

NASA Astrophysics Data System (ADS)

Piret, Cécile; Dunn, Jarrett

2016-10-01

The Radial Basis Functions Orthogonal Gradients method (RBF-OGr) was introduced in [1] to discretize differential operators defined on arbitrary manifolds defined only by a point cloud. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent complex geometries in any spatial dimension. A large limitation of the RBF-OGr method was its large computational complexity, which greatly restricted the size of the point cloud. In this paper, we apply the RBF-Finite Difference (RBF-FD) technique to the RBF-OGr method for building sparse differentiation matrices discretizing continuous differential operators such as the Laplace-Beltrami operator. This method can be applied to solving PDEs on arbitrary surfaces embedded in ℛ3. We illustrate the accuracy of our new method by solving the heat equation on the unit sphere.

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan

1989-01-01

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

Comparison of Penalty Functions for Sparse Canonical Correlation Analysis

PubMed Central

Chalise, Prabhakar; Fridley, Brooke L.

2011-01-01

Canonical correlation analysis (CCA) is a widely used multivariate method for assessing the association between two sets of variables. However, when the number of variables far exceeds the number of subjects, such in the case of large-scale genomic studies, the traditional CCA method is not appropriate. In addition, when the variables are highly correlated the sample covariance matrices become unstable or undefined. To overcome these two issues, sparse canonical correlation analysis (SCCA) for multiple data sets has been proposed using a Lasso type of penalty. However, these methods do not have direct control over sparsity of solution. An additional step that uses Bayesian Information Criterion (BIC) has also been suggested to further filter out unimportant features. In this paper, a comparison of four penalty functions (Lasso, Elastic-net, SCAD and Hard-threshold) for SCCA with and without the BIC filtering step have been carried out using both real and simulated genotypic and mRNA expression data. This study indicates that the SCAD penalty with BIC filter would be a preferable penalty function for application of SCCA to genomic data. PMID:21984855

Wavelets in electronic structure calculations

NASA Astrophysics Data System (ADS)

Modisette, Jason Perry

1997-09-01

Ab initio calculations of the electronic structure of bulk materials and large clusters are not possible on today's computers using current techniques. The storage and diagonalization of the Hamiltonian matrix are the limiting factors in both memory and execution time. The scaling of both quantities with problem size can be reduced by using approximate diagonalization or direct minimization of the total energy with respect to the density matrix in conjunction with a localized basis. Wavelet basis members are much more localized than conventional bases such as Gaussians or numerical atomic orbitals. This localization leads to sparse matrices of the operators that arise in SCF multi-electron calculations. We have investigated the construction of the one-electron Hamiltonian, and also the effective one- electron Hamiltonians that appear in density-functional and Hartree-Fock theories. We develop efficient methods for the generation of the kinetic energy and potential matrices, the Hartree and exchange potentials, and the local exchange-correlation potential of the LDA. Test calculations are performed on one-electron problems with a variety of potentials in one and three dimensions.

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.

Filling gaps in large ecological databases: consequences for the study of global-scale plant functional trait patterns

NASA Astrophysics Data System (ADS)

Schrodt, Franziska; Shan, Hanhuai; Fazayeli, Farideh; Karpatne, Anuj; Kattge, Jens; Banerjee, Arindam; Reichstein, Markus; Reich, Peter

2013-04-01

With the advent of remotely sensed data and coordinated efforts to create global databases, the ecological community has progressively become more data-intensive. However, in contrast to other disciplines, statistical ways of handling these large data sets, especially the gaps which are inherent to them, are lacking. Widely used theoretical approaches, for example model averaging based on Akaike's information criterion (AIC), are sensitive to missing values. Yet, the most common way of handling sparse matrices - the deletion of cases with missing data (complete case analysis) - is known to severely reduce statistical power as well as inducing biased parameter estimates. In order to address these issues, we present novel approaches to gap filling in large ecological data sets using matrix factorization techniques. Factorization based matrix completion was developed in a recommender system context and has since been widely used to impute missing data in fields outside the ecological community. Here, we evaluate the effectiveness of probabilistic matrix factorization techniques for imputing missing data in ecological matrices using two imputation techniques. Hierarchical Probabilistic Matrix Factorization (HPMF) effectively incorporates hierarchical phylogenetic information (phylogenetic group, family, genus, species and individual plant) into the trait imputation. Advanced Hierarchical Probabilistic Matrix Factorization (aHPMF) on the other hand includes climate and soil information into the matrix factorization by regressing the environmental variables against residuals of the HPMF. One unique opportunity opened up by aHPMF is out-of-sample prediction, where traits can be predicted for specific species at locations different to those sampled in the past. This has potentially far-reaching consequences for the study of global-scale plant functional trait patterns. We test the accuracy and effectiveness of HPMF and aHPMF in filling sparse matrices, using the TRY database of plant functional traits (http://www.try-db.org). TRY is one of the largest global compilations of plant trait databases (750 traits of 1 million plants), encompassing data on morphological, anatomical, biochemical, phenological and physiological features of plants. However, despite of unprecedented coverage, the TRY database is still very sparse, severely limiting joint trait analyses. Plant traits are the key to understanding how plants as primary producers adjust to changes in environmental conditions and in turn influence them. Forming the basis for Dynamic Global Vegetation Models (DGVMs), plant traits are also fundamental in global change studies for predicting future ecosystem changes. It is thus imperative that missing data is imputed in as accurate and precise a way as possible. In this study, we show the advantages and disadvantages of applying probabilistic matrix factorization techniques in incorporating hierarchical and environmental information for the prediction of missing plant traits as compared to conventional imputation techniques such as the complete case and mean approaches. We will discuss the implications of using gap-filled data for global-scale studies of plant functional trait - environment relationship as opposed to the above-mentioned conventional techniques, using examples of out-of-sample predictions of foliar Nitrogen across several species' ranges and biomes.

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

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« 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

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

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.

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.

Limited plasticity in the phenotypic variance-covariance matrix for male advertisement calls in the black field cricket, Teleogryllus commodus

PubMed Central

Pitchers, W. R.; Brooks, R.; Jennions, M. D.; Tregenza, T.; Dworkin, I.; Hunt, J.

2013-01-01

Phenotypic integration and plasticity are central to our understanding of how complex phenotypic traits evolve. Evolutionary change in complex quantitative traits can be predicted using the multivariate breeders’ equation, but such predictions are only accurate if the matrices involved are stable over evolutionary time. Recent work, however, suggests that these matrices are temporally plastic, spatially variable and themselves evolvable. The data available on phenotypic variance-covariance matrix (P) stability is sparse, and largely focused on morphological traits. Here we compared P for the structure of the complex sexual advertisement call of six divergent allopatric populations of the Australian black field cricket, Teleogryllus commodus. We measured a subset of calls from wild-caught crickets from each of the populations and then a second subset after rearing crickets under common-garden conditions for three generations. In a second experiment, crickets from each population were reared in the laboratory on high- and low-nutrient diets and their calls recorded. In both experiments, we estimated P for call traits and used multiple methods to compare them statistically (Flury hierarchy, geometric subspace comparisons and random skewers). Despite considerable variation in means and variances of individual call traits, the structure of P was largely conserved among populations, across generations and between our rearing diets. Our finding that P remains largely stable, among populations and between environmental conditions, suggests that selection has preserved the structure of call traits in order that they can function as an integrated unit. PMID:23530814

Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties

NASA Astrophysics Data System (ADS)

Karp, Jonathan; Torres-Herrera, Jonathan; TáVora, Marco; Santos, Lea

We study the static and dynamical properties of isolated spin 1/2 systems as prototypes of many-body quantum systems and compare the results to those of full random matrices from a Gaussian orthogonal ensemble. Full random matrices do not represent realistic systems, because they imply that all particles interact at the same time, as opposed to realistic Hamiltonians, which are sparse and have only few-body interactions. Nevertheless, with full random matrices we can derive analytical results that can be used as references and bounds for the corresponding properties of realistic systems. In particular, we show that the results for the Shannon information entropy are very similar to those for the von Neumann entanglement entropy, with the former being computationally less expensive. We also discuss the behavior of the survival probability of the initial state at different time scales and show that it contains more information about the system than the entropies. Support from the NSF Grant No. DMR-1147430.

Efficient quantum circuits for dense circulant and circulant like operators

PubMed Central

Zhou, S. S.

2017-01-01

Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily extended to the implementation of Toeplitz, Hankel and block circulant matrices. Efficient quantum algorithms to implement the inverses and products of circulant operators are also provided, and an example application in solving the equation of motion for cyclic systems is discussed. PMID:28572988

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

NASA Technical Reports Server (NTRS)

Zubair, Mohammad; Nielsen, Eric; Luitjens, Justin; Hammond, Dana

2016-01-01

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

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.

Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1989-01-01

Communication requirements of Cholesky factorization of dense and sparse symmetric, positive definite matrices are analyzed. The communication requirement is characterized by the data traffic generated on multiprocessor systems with local and shared memory. Lower bound proofs are given to show that when the load is uniformly distributed the data traffic associated with factoring an n x n dense matrix using n to the alpha power (alpha less than or equal 2) processors is omega(n to the 2 + alpha/2 power). For n x n sparse matrices representing a square root of n x square root of n regular grid graph the data traffic is shown to be omega(n to the 1 + alpha/2 power), alpha less than or equal 1. Partitioning schemes that are variations of block assignment scheme are described and it is shown that the data traffic generated by these schemes are asymptotically optimal. The schemes allow efficient use of up to O(n to the 2nd power) processors in the dense case and up to O(n) processors in the sparse case before the total data traffic reaches the maximum value of O(n to the 3rd power) and O(n to the 3/2 power), respectively. It is shown that the block based partitioning schemes allow a better utilization of the data accessed from shared memory and thus reduce the data traffic than those based on column-wise wrap around assignment schemes.

Reliability of the Colorado Family Support Assessment: A Self-Sufficiency Matrix for Families

ERIC Educational Resources Information Center

Richmond, Melissa K.; Pampel, Fred C.; Zarcula, Flavia; Howey, Virginia; McChesney, Brenda

2017-01-01

Purpose: Family support programs commonly use self-sufficiency matrices (SSMs) to measure family outcomes, however, validation research on SSMs is sparse. This study examined the reliability of the Colorado Family Support Assessment 2.0 (CFSA 2.0) to measure family self-reliance across 14 domains (e.g., employment). Methods: Ten written case…

A new method for computation of eigenvector derivatives with distinct and repeated eigenvalues in structural dynamic analysis

NASA Astrophysics Data System (ADS)

Li, Zhengguang; Lai, Siu-Kai; Wu, Baisheng

2018-07-01

Determining eigenvector derivatives is a challenging task due to the singularity of the coefficient matrices of the governing equations, especially for those structural dynamic systems with repeated eigenvalues. An effective strategy is proposed to construct a non-singular coefficient matrix, which can be directly used to obtain the eigenvector derivatives with distinct and repeated eigenvalues. This approach also has an advantage that only requires eigenvalues and eigenvectors of interest, without solving the particular solutions of eigenvector derivatives. The Symmetric Quasi-Minimal Residual (SQMR) method is then adopted to solve the governing equations, only the existing factored (shifted) stiffness matrix from an iterative eigensolution such as the subspace iteration method or the Lanczos algorithm is utilized. The present method can deal with both cases of simple and repeated eigenvalues in a unified manner. Three numerical examples are given to illustrate the accuracy and validity of the proposed algorithm. Highly accurate approximations to the eigenvector derivatives are obtained within a few iteration steps, making a significant reduction of the computational effort. This method can be incorporated into a coupled eigensolver/derivative software module. In particular, it is applicable for finite element models with large sparse matrices.

GPU-accelerated Modeling and Element-free Reverse-time Migration with Gauss Points Partition

NASA Astrophysics Data System (ADS)

Zhen, Z.; Jia, X.

2014-12-01

Element-free method (EFM) has been applied to seismic modeling and migration. Compared with finite element method (FEM) and finite difference method (FDM), it is much cheaper and more flexible because only the information of the nodes and the boundary of the study area are required in computation. In the EFM, the number of Gauss points should be consistent with the number of model nodes; otherwise the accuracy of the intermediate coefficient matrices would be harmed. Thus when we increase the nodes of velocity model in order to obtain higher resolution, we find that the size of the computer's memory will be a bottleneck. The original EFM can deal with at most 81×81 nodes in the case of 2G memory, as tested by Jia and Hu (2006). In order to solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP), and utilize the GPUs to improve the computation efficiency. Considering the characteristics of the Gaussian points, the GPP method doesn't influence the propagation of seismic wave in the velocity model. To overcome the time-consuming computation of the stiffness matrix (K) and the mass matrix (M), we also use the GPUs in our computation program. We employ the compressed sparse row (CSR) format to compress the intermediate sparse matrices and try to simplify the operations by solving the linear equations with the CULA Sparse's Conjugate Gradient (CG) solver instead of the linear sparse solver 'PARDISO'. It is observed that our strategy can significantly reduce the computational time of K and Mcompared with the algorithm based on CPU. The model tested is Marmousi model. The length of the model is 7425m and the depth is 2990m. We discretize the model with 595x298 nodes, 300x300 Gauss cells and 3x3 Gauss points in each cell. In contrast to the computational time of the conventional EFM, the GPUs-GPP approach can substantially improve the efficiency. The speedup ratio of time consumption of computing K, M is 120 and the speedup ratio time consumption of RTM is 11.5. At the same time, the accuracy of imaging is not harmed. Another advantage of the GPUs-GPP method is its easy applications in other numerical methods such as the FEM. Finally, in the GPUs-GPP method, the arrays require quite limited memory storage, which makes the method promising in dealing with large-scale 3D problems.

Sparse matrix-vector multiplication on network-on-chip

NASA Astrophysics Data System (ADS)

Sun, C.-C.; Götze, J.; Jheng, H.-Y.; Ruan, S.-J.

2010-12-01

In this paper, we present an idea for performing matrix-vector multiplication by using Network-on-Chip (NoC) architecture. In traditional IC design on-chip communications have been designed with dedicated point-to-point interconnections. Therefore, regular local data transfer is the major concept of many parallel implementations. However, when dealing with the parallel implementation of sparse matrix-vector multiplication (SMVM), which is the main step of all iterative algorithms for solving systems of linear equation, the required data transfers depend on the sparsity structure of the matrix and can be extremely irregular. Using the NoC architecture makes it possible to deal with arbitrary structure of the data transfers; i.e. with the irregular structure of the sparse matrices. So far, we have already implemented the proposed SMVM-NoC architecture with the size 4×4 and 5×5 in IEEE 754 single float point precision using FPGA.

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

Feasibility of Very Large Sparse Aperture Deployable Antennas

DTIC Science & Technology

2014-03-27

FEASIBILITY OF VERY LARGE SPARSE APERTURE DEPLOYABLE ANTENNAS THESIS Jason C. Heller, Captain...States. AFIT-ENY-14-M-24 FEASIBILITY OF VERY LARGE SPARSE APERTURE DEPLOYABLE ANTENNAS THESIS Presented to the Faculty...UNLIMITED AFIT-ENY-14-M-24 FEASIBILITY OF VERY LARGE SPARSE APERTURE DEPLOYABLE ANTENNAS Jason C. Heller, B.S., Aerospace

FINAL REPORT (MILESTONE DATE 9/30/11) FOR SUBCONTRACT NO. B594099 NUMERICAL METHODS FOR LARGE-SCALE DATA FACTORIZATION

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

De Sterck, H

2011-10-18

The following work has been performed by PI Hans De Sterck and graduate student Manda Winlaw for the required tasks 1-5 (as listed in the Statement of Work). Graduate student Manda Winlaw has visited LLNL January 31-March 11, 2011 and May 23-August 19, 2010, working with Van Henson and Mike O'Hara on non-negative matrix factorizations (NMF). She has investigated the dense subgraph clustering algorithm from 'Finding Dense Subgraphs for Sparse Undirected, Directed, and Bipartite Graphs' by Chen and Saad, testing this method on several term-document matrices and adapting it to cluster based on the rank of the subgraphs instead ofmore » the density. Manda Winlaw was awarded a first prize in the annual LLNL summer student poster competition for a poster on her NMF research. PI Hans De Sterck has developed a new adaptive algebraic multigrid algorithm for computing a few dominant or minimal singular triplets of sparse rectangular matrices. This work builds on adaptive algebraic multigrid methods that were further developed by the PI and collaborators (including Sanders and Henson) for Markov chains. The method also combines and extends existing multigrid algorithms for the symmetric eigenproblem. The PI has visited LLNL February 22-25, 2011, and has given a CASC seminar 'Algebraic Multigrid for the Singular Value Problem' on this work on February 23, 2011. During his visit, he has discussed this work and related topics with Van Henson, Geoffrey Sanders, Panayot Vassilevski, and others. He has tested the algorithm on PDE matrices and on a term-document matrix, with promising initial results. Manda Winlaw has also started to work, with O'Hara, on estimating probability distributions over undirected graph edges. The goal is to estimate probabilistic models from sets of undirected graph edges for the purpose of prediction, anomaly detection and support to supervised learning. Graduate student Manda Winlaw is writing a paper on the results obtained with O'Hara which will be submitted some time later in 2011 to a data mining conference. PI Hans De Sterck has developed a new optimization algorithm for canonical tensor approximation, formulating an extension of the nonlinear GMRES method to optimization problems. Numerical results for tensors with up to 8 modes show that this new method is efficient for sparse and dense tensors. He has written a paper on this which has been submitted to the SIAM Journal on Scientific Computing. PI Hans De Sterck has further developed his new optimization algorithm for canonical tensor approximation, formulating an extension in terms of steepest-descent preconditioning, which makes the approach generally applicable for nonlinear optimization. He has written a paper on this extension which has been submitted to Numerical Linear Algebra with Applications.« less

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data*

PubMed Central

Cai, T. Tony; Zhang, Anru

2016-01-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data. PMID:27777471

Minimax Rate-optimal Estimation of High-dimensional Covariance Matrices with Incomplete Data.

PubMed

Cai, T Tony; Zhang, Anru

2016-09-01

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the sense that the missingness is not dependent on the values of the data. Based on incomplete data, estimators for bandable and sparse covariance matrices are proposed and their theoretical and numerical properties are investigated. Minimax rates of convergence are established under the spectral norm loss and the proposed estimators are shown to be rate-optimal under mild regularity conditions. Simulation studies demonstrate that the estimators perform well numerically. The methods are also illustrated through an application to data from four ovarian cancer studies. The key technical tools developed in this paper are of independent interest and potentially useful for a range of related problems in high-dimensional statistical inference with missing data.

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%.

IQ Gains in Argentina between 1964 and 1998

ERIC Educational Resources Information Center

Flynn, James R.; Rossi-Case, Lilia

2012-01-01

The literature on IQ gains in Latin America is sparse. We estimate gains on Raven's Progressive Matrices in the city of La Plata (Argentina) between 1964 and 1998. The gains are robust at the top of the curve as well as at the bottom. Therefore, they are contrary to the hypothesis that nutrition played a major role in recent Argentine IQ gains.…

Efficient and Robust Signal Approximations

DTIC Science & Technology

2009-05-01

otherwise. Remark. Permutation matrices are both orthogonal and doubly- stochastic [62]. We will now show how to further simplify the Robust Coding...reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching...Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 Keywords: signal processing, image compression, independent component analysis , sparse

Closed-loop multiple-scattering imaging with sparse seismic measurements

NASA Astrophysics Data System (ADS)

Berkhout, A. J. Guus

2018-03-01

In the theoretical situation of noise-free, complete data volumes (`perfect data'), seismic data matrices are fully filled and multiple-scattering operators have the minimum-phase property. Perfect data allow direct inversion methods to be successful in removing surface and internal multiple scattering. Moreover, under these perfect data conditions direct source wavefields realize complete illumination (no irrecoverable shadow zones) and, therefore, primary reflections (first-order response) can provide us with the complete seismic image. However, in practice seismic measurements always contain noise and we never have complete data volumes at our disposal. We actually deal with sparse data matrices that cannot be directly inverted. The message of this paper is that in practice multiple scattering (including source ghosting) must not be removed but must be utilized. It is explained that in the real world we badly need multiple scattering to fill the illumination gaps in the subsurface. It is also explained that the proposed multiple-scattering imaging algorithm gives us the opportunity to decompose both the image and the wavefields into order-based constituents, making the multiple scattering extension easy to apply. Last but not least, the algorithm allows us to use the minimum-phase property to validate and improve images in an objective way.

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

Discrete Kalman filtering equations of second-order form for control-structure interaction simulations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alvin, K. F.; Belvin, W. Keith

1991-01-01

A second-order form of discrete Kalman filtering equations is proposed as a candidate state estimator for efficient simulations of control-structure interactions in coupled physical coordinate configurations as opposed to decoupled modal coordinates. The resulting matrix equation of the present state estimator consists of the same symmetric, sparse N x N coupled matrices of the governing structural dynamics equations as opposed to unsymmetric 2N x 2N state space-based estimators. Thus, in addition to substantial computational efficiency improvement, the present estimator can be applied to control-structure design optimization for which the physical coordinates associated with the mass, damping and stiffness matrices of the structure are needed instead of modal coordinates.

A new look at the simultaneous analysis and design of structures

NASA Technical Reports Server (NTRS)

Striz, Alfred G.

1994-01-01

The minimum weight optimization of structural systems, subject to strength and displacement constraints as well as size side constraints, was investigated by the Simultaneous ANalysis and Design (SAND) approach. As an optimizer, the code NPSOL was used which is based on a sequential quadratic programming (SQP) algorithm. The structures were modeled by the finite element method. The finite element related input to NPSOL was automatically generated from the input decks of such standard FEM/optimization codes as NASTRAN or ASTROS, with the stiffness matrices, at present, extracted from the FEM code ANALYZE. In order to avoid ill-conditioned matrices that can be encountered when the global stiffness equations are used as additional nonlinear equality constraints in the SAND approach (with the displacements as additional variables), the matrix displacement method was applied. In this approach, the element stiffness equations are used as constraints instead of the global stiffness equations, in conjunction with the nodal force equilibrium equations. This approach adds the element forces as variables to the system. Since, for complex structures and the associated large and very sparce matrices, the execution times of the optimization code became excessive due to the large number of required constraint gradient evaluations, the Kreisselmeier-Steinhauser function approach was used to decrease the computational effort by reducing the nonlinear equality constraint system to essentially a single combined constraint equation. As the linear equality and inequality constraints require much less computational effort to evaluate, they were kept in their previous form to limit the complexity of the KS function evaluation. To date, the standard three-bar, ten-bar, and 72-bar trusses have been tested. For the standard SAND approach, correct results were obtained for all three trusses although convergence became slower for the 72-bar truss. When the matrix displacement method was used, correct results were still obtained, but the execution times became excessive due to the large number of constraint gradient evaluations required. Using the KS function, the computational effort dropped, but the optimization seemed to become less robust. The investigation of this phenomenon is continuing. As an alternate approach, the code MINOS for the optimization of sparse matrices can be applied to the problem in lieu of the Kreisselmeier-Steinhauser function. This investigation is underway.

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

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.

Selecting informative subsets of sparse supermatrices increases the chance to find correct trees.

PubMed

Misof, Bernhard; Meyer, Benjamin; von Reumont, Björn Marcus; Kück, Patrick; Misof, Katharina; Meusemann, Karen

2013-12-03

Character matrices with extensive missing data are frequently used in phylogenomics with potentially detrimental effects on the accuracy and robustness of tree inference. Therefore, many investigators select taxa and genes with high data coverage. Drawbacks of these selections are their exclusive reliance on data coverage without consideration of actual signal in the data which might, thus, not deliver optimal data matrices in terms of potential phylogenetic signal. In order to circumvent this problem, we have developed a heuristics implemented in a software called mare which (1) assesses information content of genes in supermatrices using a measure of potential signal combined with data coverage and (2) reduces supermatrices with a simple hill climbing procedure to submatrices with high total information content. We conducted simulation studies using matrices of 50 taxa × 50 genes with heterogeneous phylogenetic signal among genes and data coverage between 10-30%. With matrices of 50 taxa × 50 genes with heterogeneous phylogenetic signal among genes and data coverage between 10-30% Maximum Likelihood (ML) tree reconstructions failed to recover correct trees. A selection of a data subset with the herein proposed approach increased the chance to recover correct partial trees more than 10-fold. The selection of data subsets with the herein proposed simple hill climbing procedure performed well either considering the information content or just a simple presence/absence information of genes. We also applied our approach on an empirical data set, addressing questions of vertebrate systematics. With this empirical dataset selecting a data subset with high information content and supporting a tree with high average boostrap support was most successful if information content of genes was considered. Our analyses of simulated and empirical data demonstrate that sparse supermatrices can be reduced on a formal basis outperforming the usually used simple selections of taxa and genes with high data coverage.

Fast global image smoothing based on weighted least squares.

PubMed

Min, Dongbo; Choi, Sunghwan; Lu, Jiangbo; Ham, Bumsub; Sohn, Kwanghoon; Do, Minh N

2014-12-01

This paper presents an efficient technique for performing a spatially inhomogeneous edge-preserving image smoothing, called fast global smoother. Focusing on sparse Laplacian matrices consisting of a data term and a prior term (typically defined using four or eight neighbors for 2D image), our approach efficiently solves such global objective functions. In particular, we approximate the solution of the memory-and computation-intensive large linear system, defined over a d-dimensional spatial domain, by solving a sequence of 1D subsystems. Our separable implementation enables applying a linear-time tridiagonal matrix algorithm to solve d three-point Laplacian matrices iteratively. Our approach combines the best of two paradigms, i.e., efficient edge-preserving filters and optimization-based smoothing. Our method has a comparable runtime to the fast edge-preserving filters, but its global optimization formulation overcomes many limitations of the local filtering approaches. Our method also achieves high-quality results as the state-of-the-art optimization-based techniques, but runs ∼10-30 times faster. Besides, considering the flexibility in defining an objective function, we further propose generalized fast algorithms that perform Lγ norm smoothing (0 < γ < 2) and support an aggregated (robust) data term for handling imprecise data constraints. We demonstrate the effectiveness and efficiency of our techniques in a range of image processing and computer graphics applications.

Data traffic reduction schemes for sparse Cholesky factorizations

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1988-01-01

Load distribution schemes are presented which minimize the total data traffic in the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems with local and shared memory. The total data traffic in factoring an n x n sparse, symmetric, positive definite matrix representing an n-vertex regular 2-D grid graph using n (sup alpha), alpha is equal to or less than 1, processors are shown to be O(n(sup 1 + alpha/2)). It is O(n(sup 3/2)), when n (sup alpha), alpha is equal to or greater than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal. The schemes allow efficient use of up to O(n) processors before the total data traffic reaches the maximum value of O(n(sup 3/2)). The partitioning employed within the scheme, allows a better utilization of the data accessed from shared memory than those of previously published methods.

Method and apparatus for optimized processing of sparse matrices

DOEpatents

Taylor, Valerie E.

1993-01-01

A computer architecture for processing a sparse matrix is disclosed. The apparatus stores a value-row vector corresponding to nonzero values of a sparse matrix. Each of the nonzero values is located at a defined row and column position in the matrix. The value-row vector includes a first vector including nonzero values and delimiting characters indicating a transition from one column to another. The value-row vector also includes a second vector which defines row position values in the matrix corresponding to the nonzero values in the first vector and column position values in the matrix corresponding to the column position of the nonzero values in the first vector. The architecture also includes a circuit for detecting a special character within the value-row vector. Matrix-vector multiplication is executed on the value-row vector. This multiplication is performed by multiplying an index value of the first vector value by a column value from a second matrix to form a matrix-vector product which is added to a previous matrix-vector product.

Optimal Couple Projections for Domain Adaptive Sparse Representation-based Classification.

PubMed

Zhang, Guoqing; Sun, Huaijiang; Porikli, Fatih; Liu, Yazhou; Sun, Quansen

2017-08-29

In recent years, sparse representation based classification (SRC) is one of the most successful methods and has been shown impressive performance in various classification tasks. However, when the training data has a different distribution than the testing data, the learned sparse representation may not be optimal, and the performance of SRC will be degraded significantly. To address this problem, in this paper, we propose an optimal couple projections for domain-adaptive sparse representation-based classification (OCPD-SRC) method, in which the discriminative features of data in the two domains are simultaneously learned with the dictionary that can succinctly represent the training and testing data in the projected space. OCPD-SRC is designed based on the decision rule of SRC, with the objective to learn coupled projection matrices and a common discriminative dictionary such that the between-class sparse reconstruction residuals of data from both domains are maximized, and the within-class sparse reconstruction residuals of data are minimized in the projected low-dimensional space. Thus, the resulting representations can well fit SRC and simultaneously have a better discriminant ability. In addition, our method can be easily extended to multiple domains and can be kernelized to deal with the nonlinear structure of data. The optimal solution for the proposed method can be efficiently obtained following the alternative optimization method. Extensive experimental results on a series of benchmark databases show that our method is better or comparable to many state-of-the-art methods.

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.

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

From the Rendering Equation to Stratified Light Transport Inversion

DTIC Science & Technology

2010-12-09

iteratively. These approaches relate closely to the radiosity method for diffuse global illumination in forward rendering (Hanrahan et al, 1991; Gortler et...currently simply use sparse matrices to represent T, we are also interested in exploring connections with hierar- chical and wavelet radiosity as in...Seidel iterative methods used in radiosity . 2.4 Inverse Light Transport Previous work on inverse rendering has considered inversion of the direct

Nonlinear Estimation With Sparse Temporal Measurements

DTIC Science & Technology

2016-09-01

Kalman filter , the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are commonly used in practical application. The Kalman filter is an...optimal estimator for linear systems; the EKF and UKF are sub-optimal approximations of the Kalman filter . The EKF uses a first-order Taylor series...propagated covariance is compared for similarity with a Monte Carlo propagation. The similarity of the covariance matrices is shown to predict filter

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

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.

Non-Hermitian localization in biological networks.

PubMed

Amir, Ariel; Hatano, Naomichi; Nelson, David R

2016-04-01

We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90^{∘} rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

Non-Hermitian localization in biological networks

NASA Astrophysics Data System (ADS)

Amir, Ariel; Hatano, Naomichi; Nelson, David R.

2016-04-01

We explore the spectra and localization properties of the N -site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large N , the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to 90∘ rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-N limit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the "charges" embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey "Dale's law" (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.

Joint association discovery and diagnosis of Alzheimer's disease by supervised heterogeneous multiview learning.

PubMed

Zhe, Shandian; Xu, Zenglin; Qi, Yuan; Yu, Peng

2014-01-01

A key step for Alzheimer's disease (AD) study is to identify associations between genetic variations and intermediate phenotypes (e.g., brain structures). At the same time, it is crucial to develop a noninvasive means for AD diagnosis. Although these two tasks-association discovery and disease diagnosis-have been treated separately by a variety of approaches, they are tightly coupled due to their common biological basis. We hypothesize that the two tasks can potentially benefit each other by a joint analysis, because (i) the association study discovers correlated biomarkers from different data sources, which may help improve diagnosis accuracy, and (ii) the disease status may help identify disease-sensitive associations between genetic variations and MRI features. Based on this hypothesis, we present a new sparse Bayesian approach for joint association study and disease diagnosis. In this approach, common latent features are extracted from different data sources based on sparse projection matrices and used to predict multiple disease severity levels based on Gaussian process ordinal regression; in return, the disease status is used to guide the discovery of relationships between the data sources. The sparse projection matrices not only reveal the associations but also select groups of biomarkers related to AD. To learn the model from data, we develop an efficient variational expectation maximization algorithm. Simulation results demonstrate that our approach achieves higher accuracy in both predicting ordinal labels and discovering associations between data sources than alternative methods. We apply our approach to an imaging genetics dataset of AD. Our joint analysis approach not only identifies meaningful and interesting associations between genetic variations, brain structures, and AD status, but also achieves significantly higher accuracy for predicting ordinal AD stages than the competing methods.

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.

Exponential convergence through linear finite element discretization of stratified subdomains

NASA Astrophysics Data System (ADS)

Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali

2016-10-01

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.

High-resolution wavefront reconstruction using the frozen flow hypothesis

NASA Astrophysics Data System (ADS)

Liu, Xuewen; Liang, Yonghui; Liu, Jin; Xu, Jieping

2017-10-01

This paper describes an approach to reconstructing wavefronts on finer grid using the frozen flow hypothesis (FFH), which exploits spatial and temporal correlations between consecutive wavefront sensor (WFS) frames. Under the assumption of FFH, slope data from WFS can be connected to a finer, composite slope grid using translation and down sampling, and elements in transformation matrices are determined by wind information. Frames of slopes are then combined and slopes on finer grid are reconstructed by solving a sparse, large-scale, ill-posed least squares problem. By using reconstructed finer slope data and adopting Fried geometry of WFS, high-resolution wavefronts are then reconstructed. The results show that this method is robust even with detector noise and wind information inaccuracy, and under bad seeing conditions, high-frequency information in wavefronts can be recovered more accurately compared with when correlations in WFS frames are ignored.

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.

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.

A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding.

PubMed

Scemama, Anthony; Renon, Nicolas; Rapacioli, Mathias

2014-06-10

We present an algorithm and its parallel implementation for solving a self-consistent problem as encountered in Hartree-Fock or density functional theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows one to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density-functional-based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines, (ii) calculations involving intermediate size systems (1000-100 000 atoms) are also strongly accelerated and can run efficiently on standard servers, and (iii) the error on the total energy due to the use of a cutoff in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.

Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency.

PubMed

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-05-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

Assessing Effects of Prenatal Alcohol Exposure Using Group-wise Sparse Representation of FMRI Data

PubMed Central

Lv, Jinglei; Jiang, Xi; Li, Xiang; Zhu, Dajiang; Zhao, Shijie; Zhang, Tuo; Hu, Xintao; Han, Junwei; Guo, Lei; Li, Zhihao; Coles, Claire; Hu, Xiaoping; Liu, Tianming

2015-01-01

Task-based fMRI activation mapping has been widely used in clinical neuroscience in order to assess different functional activity patterns in conditions such as prenatal alcohol exposure (PAE) affected brains and healthy controls. In this paper, we propose a novel, alternative approach of group-wise sparse representation of the fMRI data of multiple groups of subjects (healthy control, exposed non-dysmorphic PAE and exposed dysmorphic PAE) and assess the systematic functional activity differences among these three populations. Specifically, a common time series signal dictionary is learned from the aggregated fMRI signals of all three groups of subjects, and then the weight coefficient matrices (named statistical coefficient map (SCM)) associated with each common dictionary were statistically assessed for each group separately. Through inter-group comparisons based on the correspondence established by the common dictionary, our experimental results have demonstrated that the group-wise sparse coding strategy and the SCM can effectively reveal a collection of brain networks/regions that were affected by different levels of severity of PAE. PMID:26195294

A unified statistical approach to non-negative matrix factorization and probabilistic latent semantic indexing

PubMed Central

Wang, Guoli; Ebrahimi, Nader

2014-01-01

Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into the product of two nonnegative matrices, W and H, such that V ∼ W H. It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a variety of areas such as natural language processing, neuroscience, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. There has also been simultaneous development of a related statistical latent class modeling approach, namely, probabilistic latent semantic indexing (PLSI), for analyzing and interpreting co-occurrence count data arising in natural language processing. In this paper, we present a generalized statistical approach to NMF and PLSI based on Renyi's divergence between two non-negative matrices, stemming from the Poisson likelihood. Our approach unifies various competing models and provides a unique theoretical framework for these methods. We propose a unified algorithm for NMF and provide a rigorous proof of monotonicity of multiplicative updates for W and H. In addition, we generalize the relationship between NMF and PLSI within this framework. We demonstrate the applicability and utility of our approach as well as its superior performance relative to existing methods using real-life and simulated document clustering data. PMID:25821345

A unified statistical approach to non-negative matrix factorization and probabilistic latent semantic indexing.

PubMed

Devarajan, Karthik; Wang, Guoli; Ebrahimi, Nader

2015-04-01

Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into the product of two nonnegative matrices, W and H , such that V ∼ W H . It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a variety of areas such as natural language processing, neuroscience, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. There has also been simultaneous development of a related statistical latent class modeling approach, namely, probabilistic latent semantic indexing (PLSI), for analyzing and interpreting co-occurrence count data arising in natural language processing. In this paper, we present a generalized statistical approach to NMF and PLSI based on Renyi's divergence between two non-negative matrices, stemming from the Poisson likelihood. Our approach unifies various competing models and provides a unique theoretical framework for these methods. We propose a unified algorithm for NMF and provide a rigorous proof of monotonicity of multiplicative updates for W and H . In addition, we generalize the relationship between NMF and PLSI within this framework. We demonstrate the applicability and utility of our approach as well as its superior performance relative to existing methods using real-life and simulated document clustering data.

Self-consistent phonons revisited. I. The role of thermal versus quantum fluctuations on structural transitions in large Lennard-Jones clusters.

PubMed

Georgescu, Ionuţ; Mandelshtam, Vladimir A

2012-10-14

The theory of self-consistent phonons (SCP) was originally developed to address the anharmonic effects in condensed matter systems. The method seeks a harmonic, temperature-dependent Hamiltonian that provides the "best fit" for the physical Hamiltonian, the "best fit" being defined as the one that optimizes the Helmholtz free energy at a fixed temperature. The present developments provide a scalable O(N) unified framework that accounts for anharmonic effects in a many-body system, when it is probed by either thermal (ℏ → 0) or quantum fluctuations (T → 0). In these important limits, the solution of the nonlinear SCP equations can be reached in a manner that requires only the multiplication of 3N × 3N matrices, with no need of diagonalization. For short range potentials, such as Lennard-Jones, the Hessian, and other related matrices are highly sparse, so that the scaling of the matrix multiplications can be reduced from O(N(3)) to ~O(N). We investigate the role of quantum effects by continuously varying the de-Boer quantum delocalization parameter Λ and report the N-Λ (T = 0), and also the classical N-T (Λ = 0) phase diagrams for sizes up to N ~ 10(4). Our results demonstrate that the harmonic approximation becomes inadequate already for such weakly quantum systems as neon clusters, or for classical systems much below the melting temperatures.

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

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.

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.

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.

Research on numerical algorithms for large space structures

NASA Technical Reports Server (NTRS)

Denman, E. D.

1982-01-01

Numerical algorithms for large space structures were investigated with particular emphasis on decoupling method for analysis and design. Numerous aspects of the analysis of large systems ranging from the algebraic theory to lambda matrices to identification algorithms were considered. A general treatment of the algebraic theory of lambda matrices is presented and the theory is applied to second order lambda matrices.

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.

Reprint of "Two-stage sparse coding of region covariance via Log-Euclidean kernels to detect saliency".

PubMed

Zhang, Ying-Ying; Yang, Cai; Zhang, Ping

2017-08-01

In this paper, we present a novel bottom-up saliency detection algorithm from the perspective of covariance matrices on a Riemannian manifold. Each superpixel is described by a region covariance matrix on Riemannian Manifolds. We carry out a two-stage sparse coding scheme via Log-Euclidean kernels to extract salient objects efficiently. In the first stage, given background dictionary on image borders, sparse coding of each region covariance via Log-Euclidean kernels is performed. The reconstruction error on the background dictionary is regarded as the initial saliency of each superpixel. In the second stage, an improvement of the initial result is achieved by calculating reconstruction errors of the superpixels on foreground dictionary, which is extracted from the first stage saliency map. The sparse coding in the second stage is similar to the first stage, but is able to effectively highlight the salient objects uniformly from the background. Finally, three post-processing methods-highlight-inhibition function, context-based saliency weighting, and the graph cut-are adopted to further refine the saliency map. Experiments on four public benchmark datasets show that the proposed algorithm outperforms the state-of-the-art methods in terms of precision, recall and mean absolute error, and demonstrate the robustness and efficiency of the proposed method. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

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.

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.

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

Carpenter, J.A.

This report is a sequel to ORNL/CSD-106 in the ongoing supplements to Professor A.S. Householder's KWIC Index for Numerical Algebra. Beginning with the previous supplement, the subject has been restricted to Numerical Linear Algebra, roughly characterized by the American Mathematical Society's classification sections 15 and 65F but with little coverage of infinite matrices, matrices over fields of characteristics other than zero, operator theory, optimization and those parts of matrix theory primarily combinatorial in nature. Some consideration is given to the uses of graph theory in Numerical Linear Algebra, particularly with respect to algorithms for sparse matrix computations. The period coveredmore » by this report is roughly the calendar year 1982 as measured by the appearance of the articles in the American Mathematical Society's Contents of Mathematical Publications lagging actual appearance dates by up to nearly half a year. The review citations are limited to the Mathematical Reviews (MR).« less

Locality preserving non-negative basis learning with graph embedding.

PubMed

Ghanbari, Yasser; Herrington, John; Gur, Ruben C; Schultz, Robert T; Verma, Ragini

2013-01-01

The high dimensionality of connectivity networks necessitates the development of methods identifying the connectivity building blocks that not only characterize the patterns of brain pathology but also reveal representative population patterns. In this paper, we present a non-negative component analysis framework for learning localized and sparse sub-network patterns of connectivity matrices by decomposing them into two sets of discriminative and reconstructive bases. In order to obtain components that are designed towards extracting population differences, we exploit the geometry of the population by using a graphtheoretical scheme that imposes locality-preserving properties as well as maintaining the underlying distance between distant nodes in the original and the projected space. The effectiveness of the proposed framework is demonstrated by applying it to two clinical studies using connectivity matrices derived from DTI to study a population of subjects with ASD, as well as a developmental study of structural brain connectivity that extracts gender differences.

Finite Element Analysis in Concurrent Processing: Computational Issues

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Watson, Brian; Vanderplaats, Garrett

2004-01-01

The purpose of this research is to investigate the potential application of new methods for solving large-scale static structural problems on concurrent computers. It is well known that traditional single-processor computational speed will be limited by inherent physical limits. The only path to achieve higher computational speeds lies through concurrent processing. Traditional factorization solution methods for sparse matrices are ill suited for concurrent processing because the null entries get filled, leading to high communication and memory requirements. The research reported herein investigates alternatives to factorization that promise a greater potential to achieve high concurrent computing efficiency. Two methods, and their variants, based on direct energy minimization are studied: a) minimization of the strain energy using the displacement method formulation; b) constrained minimization of the complementary strain energy using the force method formulation. Initial results indicated that in the context of the direct energy minimization the displacement formulation experienced convergence and accuracy difficulties while the force formulation showed promising potential.

Elimination sequence optimization for SPAR

NASA Technical Reports Server (NTRS)

Hogan, Harry A.

1986-01-01

SPAR is a large-scale computer program for finite element structural analysis. The program allows user specification of the order in which the joints of a structure are to be eliminated since this order can have significant influence over solution performance, in terms of both storage requirements and computer time. An efficient elimination sequence can improve performance by over 50% for some problems. Obtaining such sequences, however, requires the expertise of an experienced user and can take hours of tedious effort to affect. Thus, an automatic elimination sequence optimizer would enhance productivity by reducing the analysts' problem definition time and by lowering computer costs. Two possible methods for automating the elimination sequence specifications were examined. Several algorithms based on the graph theory representations of sparse matrices were studied with mixed results. Significant improvement in the program performance was achieved, but sequencing by an experienced user still yields substantially better results. The initial results provide encouraging evidence that the potential benefits of such an automatic sequencer would be well worth the effort.

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

Multi-Source Cooperative Data Collection with a Mobile Sink for the Wireless Sensor Network.

PubMed

Han, Changcai; Yang, Jinsheng

2017-10-30

The multi-source cooperation integrating distributed low-density parity-check codes is investigated to jointly collect data from multiple sensor nodes to the mobile sink in the wireless sensor network. The one-round and two-round cooperative data collection schemes are proposed according to the moving trajectories of the sink node. Specifically, two sparse cooperation models are firstly formed based on geographical locations of sensor source nodes, the impairment of inter-node wireless channels and moving trajectories of the mobile sink. Then, distributed low-density parity-check codes are devised to match the directed graphs and cooperation matrices related with the cooperation models. In the proposed schemes, each source node has quite low complexity attributed to the sparse cooperation and the distributed processing. Simulation results reveal that the proposed cooperative data collection schemes obtain significant bit error rate performance and the two-round cooperation exhibits better performance compared with the one-round scheme. The performance can be further improved when more source nodes participate in the sparse cooperation. For the two-round data collection schemes, the performance is evaluated for the wireless sensor networks with different moving trajectories and the variant data sizes.

Multi-Source Cooperative Data Collection with a Mobile Sink for the Wireless Sensor Network

PubMed Central

Han, Changcai; Yang, Jinsheng

2017-01-01

The multi-source cooperation integrating distributed low-density parity-check codes is investigated to jointly collect data from multiple sensor nodes to the mobile sink in the wireless sensor network. The one-round and two-round cooperative data collection schemes are proposed according to the moving trajectories of the sink node. Specifically, two sparse cooperation models are firstly formed based on geographical locations of sensor source nodes, the impairment of inter-node wireless channels and moving trajectories of the mobile sink. Then, distributed low-density parity-check codes are devised to match the directed graphs and cooperation matrices related with the cooperation models. In the proposed schemes, each source node has quite low complexity attributed to the sparse cooperation and the distributed processing. Simulation results reveal that the proposed cooperative data collection schemes obtain significant bit error rate performance and the two-round cooperation exhibits better performance compared with the one-round scheme. The performance can be further improved when more source nodes participate in the sparse cooperation. For the two-round data collection schemes, the performance is evaluated for the wireless sensor networks with different moving trajectories and the variant data sizes. PMID:29084155

Large-scale two-photon imaging revealed super-sparse population codes in the V1 superficial layer of awake monkeys.

PubMed

Tang, Shiming; Zhang, Yimeng; Li, Zhihao; Li, Ming; Liu, Fang; Jiang, Hongfei; Lee, Tai Sing

2018-04-26

One general principle of sensory information processing is that the brain must optimize efficiency by reducing the number of neurons that process the same information. The sparseness of the sensory representations in a population of neurons reflects the efficiency of the neural code. Here, we employ large-scale two-photon calcium imaging to examine the responses of a large population of neurons within the superficial layers of area V1 with single-cell resolution, while simultaneously presenting a large set of natural visual stimuli, to provide the first direct measure of the population sparseness in awake primates. The results show that only 0.5% of neurons respond strongly to any given natural image - indicating a ten-fold increase in the inferred sparseness over previous measurements. These population activities are nevertheless necessary and sufficient to discriminate visual stimuli with high accuracy, suggesting that the neural code in the primary visual cortex is both super-sparse and highly efficient. © 2018, Tang et al.

Development of an EMC3-EIRENE Synthetic Imaging Diagnostic

NASA Astrophysics Data System (ADS)

Meyer, William; Allen, Steve; Samuell, Cameron; Lore, Jeremy

2017-10-01

2D and 3D flow measurements are critical for validating numerical codes such as EMC3-EIRENE. Toroidal symmetry assumptions preclude tomographic reconstruction of 3D flows from single camera views. In addition, the resolution of the grids utilized in numerical code models can easily surpass the resolution of physical camera diagnostic geometries. For these reasons we have developed a Synthetic Imaging Diagnostic capability for forward projection comparisons of EMC3-EIRENE model solutions with the line integrated images from the Doppler Coherence Imaging diagnostic on DIII-D. The forward projection matrix is 2.8 Mpixel by 6.4 Mcells for the non-axisymmetric case we present. For flow comparisons, both simple line integral, and field aligned component matrices must be calculated. The calculation of these matrices is a massive embarrassingly parallel problem and performed with a custom dispatcher that allows processing platforms to join mid-problem as they become available, or drop out if resources are needed for higher priority tasks. The matrices are handled using standard sparse matrix techniques. Prepared by LLNL under Contract DE-AC52-07NA27344. This material is based upon work supported by the U.S. DOE, Office of Science, Office of Fusion Energy Sciences. LLNL-ABS-734800.

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

NASA Astrophysics Data System (ADS)

Vanchurin, Vitaly

2018-05-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

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.

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

NASA Astrophysics Data System (ADS)

Vanchurin, Vitaly

2018-06-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

SAR matrices: automated extraction of information-rich SAR tables from large compound data sets.

PubMed

Wassermann, Anne Mai; Haebel, Peter; Weskamp, Nils; Bajorath, Jürgen

2012-07-23

We introduce the SAR matrix data structure that is designed to elucidate SAR patterns produced by groups of structurally related active compounds, which are extracted from large data sets. SAR matrices are systematically generated and sorted on the basis of SAR information content. Matrix generation is computationally efficient and enables processing of large compound sets. The matrix format is reminiscent of SAR tables, and SAR patterns revealed by different categories of matrices are easily interpretable. The structural organization underlying matrix formation is more flexible than standard R-group decomposition schemes. Hence, the resulting matrices capture SAR information in a comprehensive manner.

Sparse Covariance Matrix Estimation With Eigenvalue Constraints

PubMed Central

LIU, Han; WANG, Lie; ZHAO, Tuo

2014-01-01

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholding and projection algorithm based on the alternating direction method of multipliers. Empirically, we conduct thorough numerical experiments on simulated datasets as well as real data examples to illustrate the usefulness of our method. Supplementary materials for the article are available online. PMID:25620866

MUTILS - a set of efficient modeling tools for multi-core CPUs implemented in MEX

NASA Astrophysics Data System (ADS)

Krotkiewski, Marcin; Dabrowski, Marcin

2013-04-01

The need for computational performance is common in scientific applications, and in particular in numerical simulations, where high resolution models require efficient processing of large amounts of data. Especially in the context of geological problems the need to increase the model resolution to resolve physical and geometrical complexities seems to have no limits. Alas, the performance of new generations of CPUs does not improve any longer by simply increasing clock speeds. Current industrial trends are to increase the number of computational cores. As a result, parallel implementations are required in order to fully utilize the potential of new processors, and to study more complex models. We target simulations on small to medium scale shared memory computers: laptops and desktop PCs with ~8 CPU cores and up to tens of GB of memory to high-end servers with ~50 CPU cores and hundereds of GB of memory. In this setting MATLAB is often the environment of choice for scientists that want to implement their own models with little effort. It is a useful general purpose mathematical software package, but due to its versatility some of its functionality is not as efficient as it could be. In particular, the challanges of modern multi-core architectures are not fully addressed. We have developed MILAMIN 2 - an efficient FEM modeling environment written in native MATLAB. Amongst others, MILAMIN provides functions to define model geometry, generate and convert structured and unstructured meshes (also through interfaces to external mesh generators), compute element and system matrices, apply boundary conditions, solve the system of linear equations, address non-linear and transient problems, and perform post-processing. MILAMIN strives to combine the ease of code development and the computational efficiency. Where possible, the code is optimized and/or parallelized within the MATLAB framework. Native MATLAB is augmented with the MUTILS library - a set of MEX functions that implement the computationally intensive, performance critical parts of the code, which we have identified to be bottlenecks. Here, we discuss the functionality and performance of the MUTILS library. Currently, it includes: 1. time and memory efficient assembly of sparse matrices for FEM simulations 2. parallel sparse matrix - vector product with optimizations speficic to symmetric matrices and multiple degrees of freedom per node 3. parallel point in triangle location and point in tetrahedron location for unstructured, adaptive 2D and 3D meshes (useful for 'marker in cell' type of methods) 4. parallel FEM interpolation for 2D and 3D meshes of elements of different types and orders, and for different number of degrees of freedom per node 5. a stand-alone, MEX implementation of the Conjugate Gradients iterative solver 6. interface to METIS graph partitioning and a fast implementation of RCM reordering

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.

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.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems.

PubMed

Ravishankar, Saiprasad; Nadakuditi, Raj Rao; Fessler, Jeffrey A

2017-12-01

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction.

Efficient Sum of Outer Products Dictionary Learning (SOUP-DIL) and Its Application to Inverse Problems

PubMed Central

Ravishankar, Saiprasad; Nadakuditi, Raj Rao; Fessler, Jeffrey A.

2017-01-01

The sparsity of signals in a transform domain or dictionary has been exploited in applications such as compression, denoising and inverse problems. More recently, data-driven adaptation of synthesis dictionaries has shown promise compared to analytical dictionary models. However, dictionary learning problems are typically non-convex and NP-hard, and the usual alternating minimization approaches for these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. This paper exploits the ideas that drive algorithms such as K-SVD, and investigates in detail efficient methods for aggregate sparsity penalized dictionary learning by first approximating the data with a sum of sparse rank-one matrices (outer products) and then using a block coordinate descent approach to estimate the unknowns. The resulting block coordinate descent algorithms involve efficient closed-form solutions. Furthermore, we consider the problem of dictionary-blind image reconstruction, and propose novel and efficient algorithms for adaptive image reconstruction using block coordinate descent and sum of outer products methodologies. We provide a convergence study of the algorithms for dictionary learning and dictionary-blind image reconstruction. Our numerical experiments show the promising performance and speedups provided by the proposed methods over previous schemes in sparse data representation and compressed sensing-based image reconstruction. PMID:29376111

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.

Canny edge-based deformable image registration

NASA Astrophysics Data System (ADS)

Kearney, Vasant; Huang, Yihui; Mao, Weihua; Yuan, Baohong; Tang, Liping

2017-02-01

This work focuses on developing a 2D Canny edge-based deformable image registration (Canny DIR) algorithm to register in vivo white light images taken at various time points. This method uses a sparse interpolation deformation algorithm to sparsely register regions of the image with strong edge information. A stability criterion is enforced which removes regions of edges that do not deform in a smooth uniform manner. Using a synthetic mouse surface ground truth model, the accuracy of the Canny DIR algorithm was evaluated under axial rotation in the presence of deformation. The accuracy was also tested using fluorescent dye injections, which were then used for gamma analysis to establish a second ground truth. The results indicate that the Canny DIR algorithm performs better than rigid registration, intensity corrected Demons, and distinctive features for all evaluation matrices and ground truth scenarios. In conclusion Canny DIR performs well in the presence of the unique lighting and shading variations associated with white-light-based image registration.

A new approach for solving seismic tomography problems and assessing the uncertainty through the use of graph theory and direct methods

NASA Astrophysics Data System (ADS)

Bogiatzis, P.; Ishii, M.; Davis, T. A.

2016-12-01

Seismic tomography inverse problems are among the largest high-dimensional parameter estimation tasks in Earth science. We show how combinatorics and graph theory can be used to analyze the structure of such problems, and to effectively decompose them into smaller ones that can be solved efficiently by means of the least squares method. In combination with recent high performance direct sparse algorithms, this reduction in dimensionality allows for an efficient computation of the model resolution and covariance matrices using limited resources. Furthermore, we show that a new sparse singular value decomposition method can be used to obtain the complete spectrum of the singular values. This procedure provides the means for more objective regularization and further dimensionality reduction of the problem. We apply this methodology to a moderate size, non-linear seismic tomography problem to image the structure of the crust and the upper mantle beneath Japan using local deep earthquakes recorded by the High Sensitivity Seismograph Network stations.

HPC-NMF: A High-Performance Parallel Algorithm for Nonnegative Matrix Factorization

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

Kannan, Ramakrishnan; Sukumar, Sreenivas R.; Ballard, Grey M.

NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient distributed algorithms to solve the problem for big data sets. We propose a high-performance distributed-memory parallel algorithm that computes the factorization by iteratively solving alternating non-negative least squares (NLS) subproblems formore » $$\\WW$$ and $$\\HH$$. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). As opposed to previous implementation, our algorithm is also flexible: It performs well for both dense and sparse matrices, and allows the user to choose any one of the multiple algorithms for solving the updates to low rank factors $$\\WW$$ and $$\\HH$$ within the alternating iterations.« less

A Partitioning Algorithm for Block-Diagonal Matrices With Overlap

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

Guy Antoine Atenekeng Kahou; Laura Grigori; Masha Sosonkina

2008-02-02

We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition {Omega}{sub i} has at most two neighbors {Omega}{sub i-1} and {Omega}{sub i+1}. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile ismore » performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transferred between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach.« less

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

PubMed Central

2017-01-01

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions. PMID:29267329

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

NASA Technical Reports Server (NTRS)

Beam, Richard M.; Warming, Robert F.

1991-01-01

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Domain decomposition methods for the parallel computation of reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.

1988-01-01

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Spectral Calculation of ICRF Wave Propagation and Heating in 2-D Using Massively Parallel Computers

NASA Astrophysics Data System (ADS)

Jaeger, E. F.; D'Azevedo, E.; Berry, L. A.; Carter, M. D.; Batchelor, D. B.

2000-10-01

Spectral calculations of ICRF wave propagation in plasmas have the natural advantage that they require no assumption regarding the smallness of the ion Larmor radius ρ relative to wavelength λ. Results are therefore applicable to all orders in k_bot ρ where k_bot = 2π/λ. But because all modes in the spectral representation are coupled, the solution requires inversion of a large dense matrix. In contrast, finite difference algorithms involve only matrices that are sparse and banded. Thus, spectral calculations of wave propagation and heating in tokamak plasmas have so far been limited to 1-D. In this paper, we extend the spectral method to 2-D by taking advantage of new matrix inversion techniques that utilize massively parallel computers. By spreading the dense matrix over 576 processors on the ORNL IBM RS/6000 SP supercomputer, we are able to solve up to 120,000 coupled complex equations requiring 230 GBytes of memory and achieving over 500 Gflops/sec. Initial results for ASDEX and NSTX will be presented using up to 200 modes in both the radial and vertical dimensions.

High-Dimensional Bayesian Geostatistics

PubMed Central

Banerjee, Sudipto

2017-01-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as “priors” for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings. PMID:29391920

High-Dimensional Bayesian Geostatistics.

PubMed

Banerjee, Sudipto

2017-06-01

With the growing capabilities of Geographic Information Systems (GIS) and user-friendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatiotemporal process models have become widely deployed statistical tools for researchers to better understand the complex nature of spatial and temporal variability. However, fitting hierarchical spatiotemporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. This article offers a focused review of two methods for constructing well-defined highly scalable spatiotemporal stochastic processes. Both these processes can be used as "priors" for spatiotemporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that ensures sparse precision matrices for its finite realizations. Both processes can be exploited as a scalable prior embedded within a rich hierarchical modeling framework to deliver full Bayesian inference. These approaches can be described as model-based solutions for big spatiotemporal datasets. The models ensure that the algorithmic complexity has ~ n floating point operations (flops), where n the number of spatial locations (per iteration). We compare these methods and provide some insight into their methodological underpinnings.

Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering.

PubMed

Chang, Jinyuan; Zhou, Wen; Zhou, Wen-Xin; Wang, Lan

2017-03-01

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence, the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and are available on CRAN. © 2016, The International Biometric Society.

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

NASA Astrophysics Data System (ADS)

Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng

2017-01-01

Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.

An efficient parallel-processing method for transposing large matrices in place.

PubMed

Portnoff, M R

1999-01-01

We have developed an efficient algorithm for transposing large matrices in place. The algorithm is efficient because data are accessed either sequentially in blocks or randomly within blocks small enough to fit in cache, and because the same indexing calculations are shared among identical procedures operating on independent subsets of the data. This inherent parallelism makes the method well suited for a multiprocessor computing environment. The algorithm is easy to implement because the same two procedures are applied to the data in various groupings to carry out the complete transpose operation. Using only a single processor, we have demonstrated nearly an order of magnitude increase in speed over the previously published algorithm by Gate and Twigg for transposing a large rectangular matrix in place. With multiple processors operating in parallel, the processing speed increases almost linearly with the number of processors. A simplified version of the algorithm for square matrices is presented as well as an extension for matrices large enough to require virtual memory.

Structure-preserving and rank-revealing QR-factorizations

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

Bischof, C.H.; Hansen, P.C.

1991-11-01

The rank-revealing QR-factorization (RRQR-factorization) is a special QR-factorization that is guaranteed to reveal the numerical rank of the matrix under consideration. This makes the RRQR-factorization a useful tool in the numerical treatment of many rank-deficient problems in numerical linear algebra. In this paper, a framework is presented for the efficient implementation of RRQR algorithms, in particular, for sparse matrices. A sparse RRQR-algorithm should seek to preserve the structure and sparsity of the matrix as much as possible while retaining the ability to capture safely the numerical rank. To this end, the paper proposes to compute an initial QR-factorization using amore » restricted pivoting strategy guarded by incremental condition estimation (ICE), and then applies the algorithm suggested by Chan and Foster to this QR-factorization. The column exchange strategy used in the initial QR factorization will exploit the fact that certain column exchanges do not change the sparsity structure, and compute a sparse QR-factorization that is a good approximation of the sought-after RRQR-factorization. Due to quantities produced by ICE, the Chan/Foster RRQR algorithm can be implemented very cheaply, thus verifying that the sought-after RRQR-factorization has indeed been computed. Experimental results on a model problem show that the initial QR-factorization is indeed very likely to produce RRQR-factorization.« less

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

NASA Technical Reports Server (NTRS)

Poole, E. L.

1986-01-01

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

Fast sparsely synchronized brain rhythms in a scale-free neural network

NASA Astrophysics Data System (ADS)

Kim, Sang-Yoon; Lim, Woochang

2015-08-01

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D . For small D , full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp> ( : ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For D

Low-rank network decomposition reveals structural characteristics of small-world networks

NASA Astrophysics Data System (ADS)

Barranca, Victor J.; Zhou, Douglas; Cai, David

2015-12-01

Small-world networks occur naturally throughout biological, technological, and social systems. With their prevalence, it is particularly important to prudently identify small-world networks and further characterize their unique connection structure with respect to network function. In this work we develop a formalism for classifying networks and identifying small-world structure using a decomposition of network connectivity matrices into low-rank and sparse components, corresponding to connections within clusters of highly connected nodes and sparse interconnections between clusters, respectively. We show that the network decomposition is independent of node indexing and define associated bounded measures of connectivity structure, which provide insight into the clustering and regularity of network connections. While many existing network characterizations rely on constructing benchmark networks for comparison or fail to describe the structural properties of relatively densely connected networks, our classification relies only on the intrinsic network structure and is quite robust with respect to changes in connection density, producing stable results across network realizations. Using this framework, we analyze several real-world networks and reveal new structural properties, which are often indiscernible by previously established characterizations of network connectivity.

An efficient gridding reconstruction method for multishot non-Cartesian imaging with correction of off-resonance artifacts.

PubMed

Meng, Yuguang; Lei, Hao

2010-06-01

An efficient iterative gridding reconstruction method with correction of off-resonance artifacts was developed, which is especially tailored for multiple-shot non-Cartesian imaging. The novelty of the method lies in that the transformation matrix for gridding (T) was constructed as the convolution of two sparse matrices, among which the former is determined by the sampling interval and the spatial distribution of the off-resonance frequencies and the latter by the sampling trajectory and the target grid in the Cartesian space. The resulting T matrix is also sparse and can be solved efficiently with the iterative conjugate gradient algorithm. It was shown that, with the proposed method, the reconstruction speed in multiple-shot non-Cartesian imaging can be improved significantly while retaining high reconstruction fidelity. More important, the method proposed allows tradeoff between the accuracy and the computation time of reconstruction, making customization of the use of such a method in different applications possible. The performance of the proposed method was demonstrated by numerical simulation and multiple-shot spiral imaging on rat brain at 4.7 T. (c) 2010 Wiley-Liss, Inc.

Sequential time interleaved random equivalent sampling for repetitive signal.

PubMed

Zhao, Yijiu; Liu, Jingjing

2016-12-01

Compressed sensing (CS) based sampling techniques exhibit many advantages over other existing approaches for sparse signal spectrum sensing; they are also incorporated into non-uniform sampling signal reconstruction to improve the efficiency, such as random equivalent sampling (RES). However, in CS based RES, only one sample of each acquisition is considered in the signal reconstruction stage, and it will result in more acquisition runs and longer sampling time. In this paper, a sampling sequence is taken in each RES acquisition run, and the corresponding block measurement matrix is constructed using a Whittaker-Shannon interpolation formula. All the block matrices are combined into an equivalent measurement matrix with respect to all sampling sequences. We implemented the proposed approach with a multi-cores analog-to-digital converter (ADC), whose ADC cores are time interleaved. A prototype realization of this proposed CS based sequential random equivalent sampling method has been developed. It is able to capture an analog waveform at an equivalent sampling rate of 40 GHz while sampled at 1 GHz physically. Experiments indicate that, for a sparse signal, the proposed CS based sequential random equivalent sampling exhibits high efficiency.

An Object-Oriented Collection of Minimum Degree Algorithms: Design, Implementation, and Experiences

NASA Technical Reports Server (NTRS)

Kumfert, Gary; Pothen, Alex

1999-01-01

The multiple minimum degree (MMD) algorithm and its variants have enjoyed 20+ years of research and progress in generating fill-reducing orderings for sparse, symmetric positive definite matrices. Although conceptually simple, efficient implementations of these algorithms are deceptively complex and highly specialized. In this case study, we present an object-oriented library that implements several recent minimum degree-like algorithms. We discuss how object-oriented design forces us to decompose these algorithms in a different manner than earlier codes and demonstrate how this impacts the flexibility and efficiency of our C++ implementation. We compare the performance of our code against other implementations in C or Fortran.

Symmetrical group theory for mathematical complexity reduction of digital holograms

NASA Astrophysics Data System (ADS)

Perez-Ramirez, A.; Guerrero-Juk, J.; Sanchez-Lara, R.; Perez-Ramirez, M.; Rodriguez-Blanco, M. A.; May-Alarcon, M.

2017-10-01

This work presents the use of mathematical group theory through an algorithm to reduce the multiplicative computational complexity in the process of creating digital holograms. An object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image, where the image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity ( k - 1) × N for the case of sparse matrices and binary images, where k is the number of pixels other than zero and N is the total points in the image.

Peculiar spectral statistics of ensembles of trees and star-like graphs

NASA Astrophysics Data System (ADS)

Kovaleva, V.; Maximov, Yu; Nechaev, S.; Valba, O.

2017-07-01

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the ‘Lifshitz singularity’ emerging in the one-dimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However, the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, reflecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of an ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.

Peculiar spectral statistics of ensembles of trees and star-like graphs

DOE PAGES

Kovaleva, V.; Maximov, Yu; Nechaev, S.; ...

2017-07-11

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \\Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However,more » the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.« less

Peculiar spectral statistics of ensembles of trees and star-like graphs

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

Kovaleva, V.; Maximov, Yu; Nechaev, S.

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \\Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However,more » the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.« less

Revealing the Hidden Relationship by Sparse Modules in Complex Networks with a Large-Scale Analysis

PubMed Central

Jiao, Qing-Ju; Huang, Yan; Liu, Wei; Wang, Xiao-Fan; Chen, Xiao-Shuang; Shen, Hong-Bin

2013-01-01

One of the remarkable features of networks is module that can provide useful insights into not only network organizations but also functional behaviors between their components. Comprehensive efforts have been devoted to investigating cohesive modules in the past decade. However, it is still not clear whether there are important structural characteristics of the nodes that do not belong to any cohesive module. In order to answer this question, we performed a large-scale analysis on 25 complex networks with different types and scales using our recently developed BTS (bintree seeking) algorithm, which is able to detect both cohesive and sparse modules in the network. Our results reveal that the sparse modules composed by the cohesively isolated nodes widely co-exist with the cohesive modules. Detailed analysis shows that both types of modules provide better characterization for the division of a network into functional units than merely cohesive modules, because the sparse modules possibly re-organize the nodes in the so-called cohesive modules, which lack obvious modular significance, into meaningful groups. Compared with cohesive modules, the sizes of sparse ones are generally smaller. Sparse modules are also found to have preferences in social and biological networks than others. PMID:23762457

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.

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

JiTTree: A Just-in-Time Compiled Sparse GPU Volume Data Structure.

PubMed

Labschütz, Matthias; Bruckner, Stefan; Gröller, M Eduard; Hadwiger, Markus; Rautek, Peter

2016-01-01

Sparse volume data structures enable the efficient representation of large but sparse volumes in GPU memory for computation and visualization. However, the choice of a specific data structure for a given data set depends on several factors, such as the memory budget, the sparsity of the data, and data access patterns. In general, there is no single optimal sparse data structure, but a set of several candidates with individual strengths and drawbacks. One solution to this problem are hybrid data structures which locally adapt themselves to the sparsity. However, they typically suffer from increased traversal overhead which limits their utility in many applications. This paper presents JiTTree, a novel sparse hybrid volume data structure that uses just-in-time compilation to overcome these problems. By combining multiple sparse data structures and reducing traversal overhead we leverage their individual advantages. We demonstrate that hybrid data structures adapt well to a large range of data sets. They are especially superior to other sparse data structures for data sets that locally vary in sparsity. Possible optimization criteria are memory, performance and a combination thereof. Through just-in-time (JIT) compilation, JiTTree reduces the traversal overhead of the resulting optimal data structure. As a result, our hybrid volume data structure enables efficient computations on the GPU, while being superior in terms of memory usage when compared to non-hybrid data structures.

Thresholding functional connectomes by means of mixture modeling.

PubMed

Bielczyk, Natalia Z; Walocha, Fabian; Ebel, Patrick W; Haak, Koen V; Llera, Alberto; Buitelaar, Jan K; Glennon, Jeffrey C; Beckmann, Christian F

2018-05-01

Functional connectivity has been shown to be a very promising tool for studying the large-scale functional architecture of the human brain. In network research in fMRI, functional connectivity is considered as a set of pair-wise interactions between the nodes of the network. These interactions are typically operationalized through the full or partial correlation between all pairs of regional time series. Estimating the structure of the latent underlying functional connectome from the set of pair-wise partial correlations remains an open research problem though. Typically, this thresholding problem is approached by proportional thresholding, or by means of parametric or non-parametric permutation testing across a cohort of subjects at each possible connection. As an alternative, we propose a data-driven thresholding approach for network matrices on the basis of mixture modeling. This approach allows for creating subject-specific sparse connectomes by modeling the full set of partial correlations as a mixture of low correlation values associated with weak or unreliable edges in the connectome and a sparse set of reliable connections. Consequently, we propose to use alternative thresholding strategy based on the model fit using pseudo-False Discovery Rates derived on the basis of the empirical null estimated as part of the mixture distribution. We evaluate the method on synthetic benchmark fMRI datasets where the underlying network structure is known, and demonstrate that it gives improved performance with respect to the alternative methods for thresholding connectomes, given the canonical thresholding levels. We also demonstrate that mixture modeling gives highly reproducible results when applied to the functional connectomes of the visual system derived from the n-back Working Memory task in the Human Connectome Project. The sparse connectomes obtained from mixture modeling are further discussed in the light of the previous knowledge of the functional architecture of the visual system in humans. We also demonstrate that with use of our method, we are able to extract similar information on the group level as can be achieved with permutation testing even though these two methods are not equivalent. We demonstrate that with both of these methods, we obtain functional decoupling between the two hemispheres in the higher order areas of the visual cortex during visual stimulation as compared to the resting state, which is in line with previous studies suggesting lateralization in the visual processing. However, as opposed to permutation testing, our approach does not require inference at the cohort level and can be used for creating sparse connectomes at the level of a single subject. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

SparRec: An effective matrix completion framework of missing data imputation for GWAS

NASA Astrophysics Data System (ADS)

Jiang, Bo; Ma, Shiqian; Causey, Jason; Qiao, Linbo; Hardin, Matthew Price; Bitts, Ian; Johnson, Daniel; Zhang, Shuzhong; Huang, Xiuzhen

2016-10-01

Genome-wide association studies present computational challenges for missing data imputation, while the advances of genotype technologies are generating datasets of large sample sizes with sample sets genotyped on multiple SNP chips. We present a new framework SparRec (Sparse Recovery) for imputation, with the following properties: (1) The optimization models of SparRec, based on low-rank and low number of co-clusters of matrices, are different from current statistics methods. While our low-rank matrix completion (LRMC) model is similar to Mendel-Impute, our matrix co-clustering factorization (MCCF) model is completely new. (2) SparRec, as other matrix completion methods, is flexible to be applied to missing data imputation for large meta-analysis with different cohorts genotyped on different sets of SNPs, even when there is no reference panel. This kind of meta-analysis is very challenging for current statistics based methods. (3) SparRec has consistent performance and achieves high recovery accuracy even when the missing data rate is as high as 90%. Compared with Mendel-Impute, our low-rank based method achieves similar accuracy and efficiency, while the co-clustering based method has advantages in running time. The testing results show that SparRec has significant advantages and competitive performance over other state-of-the-art existing statistics methods including Beagle and fastPhase.

Discriminant WSRC for Large-Scale Plant Species Recognition.

PubMed

Zhang, Shanwen; Zhang, Chuanlei; Zhu, Yihai; You, Zhuhong

2017-01-01

In sparse representation based classification (SRC) and weighted SRC (WSRC), it is time-consuming to solve the global sparse representation problem. A discriminant WSRC (DWSRC) is proposed for large-scale plant species recognition, including two stages. Firstly, several subdictionaries are constructed by dividing the dataset into several similar classes, and a subdictionary is chosen by the maximum similarity between the test sample and the typical sample of each similar class. Secondly, the weighted sparse representation of the test image is calculated with respect to the chosen subdictionary, and then the leaf category is assigned through the minimum reconstruction error. Different from the traditional SRC and its improved approaches, we sparsely represent the test sample on a subdictionary whose base elements are the training samples of the selected similar class, instead of using the generic overcomplete dictionary on the entire training samples. Thus, the complexity to solving the sparse representation problem is reduced. Moreover, DWSRC is adapted to newly added leaf species without rebuilding the dictionary. Experimental results on the ICL plant leaf database show that the method has low computational complexity and high recognition rate and can be clearly interpreted.

Locating multiple diffusion sources in time varying networks from sparse observations.

PubMed

Hu, Zhao-Long; Shen, Zhesi; Cao, Shinan; Podobnik, Boris; Yang, Huijie; Wang, Wen-Xu; Lai, Ying-Cheng

2018-02-08

Data based source localization in complex networks has a broad range of applications. Despite recent progress, locating multiple diffusion sources in time varying networks remains to be an outstanding problem. Bridging structural observability and sparse signal reconstruction theories, we develop a general framework to locate diffusion sources in time varying networks based solely on sparse data from a small set of messenger nodes. A general finding is that large degree nodes produce more valuable information than small degree nodes, a result that contrasts that for static networks. Choosing large degree nodes as the messengers, we find that sparse observations from a few such nodes are often sufficient for any number of diffusion sources to be located for a variety of model and empirical networks. Counterintuitively, sources in more rapidly varying networks can be identified more readily with fewer required messenger nodes.

Ground State and Finite Temperature Lanczos Methods

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Bonča, J.

The present review will focus on recent development of exact- diagonalization (ED) methods that use Lanczos algorithm to transform large sparse matrices onto the tridiagonal form. We begin with a review of basic principles of the Lanczos method for computing ground-state static as well as dynamical properties. Next, generalization to finite-temperatures in the form of well established finite-temperature Lanczos method is described. The latter allows for the evaluation of temperatures T>0 static and dynamic quantities within various correlated models. Several extensions and modification of the latter method introduced more recently are analysed. In particular, the low-temperature Lanczos method and the microcanonical Lanczos method, especially applicable within the high-T regime. In order to overcome the problems of exponentially growing Hilbert spaces that prevent ED calculations on larger lattices, different approaches based on Lanczos diagonalization within the reduced basis have been developed. In this context, recently developed method based on ED within a limited functional space is reviewed. Finally, we briefly discuss the real-time evolution of correlated systems far from equilibrium, which can be simulated using the ED and Lanczos-based methods, as well as approaches based on the diagonalization in a reduced basis.

Bézier B¯ projection

NASA Astrophysics Data System (ADS)

Miao, Di; Borden, Michael J.; Scott, Michael A.; Thomas, Derek C.

2018-06-01

In this paper we demonstrate the use of B\\'{e}zier projection to alleviate locking phenomena in structural mechanics applications of isogeometric analysis. Interpreting the well-known $\\bar{B}$ projection in two different ways we develop two formulations for locking problems in beams and nearly incompressible elastic solids. One formulation leads to a sparse symmetric symmetric system and the other leads to a sparse non-symmetric system. To demonstrate the utility of B\\'{e}zier projection for both geometry and material locking phenomena we focus on transverse shear locking in Timoshenko beams and volumetric locking in nearly compressible linear elasticity although the approach can be applied generally to other types of locking phenemona as well. B\\'{e}zier projection is a local projection technique with optimal approximation properties, which in many cases produces solutions that are comparable to global $L^2$ projection. In the context of $\\bar{B}$ methods, the use of B\\'ezier projection produces sparse stiffness matrices with only a slight increase in bandwidth when compared to standard displacement-based methods. Of particular importance is that the approach is applicable to any spline representation that can be written in B\\'ezier form like NURBS, T-splines, LR-splines, etc. We discuss in detail how to integrate this approach into an existing finite element framework with minimal disruption through the use of B\\'ezier extraction operators and a newly introduced dual basis for the B\\'{e}zierprojection operator. We then demonstrate the behavior of the two proposed formulations through several challenging benchmark problems.

Evaluating the efficacy of a structure-derived amino acid substitution matrix in detecting protein homologs by BLAST and PSI-BLAST.

PubMed

Goonesekere, Nalin Cw

2009-01-01

The large numbers of protein sequences generated by whole genome sequencing projects require rapid and accurate methods of annotation. The detection of homology through computational sequence analysis is a powerful tool in determining the complex evolutionary and functional relationships that exist between proteins. Homology search algorithms employ amino acid substitution matrices to detect similarity between proteins sequences. The substitution matrices in common use today are constructed using sequences aligned without reference to protein structure. Here we present amino acid substitution matrices constructed from the alignment of a large number of protein domain structures from the structural classification of proteins (SCOP) database. We show that when incorporated into the homology search algorithms BLAST and PSI-blast, the structure-based substitution matrices enhance the efficacy of detecting remote homologs.

Fast sparsely synchronized brain rhythms in a scale-free neural network.

PubMed

Kim, Sang-Yoon; Lim, Woochang

2015-08-01

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D. For small D, full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp>〈fi〉 (〈fi〉: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4〈fi〉 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For D

Novel sustained-release dosage forms of proteins using polyglycerol esters of fatty acids.

PubMed

Yamagata, Y; Iga, K; Ogawa, Y

2000-02-03

In order to develop a novel delivery system for proteins based on polyglycerol esters of fatty acids (PGEFs), we studied a model system using interferon-alpha (IFN-alpha) as the test protein. A cylindrical matrix was prepared by a heat extrusion technique using a lyophilized powder of the protein and 11 different types of synthetic PGEFs, which varied in degree of glycerol polymerization (di- and tetra-), chain length of fatty acids (myristate, palmitate and stearate) and degree of fatty acid esterification (mono-, di- and tri-). In an in-vitro release study using an enzyme-linked immunosorbent assay (ELISA) as a detection method, the matrices prepared from a monoglyceride (used for comparison) and from diglycerol esters exhibited a biphasic release pattern with a large initial burst followed by slow release. In contrast, the matrices prepared from tetraglycerol esters showed a steady rate of release without a large initial burst. In an in vivo release study, initial bursts of IFN-alpha release were, also, dramatically reduced when the matrices were prepared from the tetraglycerol esters of palmitate and stearate, and the mean residence time (MRT) of IFN-alpha was prolonged, whereas the matrices prepared from monoglyceride and from diglycerol esters showed large initial bursts of IFN-alpha release. Since the release rates from the matrices prepared from the tetraglycerol esters of palmitate and stearate were governed by Jander's equation modified for a cylindrical matrix, the release from those matrices was concluded to be a diffusion-controlled process. The bioavailability of IFN-alpha after implantation of the matrix formulation prepared using all types of PGEFs, except for tetraglycerol triesters, was almost equivalent to that after injection of IFN-alpha solution; consequently, IFN-alpha in these matrices appears to remain stable during the release period.

Large-region acoustic source mapping using a movable array and sparse covariance fitting.

PubMed

Zhao, Shengkui; Tuna, Cagdas; Nguyen, Thi Ngoc Tho; Jones, Douglas L

2017-01-01

Large-region acoustic source mapping is important for city-scale noise monitoring. Approaches using a single-position measurement scheme to scan large regions using small arrays cannot provide clean acoustic source maps, while deploying large arrays spanning the entire region of interest is prohibitively expensive. A multiple-position measurement scheme is applied to scan large regions at multiple spatial positions using a movable array of small size. Based on the multiple-position measurement scheme, a sparse-constrained multiple-position vectorized covariance matrix fitting approach is presented. In the proposed approach, the overall sample covariance matrix of the incoherent virtual array is first estimated using the multiple-position array data and then vectorized using the Khatri-Rao (KR) product. A linear model is then constructed for fitting the vectorized covariance matrix and a sparse-constrained reconstruction algorithm is proposed for recovering source powers from the model. The user parameter settings are discussed. The proposed approach is tested on a 30 m × 40 m region and a 60 m × 40 m region using simulated and measured data. Much cleaner acoustic source maps and lower sound pressure level errors are obtained compared to the beamforming approaches and the previous sparse approach [Zhao, Tuna, Nguyen, and Jones, Proc. IEEE Intl. Conf. on Acoustics, Speech and Signal Processing (ICASSP) (2016)].

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.

A Relaxation Method for Nonlocal and Non-Hermitian Operators

NASA Astrophysics Data System (ADS)

Lagaris, I. E.; Papageorgiou, D. G.; Braun, M.; Sofianos, S. A.

1996-06-01

We present a grid method to solve the time dependent Schrödinger equation (TDSE). It uses the Crank-Nicholson scheme to propagate the wavefunction forward in time and finite differences to approximate the derivative operators. The resulting sparse linear system is solved by the symmetric successive overrelaxation iterative technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-Hermitian matrices with real eigenvalues. We test the method by solving the TDSE in the imaginary time domain, thus converting the time propagation to asymptotic relaxation. Benchmark problems solved are both in one and two dimensions, with local, nonlocal, Hermitian and non-Hermitian Hamiltonians.

Performance effects of irregular communications patterns on massively parallel multiprocessors

NASA Technical Reports Server (NTRS)

Saltz, Joel; Petiton, Serge; Berryman, Harry; Rifkin, Adam

1991-01-01

A detailed study of the performance effects of irregular communications patterns on the CM-2 was conducted. The communications capabilities of the CM-2 were characterized under a variety of controlled conditions. In the process of carrying out the performance evaluation, extensive use was made of a parameterized synthetic mesh. In addition, timings with unstructured meshes generated for aerodynamic codes and a set of sparse matrices with banded patterns on non-zeroes were performed. This benchmarking suite stresses the communications capabilities of the CM-2 in a range of different ways. Benchmark results demonstrate that it is possible to make effective use of much of the massive concurrency available in the communications network.

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.

Sparse, decorrelated odor coding in the mushroom body enhances learned odor discrimination.

PubMed

Lin, Andrew C; Bygrave, Alexei M; de Calignon, Alix; Lee, Tzumin; Miesenböck, Gero

2014-04-01

Sparse coding may be a general strategy of neural systems for augmenting memory capacity. In Drosophila melanogaster, sparse odor coding by the Kenyon cells of the mushroom body is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. However, it remains untested how sparse coding relates to behavioral performance. Here we demonstrate that sparseness is controlled by a negative feedback circuit between Kenyon cells and the GABAergic anterior paired lateral (APL) neuron. Systematic activation and blockade of each leg of this feedback circuit showed that Kenyon cells activated APL and APL inhibited Kenyon cells. Disrupting the Kenyon cell-APL feedback loop decreased the sparseness of Kenyon cell odor responses, increased inter-odor correlations and prevented flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor specificity of memories.

Large Scale Density Estimation of Blue and Fin Whales: Utilizing Sparse Array Data to Develop and Implement a New Method for Estimating Blue and Fin Whale Density

DTIC Science & Technology

2015-09-30

1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Large Scale Density Estimation of Blue and Fin Whales ...Utilizing Sparse Array Data to Develop and Implement a New Method for Estimating Blue and Fin Whale Density Len Thomas & Danielle Harris Centre...to develop and implement a new method for estimating blue and fin whale density that is effective over large spatial scales and is designed to cope

Deformable segmentation via sparse representation and dictionary learning.

PubMed

Zhang, Shaoting; Zhan, Yiqiang; Metaxas, Dimitris N

2012-10-01

"Shape" and "appearance", the two pillars of a deformable model, complement each other in object segmentation. In many medical imaging applications, while the low-level appearance information is weak or mis-leading, shape priors play a more important role to guide a correct segmentation, thanks to the strong shape characteristics of biological structures. Recently a novel shape prior modeling method has been proposed based on sparse learning theory. Instead of learning a generative shape model, shape priors are incorporated on-the-fly through the sparse shape composition (SSC). SSC is robust to non-Gaussian errors and still preserves individual shape characteristics even when such characteristics is not statistically significant. Although it seems straightforward to incorporate SSC into a deformable segmentation framework as shape priors, the large-scale sparse optimization of SSC has low runtime efficiency, which cannot satisfy clinical requirements. In this paper, we design two strategies to decrease the computational complexity of SSC, making a robust, accurate and efficient deformable segmentation system. (1) When the shape repository contains a large number of instances, which is often the case in 2D problems, K-SVD is used to learn a more compact but still informative shape dictionary. (2) If the derived shape instance has a large number of vertices, which often appears in 3D problems, an affinity propagation method is used to partition the surface into small sub-regions, on which the sparse shape composition is performed locally. Both strategies dramatically decrease the scale of the sparse optimization problem and hence speed up the algorithm. Our method is applied on a diverse set of biomedical image analysis problems. Compared to the original SSC, these two newly-proposed modules not only significant reduce the computational complexity, but also improve the overall accuracy. Copyright © 2012 Elsevier B.V. All rights reserved.

Medical image classification based on multi-scale non-negative sparse coding.

PubMed

Zhang, Ruijie; Shen, Jian; Wei, Fushan; Li, Xiong; Sangaiah, Arun Kumar

2017-11-01

With the rapid development of modern medical imaging technology, medical image classification has become more and more important in medical diagnosis and clinical practice. Conventional medical image classification algorithms usually neglect the semantic gap problem between low-level features and high-level image semantic, which will largely degrade the classification performance. To solve this problem, we propose a multi-scale non-negative sparse coding based medical image classification algorithm. Firstly, Medical images are decomposed into multiple scale layers, thus diverse visual details can be extracted from different scale layers. Secondly, for each scale layer, the non-negative sparse coding model with fisher discriminative analysis is constructed to obtain the discriminative sparse representation of medical images. Then, the obtained multi-scale non-negative sparse coding features are combined to form a multi-scale feature histogram as the final representation for a medical image. Finally, SVM classifier is combined to conduct medical image classification. The experimental results demonstrate that our proposed algorithm can effectively utilize multi-scale and contextual spatial information of medical images, reduce the semantic gap in a large degree and improve medical image classification performance. Copyright © 2017 Elsevier B.V. All rights reserved.

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.

Multimodal sparse reconstruction in guided wave imaging of defects in plates

NASA Astrophysics Data System (ADS)

Golato, Andrew; Santhanam, Sridhar; Ahmad, Fauzia; Amin, Moeness G.

2016-07-01

A multimodal sparse reconstruction approach is proposed for localizing defects in thin plates in Lamb wave-based structural health monitoring. The proposed approach exploits both the sparsity of the defects and the multimodal nature of Lamb wave propagation in plates. It takes into account the variation of the defects' aspect angles across the various transducer pairs. At low operating frequencies, only the fundamental symmetric and antisymmetric Lamb modes emanate from a transmitting transducer. Asymmetric defects scatter these modes and spawn additional converted fundamental modes. Propagation models are developed for each of these scattered and spawned modes arriving at the various receiving transducers. This enables the construction of modal dictionary matrices spanning a two-dimensional array of pixels representing potential defect locations in the region of interest. Reconstruction of the region of interest is achieved by inverting the resulting linear model using the group sparsity constraint, where the groups extend across the various transducer pairs and the different modes. The effectiveness of the proposed approach is established with finite-element scattering simulations of the fundamental Lamb wave modes by crack-like defects in a plate. The approach is subsequently validated with experimental results obtained from an aluminum plate with asymmetric defects.

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.

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

Interferometric synthetic aperture radar phase unwrapping based on sparse Markov random fields by graph cuts

NASA Astrophysics Data System (ADS)

Zhou, Lifan; Chai, Dengfeng; Xia, Yu; Ma, Peifeng; Lin, Hui

2018-01-01

Phase unwrapping (PU) is one of the key processes in reconstructing the digital elevation model of a scene from its interferometric synthetic aperture radar (InSAR) data. It is known that two-dimensional (2-D) PU problems can be formulated as maximum a posteriori estimation of Markov random fields (MRFs). However, considering that the traditional MRF algorithm is usually defined on a rectangular grid, it fails easily if large parts of the wrapped data are dominated by noise caused by large low-coherence area or rapid-topography variation. A PU solution based on sparse MRF is presented to extend the traditional MRF algorithm to deal with sparse data, which allows the unwrapping of InSAR data dominated by high phase noise. To speed up the graph cuts algorithm for sparse MRF, we designed dual elementary graphs and merged them to obtain the Delaunay triangle graph, which is used to minimize the energy function efficiently. The experiments on simulated and real data, compared with other existing algorithms, both confirm the effectiveness of the proposed MRF approach, which suffers less from decorrelation effects caused by large low-coherence area or rapid-topography variation.

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.

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

Carpenter, J.A.

This report is a sequel to ORNL/CSD-96 in the ongoing supplements to Professor A.S. Householder's KWIC Index for Numerical Algebra. With this supplement, the coverage has been restricted to Numerical Linear Algebra and is now roughly characterized by the American Mathematical Society's classification section 15 and 65F but with little coverage of inifinite matrices, matrices over fields of characteristics other than zero, operator theory, optimization and those parts of matrix theory primarily combinatorial in nature. Some recognition is made of the uses of graph theory in Numerical Linear Algebra, particularly as regards their use in algorithms for sparse matrix computations.more » The period covered by this report is roughly the calendar year 1981 as measured by the appearance of the articles in the American Mathematical Society's Contents of Mathematical Publications. The review citations are limited to the Mathematical Reviews (MR) and Das Zentralblatt fur Mathematik und Ihre Grenzgebiete (ZBL). Future reports will be made more timely by closer ovservation of the few journals which supply the bulk of the listings rather than what appears to be too much reliance on secondary sources. Some thought is being given to the physical appearance of these reports and the author welcomes comments concerning both their appearance and contents.« less

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.

Hybrid reconstruction of quantum density matrix: when low-rank meets sparsity

NASA Astrophysics Data System (ADS)

Li, Kezhi; Zheng, Kai; Yang, Jingbei; Cong, Shuang; Liu, Xiaomei; Li, Zhaokai

2017-12-01

Both the mathematical theory and experiments have verified that the quantum state tomography based on compressive sensing is an efficient framework for the reconstruction of quantum density states. In recent physical experiments, we found that many unknown density matrices in which people are interested in are low-rank as well as sparse. Bearing this information in mind, in this paper we propose a reconstruction algorithm that combines the low-rank and the sparsity property of density matrices and further theoretically prove that the solution of the optimization function can be, and only be, the true density matrix satisfying the model with overwhelming probability, as long as a necessary number of measurements are allowed. The solver leverages the fixed-point equation technique in which a step-by-step strategy is developed by utilizing an extended soft threshold operator that copes with complex values. Numerical experiments of the density matrix estimation for real nuclear magnetic resonance devices reveal that the proposed method achieves a better accuracy compared to some existing methods. We believe that the proposed method could be leveraged as a generalized approach and widely implemented in the quantum state estimation.

Applications of multiple-constraint matrix updates to the optimal control of large structures

NASA Technical Reports Server (NTRS)

Smith, S. W.; Walcott, B. L.

1992-01-01

Low-authority control or vibration suppression in large, flexible space structures can be formulated as a linear feedback control problem requiring computation of displacement and velocity feedback gain matrices. To ensure stability in the uncontrolled modes, these gain matrices must be symmetric and positive definite. In this paper, efficient computation of symmetric, positive-definite feedback gain matrices is accomplished through the use of multiple-constraint matrix update techniques originally developed for structural identification applications. Two systems were used to illustrate the application: a simple spring-mass system and a planar truss. From these demonstrations, use of this multiple-constraint technique is seen to provide a straightforward approach for computing the low-authority gains.

Thin-film sparse boundary array design for passive acoustic mapping during ultrasound therapy.

PubMed

Coviello, Christian M; Kozick, Richard J; Hurrell, Andrew; Smith, Penny Probert; Coussios, Constantin-C

2012-10-01

A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array's geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology.

Sparse gammatone signal model optimized for English speech does not match the human auditory filters.

PubMed

Strahl, Stefan; Mertins, Alfred

2008-07-18

Evidence that neurosensory systems use sparse signal representations as well as improved performance of signal processing algorithms using sparse signal models raised interest in sparse signal coding in the last years. For natural audio signals like speech and environmental sounds, gammatone atoms have been derived as expansion functions that generate a nearly optimal sparse signal model (Smith, E., Lewicki, M., 2006. Efficient auditory coding. Nature 439, 978-982). Furthermore, gammatone functions are established models for the human auditory filters. Thus far, a practical application of a sparse gammatone signal model has been prevented by the fact that deriving the sparsest representation is, in general, computationally intractable. In this paper, we applied an accelerated version of the matching pursuit algorithm for gammatone dictionaries allowing real-time and large data set applications. We show that a sparse signal model in general has advantages in audio coding and that a sparse gammatone signal model encodes speech more efficiently in terms of sparseness than a sparse modified discrete cosine transform (MDCT) signal model. We also show that the optimal gammatone parameters derived for English speech do not match the human auditory filters, suggesting for signal processing applications to derive the parameters individually for each applied signal class instead of using psychometrically derived parameters. For brain research, it means that care should be taken with directly transferring findings of optimality for technical to biological systems.

Use of job-exposure matrices to estimate occupational exposure to pesticides: A review.

PubMed

Carles, Camille; Bouvier, Ghislaine; Lebailly, Pierre; Baldi, Isabelle

2017-03-01

The health effects of pesticides have been extensively studied in epidemiology, mainly in agricultural populations. However, pesticide exposure assessment remains a key methodological issue for epidemiological studies. Besides self-reported information, expert assessment or metrology, job-exposure matrices still appear to be an interesting tool. We reviewed all existing matrices assessing occupational exposure to pesticides in epidemiological studies and described the exposure parameters they included. We identified two types of matrices, (i) generic ones that are generally used in case-control studies and document broad categories of pesticides in a large range of jobs, and (ii) specific matrices, developed for use in agricultural cohorts, that generally provide exposure metrics at the active ingredient level. The various applications of these matrices in epidemiological studies have proven that they are valuable tools to assess pesticide exposure. Specific matrices are particularly promising for use in agricultural cohorts. However, results obtained with matrices have rarely been compared with those obtained with other tools. In addition, the external validity of the given estimates has not been adequately discussed. Yet, matrices would help in reducing misclassification and in quantifying cumulated exposures, to improve knowledge about the chronic health effects of pesticides.

High Angular Resolution Microwave Sensing with Large, Sparse, Random Arrays

DTIC Science & Technology

1983-11-01

RESEARCH AFOSR 82-0012 DTIC s" A6 19M UNIVERSITY of PENNSYLVANIA VALLEY FORGE RESEARCH CENTER THE MOORE SCHOOL OF ELECTRICAL ENGINEERING PHILADELPHIA...MICROWAVE SENSING WITH LARGE, SPARSE, RANDOM ARRAYS Final Scientific Report AIR FORCE OFFICE OF SCIENTIFIC RESEARCH AFOSR 82-0012 Valley Forge Research ...CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Air Force Office of Scientific Research /NE Nov 1983 - . Bildin 41073. NUMBER Or PAG ES BOllinZ AFB, DIC

Curvelet-based compressive sensing for InSAR raw data

NASA Astrophysics Data System (ADS)

Costa, Marcello G.; da Silva Pinho, Marcelo; Fernandes, David

2015-10-01

The aim of this work is to evaluate the compression performance of SAR raw data for interferometry applications collected by airborne from BRADAR (Brazilian SAR System operating in X and P bands) using the new approach based on compressive sensing (CS) to achieve an effective recovery with a good phase preserving. For this framework is desirable a real-time capability, where the collected data can be compressed to reduce onboard storage and bandwidth required for transmission. In the CS theory, a sparse unknown signals can be recovered from a small number of random or pseudo-random measurements by sparsity-promoting nonlinear recovery algorithms. Therefore, the original signal can be significantly reduced. To achieve the sparse representation of SAR signal, was done a curvelet transform. The curvelets constitute a directional frame, which allows an optimal sparse representation of objects with discontinuities along smooth curves as observed in raw data and provides an advanced denoising optimization. For the tests were made available a scene of 8192 x 2048 samples in range and azimuth in X-band with 2 m of resolution. The sparse representation was compressed using low dimension measurements matrices in each curvelet subband. Thus, an iterative CS reconstruction method based on IST (iterative soft/shrinkage threshold) was adjusted to recover the curvelets coefficients and then the original signal. To evaluate the compression performance were computed the compression ratio (CR), signal to noise ratio (SNR), and because the interferometry applications require more reconstruction accuracy the phase parameters like the standard deviation of the phase (PSD) and the mean phase error (MPE) were also computed. Moreover, in the image domain, a single-look complex image was generated to evaluate the compression effects. All results were computed in terms of sparsity analysis to provides an efficient compression and quality recovering appropriated for inSAR applications, therefore, providing a feasibility for compressive sensing application.

Exhaustive Search for Sparse Variable Selection in Linear Regression

NASA Astrophysics Data System (ADS)

Igarashi, Yasuhiko; Takenaka, Hikaru; Nakanishi-Ohno, Yoshinori; Uemura, Makoto; Ikeda, Shiro; Okada, Masato

2018-04-01

We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.

Novel image compression-encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing

NASA Astrophysics Data System (ADS)

Zhou, Nanrun; Zhang, Aidi; Zheng, Fen; Gong, Lihua

2014-10-01

The existing ways to encrypt images based on compressive sensing usually treat the whole measurement matrix as the key, which renders the key too large to distribute and memorize or store. To solve this problem, a new image compression-encryption hybrid algorithm is proposed to realize compression and encryption simultaneously, where the key is easily distributed, stored or memorized. The input image is divided into 4 blocks to compress and encrypt, then the pixels of the two adjacent blocks are exchanged randomly by random matrices. The measurement matrices in compressive sensing are constructed by utilizing the circulant matrices and controlling the original row vectors of the circulant matrices with logistic map. And the random matrices used in random pixel exchanging are bound with the measurement matrices. Simulation results verify the effectiveness, security of the proposed algorithm and the acceptable compression performance.

Thirty Years of Nonparametric Item Response Theory.

ERIC Educational Resources Information Center

Molenaar, Ivo W.

2001-01-01

Discusses relationships between a mathematical measurement model and its real-world applications. Makes a distinction between large-scale data matrices commonly found in educational measurement and smaller matrices found in attitude and personality measurement. Also evaluates nonparametric methods for estimating item response functions and…

Statistical model for the mechanical behavior of the tissue engineering non-woven fibrous matrices under large deformation.

PubMed

Rizvi, Mohd Suhail; Pal, Anupam

2014-09-01

The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex three-dimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structure-mechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

BI-sparsity pursuit for robust subspace recovery

DOE PAGES

Bian, Xiao; Krim, Hamid

2015-09-01

Here, the success of sparse models in computer vision and machine learning in many real-world applications, may be attributed in large part, to the fact that many high dimensional data are distributed in a union of low dimensional subspaces. The underlying structure may, however, be adversely affected by sparse errors, thus inducing additional complexity in recovering it. In this paper, we propose a bi-sparse model as a framework to investigate and analyze this problem, and provide as a result , a novel algorithm to recover the union of subspaces in presence of sparse corruptions. We additionally demonstrate the effectiveness ofmore » our method by experiments on real-world vision data.« less

Learning in the Machine: Random Backpropagation and the Deep Learning Channel.

PubMed

Baldi, Pierre; Sadowski, Peter; Lu, Zhiqin

2018-07-01

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is remarkable both because of its effectiveness, in spite of using random matrices to communicate error information, and because it completely removes the taxing requirement of maintaining symmetric weights in a physical neural system. To better understand random backpropagation, we first connect it to the notions of local learning and learning channels. Through this connection, we derive several alternatives to RBP, including skipped RBP (SRPB), adaptive RBP (ARBP), sparse RBP, and their combinations (e.g. ASRBP) and analyze their computational complexity. We then study their behavior through simulations using the MNIST and CIFAR-10 bechnmark datasets. These simulations show that most of these variants work robustly, almost as well as backpropagation, and that multiplication by the derivatives of the activation functions is important. As a follow-up, we study also the low-end of the number of bits required to communicate error information over the learning channel. We then provide partial intuitive explanations for some of the remarkable properties of RBP and its variations. Finally, we prove several mathematical results, including the convergence to fixed points of linear chains of arbitrary length, the convergence to fixed points of linear autoencoders with decorrelated data, the long-term existence of solutions for linear systems with a single hidden layer and convergence in special cases, and the convergence to fixed points of non-linear chains, when the derivative of the activation functions is included.

Implicit Kalman filtering

NASA Technical Reports Server (NTRS)

Skliar, M.; Ramirez, W. F.

1997-01-01

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Fidelity under isospectral perturbations: a random matrix study

NASA Astrophysics Data System (ADS)

Leyvraz, F.; García, A.; Kohler, H.; Seligman, T. H.

2013-07-01

The set of Hamiltonians generated by all unitary transformations from a single Hamiltonian is the largest set of isospectral Hamiltonians we can form. Taking advantage of the fact that the unitary group can be generated from Hermitian matrices we can take the ones generated by the Gaussian unitary ensemble with a small parameter as small perturbations. Similarly, the transformations generated by Hermitian antisymmetric matrices from orthogonal matrices form isospectral transformations among symmetric matrices. Based on this concept we can obtain the fidelity decay of a system that decays under a random isospectral perturbation with well-defined properties regarding time-reversal invariance. If we choose the Hamiltonian itself also from a classical random matrix ensemble, then we obtain solutions in terms of form factors in the limit of large matrices.

Sparse reconstruction localization of multiple acoustic emissions in large diameter pipelines

NASA Astrophysics Data System (ADS)

Dubuc, Brennan; Ebrahimkhanlou, Arvin; Salamone, Salvatore

2017-04-01

A sparse reconstruction localization method is proposed, which is capable of localizing multiple acoustic emission events occurring closely in time. The events may be due to a number of sources, such as the growth of corrosion patches or cracks. Such acoustic emissions may yield localization failure if a triangulation method is used. The proposed method is implemented both theoretically and experimentally on large diameter thin-walled pipes. Experimental examples are presented, which demonstrate the failure of a triangulation method when multiple sources are present in this structure, while highlighting the capabilities of the proposed method. The examples are generated from experimental data of simulated acoustic emission events. The data corresponds to helical guided ultrasonic waves generated in a 3 m long large diameter pipe by pencil lead breaks on its outer surface. Acoustic emission waveforms are recorded by six sparsely distributed low-profile piezoelectric transducers instrumented on the outer surface of the pipe. The same array of transducers is used for both the proposed and the triangulation method. It is demonstrated that the proposed method is able to localize multiple events occurring closely in time. Furthermore, the matching pursuit algorithm and the basis pursuit densoising approach are each evaluated as potential numerical tools in the proposed sparse reconstruction method.

Feature Selection and Pedestrian Detection Based on Sparse Representation.

PubMed

Yao, Shihong; Wang, Tao; Shen, Weiming; Pan, Shaoming; Chong, Yanwen; Ding, Fei

2015-01-01

Pedestrian detection have been currently devoted to the extraction of effective pedestrian features, which has become one of the obstacles in pedestrian detection application according to the variety of pedestrian features and their large dimension. Based on the theoretical analysis of six frequently-used features, SIFT, SURF, Haar, HOG, LBP and LSS, and their comparison with experimental results, this paper screens out the sparse feature subsets via sparse representation to investigate whether the sparse subsets have the same description abilities and the most stable features. When any two of the six features are fused, the fusion feature is sparsely represented to obtain its important components. Sparse subsets of the fusion features can be rapidly generated by avoiding calculation of the corresponding index of dimension numbers of these feature descriptors; thus, the calculation speed of the feature dimension reduction is improved and the pedestrian detection time is reduced. Experimental results show that sparse feature subsets are capable of keeping the important components of these six feature descriptors. The sparse features of HOG and LSS possess the same description ability and consume less time compared with their full features. The ratios of the sparse feature subsets of HOG and LSS to their full sets are the highest among the six, and thus these two features can be used to best describe the characteristics of the pedestrian and the sparse feature subsets of the combination of HOG-LSS show better distinguishing ability and parsimony.

The algebraic theory of latent projectors in lambda matrices

NASA Technical Reports Server (NTRS)

Denman, E. D.; Leyva-Ramos, J.; Jeon, G. J.

1981-01-01

Multivariable systems such as a finite-element model of vibrating structures, control systems, and large-scale systems are often formulated in terms of differential equations which give rise to lambda matrices. The present investigation is concerned with the formulation of the algebraic theory of lambda matrices and the relationship of latent roots, latent vectors, and latent projectors to the eigenvalues, eigenvectors, and eigenprojectors of the companion form. The chain rule for latent projectors and eigenprojectors for the repeated latent root or eigenvalues is given.

Evidence for sparse synergies in grasping actions.

PubMed

Prevete, Roberto; Donnarumma, Francesco; d'Avella, Andrea; Pezzulo, Giovanni

2018-01-12

Converging evidence shows that hand-actions are controlled at the level of synergies and not single muscles. One intriguing aspect of synergy-based action-representation is that it may be intrinsically sparse and the same synergies can be shared across several distinct types of hand-actions. Here, adopting a normative angle, we consider three hypotheses for hand-action optimal-control: sparse-combination hypothesis (SC) - sparsity in the mapping between synergies and actions - i.e., actions implemented using a sparse combination of synergies; sparse-elements hypothesis (SE) - sparsity in synergy representation - i.e., the mapping between degrees-of-freedom (DoF) and synergies is sparse; double-sparsity hypothesis (DS) - a novel view combining both SC and SE - i.e., both the mapping between DoF and synergies and between synergies and actions are sparse, each action implementing a sparse combination of synergies (as in SC), each using a limited set of DoFs (as in SE). We evaluate these hypotheses using hand kinematic data from six human subjects performing nine different types of reach-to-grasp actions. Our results support DS, suggesting that the best action representation is based on a relatively large set of synergies, each involving a reduced number of degrees-of-freedom, and that distinct sets of synergies may be involved in distinct tasks.

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering.

PubMed

Sicat, Ronell; Krüger, Jens; Möller, Torsten; Hadwiger, Markus

2014-12-01

This paper presents a new multi-resolution volume representation called sparse pdf volumes, which enables consistent multi-resolution volume rendering based on probability density functions (pdfs) of voxel neighborhoods. These pdfs are defined in the 4D domain jointly comprising the 3D volume and its 1D intensity range. Crucially, the computation of sparse pdf volumes exploits data coherence in 4D, resulting in a sparse representation with surprisingly low storage requirements. At run time, we dynamically apply transfer functions to the pdfs using simple and fast convolutions. Whereas standard low-pass filtering and down-sampling incur visible differences between resolution levels, the use of pdfs facilitates consistent results independent of the resolution level used. We describe the efficient out-of-core computation of large-scale sparse pdf volumes, using a novel iterative simplification procedure of a mixture of 4D Gaussians. Finally, our data structure is optimized to facilitate interactive multi-resolution volume rendering on GPUs.

Sample-Starved Large Scale Network Analysis

DTIC Science & Technology

2016-05-05

As reported in our journal publication (G. Marjanovic and A. O. Hero, ”l0 Sparse Inverse Covariance Estimation,” IEEE Trans on Signal Processing, vol... Marjanovic and A. O. Hero, ”l0 Sparse Inverse Covariance Estimation,” in IEEE Trans on Signal Processing, vol. 63, no. 12, pp. 3218-3231, May 2015. 6. G

Compressed Sensing for Chemistry

NASA Astrophysics Data System (ADS)

Sanders, Jacob Nathan

Many chemical applications, from spectroscopy to quantum chemistry, involve measuring or computing a large amount of data, and then compressing this data to retain the most chemically-relevant information. In contrast, compressed sensing is an emergent technique that makes it possible to measure or compute an amount of data that is roughly proportional to its information content. In particular, compressed sensing enables the recovery of a sparse quantity of information from significantly undersampled data by solving an ℓ 1-optimization problem. This thesis represents the application of compressed sensing to problems in chemistry. The first half of this thesis is about spectroscopy. Compressed sensing is used to accelerate the computation of vibrational and electronic spectra from real-time time-dependent density functional theory simulations. Using compressed sensing as a drop-in replacement for the discrete Fourier transform, well-resolved frequency spectra are obtained at one-fifth the typical simulation time and computational cost. The technique is generalized to multiple dimensions and applied to two-dimensional absorption spectroscopy using experimental data collected on atomic rubidium vapor. Finally, a related technique known as super-resolution is applied to open quantum systems to obtain realistic models of a protein environment, in the form of atomistic spectral densities, at lower computational cost. The second half of this thesis deals with matrices in quantum chemistry. It presents a new use of compressed sensing for more efficient matrix recovery whenever the calculation of individual matrix elements is the computational bottleneck. The technique is applied to the computation of the second-derivative Hessian matrices in electronic structure calculations to obtain the vibrational modes and frequencies of molecules. When applied to anthracene, this technique results in a threefold speed-up, with greater speed-ups possible for larger molecules. The implementation of the method in the Q-Chem commercial software package is described. Moreover, the method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations.

A Large Sparse Aperture Densified Pupil Hypertelescope Concept for Ground Based Detection of Extra-Solar Earth-Like Planets

NASA Technical Reports Server (NTRS)

Gezari, D.; Lyon, R.; Woodruff, R.; Labeyrie, A.; Oegerle, William (Technical Monitor)

2002-01-01

A concept is presented for a large (10 - 30 meter) sparse aperture hyper telescope to image extrasolar earth-like planets from the ground in the presence of atmospheric seeing. The telescope achieves high dynamic range very close to bright stellar sources with good image quality using pupil densification techniques. Active correction of the perturbed wavefront is simplified by using 36 small flat mirrors arranged in a parabolic steerable array structure, eliminating the need for large delat lines and operating at near-infrared (1 - 3 Micron) wavelengths with flats comparable in size to the seeing cells.

The food matrix affects the anthocyanin profile of fortified egg and dairy matrices during processing and in vitro digestion.

PubMed

Pineda-Vadillo, Carlos; Nau, Françoise; Guerin-Dubiard, Catherin; Jardin, Julien; Lechevalier, Valérie; Sanz-Buenhombre, Marisa; Guadarrama, Alberto; Tóth, Tamás; Csavajda, Éva; Hingyi, Hajnalka; Karakaya, Sibel; Sibakov, Juhani; Capozzi, Francesco; Bordoni, Alessandra; Dupont, Didier

2017-01-01

The aim of the present study was to understand to what extent the inclusion of anthocyanins into dairy and egg matrices could affect their stability after processing and their release and solubility during digestion. For this purpose, individual and total anthocyanin content of four different enriched matrices, namely custard dessert, milkshake, pancake and omelettete, was determined after their manufacturing and during in vitro digestion. Results showed that anthocyanin recovery after processing largely varied among matrices, mainly due to the treatments applied and the interactions developed with other food components. In terms of digestion, the present study showed that the inclusion of anthocyanins into food matrices could be an effective way to protect them against intestinal degradation, and also the incorporation of anthocyanins into matrices with different compositions and structures could represent an interesting and effective method to control the delivery of anthocyanins within the different compartments of the digestive tract. Copyright © 2016 Elsevier Ltd. All rights reserved.

Nonnegative matrix factorization and sparse representation for the automated detection of periodic limb movements in sleep.

PubMed

Shokrollahi, Mehrnaz; Krishnan, Sridhar; Dopsa, Dustin D; Muir, Ryan T; Black, Sandra E; Swartz, Richard H; Murray, Brian J; Boulos, Mark I

2016-11-01

Stroke is a leading cause of death and disability in adults, and incurs a significant economic burden to society. Periodic limb movements (PLMs) in sleep are repetitive movements involving the great toe, ankle, and hip. Evolving evidence suggests that PLMs may be associated with high blood pressure and stroke, but this relationship remains underexplored. Several issues limit the study of PLMs including the need to manually score them, which is time-consuming and costly. For this reason, we developed a novel automated method for nocturnal PLM detection, which was shown to be correlated with (a) the manually scored PLM index on polysomnography, and (b) white matter hyperintensities on brain imaging, which have been demonstrated to be associated with PLMs. Our proposed algorithm consists of three main stages: (1) representing the signal in the time-frequency plane using time-frequency matrices (TFM), (2) applying K-nonnegative matrix factorization technique to decompose the TFM matrix into its significant components, and (3) applying kernel sparse representation for classification (KSRC) to the decomposed signal. Our approach was applied to a dataset that consisted of 65 subjects who underwent polysomnography. An overall classification of 97 % was achieved for discrimination of the aforementioned signals, demonstrating the potential of the presented method.

A modified sparse reconstruction method for three-dimensional synthetic aperture radar image

NASA Astrophysics Data System (ADS)

Zhang, Ziqiang; Ji, Kefeng; Song, Haibo; Zou, Huanxin

2018-03-01

There is an increasing interest in three-dimensional Synthetic Aperture Radar (3-D SAR) imaging from observed sparse scattering data. However, the existing 3-D sparse imaging method requires large computing times and storage capacity. In this paper, we propose a modified method for the sparse 3-D SAR imaging. The method processes the collection of noisy SAR measurements, usually collected over nonlinear flight paths, and outputs 3-D SAR imagery. Firstly, the 3-D sparse reconstruction problem is transformed into a series of 2-D slices reconstruction problem by range compression. Then the slices are reconstructed by the modified SL0 (smoothed l0 norm) reconstruction algorithm. The improved algorithm uses hyperbolic tangent function instead of the Gaussian function to approximate the l0 norm and uses the Newton direction instead of the steepest descent direction, which can speed up the convergence rate of the SL0 algorithm. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm. It is shown that our method, compared with existing 3-D sparse imaging method, performs better in reconstruction quality and the reconstruction time.

Exploratory graphical models of functional and structural connectivity patterns for Alzheimer's Disease diagnosis.

PubMed

Ortiz, Andrés; Munilla, Jorge; Álvarez-Illán, Ignacio; Górriz, Juan M; Ramírez, Javier

2015-01-01

Alzheimer's Disease (AD) is the most common neurodegenerative disease in elderly people. Its development has been shown to be closely related to changes in the brain connectivity network and in the brain activation patterns along with structural changes caused by the neurodegenerative process. Methods to infer dependence between brain regions are usually derived from the analysis of covariance between activation levels in the different areas. However, these covariance-based methods are not able to estimate conditional independence between variables to factor out the influence of other regions. Conversely, models based on the inverse covariance, or precision matrix, such as Sparse Gaussian Graphical Models allow revealing conditional independence between regions by estimating the covariance between two variables given the rest as constant. This paper uses Sparse Inverse Covariance Estimation (SICE) methods to learn undirected graphs in order to derive functional and structural connectivity patterns from Fludeoxyglucose (18F-FDG) Position Emission Tomography (PET) data and segmented Magnetic Resonance images (MRI), drawn from the ADNI database, for Control, MCI (Mild Cognitive Impairment Subjects), and AD subjects. Sparse computation fits perfectly here as brain regions usually only interact with a few other areas. The models clearly show different metabolic covariation patters between subject groups, revealing the loss of strong connections in AD and MCI subjects when compared to Controls. Similarly, the variance between GM (Gray Matter) densities of different regions reveals different structural covariation patterns between the different groups. Thus, the different connectivity patterns for controls and AD are used in this paper to select regions of interest in PET and GM images with discriminative power for early AD diagnosis. Finally, functional an structural models are combined to leverage the classification accuracy. The results obtained in this work show the usefulness of the Sparse Gaussian Graphical models to reveal functional and structural connectivity patterns. This information provided by the sparse inverse covariance matrices is not only used in an exploratory way but we also propose a method to use it in a discriminative way. Regression coefficients are used to compute reconstruction errors for the different classes that are then introduced in a SVM for classification. Classification experiments performed using 68 Controls, 70 AD, and 111 MCI images and assessed by cross-validation show the effectiveness of the proposed method.

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.

Deep feature representation with stacked sparse auto-encoder and convolutional neural network for hyperspectral imaging-based detection of cucumber defects

USDA-ARS?s Scientific Manuscript database

It is challenging to achieve rapid and accurate processing of large amounts of hyperspectral image data. This research was aimed to develop a novel classification method by employing deep feature representation with the stacked sparse auto-encoder (SSAE) and the SSAE combined with convolutional neur...

Basal Cell Carcinoma With Matrical Differentiation: Clinicopathologic, Immunohistochemical, and Molecular Biological Study of 22 Cases.

PubMed

Kyrpychova, Liubov; Carr, Richard A; Martinek, Petr; Vanecek, Tomas; Perret, Raul; Chottová-Dvořáková, Magdalena; Zamecnik, Michal; Hadravsky, Ladislav; Michal, Michal; Kazakov, Dmitry V

2017-06-01

Basal cell carcinoma (BCC) with matrical differentiation is a fairly rare neoplasm, with about 30 cases documented mainly as isolated case reports. We studied a series of this neoplasm, including cases with an atypical matrical component, a hitherto unreported feature. Lesions coded as BCC with matrical differentiation were reviewed; 22 cases were included. Immunohistochemical studies were performed using antibodies against BerEp4, β-catenin, and epithelial membrane antigen (EMA). Molecular genetic studies using Ion AmpliSeq Cancer Hotspot Panel v2 by massively parallel sequencing on Ion Torrent PGM were performed in 2 cases with an atypical matrical component (1 was previously subjected to microdissection to sample the matrical and BCC areas separately). There were 13 male and 9 female patients, ranging in age from 41 to 89 years. Microscopically, all lesions manifested at least 2 components, a BCC area (follicular germinative differentiation) and areas with matrical differentiation. A BCC component dominated in 14 cases, whereas a matrical component dominated in 4 cases. Matrical differentiation was recognized as matrical/supramatrical cells (n=21), shadow cells (n=21), bright red trichohyaline granules (n=18), and blue-gray corneocytes (n=18). In 2 cases, matrical areas manifested cytologic atypia, and a third case exhibited an infiltrative growth pattern, with the tumor metastasizing to a lymph node. BerEP4 labeled the follicular germinative cells, whereas it was markedly reduced or negative in matrical areas. The reverse pattern was seen with β-catenin. EMA was negative in BCC areas but stained a proportion of matrical/supramatrical cells. Genetic studies revealed mutations of the following genes: CTNNB1, KIT, CDKN2A, TP53, SMAD4, ERBB4, and PTCH1, with some differences between the matrical and BCC components. It is concluded that matrical differentiation in BCC in most cases occurs as multiple foci. Rare neoplasms manifest atypia in the matrical areas. Immunohistochemical analysis for BerEP4, EMA, and β-catenin can be helpful in limited biopsy specimens. From a molecular biological prospective, BCC and matrical components appear to share some of the gene mutations but have differences in others, but this observation must be validated in a large series.

Optimal neighborhood indexing for protein similarity search.

PubMed

Peterlongo, Pierre; Noé, Laurent; Lavenier, Dominique; Nguyen, Van Hoa; Kucherov, Gregory; Giraud, Mathieu

2008-12-16

Similarity inference, one of the main bioinformatics tasks, has to face an exponential growth of the biological data. A classical approach used to cope with this data flow involves heuristics with large seed indexes. In order to speed up this technique, the index can be enhanced by storing additional information to limit the number of random memory accesses. However, this improvement leads to a larger index that may become a bottleneck. In the case of protein similarity search, we propose to decrease the index size by reducing the amino acid alphabet. The paper presents two main contributions. First, we show that an optimal neighborhood indexing combining an alphabet reduction and a longer neighborhood leads to a reduction of 35% of memory involved into the process, without sacrificing the quality of results nor the computational time. Second, our approach led us to develop a new kind of substitution score matrices and their associated e-value parameters. In contrast to usual matrices, these matrices are rectangular since they compare amino acid groups from different alphabets. We describe the method used for computing those matrices and we provide some typical examples that can be used in such comparisons. Supplementary data can be found on the website http://bioinfo.lifl.fr/reblosum. We propose a practical index size reduction of the neighborhood data, that does not negatively affect the performance of large-scale search in protein sequences. Such an index can be used in any study involving large protein data. Moreover, rectangular substitution score matrices and their associated statistical parameters can have applications in any study involving an alphabet reduction.

Optimal neighborhood indexing for protein similarity search

PubMed Central

Peterlongo, Pierre; Noé, Laurent; Lavenier, Dominique; Nguyen, Van Hoa; Kucherov, Gregory; Giraud, Mathieu

2008-01-01

Background Similarity inference, one of the main bioinformatics tasks, has to face an exponential growth of the biological data. A classical approach used to cope with this data flow involves heuristics with large seed indexes. In order to speed up this technique, the index can be enhanced by storing additional information to limit the number of random memory accesses. However, this improvement leads to a larger index that may become a bottleneck. In the case of protein similarity search, we propose to decrease the index size by reducing the amino acid alphabet. Results The paper presents two main contributions. First, we show that an optimal neighborhood indexing combining an alphabet reduction and a longer neighborhood leads to a reduction of 35% of memory involved into the process, without sacrificing the quality of results nor the computational time. Second, our approach led us to develop a new kind of substitution score matrices and their associated e-value parameters. In contrast to usual matrices, these matrices are rectangular since they compare amino acid groups from different alphabets. We describe the method used for computing those matrices and we provide some typical examples that can be used in such comparisons. Supplementary data can be found on the website . Conclusion We propose a practical index size reduction of the neighborhood data, that does not negatively affect the performance of large-scale search in protein sequences. Such an index can be used in any study involving large protein data. Moreover, rectangular substitution score matrices and their associated statistical parameters can have applications in any study involving an alphabet reduction. PMID:19087280

Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

NASA Astrophysics Data System (ADS)

Náprstek, J.; Král, R.

2016-09-01

The Fokker-Planck equation (FPE) is a frequently used tool for the solution of cross probability density function (PDF) of a dynamic system response excited by a vector of random processes. FEM represents a very effective solution possibility, particularly when transition processes are investigated or a more detailed solution is needed. Actual papers deal with single degree of freedom (SDOF) systems only. So the respective FPE includes two independent space variables only. Stepping over this limit into MDOF systems a number of specific problems related to a true multi-dimensionality must be overcome. Unlike earlier studies, multi-dimensional simplex elements in any arbitrary dimension should be deployed and rectangular (multi-brick) elements abandoned. Simple closed formulae of integration in multi-dimension domain have been derived. Another specific problem represents the generation of multi-dimensional finite element mesh. Assembling of system global matrices should be subjected to newly composed algorithms due to multi-dimensionality. The system matrices are quite full and no advantages following from their sparse character can be profited from, as is commonly used in conventional FEM applications in 2D/3D problems. After verification of partial algorithms, an illustrative example dealing with a 2DOF non-linear aeroelastic system in combination with random and deterministic excitations is discussed.

Compressed sensing with cyclic-S Hadamard matrix for terahertz imaging applications

NASA Astrophysics Data System (ADS)

Ermeydan, Esra Şengün; ćankaya, Ilyas

2018-01-01

Compressed Sensing (CS) with Cyclic-S Hadamard matrix is proposed for single pixel imaging applications in this study. In single pixel imaging scheme, N = r . c samples should be taken for r×c pixel image where . denotes multiplication. CS is a popular technique claiming that the sparse signals can be reconstructed with samples under Nyquist rate. Therefore to solve the slow data acquisition problem in Terahertz (THz) single pixel imaging, CS is a good candidate. However, changing mask for each measurement is a challenging problem since there is no commercial Spatial Light Modulators (SLM) for THz band yet, therefore circular masks are suggested so that for each measurement one or two column shifting will be enough to change the mask. The CS masks are designed using cyclic-S matrices based on Hadamard transform for 9 × 7 and 15 × 17 pixel images within the framework of this study. The %50 compressed images are reconstructed using total variation based TVAL3 algorithm. Matlab simulations demonstrates that cyclic-S matrices can be used for single pixel imaging based on CS. The circular masks have the advantage to reduce the mechanical SLMs to a single sliding strip, whereas the CS helps to reduce acquisition time and energy since it allows to reconstruct the image from fewer samples.

Compound matrices

NASA Astrophysics Data System (ADS)

Kravvaritis, Christos; Mitrouli, Marilena

2009-02-01

This paper studies the possibility to calculate efficiently compounds of real matrices which have a special form or structure. The usefulness of such an effort lies in the fact that the computation of compound matrices, which is generally noneffective due to its high complexity, is encountered in several applications. A new approach for computing the Singular Value Decompositions (SVD's) of the compounds of a matrix is proposed by establishing the equality (up to a permutation) between the compounds of the SVD of a matrix and the SVD's of the compounds of the matrix. The superiority of the new idea over the standard method is demonstrated. Similar approaches with some limitations can be adopted for other matrix factorizations, too. Furthermore, formulas for the n - 1 compounds of Hadamard matrices are derived, which dodge the strenuous computations of the respective numerous large determinants. Finally, a combinatorial counting technique for finding the compounds of diagonal matrices is illustrated.

Three-dimensional polarization algebra.

PubMed

R Sheppard, Colin J; Castello, Marco; Diaspro, Alberto

2016-10-01

If light is focused or collected with a high numerical aperture lens, as may occur in imaging and optical encryption applications, polarization should be considered in three dimensions (3D). The matrix algebra of polarization behavior in 3D is discussed. It is useful to convert between the Mueller matrix and two different Hermitian matrices, representing an optical material or system, which are in the literature. Explicit transformation matrices for converting the column vector form of these different matrices are extended to the 3D case, where they are large (81×81) but can be generated using simple rules. It is found that there is some advantage in using a generalization of the Chandrasekhar phase matrix treatment, rather than that based on Gell-Mann matrices, as the resultant matrices are of simpler form and reduce to the two-dimensional case more easily. Explicit expressions are given for 3D complex field components in terms of Chandrasekhar-Stokes parameters.

Regularized Embedded Multiple Kernel Dimensionality Reduction for Mine Signal Processing.

PubMed

Li, Shuang; Liu, Bing; Zhang, Chen

2016-01-01

Traditional multiple kernel dimensionality reduction models are generally based on graph embedding and manifold assumption. But such assumption might be invalid for some high-dimensional or sparse data due to the curse of dimensionality, which has a negative influence on the performance of multiple kernel learning. In addition, some models might be ill-posed if the rank of matrices in their objective functions was not high enough. To address these issues, we extend the traditional graph embedding framework and propose a novel regularized embedded multiple kernel dimensionality reduction method. Different from the conventional convex relaxation technique, the proposed algorithm directly takes advantage of a binary search and an alternative optimization scheme to obtain optimal solutions efficiently. The experimental results demonstrate the effectiveness of the proposed method for supervised, unsupervised, and semisupervised scenarios.

Optimal interpolation and the Kalman filter. [for analysis of numerical weather predictions

NASA Technical Reports Server (NTRS)

Cohn, S.; Isaacson, E.; Ghil, M.

1981-01-01

The estimation theory of stochastic-dynamic systems is described and used in a numerical study of optimal interpolation. The general form of data assimilation methods is reviewed. The Kalman-Bucy, KB filter, and optimal interpolation (OI) filters are examined for effectiveness in performance as gain matrices using a one-dimensional form of the shallow-water equations. Control runs in the numerical analyses were performed for a ten-day forecast in concert with the OI method. The effects of optimality, initialization, and assimilation were studied. It was found that correct initialization is necessary in order to localize errors, especially near boundary points. Also, the use of small forecast error growth rates over data-sparse areas was determined to offset inaccurate modeling of correlation functions near boundaries.

Comparability of item quality indices from sparse data matrices with random and non-random missing data patterns.

PubMed

Wolfe, Edward W; McGill, Michael T

2011-01-01

This article summarizes a simulation study of the performance of five item quality indicators (the weighted and unweighted versions of the mean square and standardized mean square fit indices and the point-measure correlation) under conditions of relatively high and low amounts of missing data under both random and conditional patterns of missing data for testing contexts such as those encountered in operational administrations of a computerized adaptive certification or licensure examination. The results suggest that weighted fit indices, particularly the standardized mean square index, and the point-measure correlation provide the most consistent information between random and conditional missing data patterns and that these indices perform more comparably for items near the passing score than for items with extreme difficulty values.

History of the Nuclei Important for Cosmochemistry

NASA Technical Reports Server (NTRS)

Meyer, Bradley S.

2004-01-01

An essential aspect of studying the nuclei important for cosmochemistry is their production in stars. Over the grant period, we have further developed the Clemson/American University of Beirut stellar evolution code. Through use of a biconjugate-gradient matrix solver, we now routinely solve l0(exp 6) x l0(exp 6) sparse matrices on our desktop computers. This has allowed us to couple nucleosynthesis and convection fully in the 1-D star, which, in turn, provides better estimates of nuclear yields when the mixing and nuclear burning timescales are comparable. We also have incorporated radiation transport into our 1-D supernova explosion code. We used the stellar evolution and explosion codes to compute iron abundances in a 25 Solar mass star and compared the results to data from RIMS.

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map.

PubMed

Park, Wooram; Liu, Yan; Zhou, Yu; Moses, Matthew; Chirikjian, Gregory S

2008-04-11

A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker-Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.

Lecture Notes on Multigrid Methods

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

Vassilevski, P S

The Lecture Notes are primarily based on a sequence of lectures given by the author while been a Fulbright scholar at 'St. Kliment Ohridski' University of Sofia, Sofia, Bulgaria during the winter semester of 2009-2010 academic year. The notes are somewhat expanded version of the actual one semester class he taught there. The material covered is slightly modified and adapted version of similar topics covered in the author's monograph 'Multilevel Block-Factorization Preconditioners' published in 2008 by Springer. The author tried to keep the notes as self-contained as possible. That is why the lecture notes begin with some basic introductory matrix-vectormore » linear algebra, numerical PDEs (finite element) facts emphasizing the relations between functions in finite dimensional spaces and their coefficient vectors and respective norms. Then, some additional facts on the implementation of finite elements based on relation tables using the popular compressed sparse row (CSR) format are given. Also, typical condition number estimates of stiffness and mass matrices, the global matrix assembly from local element matrices are given as well. Finally, some basic introductory facts about stationary iterative methods, such as Gauss-Seidel and its symmetrized version are presented. The introductory material ends up with the smoothing property of the classical iterative methods and the main definition of two-grid iterative methods. From here on, the second part of the notes begins which deals with the various aspects of the principal TG and the numerous versions of the MG cycles. At the end, in part III, we briefly introduce algebraic versions of MG referred to as AMG, focusing on classes of AMG specialized for finite element matrices.« less

Recursive partitioned inversion of large (1500 x 1500) symmetric matrices

NASA Technical Reports Server (NTRS)

Putney, B. H.; Brownd, J. E.; Gomez, R. A.

1976-01-01

A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.

Bayesian sparse channel estimation

NASA Astrophysics Data System (ADS)

Chen, Chulong; Zoltowski, Michael D.

2012-05-01

In Orthogonal Frequency Division Multiplexing (OFDM) systems, the technique used to estimate and track the time-varying multipath channel is critical to ensure reliable, high data rate communications. It is recognized that wireless channels often exhibit a sparse structure, especially for wideband and ultra-wideband systems. In order to exploit this sparse structure to reduce the number of pilot tones and increase the channel estimation quality, the application of compressed sensing to channel estimation is proposed. In this article, to make the compressed channel estimation more feasible for practical applications, it is investigated from a perspective of Bayesian learning. Under the Bayesian learning framework, the large-scale compressed sensing problem, as well as large time delay for the estimation of the doubly selective channel over multiple consecutive OFDM symbols, can be avoided. Simulation studies show a significant improvement in channel estimation MSE and less computing time compared to the conventional compressed channel estimation techniques.

Fine structure of spectral properties for random correlation matrices: An application to financial markets

NASA Astrophysics Data System (ADS)

Livan, Giacomo; Alfarano, Simone; Scalas, Enrico

2011-07-01

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

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.

Sparse partial least squares regression for simultaneous dimension reduction and variable selection

PubMed Central

Chun, Hyonho; Keleş, Sündüz

2010-01-01

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data. PMID:20107611

Synaptic and Network Mechanisms of Sparse and Reliable Visual Cortical Activity during Nonclassical Receptive Field Stimulation

PubMed Central

Haider, Bilal; Krause, Matthew R.; Duque, Alvaro; Yu, Yuguo; Touryan, Jonathan; Mazer, James A.; McCormick, David A.

2011-01-01

SUMMARY During natural vision, the entire visual field is stimulated by images rich in spatiotemporal structure. Although many visual system studies restrict stimuli to the classical receptive field (CRF), it is known that costimulation of the CRF and the surrounding nonclassical receptive field (nCRF) increases neuronal response sparseness. The cellular and network mechanisms underlying increased response sparseness remain largely unexplored. Here we show that combined CRF + nCRF stimulation increases the sparseness, reliability, and precision of spiking and membrane potential responses in classical regular spiking (RSC) pyramidal neurons of cat primary visual cortex. Conversely, fast-spiking interneurons exhibit increased activity and decreased selectivity during CRF + nCRF stimulation. The increased sparseness and reliability of RSC neuron spiking is associated with increased inhibitory barrages and narrower visually evoked synaptic potentials. Our experimental observations were replicated with a simple computational model, suggesting that network interactions among neuronal subtypes ultimately sharpen recurrent excitation, producing specific and reliable visual responses. PMID:20152117

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering

PubMed Central

Sicat, Ronell; Krüger, Jens; Möller, Torsten; Hadwiger, Markus

2015-01-01

This paper presents a new multi-resolution volume representation called sparse pdf volumes, which enables consistent multi-resolution volume rendering based on probability density functions (pdfs) of voxel neighborhoods. These pdfs are defined in the 4D domain jointly comprising the 3D volume and its 1D intensity range. Crucially, the computation of sparse pdf volumes exploits data coherence in 4D, resulting in a sparse representation with surprisingly low storage requirements. At run time, we dynamically apply transfer functions to the pdfs using simple and fast convolutions. Whereas standard low-pass filtering and down-sampling incur visible differences between resolution levels, the use of pdfs facilitates consistent results independent of the resolution level used. We describe the efficient out-of-core computation of large-scale sparse pdf volumes, using a novel iterative simplification procedure of a mixture of 4D Gaussians. Finally, our data structure is optimized to facilitate interactive multi-resolution volume rendering on GPUs. PMID:26146475

Recognizing the ‘sparsely settled forest’: Multi-decade socioecological change dynamics and community exemplars

Treesearch

Derek B. Van Berkel; Bronwyn Rayfield; Sebastián Martinuzzi; Martin J. Lechowicz; Eric White; Kathleen P. Bell; Chris R. Colocousis; Kent F. Kovacs; Anita T. Morzillo; Darla K. Munroe; Benoit Parmentier; Volker C. Radeloff; Brian J. McGill

2018-01-01

Sparsely settled forests (SSF) are poorly studied, coupled natural and human systems involving rural communities in forest ecosystems that are neither largely uninhabited wildland nor forests on the edges of urban areas. We developed and applied a multidisciplinary approach to define, map, and examine changes in the spatial extent and structure of both the landscapes...

Energy Balanced Strategies for Maximizing the Lifetime of Sparsely Deployed Underwater Acoustic Sensor Networks

PubMed Central

Luo, Hanjiang; Guo, Zhongwen; Wu, Kaishun; Hong, Feng; Feng, Yuan

2009-01-01

Underwater acoustic sensor networks (UWA-SNs) are envisioned to perform monitoring tasks over the large portion of the world covered by oceans. Due to economics and the large area of the ocean, UWA-SNs are mainly sparsely deployed networks nowadays. The limited battery resources is a big challenge for the deployment of such long-term sensor networks. Unbalanced battery energy consumption will lead to early energy depletion of nodes, which partitions the whole networks and impairs the integrity of the monitoring datasets or even results in the collapse of the entire networks. On the contrary, balanced energy dissipation of nodes can prolong the lifetime of such networks. In this paper, we focus on the energy balance dissipation problem of two types of sparsely deployed UWA-SNs: underwater moored monitoring systems and sparsely deployed two-dimensional UWA-SNs. We first analyze the reasons of unbalanced energy consumption in such networks, then we propose two energy balanced strategies to maximize the lifetime of networks both in shallow and deep water. Finally, we evaluate our methods by simulations and the results show that the two strategies can achieve balanced energy consumption per node while at the same time prolong the networks lifetime. PMID:22399970

Comparison of Different Matrices as Potential Quality Control Samples for Neurochemical Dementia Diagnostics.

PubMed

Lelental, Natalia; Brandner, Sebastian; Kofanova, Olga; Blennow, Kaj; Zetterberg, Henrik; Andreasson, Ulf; Engelborghs, Sebastiaan; Mroczko, Barbara; Gabryelewicz, Tomasz; Teunissen, Charlotte; Mollenhauer, Brit; Parnetti, Lucilla; Chiasserini, Davide; Molinuevo, Jose Luis; Perret-Liaudet, Armand; Verbeek, Marcel M; Andreasen, Niels; Brosseron, Frederic; Bahl, Justyna M C; Herukka, Sanna-Kaisa; Hausner, Lucrezia; Frölich, Lutz; Labonte, Anne; Poirier, Judes; Miller, Anne-Marie; Zilka, Norbert; Kovacech, Branislav; Urbani, Andrea; Suardi, Silvia; Oliveira, Catarina; Baldeiras, Ines; Dubois, Bruno; Rot, Uros; Lehmann, Sylvain; Skinningsrud, Anders; Betsou, Fay; Wiltfang, Jens; Gkatzima, Olymbia; Winblad, Bengt; Buchfelder, Michael; Kornhuber, Johannes; Lewczuk, Piotr

2016-03-01

Assay-vendor independent quality control (QC) samples for neurochemical dementia diagnostics (NDD) biomarkers are so far commercially unavailable. This requires that NDD laboratories prepare their own QC samples, for example by pooling leftover cerebrospinal fluid (CSF) samples. To prepare and test alternative matrices for QC samples that could facilitate intra- and inter-laboratory QC of the NDD biomarkers. Three matrices were validated in this study: (A) human pooled CSF, (B) Aβ peptides spiked into human prediluted plasma, and (C) Aβ peptides spiked into solution of bovine serum albumin in phosphate-buffered saline. All matrices were tested also after supplementation with an antibacterial agent (sodium azide). We analyzed short- and long-term stability of the biomarkers with ELISA and chemiluminescence (Fujirebio Europe, MSD, IBL International), and performed an inter-laboratory variability study. NDD biomarkers turned out to be stable in almost all samples stored at the tested conditions for up to 14 days as well as in samples stored deep-frozen (at - 80°C) for up to one year. Sodium azide did not influence biomarker stability. Inter-center variability of the samples sent at room temperature (pooled CSF, freeze-dried CSF, and four artificial matrices) was comparable to the results obtained on deep-frozen samples in other large-scale projects. Our results suggest that it is possible to replace self-made, CSF-based QC samples with large-scale volumes of QC materials prepared with artificial peptides and matrices. This would greatly facilitate intra- and inter-laboratory QC schedules for NDD measurements.

Discrete Sparse Coding.

PubMed

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

Fast evaluation of scaled opposite spin second-order Møller-Plesset correlation energies using auxiliary basis expansions and exploiting sparsity.

PubMed

Jung, Yousung; Shao, Yihan; Head-Gordon, Martin

2007-09-01

The scaled opposite spin Møller-Plesset method (SOS-MP2) is an economical way of obtaining correlation energies that are computationally cheaper, and yet, in a statistical sense, of higher quality than standard MP2 theory, by introducing one empirical parameter. But SOS-MP2 still has a fourth-order scaling step that makes the method inapplicable to very large molecular systems. We reduce the scaling of SOS-MP2 by exploiting the sparsity of expansion coefficients and local integral matrices, by performing local auxiliary basis expansions for the occupied-virtual product distributions. To exploit sparsity of 3-index local quantities, we use a blocking scheme in which entire zero-rows and columns, for a given third global index, are deleted by comparison against a numerical threshold. This approach minimizes sparse matrix book-keeping overhead, and also provides sufficiently large submatrices after blocking, to allow efficient matrix-matrix multiplies. The resulting algorithm is formally cubic scaling, and requires only moderate computational resources (quadratic memory and disk space) and, in favorable cases, is shown to yield effective quadratic scaling behavior in the size regime we can apply it to. Errors associated with local fitting using the attenuated Coulomb metric and numerical thresholds in the blocking procedure are found to be insignificant in terms of the predicted relative energies. A diverse set of test calculations shows that the size of system where significant computational savings can be achieved depends strongly on the dimensionality of the system, and the extent of localizability of the molecular orbitals. Copyright 2007 Wiley Periodicals, Inc.

Sparse distributed memory overview

NASA Technical Reports Server (NTRS)

Raugh, Mike

1990-01-01

The Sparse Distributed Memory (SDM) project is investigating the theory and applications of massively parallel computing architecture, called sparse distributed memory, that will support the storage and retrieval of sensory and motor patterns characteristic of autonomous systems. The immediate objectives of the project are centered in studies of the memory itself and in the use of the memory to solve problems in speech, vision, and robotics. Investigation of methods for encoding sensory data is an important part of the research. Examples of NASA missions that may benefit from this work are Space Station, planetary rovers, and solar exploration. Sparse distributed memory offers promising technology for systems that must learn through experience and be capable of adapting to new circumstances, and for operating any large complex system requiring automatic monitoring and control. Sparse distributed memory is a massively parallel architecture motivated by efforts to understand how the human brain works. Sparse distributed memory is an associative memory, able to retrieve information from cues that only partially match patterns stored in the memory. It is able to store long temporal sequences derived from the behavior of a complex system, such as progressive records of the system's sensory data and correlated records of the system's motor controls.

Reconstructing cortical current density by exploring sparseness in the transform domain

NASA Astrophysics Data System (ADS)

Ding, Lei

2009-05-01

In the present study, we have developed a novel electromagnetic source imaging approach to reconstruct extended cortical sources by means of cortical current density (CCD) modeling and a novel EEG imaging algorithm which explores sparseness in cortical source representations through the use of L1-norm in objective functions. The new sparse cortical current density (SCCD) imaging algorithm is unique since it reconstructs cortical sources by attaining sparseness in a transform domain (the variation map of cortical source distributions). While large variations are expected to occur along boundaries (sparseness) between active and inactive cortical regions, cortical sources can be reconstructed and their spatial extents can be estimated by locating these boundaries. We studied the SCCD algorithm using numerous simulations to investigate its capability in reconstructing cortical sources with different extents and in reconstructing multiple cortical sources with different extent contrasts. The SCCD algorithm was compared with two L2-norm solutions, i.e. weighted minimum norm estimate (wMNE) and cortical LORETA. Our simulation data from the comparison study show that the proposed sparse source imaging algorithm is able to accurately and efficiently recover extended cortical sources and is promising to provide high-accuracy estimation of cortical source extents.

Sparse ice: Geophysical, biological and Indigenous knowledge perspectives on a habitat for ice-associated fauna

NASA Astrophysics Data System (ADS)

Lee, O. A.; Eicken, H.; Weyapuk, W., Jr.; Adams, B.; Mohoney, A. R.

2015-12-01

The significance of highly dispersed, remnant Arctic sea ice as a platform for marine mammals and indigenous hunters in spring and summer may have increased disproportionately with changes in the ice cover. As dispersed remnant ice becomes more common in the future it will be increasingly important to understand its ecological role for upper trophic levels such as marine mammals and its role for supporting primary productivity of ice-associated algae. Potential sparse ice habitat at sea ice concentrations below 15% is difficult to detect using remote sensing data alone. A combination of high resolution satellite imagery (including Synthetic Aperture Radar), data from the Barrow sea ice radar, and local observations from indigenous sea ice experts was used to detect sparse sea ice in the Alaska Arctic. Traditional knowledge on sea ice use by marine mammals was used to delimit the scales where sparse ice could still be used as habitat for seals and walrus. Potential sparse ice habitat was quantified with respect to overall spatial extent, size of ice floes, and density of floes. Sparse ice persistence offshore did not prevent the occurrence of large coastal walrus haul outs, but the lack of sparse ice and early sea ice retreat coincided with local observations of ringed seal pup mortality. Observations from indigenous hunters will continue to be an important source of information for validating remote sensing detections of sparse ice, and improving understanding of marine mammal adaptations to sea ice change.

Structures and textures of the Murchison and Mighei carbonaceous chondrite matrices

NASA Technical Reports Server (NTRS)

Mackinnon, I. D. R.

1980-01-01

High-resolution transmission electron microscopy has confirmed earlier observations that the character of the Murchison and Mighei fine-grained matrices is complex in mineralogy and texture. Layer structure minerals occur as planar laths, rounded grains or subhedral grains, and range in size from less than 100 A to about 1 micrometer. Serpentine-type and brucite-type structures predominate in the CM matrices. The occurrence of Povlen chrysolite and a vein of disordered mixed-layer and brucite-type material cutting a large lizardite-type grain suggests that at least some of the matrix materials were formed by alteration of preexisting material.

Efficient similarity-based data clustering by optimal object to cluster reallocation.

PubMed

Rossignol, Mathias; Lagrange, Mathieu; Cont, Arshia

2018-01-01

We present an iterative flat hard clustering algorithm designed to operate on arbitrary similarity matrices, with the only constraint that these matrices be symmetrical. Although functionally very close to kernel k-means, our proposal performs a maximization of average intra-class similarity, instead of a squared distance minimization, in order to remain closer to the semantics of similarities. We show that this approach permits the relaxing of some conditions on usable affinity matrices like semi-positiveness, as well as opening possibilities for computational optimization required for large datasets. Systematic evaluation on a variety of data sets shows that compared with kernel k-means and the spectral clustering methods, the proposed approach gives equivalent or better performance, while running much faster. Most notably, it significantly reduces memory access, which makes it a good choice for large data collections. Material enabling the reproducibility of the results is made available online.

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

Concurrent and Predictive Validity of the Raven Progressive Matrices and the Naglieri Nonverbal Ability Test

ERIC Educational Resources Information Center

Balboni, Giulia; Naglieri, Jack A.; Cubelli, Roberto

2010-01-01

The concurrent and predictive validities of the Naglieri Nonverbal Ability Test (NNAT) and Raven's Colored Progressive Matrices (CPM) were investigated in a large group of Italian third-and fifth-grade students with different sociocultural levels evaluated at the beginning and end of the school year. CPM and NNAT scores were related to math and…

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.

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.

Hierarchical matrices implemented into the boundary integral approaches for gravity field modelling

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Vipiana, Francesca

2017-04-01

Boundary integral approaches applied for gravity field modelling have been recently developed to solve the geodetic boundary value problems numerically, or to process satellite observations, e.g. from the GOCE satellite mission. In order to obtain numerical solutions of "cm-level" accuracy, such approaches require very refined level of the disretization or resolution. This leads to enormous memory requirements that need to be reduced. An implementation of the Hierarchical Matrices (H-matrices) can significantly reduce a numerical complexity of these approaches. A main idea of the H-matrices is based on an approximation of the entire system matrix that is split into a family of submatrices. Large submatrices are stored in factorized representation, while small submatrices are stored in standard representation. This allows reducing memory requirements significantly while improving the efficiency. The poster presents our preliminary results of implementations of the H-matrices into the existing boundary integral approaches based on the boundary element method or the method of fundamental solution.

Efficient large-scale graph data optimization for intelligent video surveillance

NASA Astrophysics Data System (ADS)

Shang, Quanhong; Zhang, Shujun; Wang, Yanbo; Sun, Chen; Wang, Zepeng; Zhang, Luming

2017-08-01

Society is rapidly accepting the use of a wide variety of cameras Location and applications: site traffic monitoring, parking Lot surveillance, car and smart space. These ones here the camera provides data every day in an analysis Effective way. Recent advances in sensor technology Manufacturing, communications and computing are stimulating.The development of new applications that can change the traditional Vision system incorporating universal smart camera network. This Analysis of visual cues in multi camera networks makes wide Applications ranging from smart home and office automation to large area surveillance and traffic surveillance. In addition, dense Camera networks, most of which have large overlapping areas of cameras. In the view of good research, we focus on sparse camera networks. One Sparse camera network using large area surveillance. As few cameras as possible, most cameras do not overlap Each other’s field of vision. This task is challenging Lack of knowledge of topology Network, the specific changes in appearance and movement Track different opinions of the target, as well as difficulties Understanding complex events in a network. In this review in this paper, we present a comprehensive survey of recent studies Results to solve the problem of topology learning, Object appearance modeling and global activity understanding sparse camera network. In addition, some of the current open Research issues are discussed.

Graph theory approach to the eigenvalue problem of large space structures

NASA Technical Reports Server (NTRS)

Reddy, A. S. S. R.; Bainum, P. M.

1981-01-01

Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.

A critical analysis of computational protein design with sparse residue interaction graphs

PubMed Central

Georgiev, Ivelin S.

2017-01-01

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies. PMID:28358804

Rare-event statistics and modular invariance

NASA Astrophysics Data System (ADS)

Nechaev, S. K.; Polovnikov, K.

2018-01-01

Simple geometric arguments based on constructing the Euclid orchard are presented, which explain the equivalence of various types of distributions that result from rare-event statistics. In particular, the spectral density of the exponentially weighted ensemble of linear polymer chains is examined for its number-theoretic properties. It can be shown that the eigenvalue statistics of the corresponding adjacency matrices in the sparse regime show a peculiar hierarchical structure and are described by the popcorn (Thomae) function discontinuous in the dense set of rational numbers. Moreover, the spectral edge density distribution exhibits Lifshitz tails, reminiscent of 1D Anderson localization. Finally, a continuous approximation for the popcorn function is suggested based on the Dedekind η-function, and the hierarchical ultrametric structure of the popcorn-like distributions is demonstrated to be related to hidden SL(2,Z) modular symmetry.

Jacobi spectral Galerkin method for elliptic Neumann problems

NASA Astrophysics Data System (ADS)

Doha, E.; Bhrawy, A.; Abd-Elhameed, W.

2009-01-01

This paper is concerned with fast spectral-Galerkin Jacobi algorithms for solving one- and two-dimensional elliptic equations with homogeneous and nonhomogeneous Neumann boundary conditions. The paper extends the algorithms proposed by Shen (SIAM J Sci Comput 15:1489-1505, 1994) and Auteri et al. (J Comput Phys 185:427-444, 2003), based on Legendre polynomials, to Jacobi polynomials with arbitrary α and β. The key to the efficiency of our algorithms is to construct appropriate basis functions with zero slope at the endpoints, which lead to systems with sparse matrices for the discrete variational formulations. The direct solution algorithm developed for the homogeneous Neumann problem in two-dimensions relies upon a tensor product process. Nonhomogeneous Neumann data are accounted for by means of a lifting. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented.

Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric.

PubMed

Luenser, Arne; Schurkus, Henry F; Ochsenfeld, Christian

2017-04-11

A reformulation of the random phase approximation within the resolution-of-the-identity (RI) scheme is presented, that is competitive to canonical molecular orbital RI-RPA already for small- to medium-sized molecules. For electronically sparse systems drastic speedups due to the reduced scaling behavior compared to the molecular orbital formulation are demonstrated. Our reformulation is based on two ideas, which are independently useful: First, a Cholesky decomposition of density matrices that reduces the scaling with basis set size for a fixed-size molecule by one order, leading to massive performance improvements. Second, replacement of the overlap RI metric used in the original AO-RPA by an attenuated Coulomb metric. Accuracy is significantly improved compared to the overlap metric, while locality and sparsity of the integrals are retained, as is the effective linear scaling behavior.

Direct numerical simulation of incompressible axisymmetric flows

NASA Technical Reports Server (NTRS)

Loulou, Patrick

1994-01-01

In the present work, we propose to conduct direct numerical simulations (DNS) of incompressible turbulent axisymmetric jets and wakes. The objectives of the study are to understand the fundamental behavior of axisymmetric jets and wakes, which are perhaps the most technologically relevant free shear flows (e.g. combuster injectors, propulsion jet). Among the data to be generated are various statistical quantities of importance in turbulence modeling, like the mean velocity, turbulent stresses, and all the terms in the Reynolds-stress balance equations. In addition, we will be interested in the evolution of large-scale structures that are common in free shear flow. The axisymmetric jet or wake is also a good problem in which to try the newly developed b-spline numerical method. Using b-splines as interpolating functions in the non-periodic direction offers many advantages. B-splines have local support, which leads to sparse matrices that can be efficiently stored and solved. Also, they offer spectral-like accuracy that are C(exp O-1) continuous, where O is the order of the spline used; this means that derivatives of the velocity such as the vorticity are smoothly and accurately represented. For purposes of validation against existing results, the present code will also be able to simulate internal flows (ones that require a no-slip boundary condition). Implementation of no-slip boundary condition is trivial in the context of the b-splines.

Robust k-mer frequency estimation using gapped k-mers

PubMed Central

Ghandi, Mahmoud; Mohammad-Noori, Morteza

2013-01-01

Oligomers of fixed length, k, commonly known as k-mers, are often used as fundamental elements in the description of DNA sequence features of diverse biological function, or as intermediate elements in the constuction of more complex descriptors of sequence features such as position weight matrices. k-mers are very useful as general sequence features because they constitute a complete and unbiased feature set, and do not require parameterization based on incomplete knowledge of biological mechanisms. However, a fundamental limitation in the use of k-mers as sequence features is that as k is increased, larger spatial correlations in DNA sequence elements can be described, but the frequency of observing any specific k-mer becomes very small, and rapidly approaches a sparse matrix of binary counts. Thus any statistical learning approach using k-mers will be susceptible to noisy estimation of k-mer frequencies once k becomes large. Because all molecular DNA interactions have limited spatial extent, gapped k-mers often carry the relevant biological signal. Here we use gapped k-mer counts to more robustly estimate the ungapped k-mer frequencies, by deriving an equation for the minimum norm estimate of k-mer frequencies given an observed set of gapped k-mer frequencies. We demonstrate that this approach provides a more accurate estimate of the k-mer frequencies in real biological sequences using a sample of CTCF binding sites in the human genome. PMID:23861010

Robust k-mer frequency estimation using gapped k-mers.

PubMed

Ghandi, Mahmoud; Mohammad-Noori, Morteza; Beer, Michael A

2014-08-01

Oligomers of fixed length, k, commonly known as k-mers, are often used as fundamental elements in the description of DNA sequence features of diverse biological function, or as intermediate elements in the constuction of more complex descriptors of sequence features such as position weight matrices. k-mers are very useful as general sequence features because they constitute a complete and unbiased feature set, and do not require parameterization based on incomplete knowledge of biological mechanisms. However, a fundamental limitation in the use of k-mers as sequence features is that as k is increased, larger spatial correlations in DNA sequence elements can be described, but the frequency of observing any specific k-mer becomes very small, and rapidly approaches a sparse matrix of binary counts. Thus any statistical learning approach using k-mers will be susceptible to noisy estimation of k-mer frequencies once k becomes large. Because all molecular DNA interactions have limited spatial extent, gapped k-mers often carry the relevant biological signal. Here we use gapped k-mer counts to more robustly estimate the ungapped k-mer frequencies, by deriving an equation for the minimum norm estimate of k-mer frequencies given an observed set of gapped k-mer frequencies. We demonstrate that this approach provides a more accurate estimate of the k-mer frequencies in real biological sequences using a sample of CTCF binding sites in the human genome.

Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow

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

Vitello, P; Fried, L E; Pudliner, B

2003-07-14

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values, called the ''cache'' is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamicmore » calculations, CHEETAH uses MPI communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.« less

Sparse Partial Equilibrium Tables in Chemically Resolved Reactive Flow

NASA Astrophysics Data System (ADS)

Vitello, Peter; Fried, Laurence E.; Pudliner, Brian; McAbee, Tom

2004-07-01

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and hydrodynamics. Unfortunately, little is known concerning the detailed chemical kinetics of detonations in energetic materials. CHEETAH uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. CHEETAH supports a wide range of elements and condensed detonation products and can also be applied to gas detonations. A sparse hash table of equation of state values is used in CHEETAH to enhance the efficiency of kinetic reaction calculations. For large-scale parallel hydrodynamic calculations, CHEETAH uses parallel communication to updates to the cache. We present here details of the sparse caching model used in the CHEETAH coupled to an ALE hydrocode. To demonstrate the efficiency of modeling using a sparse cache model we consider detonations in energetic materials.

Assessment of actual evapotranspiration over a semiarid heterogeneous land surface by means of coupled low-resolution remote sensing data with an energy balance model: comparison to extra-large aperture scintillometer measurements

NASA Astrophysics Data System (ADS)

Saadi, Sameh; Boulet, Gilles; Bahir, Malik; Brut, Aurore; Delogu, Émilie; Fanise, Pascal; Mougenot, Bernard; Simonneaux, Vincent; Lili Chabaane, Zohra

2018-04-01

In semiarid areas, agricultural production is restricted by water availability; hence, efficient agricultural water management is a major issue. The design of tools providing regional estimates of evapotranspiration (ET), one of the most relevant water balance fluxes, may help the sustainable management of water resources. Remote sensing provides periodic data about actual vegetation temporal dynamics (through the normalized difference vegetation index, NDVI) and water availability under water stress (through the surface temperature Tsurf), which are crucial factors controlling ET. In this study, spatially distributed estimates of ET (or its energy equivalent, the latent heat flux LE) in the Kairouan plain (central Tunisia) were computed by applying the Soil Plant Atmosphere and Remote Sensing Evapotranspiration (SPARSE) model fed by low-resolution remote sensing data (Terra and Aqua MODIS). The work's goal was to assess the operational use of the SPARSE model and the accuracy of the modeled (i) sensible heat flux (H) and (ii) daily ET over a heterogeneous semiarid landscape with complex land cover (i.e., trees, winter cereals, summer vegetables). SPARSE was run to compute instantaneous estimates of H and LE fluxes at the satellite overpass times. The good correspondence (R2 = 0.60 and 0.63 and RMSE = 57.89 and 53.85 W m-2 for Terra and Aqua, respectively) between instantaneous H estimates and large aperture scintillometer (XLAS) H measurements along a path length of 4 km over the study area showed that the SPARSE model presents satisfactory accuracy. Results showed that, despite the fairly large scatter, the instantaneous LE can be suitably estimated at large scales (RMSE = 47.20 and 43.20 W m-2 for Terra and Aqua, respectively, and R2 = 0.55 for both satellites). Additionally, water stress was investigated by comparing modeled (SPARSE) and observed (XLAS) water stress values; we found that most points were located within a 0.2 confidence interval, thus the general tendencies are well reproduced. Even though extrapolation of instantaneous latent heat flux values to daily totals was less obvious, daily ET estimates are deemed acceptable.

Return probabilities and hitting times of random walks on sparse Erdös-Rényi graphs.

PubMed

Martin, O C; Sulc, P

2010-03-01

We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdös-Rényi graphs. Using the tree approach, which is expected to be exact in the large graph limit, we show how to solve for the distribution of these quantities and we find that these distributions exhibit a form of self-similarity.

Sparsity-Based Representation for Classification Algorithms and Comparison Results for Transient Acoustic Signals

DTIC Science & Technology

2016-05-01

large but correlated noise and signal interference (i.e., low -rank interference). Another contribution is the implementation of deep learning...representation, low rank, deep learning 52 Tung-Duong Tran-Luu 301-394-3082Unclassified Unclassified Unclassified UU ii Approved for public release; distribution...Classification of Acoustic Transients 6 3.2 Joint Sparse Representation with Low -Rank Interference 7 3.3 Simultaneous Group-and-Joint Sparse Representation

Unsupervised Learning for Monaural Source Separation Using Maximization–Minimization Algorithm with Time–Frequency Deconvolution †

PubMed Central

Bouridane, Ahmed; Ling, Bingo Wing-Kuen

2018-01-01

This paper presents an unsupervised learning algorithm for sparse nonnegative matrix factor time–frequency deconvolution with optimized fractional β-divergence. The β-divergence is a group of cost functions parametrized by a single parameter β. The Itakura–Saito divergence, Kullback–Leibler divergence and Least Square distance are special cases that correspond to β=0, 1, 2, respectively. This paper presents a generalized algorithm that uses a flexible range of β that includes fractional values. It describes a maximization–minimization (MM) algorithm leading to the development of a fast convergence multiplicative update algorithm with guaranteed convergence. The proposed model operates in the time–frequency domain and decomposes an information-bearing matrix into two-dimensional deconvolution of factor matrices that represent the spectral dictionary and temporal codes. The deconvolution process has been optimized to yield sparse temporal codes through maximizing the likelihood of the observations. The paper also presents a method to estimate the fractional β value. The method is demonstrated on separating audio mixtures recorded from a single channel. The paper shows that the extraction of the spectral dictionary and temporal codes is significantly more efficient by using the proposed algorithm and subsequently leads to better source separation performance. Experimental tests and comparisons with other factorization methods have been conducted to verify its efficacy. PMID:29702629

Image super-resolution via sparse representation.

PubMed

Yang, Jianchao; Wright, John; Huang, Thomas S; Ma, Yi

2010-11-01

This paper presents a new approach to single-image super-resolution, based on sparse signal representation. Research on image statistics suggests that image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary. Inspired by this observation, we seek a sparse representation for each patch of the low-resolution input, and then use the coefficients of this representation to generate the high-resolution output. Theoretical results from compressed sensing suggest that under mild conditions, the sparse representation can be correctly recovered from the downsampled signals. By jointly training two dictionaries for the low- and high-resolution image patches, we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries. Therefore, the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch. The learned dictionary pair is a more compact representation of the patch pairs, compared to previous approaches, which simply sample a large amount of image patch pairs, reducing the computational cost substantially. The effectiveness of such a sparsity prior is demonstrated for both general image super-resolution and the special case of face hallucination. In both cases, our algorithm generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods. In addition, the local sparse modeling of our approach is naturally robust to noise, and therefore the proposed algorithm can handle super-resolution with noisy inputs in a more unified framework.

Sparse modeling of spatial environmental variables associated with asthma

PubMed Central

Chang, Timothy S.; Gangnon, Ronald E.; Page, C. David; Buckingham, William R.; Tandias, Aman; Cowan, Kelly J.; Tomasallo, Carrie D.; Arndt, Brian G.; Hanrahan, Lawrence P.; Guilbert, Theresa W.

2014-01-01

Geographically distributed environmental factors influence the burden of diseases such as asthma. Our objective was to identify sparse environmental variables associated with asthma diagnosis gathered from a large electronic health record (EHR) dataset while controlling for spatial variation. An EHR dataset from the University of Wisconsin’s Family Medicine, Internal Medicine and Pediatrics Departments was obtained for 199,220 patients aged 5–50 years over a three-year period. Each patient’s home address was geocoded to one of 3,456 geographic census block groups. Over one thousand block group variables were obtained from a commercial database. We developed a Sparse Spatial Environmental Analysis (SASEA). Using this method, the environmental variables were first dimensionally reduced with sparse principal component analysis. Logistic thin plate regression spline modeling was then used to identify block group variables associated with asthma from sparse principal components. The addresses of patients from the EHR dataset were distributed throughout the majority of Wisconsin’s geography. Logistic thin plate regression spline modeling captured spatial variation of asthma. Four sparse principal components identified via model selection consisted of food at home, dog ownership, household size, and disposable income variables. In rural areas, dog ownership and renter occupied housing units from significant sparse principal components were associated with asthma. Our main contribution is the incorporation of sparsity in spatial modeling. SASEA sequentially added sparse principal components to Logistic thin plate regression spline modeling. This method allowed association of geographically distributed environmental factors with asthma using EHR and environmental datasets. SASEA can be applied to other diseases with environmental risk factors. PMID:25533437

Sparse modeling of spatial environmental variables associated with asthma.

PubMed

Chang, Timothy S; Gangnon, Ronald E; David Page, C; Buckingham, William R; Tandias, Aman; Cowan, Kelly J; Tomasallo, Carrie D; Arndt, Brian G; Hanrahan, Lawrence P; Guilbert, Theresa W

2015-02-01

Geographically distributed environmental factors influence the burden of diseases such as asthma. Our objective was to identify sparse environmental variables associated with asthma diagnosis gathered from a large electronic health record (EHR) dataset while controlling for spatial variation. An EHR dataset from the University of Wisconsin's Family Medicine, Internal Medicine and Pediatrics Departments was obtained for 199,220 patients aged 5-50years over a three-year period. Each patient's home address was geocoded to one of 3456 geographic census block groups. Over one thousand block group variables were obtained from a commercial database. We developed a Sparse Spatial Environmental Analysis (SASEA). Using this method, the environmental variables were first dimensionally reduced with sparse principal component analysis. Logistic thin plate regression spline modeling was then used to identify block group variables associated with asthma from sparse principal components. The addresses of patients from the EHR dataset were distributed throughout the majority of Wisconsin's geography. Logistic thin plate regression spline modeling captured spatial variation of asthma. Four sparse principal components identified via model selection consisted of food at home, dog ownership, household size, and disposable income variables. In rural areas, dog ownership and renter occupied housing units from significant sparse principal components were associated with asthma. Our main contribution is the incorporation of sparsity in spatial modeling. SASEA sequentially added sparse principal components to Logistic thin plate regression spline modeling. This method allowed association of geographically distributed environmental factors with asthma using EHR and environmental datasets. SASEA can be applied to other diseases with environmental risk factors. Copyright © 2014 Elsevier Inc. All rights reserved.

Noisy covariance matrices and portfolio optimization

NASA Astrophysics Data System (ADS)

Pafka, S.; Kondor, I.

2002-05-01

According to recent findings [#!bouchaud!#,#!stanley!#], empirical covariance matrices deduced from financial return series contain such a high amount of noise that, apart from a few large eigenvalues and the corresponding eigenvectors, their structure can essentially be regarded as random. In [#!bouchaud!#], e.g., it is reported that about 94% of the spectrum of these matrices can be fitted by that of a random matrix drawn from an appropriately chosen ensemble. In view of the fundamental role of covariance matrices in the theory of portfolio optimization as well as in industry-wide risk management practices, we analyze the possible implications of this effect. Simulation experiments with matrices having a structure such as described in [#!bouchaud!#,#!stanley!#] lead us to the conclusion that in the context of the classical portfolio problem (minimizing the portfolio variance under linear constraints) noise has relatively little effect. To leading order the solutions are determined by the stable, large eigenvalues, and the displacement of the solution (measured in variance) due to noise is rather small: depending on the size of the portfolio and on the length of the time series, it is of the order of 5 to 15%. The picture is completely different, however, if we attempt to minimize the variance under non-linear constraints, like those that arise e.g. in the problem of margin accounts or in international capital adequacy regulation. In these problems the presence of noise leads to a serious instability and a high degree of degeneracy of the solutions.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

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

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

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

Zhu, Xiaojun; Lei, Guangtsai; Pan, Guangwen

In this paper, the continuous operator is discretized into matrix forms by Galerkin`s procedure, using periodic Battle-Lemarie wavelets as basis/testing functions. The polynomial decomposition of wavelets is applied to the evaluation of matrix elements, which makes the computational effort of the matrix elements no more expensive than that of method of moments (MoM) with conventional piecewise basis/testing functions. A new algorithm is developed employing the fast wavelet transform (FWT). Owing to localization, cancellation, and orthogonal properties of wavelets, very sparse matrices have been obtained, which are then solved by the LSQR iterative method. This algorithm is also adaptive in thatmore » one can add at will finer wavelet bases in the regions where fields vary rapidly, without any damage to the system orthogonality of the wavelet basis functions. To demonstrate the effectiveness of the new algorithm, we applied it to the evaluation of frequency-dependent resistance and inductance matrices of multiple lossy transmission lines. Numerical results agree with previously published data and laboratory measurements. The valid frequency range of the boundary integral equation results has been extended two to three decades in comparison with the traditional MoM approach. The new algorithm has been integrated into the computer aided design tool, MagiCAD, which is used for the design and simulation of high-speed digital systems and multichip modules Pan et al. 29 refs., 7 figs., 6 tabs.« less

Resolution enhancement of tri-stereo remote sensing images by super resolution methods

NASA Astrophysics Data System (ADS)

Tuna, Caglayan; Akoguz, Alper; Unal, Gozde; Sertel, Elif

2016-10-01

Super resolution (SR) refers to generation of a High Resolution (HR) image from a decimated, blurred, low-resolution (LR) image set, which can be either a single frame or multi-frame that contains a collection of several images acquired from slightly different views of the same observation area. In this study, we propose a novel application of tri-stereo Remote Sensing (RS) satellite images to the super resolution problem. Since the tri-stereo RS images of the same observation area are acquired from three different viewing angles along the flight path of the satellite, these RS images are properly suited to a SR application. We first estimate registration between the chosen reference LR image and other LR images to calculate the sub pixel shifts among the LR images. Then, the warping, blurring and down sampling matrix operators are created as sparse matrices to avoid high memory and computational requirements, which would otherwise make the RS-SR solution impractical. Finally, the overall system matrix, which is constructed based on the obtained operator matrices is used to obtain the estimate HR image in one step in each iteration of the SR algorithm. Both the Laplacian and total variation regularizers are incorporated separately into our algorithm and the results are presented to demonstrate an improved quantitative performance against the standard interpolation method as well as improved qualitative results due expert evaluations.

MPI-FAUN: An MPI-Based Framework for Alternating-Updating Nonnegative Matrix Factorization

DOE PAGES

Kannan, Ramakrishnan; Ballard, Grey; Park, Haesun

2017-10-30

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data mining community, there is a lack of efficient parallel algorithms to solve the problem for big data sets. The main contribution of this work is a new, high-performance parallel computational framework for a broad class of NMF algorithms thatmore » iteratively solves alternating non-negative least squares (NLS) subproblems for W and H. It maintains the data and factor matrices in memory (distributed across processors), uses MPI for interprocessor communication, and, in the dense case, provably minimizes communication costs (under mild assumptions). The framework is flexible and able to leverage a variety of NMF and NLS algorithms, including Multiplicative Update, Hierarchical Alternating Least Squares, and Block Principal Pivoting. Our implementation allows us to benchmark and compare different algorithms on massive dense and sparse data matrices of size that spans from few hundreds of millions to billions. We demonstrate the scalability of our algorithm and compare it with baseline implementations, showing significant performance improvements. The code and the datasets used for conducting the experiments are available online.« less

Mid-frequency MTF compensation of optical sparse aperture system.

PubMed

Zhou, Chenghao; Wang, Zhile

2018-03-19

Optical sparse aperture (OSA) can greatly improve the spatial resolution of optical system. However, because of its aperture dispersion and sparse, its mid-frequency modulation transfer function (MTF) are significantly lower than that of a single aperture system. The main focus of this paper is on the mid-frequency MTF compensation of the optical sparse aperture system. Firstly, the principle of the mid-frequency MTF decreasing and missing of optical sparse aperture are analyzed. This paper takes the filling factor as a clue. The method of processing the mid-frequency MTF decreasing with large filling factor and method of compensation mid-frequency MTF with small filling factor are given respectively. For the MTF mid-frequency decreasing, the image spatial-variant restoration method is proposed to restore the mid-frequency information in the image; for the mid-frequency MTF missing, two images obtained by two system respectively are fused to compensate the mid-frequency information in optical sparse aperture image. The feasibility of the two method are analyzed in this paper. The numerical simulation of the system and algorithm of the two cases are presented using Zemax and Matlab. The results demonstrate that by these two methods the mid-frequency MTF of OSA system can be compensated effectively.

Sparse brain network using penalized linear regression

NASA Astrophysics Data System (ADS)

Lee, Hyekyoung; Lee, Dong Soo; Kang, Hyejin; Kim, Boong-Nyun; Chung, Moo K.

2011-03-01

Sparse partial correlation is a useful connectivity measure for brain networks when it is difficult to compute the exact partial correlation in the small-n large-p setting. In this paper, we formulate the problem of estimating partial correlation as a sparse linear regression with a l1-norm penalty. The method is applied to brain network consisting of parcellated regions of interest (ROIs), which are obtained from FDG-PET images of the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. To validate the results, we check their reproducibilities of the obtained brain networks by the leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.

Shape prior modeling using sparse representation and online dictionary learning.

PubMed

Zhang, Shaoting; Zhan, Yiqiang; Zhou, Yan; Uzunbas, Mustafa; Metaxas, Dimitris N

2012-01-01

The recently proposed sparse shape composition (SSC) opens a new avenue for shape prior modeling. Instead of assuming any parametric model of shape statistics, SSC incorporates shape priors on-the-fly by approximating a shape instance (usually derived from appearance cues) by a sparse combination of shapes in a training repository. Theoretically, one can increase the modeling capability of SSC by including as many training shapes in the repository. However, this strategy confronts two limitations in practice. First, since SSC involves an iterative sparse optimization at run-time, the more shape instances contained in the repository, the less run-time efficiency SSC has. Therefore, a compact and informative shape dictionary is preferred to a large shape repository. Second, in medical imaging applications, training shapes seldom come in one batch. It is very time consuming and sometimes infeasible to reconstruct the shape dictionary every time new training shapes appear. In this paper, we propose an online learning method to address these two limitations. Our method starts from constructing an initial shape dictionary using the K-SVD algorithm. When new training shapes come, instead of re-constructing the dictionary from the ground up, we update the existing one using a block-coordinates descent approach. Using the dynamically updated dictionary, sparse shape composition can be gracefully scaled up to model shape priors from a large number of training shapes without sacrificing run-time efficiency. Our method is validated on lung localization in X-Ray and cardiac segmentation in MRI time series. Compared to the original SSC, it shows comparable performance while being significantly more efficient.

Alternatively Constrained Dictionary Learning For Image Superresolution.

PubMed

Lu, Xiaoqiang; Yuan, Yuan; Yan, Pingkun

2014-03-01

Dictionaries are crucial in sparse coding-based algorithm for image superresolution. Sparse coding is a typical unsupervised learning method to study the relationship between the patches of high-and low-resolution images. However, most of the sparse coding methods for image superresolution fail to simultaneously consider the geometrical structure of the dictionary and the corresponding coefficients, which may result in noticeable superresolution reconstruction artifacts. In other words, when a low-resolution image and its corresponding high-resolution image are represented in their feature spaces, the two sets of dictionaries and the obtained coefficients have intrinsic links, which has not yet been well studied. Motivated by the development on nonlocal self-similarity and manifold learning, a novel sparse coding method is reported to preserve the geometrical structure of the dictionary and the sparse coefficients of the data. Moreover, the proposed method can preserve the incoherence of dictionary entries and provide the sparse coefficients and learned dictionary from a new perspective, which have both reconstruction and discrimination properties to enhance the learning performance. Furthermore, to utilize the model of the proposed method more effectively for single-image superresolution, this paper also proposes a novel dictionary-pair learning method, which is named as two-stage dictionary training. Extensive experiments are carried out on a large set of images comparing with other popular algorithms for the same purpose, and the results clearly demonstrate the effectiveness of the proposed sparse representation model and the corresponding dictionary learning algorithm.

Broken flavor 2↔3 symmetry and phenomenological approach for universal quark and lepton mass matrices

NASA Astrophysics Data System (ADS)

Matsuda, Koichi; Nishiura, Hiroyuki

2006-01-01

A phenomenological approach for the universal mass matrix model with a broken flavor 2↔3 symmetry is explored by introducing the 2↔3 antisymmetric parts of mass matrices for quarks and charged leptons. We present explicit texture components of the mass matrices, which are consistent with all the neutrino oscillation experiments and quark mixing data. The mass matrices have a common structure for quarks and leptons, while the large lepton mixings and the small quark mixings are derived with no fine-tuning due to the difference of the phase factors. The model predicts a value 2.4×10-3 for the lepton mixing matrix element square |U13|2, and also ⟨mν⟩=(0.89-1.4)×10-4eV for the averaged neutrino mass which appears in the neutrinoless double beta decay.

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

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry

NASA Astrophysics Data System (ADS)

Shiozaki, Toru

2017-01-01

We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalisation of matrices of dimension N > 10, 000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige-Van Loan algorithm, which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of 2 than state-of-the-art implementations of complex Hermitian diagonalisation; diagonalising a 12, 800 × 12, 800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel Math Kernel Library's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD licence.

Disconnected Diagrams in Lattice QCD

NASA Astrophysics Data System (ADS)

Gambhir, Arjun Singh

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

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.

Disconnected Diagrams in Lattice QCD

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

Gambhir, Arjun

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagramsmore » is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.« less

Practical recipes for the model order reduction, dynamical simulation and compressive sampling of large-scale open quantum systems

NASA Astrophysics Data System (ADS)

Sidles, John A.; Garbini, Joseph L.; Harrell, Lee E.; Hero, Alfred O.; Jacky, Jonathan P.; Malcomb, Joseph R.; Norman, Anthony G.; Williamson, Austin M.

2009-06-01

Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto state-space manifolds having reduced dimensionality and possessing a Kähler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kählerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality Kähler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candès-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given and methods for quantum state optimization by Dantzig selection are given.

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.

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 split band-Cholesky equation solving strategy for finite element analysis of transient field problems. [in fluid mechanics

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1978-01-01

The paper describes the split-Cholesky strategy for banded matrices arising from the large systems of equations in certain fluid mechanics problems. The basic idea is that for a banded matrix the computation can be carried out in pieces, with only a small portion of the matrix residing in core. Mesh considerations are discussed by demonstrating the manner in which the assembly of finite element equations proceeds for linear trial functions on a triangular mesh. The FORTRAN code which implements the out-of-core decomposition strategy for banded symmetric positive definite matrices (mass matrices) of a coupled initial value problem is given.

Spectroscopy of Cosmic Carbon Analogs in Inert-Gas Matrices and in the Gas-Phase: Comparative Results and Perspectives for Astrophysics

NASA Technical Reports Server (NTRS)

Salama, Farid; DeVincenzi, Donald L. (Technical Monitor)

2001-01-01

Recent studies of the spectroscopy of large (up to approx. 50 carbon atoms) neutral and Ionized polycyclic aromatic hydrocarbons (PAHs) and Fullerenes isolated in inert gas matrices will be presented. The advantages and the limitations of matrix isolation spectroscopy for the study of the molecular spectroscopy of interstellar dust analogs will be discussed. The laboratory data will be compared to the astronomical spectra (the interstellar extinction, the diffuse interstellar bands). Finally, the spectra of PAH ions isolated in neon/argon matrices will be compared to the spectra obtained for PAH ion seeded in a supersonic expansion. The astrophysical implications and future perspectives will be discussed.

TiO₂-Based Photocatalytic Geopolymers for Nitric Oxide Degradation.

PubMed

Strini, Alberto; Roviello, Giuseppina; Ricciotti, Laura; Ferone, Claudio; Messina, Francesco; Schiavi, Luca; Corsaro, Davide; Cioffi, Raffaele

2016-06-24

This study presents an experimental overview for the development of photocatalytic materials based on geopolymer binders as catalyst support matrices. Particularly, geopolymer matrices obtained from different solid precursors (fly ash and metakaolin), composite systems (siloxane-hybrid, foamed hybrid), and curing temperatures (room temperature and 60 °C) were investigated for the same photocatalyst content (i.e., 3% TiO₂ by weight of paste). The geopolymer matrices were previously designed for different applications, ranging from insulating (foam) to structural materials. The photocatalytic activity was evaluated as NO degradation in air, and the results were compared with an ordinary Portland cement reference. The studied matrices demonstrated highly variable photocatalytic performance depending on both matrix constituents and the curing temperature, with promising activity revealed by the geopolymers based on fly ash and metakaolin. Furthermore, microstructural features and titania dispersion in the matrices were assessed by scanning electron microscopy (SEM) and energy dispersive X-ray (EDS) analyses. Particularly, EDS analyses of sample sections indicated segregation effects of titania in the surface layer, with consequent enhancement or depletion of the catalyst concentration in the active sample region, suggesting non-negligible transport phenomena during the curing process. The described results demonstrated that geopolymer binders can be interesting catalyst support matrices for the development of photocatalytic materials and indicated a large potential for the exploitation of their peculiar features.

Conserved G-matrices of morphological and life-history traits among continental and island blue tit populations.

PubMed

Delahaie, B; Charmantier, A; Chantepie, S; Garant, D; Porlier, M; Teplitsky, C

2017-08-01

The genetic variance-covariance matrix (G-matrix) summarizes the genetic architecture of multiple traits. It has a central role in the understanding of phenotypic divergence and the quantification of the evolutionary potential of populations. Laboratory experiments have shown that G-matrices can vary rapidly under divergent selective pressures. However, because of the demanding nature of G-matrix estimation and comparison in wild populations, the extent of its spatial variability remains largely unknown. In this study, we investigate spatial variation in G-matrices for morphological and life-history traits using long-term data sets from one continental and three island populations of blue tit (Cyanistes caeruleus) that have experienced contrasting population history and selective environment. We found no evidence for differences in G-matrices among populations. Interestingly, the phenotypic variance-covariance matrices (P) were divergent across populations, suggesting that using P as a substitute for G may be inadequate. These analyses also provide the first evidence in wild populations for additive genetic variation in the incubation period (that is, the period between last egg laid and hatching) in all four populations. Altogether, our results suggest that G-matrices may be stable across populations inhabiting contrasted environments, therefore challenging the results of previous simulation studies and laboratory experiments.

Construction of type-II QC-LDPC codes with fast encoding based on perfect cyclic difference sets

NASA Astrophysics Data System (ADS)

Li, Ling-xiang; Li, Hai-bing; Li, Ji-bi; Jiang, Hua

2017-09-01

In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check (QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-II QC-LDPC codes based on perfect cyclic difference sets (CDSs) are constructed. The parity check matrices of these type-II QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices (CPMs) with weight of 1 and the circulant matrices with weight of 2 (W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error- correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-II QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise (AWGN) channel with sum-product algorithm (SPA) iterative decoding.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Sparsely sampling the sky: a Bayesian experimental design approach

NASA Astrophysics Data System (ADS)

Paykari, P.; Jaffe, A. H.

2013-08-01

The next generation of galaxy surveys will observe millions of galaxies over large volumes of the Universe. These surveys are expensive both in time and cost, raising questions regarding the optimal investment of this time and money. In this work, we investigate criteria for selecting amongst observing strategies for constraining the galaxy power spectrum and a set of cosmological parameters. Depending on the parameters of interest, it may be more efficient to observe a larger, but sparsely sampled, area of sky instead of a smaller contiguous area. In this work, by making use of the principles of Bayesian experimental design, we will investigate the advantages and disadvantages of the sparse sampling of the sky and discuss the circumstances in which a sparse survey is indeed the most efficient strategy. For the Dark Energy Survey (DES), we find that by sparsely observing the same area in a smaller amount of time, we only increase the errors on the parameters by a maximum of 0.45 per cent. Conversely, investing the same amount of time as the original DES to observe a sparser but larger area of sky, we can in fact constrain the parameters with errors reduced by 28 per cent.

Signal Sampling for Efficient Sparse Representation of Resting State FMRI Data

PubMed Central

Ge, Bao; Makkie, Milad; Wang, Jin; Zhao, Shijie; Jiang, Xi; Li, Xiang; Lv, Jinglei; Zhang, Shu; Zhang, Wei; Han, Junwei; Guo, Lei; Liu, Tianming

2015-01-01

As the size of brain imaging data such as fMRI grows explosively, it provides us with unprecedented and abundant information about the brain. How to reduce the size of fMRI data but not lose much information becomes a more and more pressing issue. Recent literature studies tried to deal with it by dictionary learning and sparse representation methods, however, their computation complexities are still high, which hampers the wider application of sparse representation method to large scale fMRI datasets. To effectively address this problem, this work proposes to represent resting state fMRI (rs-fMRI) signals of a whole brain via a statistical sampling based sparse representation. First we sampled the whole brain’s signals via different sampling methods, then the sampled signals were aggregate into an input data matrix to learn a dictionary, finally this dictionary was used to sparsely represent the whole brain’s signals and identify the resting state networks. Comparative experiments demonstrate that the proposed signal sampling framework can speed-up by ten times in reconstructing concurrent brain networks without losing much information. The experiments on the 1000 Functional Connectomes Project further demonstrate its effectiveness and superiority. PMID:26646924

Effective channel estimation and efficient symbol detection for multi-input multi-output underwater acoustic communications

NASA Astrophysics Data System (ADS)

Ling, Jun

Achieving reliable underwater acoustic communications (UAC) has long been recognized as a challenging problem owing to the scarce bandwidth available and the reverberant spread in both time and frequency domains. To pursue high data rates, we consider a multi-input multi-output (MIMO) UAC system, and our focus is placed on two main issues regarding a MIMO UAC system: (1) channel estimation, which involves the design of the training sequences and the development of a reliable channel estimation algorithm, and (2) symbol detection, which requires interference cancelation schemes due to simultaneous transmission from multiple transducers. To enhance channel estimation performance, we present a cyclic approach for designing training sequences with good auto- and cross-correlation properties, and a channel estimation algorithm called the iterative adaptive approach (IAA). Sparse channel estimates can be obtained by combining IAA with the Bayesian information criterion (BIC). Moreover, we present sparse learning via iterative minimization (SLIM) and demonstrate that SLIM gives similar performance to IAA but at a much lower computational cost. Furthermore, an extension of the SLIM algorithm is introduced to estimate the sparse and frequency modulated acoustic channels. The extended algorithm is referred to as generalization of SLIM (GoSLIM). Regarding symbol detection, a linear minimum mean-squared error based detection scheme, called RELAX-BLAST, which is a combination of vertical Bell Labs layered space-time (V-BLAST) algorithm and the cyclic principle of the RELAX algorithm, is presented and it is shown that RELAX-BLAST outperforms V-BLAST. We show that RELAX-BLAST can be implemented efficiently by making use of the conjugate gradient method and diagonalization properties of circulant matrices. This fast implementation approach requires only simple fast Fourier transform operations and facilitates parallel implementations. The effectiveness of the proposed MIMO schemes is verified by both computer simulations and experimental results obtained by analyzing the measurements acquired in multiple in-water experiments.

Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems

NASA Astrophysics Data System (ADS)

Jia, C. J.; Wang, Y.; Mendl, C. B.; Moritz, B.; Devereaux, T. P.

2018-03-01

We describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the "checkerboard" decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.

Dictionary learning-based CT detection of pulmonary nodules

NASA Astrophysics Data System (ADS)

Wu, Panpan; Xia, Kewen; Zhang, Yanbo; Qian, Xiaohua; Wang, Ge; Yu, Hengyong

2016-10-01

Segmentation of lung features is one of the most important steps for computer-aided detection (CAD) of pulmonary nodules with computed tomography (CT). However, irregular shapes, complicated anatomical background and poor pulmonary nodule contrast make CAD a very challenging problem. Here, we propose a novel scheme for feature extraction and classification of pulmonary nodules through dictionary learning from training CT images, which does not require accurately segmented pulmonary nodules. Specifically, two classification-oriented dictionaries and one background dictionary are learnt to solve a two-category problem. In terms of the classification-oriented dictionaries, we calculate sparse coefficient matrices to extract intrinsic features for pulmonary nodule classification. The support vector machine (SVM) classifier is then designed to optimize the performance. Our proposed methodology is evaluated with the lung image database consortium and image database resource initiative (LIDC-IDRI) database, and the results demonstrate that the proposed strategy is promising.

A new Python library to analyse skeleton images confirms malaria parasite remodelling of the red blood cell membrane skeleton.

PubMed

Nunez-Iglesias, Juan; Blanch, Adam J; Looker, Oliver; Dixon, Matthew W; Tilley, Leann

2018-01-01

We present Skan (Skeleton analysis), a Python library for the analysis of the skeleton structures of objects. It was inspired by the "analyse skeletons" plugin for the Fiji image analysis software, but its extensive Application Programming Interface (API) allows users to examine and manipulate any intermediate data structures produced during the analysis. Further, its use of common Python data structures such as SciPy sparse matrices and pandas data frames opens the results to analysis within the extensive ecosystem of scientific libraries available in Python. We demonstrate the validity of Skan's measurements by comparing its output to the established Analyze Skeletons Fiji plugin, and, with a new scanning electron microscopy (SEM)-based method, we confirm that the malaria parasite Plasmodium falciparum remodels the host red blood cell cytoskeleton, increasing the average distance between spectrin-actin junctions.

Enhanced Detectability of Community Structure in Multilayer Networks through Layer Aggregation.

PubMed

Taylor, Dane; Shai, Saray; Stanley, Natalie; Mucha, Peter J

2016-06-03

Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability of community structure in these networks. Using random matrix theory, we analyze detectability limitations for multilayer (specifically, multiplex) stochastic block models (SBMs) in which L layers are derived from a common SBM. We study the effect of layer aggregation on detectability for several aggregation methods, including summation of the layers' adjacency matrices for which we show the detectability limit vanishes as O(L^{-1/2}) with increasing number of layers, L. Importantly, we find a similar scaling behavior when the summation is thresholded at an optimal value, providing insight into the common-but not well understood-practice of thresholding pairwise-interaction data to obtain sparse network representations.

Three-dimensional modeling, estimation, and fault diagnosis of spacecraft air contaminants.

PubMed

Narayan, A P; Ramirez, W F

1998-01-01

A description is given of the design and implementation of a method to track the presence of air contaminants aboard a spacecraft using an accurate physical model and of a procedure that would raise alarms when certain tolerance levels are exceeded. Because our objective is to monitor the contaminants in real time, we make use of a state estimation procedure that filters measurements from a sensor system and arrives at an optimal estimate of the state of the system. The model essentially consists of a convection-diffusion equation in three dimensions, solved implicitly using the principle of operator splitting, and uses a flowfield obtained by the solution of the Navier-Stokes equations for the cabin geometry, assuming steady-state conditions. A novel implicit Kalman filter has been used for fault detection, a procedure that is an efficient way to track the state of the system and that uses the sparse nature of the state transition matrices.

A 3D finite-difference BiCG iterative solver with the Fourier-Jacobi preconditioner for the anisotropic EIT/EEG forward problem.

PubMed

Turovets, Sergei; Volkov, Vasily; Zherdetsky, Aleksej; Prakonina, Alena; Malony, Allen D

2014-01-01

The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

Selected inversion as key to a stable Langevin evolution across the QCD phase boundary

NASA Astrophysics Data System (ADS)

Bloch, Jacques; Schenk, Olaf

2018-03-01

We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.

A new Python library to analyse skeleton images confirms malaria parasite remodelling of the red blood cell membrane skeleton

PubMed Central

Looker, Oliver; Dixon, Matthew W.; Tilley, Leann

2018-01-01

We present Skan (Skeleton analysis), a Python library for the analysis of the skeleton structures of objects. It was inspired by the “analyse skeletons” plugin for the Fiji image analysis software, but its extensive Application Programming Interface (API) allows users to examine and manipulate any intermediate data structures produced during the analysis. Further, its use of common Python data structures such as SciPy sparse matrices and pandas data frames opens the results to analysis within the extensive ecosystem of scientific libraries available in Python. We demonstrate the validity of Skan’s measurements by comparing its output to the established Analyze Skeletons Fiji plugin, and, with a new scanning electron microscopy (SEM)-based method, we confirm that the malaria parasite Plasmodium falciparum remodels the host red blood cell cytoskeleton, increasing the average distance between spectrin-actin junctions. PMID:29472997

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

New imaging algorithm in diffusion tomography

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Lucas, Thomas R.; Frank, Robert M.

1997-08-01

A novel imaging algorithm for diffusion/optical tomography is presented for the case of the time dependent diffusion equation. Numerical tests are conducted for ranges of parameters realistic for applications to an early breast cancer diagnosis using ultrafast laser pulses. This is a perturbation-like method which works for both homogeneous a heterogeneous background media. Its main innovation lies in a new approach for a novel linearized problem (LP). Such an LP is derived and reduced to a boundary value problem for a coupled system of elliptic partial differential equations. As is well known, the solution of such a system amounts to the factorization of well conditioned, sparse matrices with few non-zero entries clustered along the diagonal, which can be done very rapidly. Thus, the main advantages of this technique are that it is fast and accurate. The authors call this approach the elliptic systems method (ESM). The ESM can be extended for other data collection schemes.

Isolation and Identification of Proteins Secreted by Cells Cultured within Synthetic Hydrogel-Based Matrices

PubMed Central

2018-01-01

Cells interact with and remodel their microenvironment, degrading large extracellular matrix (ECM) proteins (e.g., fibronectin, collagens) and secreting new ECM proteins and small soluble factors (e.g., growth factors, cytokines). Synthetic mimics of the ECM have been developed as controlled cell culture platforms for use in both fundamental and applied studies. However, how cells broadly remodel these initially well-defined matrices remains poorly understood and difficult to probe. In this work, we have established methods for widely examining both large and small proteins that are secreted by cells within synthetic matrices. Specifically, human mesenchymal stem cells (hMSCs), a model primary cell type, were cultured within well-defined poly(ethylene glycol) (PEG)-peptide hydrogels, and these cell-matrix constructs were decellularized and degraded for subsequent isolation and analysis of deposited proteins. Shotgun proteomics using liquid chromatography and mass spectrometry identified a variety of proteins, including the large ECM proteins fibronectin and collagen VI. Immunostaining and confocal imaging confirmed these results and provided visualization of protein organization within the synthetic matrices. Additionally, culture medium was collected from the encapsulated hMSCs, and a Luminex assay was performed to identify secreted soluble factors, including vascular endothelial growth factor (VEGF), endothelial growth factor (EGF), basic fibroblast growth factor (FGF-2), interleukin 8 (IL-8), and tumor necrosis factor alpha (TNF-α). Together, these methods provide a unique approach for studying dynamic reciprocity between cells and synthetic microenvironments and have the potential to provide new biological insights into cell responses during three-dimensional (3D) controlled cell culture. PMID:29552635

Isolation and Identification of Proteins Secreted by Cells Cultured within Synthetic Hydrogel-Based Matrices.

PubMed

Sawicki, Lisa A; Choe, Leila H; Wiley, Katherine L; Lee, Kelvin H; Kloxin, April M

2018-03-12

Cells interact with and remodel their microenvironment, degrading large extracellular matrix (ECM) proteins (e.g., fibronectin, collagens) and secreting new ECM proteins and small soluble factors (e.g., growth factors, cytokines). Synthetic mimics of the ECM have been developed as controlled cell culture platforms for use in both fundamental and applied studies. However, how cells broadly remodel these initially well-defined matrices remains poorly understood and difficult to probe. In this work, we have established methods for widely examining both large and small proteins that are secreted by cells within synthetic matrices. Specifically, human mesenchymal stem cells (hMSCs), a model primary cell type, were cultured within well-defined poly(ethylene glycol) (PEG)-peptide hydrogels, and these cell-matrix constructs were decellularized and degraded for subsequent isolation and analysis of deposited proteins. Shotgun proteomics using liquid chromatography and mass spectrometry identified a variety of proteins, including the large ECM proteins fibronectin and collagen VI. Immunostaining and confocal imaging confirmed these results and provided visualization of protein organization within the synthetic matrices. Additionally, culture medium was collected from the encapsulated hMSCs, and a Luminex assay was performed to identify secreted soluble factors, including vascular endothelial growth factor (VEGF), endothelial growth factor (EGF), basic fibroblast growth factor (FGF-2), interleukin 8 (IL-8), and tumor necrosis factor alpha (TNF-α). Together, these methods provide a unique approach for studying dynamic reciprocity between cells and synthetic microenvironments and have the potential to provide new biological insights into cell responses during three-dimensional (3D) controlled cell culture.

Natural image sequences constrain dynamic receptive fields and imply a sparse code.

PubMed

Häusler, Chris; Susemihl, Alex; Nawrot, Martin P

2013-11-06

In their natural environment, animals experience a complex and dynamic visual scenery. Under such natural stimulus conditions, neurons in the visual cortex employ a spatially and temporally sparse code. For the input scenario of natural still images, previous work demonstrated that unsupervised feature learning combined with the constraint of sparse coding can predict physiologically measured receptive fields of simple cells in the primary visual cortex. This convincingly indicated that the mammalian visual system is adapted to the natural spatial input statistics. Here, we extend this approach to the time domain in order to predict dynamic receptive fields that can account for both spatial and temporal sparse activation in biological neurons. We rely on temporal restricted Boltzmann machines and suggest a novel temporal autoencoding training procedure. When tested on a dynamic multi-variate benchmark dataset this method outperformed existing models of this class. Learning features on a large dataset of natural movies allowed us to model spatio-temporal receptive fields for single neurons. They resemble temporally smooth transformations of previously obtained static receptive fields and are thus consistent with existing theories. A neuronal spike response model demonstrates how the dynamic receptive field facilitates temporal and population sparseness. We discuss the potential mechanisms and benefits of a spatially and temporally sparse representation of natural visual input. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.

BCH codes for large IC random-access memory systems

NASA Technical Reports Server (NTRS)

Lin, S.; Costello, D. J., Jr.

1983-01-01

In this report some shortened BCH codes for possible applications to large IC random-access memory systems are presented. These codes are given by their parity-check matrices. Encoding and decoding of these codes are discussed.

Framing U-Net via Deep Convolutional Framelets: Application to Sparse-View CT.

PubMed

Han, Yoseob; Ye, Jong Chul

2018-06-01

X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse-view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and tight frame U-Nets satisfy the so-called frame condition which makes them better for effective recovery of high frequency edges in sparse-view CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.

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

Elastic plate spallation

NASA Technical Reports Server (NTRS)

Oline, L.; Medaglia, J.

1972-01-01

The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.

Arrangement of the myenteric plexus throughout the gastrointestinal tract of the opossum.

PubMed

Christensen, J; Rick, G A; Robison, B A; Stiles, M J; Wix, M A

1983-10-01

Silver impregnation of the myenteric plexus of the opossum gut was used to find differences among various regions. In the esophagus, the plexus was sparse and ganglia were spaced irregularly, many being parafascicular. Ganglia were sparse in the striated-muscle region, but more frequent in the smooth-muscle region. In the stomach, uniformly spaced ganglia were large and intrafascicular; ganglia were larger in the distal stomach than in the proximal stomach. The proximal stomach contained thick fascicles, called shunt fascicles, radiating from the lesser to the greater curvatures and bypassing ganglia. A thick nerve bundle encircled the pylorus. In the small intestine, the regularly spaced ganglia were large and intrafascicular. In the cecum, they were small and intrafascicular. In the colon, they were large and intrafascicular. Shunt fascicles, like those of the proximal stomach, extended from the rectum into the distal colon. In the rectum, the plexus was sparse, and ganglia were small and distributed irregularly. Many ganglia were parafascicular. Unique knots of tangled fascicles were frequent in the rectum; these were called labyrinthine nodes. The least densely innervated regions of the gut are the lower esophageal sphincter and the rectum. Major differences in the anatomy of the plexus characterize the different regions of the gut.

Amino Acid Properties Conserved in Molecular Evolution

PubMed Central

Rudnicki, Witold R.; Mroczek, Teresa; Cudek, Paweł

2014-01-01

That amino acid properties are responsible for the way protein molecules evolve is natural and is also reasonably well supported both by the structure of the genetic code and, to a large extent, by the experimental measures of the amino acid similarity. Nevertheless, there remains a significant gap between observed similarity matrices and their reconstructions from amino acid properties. Therefore, we introduce a simple theoretical model of amino acid similarity matrices, which allows splitting the matrix into two parts – one that depends only on mutabilities of amino acids and another that depends on pairwise similarities between them. Then the new synthetic amino acid properties are derived from the pairwise similarities and used to reconstruct similarity matrices covering a wide range of information entropies. Our model allows us to explain up to 94% of the variability in the BLOSUM family of the amino acids similarity matrices in terms of amino acid properties. The new properties derived from amino acid similarity matrices correlate highly with properties known to be important for molecular evolution such as hydrophobicity, size, shape and charge of amino acids. This result closes the gap in our understanding of the influence of amino acids on evolution at the molecular level. The methods were applied to the single family of similarity matrices used often in general sequence homology searches, but it is general and can be used also for more specific matrices. The new synthetic properties can be used in analyzes of protein sequences in various biological applications. PMID:24967708

Reconstructing three-dimensional protein crystal intensities from sparse unoriented two-axis X-ray diffraction patterns

PubMed Central

Lan, Ti-Yen; Wierman, Jennifer L.; Tate, Mark W.; Philipp, Hugh T.; Elser, Veit

2017-01-01

Recently, there has been a growing interest in adapting serial microcrystallography (SMX) experiments to existing storage ring (SR) sources. For very small crystals, however, radiation damage occurs before sufficient numbers of photons are diffracted to determine the orientation of the crystal. The challenge is to merge data from a large number of such ‘sparse’ frames in order to measure the full reciprocal space intensity. To simulate sparse frames, a dataset was collected from a large lysozyme crystal illuminated by a dim X-ray source. The crystal was continuously rotated about two orthogonal axes to sample a subset of the rotation space. With the EMC algorithm [expand–maximize–compress; Loh & Elser (2009). Phys. Rev. E, 80, 026705], it is shown that the diffracted intensity of the crystal can still be reconstructed even without knowledge of the orientation of the crystal in any sparse frame. Moreover, parallel computation implementations were designed to considerably improve the time and memory scaling of the algorithm. The results show that EMC-based SMX experiments should be feasible at SR sources. PMID:28808431

Sparse imaging for fast electron microscopy

NASA Astrophysics Data System (ADS)

Anderson, Hyrum S.; Ilic-Helms, Jovana; Rohrer, Brandon; Wheeler, Jason; Larson, Kurt

2013-02-01

Scanning electron microscopes (SEMs) are used in neuroscience and materials science to image centimeters of sample area at nanometer scales. Since imaging rates are in large part SNR-limited, large collections can lead to weeks of around-the-clock imaging time. To increase data collection speed, we propose and demonstrate on an operational SEM a fast method to sparsely sample and reconstruct smooth images. To accurately localize the electron probe position at fast scan rates, we model the dynamics of the scan coils, and use the model to rapidly and accurately visit a randomly selected subset of pixel locations. Images are reconstructed from the undersampled data by compressed sensing inversion using image smoothness as a prior. We report image fidelity as a function of acquisition speed by comparing traditional raster to sparse imaging modes. Our approach is equally applicable to other domains of nanometer microscopy in which the time to position a probe is a limiting factor (e.g., atomic force microscopy), or in which excessive electron doses might otherwise alter the sample being observed (e.g., scanning transmission electron microscopy).

Statistics of single unit responses in the human medial temporal lobe: A sparse and overdispersed code

NASA Astrophysics Data System (ADS)

Magyar, Andrew

The recent discovery of cells that respond to purely conceptual features of the environment (particular people, landmarks, objects, etc) in the human medial temporal lobe (MTL), has raised many questions about the nature of the neural code in humans. The goal of this dissertation is to develop a novel statistical method based upon maximum likelihood regression which will then be applied to these experiments in order to produce a quantitative description of the coding properties of the human MTL. In general, the method is applicable to any experiments in which a sequence of stimuli are presented to an organism while the binary responses of a large number of cells are recorded in parallel. The central concept underlying the approach is the total probability that a neuron responds to a random stimulus, called the neuronal sparsity. The model then estimates the distribution of response probabilities across the population of cells. Applying the method to single-unit recordings from the human medial temporal lobe, estimates of the sparsity distributions are acquired in four regions: the hippocampus, the entorhinal cortex, the amygdala, and the parahippocampal cortex. The resulting distributions are found to be sparse (large fraction of cells with a low response probability) and highly non-uniform, with a large proportion of ultra-sparse neurons that possess a very low response probability, and a smaller population of cells which respond much more frequently. Rammifications of the results are discussed in relation to the sparse coding hypothesis, and comparisons are made between the statistics of the human medial temporal lobe cells and place cells observed in the rodent hippocampus.

Clustering by reordering of similarity and Laplacian matrices: Application to galaxy clusters

NASA Astrophysics Data System (ADS)

Mahmoud, E.; Shoukry, A.; Takey, A.

2018-04-01

Similarity metrics, kernels and similarity-based algorithms have gained much attention due to their increasing applications in information retrieval, data mining, pattern recognition and machine learning. Similarity Graphs are often adopted as the underlying representation of similarity matrices and are at the origin of known clustering algorithms such as spectral clustering. Similarity matrices offer the advantage of working in object-object (two-dimensional) space where visualization of clusters similarities is available instead of object-features (multi-dimensional) space. In this paper, sparse ɛ-similarity graphs are constructed and decomposed into strong components using appropriate methods such as Dulmage-Mendelsohn permutation (DMperm) and/or Reverse Cuthill-McKee (RCM) algorithms. The obtained strong components correspond to groups (clusters) in the input (feature) space. Parameter ɛi is estimated locally, at each data point i from a corresponding narrow range of the number of nearest neighbors. Although more advanced clustering techniques are available, our method has the advantages of simplicity, better complexity and direct visualization of the clusters similarities in a two-dimensional space. Also, no prior information about the number of clusters is needed. We conducted our experiments on two and three dimensional, low and high-sized synthetic datasets as well as on an astronomical real-dataset. The results are verified graphically and analyzed using gap statistics over a range of neighbors to verify the robustness of the algorithm and the stability of the results. Combining the proposed algorithm with gap statistics provides a promising tool for solving clustering problems. An astronomical application is conducted for confirming the existence of 45 galaxy clusters around the X-ray positions of galaxy clusters in the redshift range [0.1..0.8]. We re-estimate the photometric redshifts of the identified galaxy clusters and obtain acceptable values compared to published spectroscopic redshifts with a 0.029 standard deviation of their differences.

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

PubMed Central

Park, Wooram; Liu, Yan; Zhou, Yu; Moses, Matthew; Chirikjian, Gregory S.

2010-01-01

SUMMARY A nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker–Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes. PMID:20454468

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

Joint sparsity based heterogeneous data-level fusion for target detection and estimation

NASA Astrophysics Data System (ADS)

Niu, Ruixin; Zulch, Peter; Distasio, Marcello; Blasch, Erik; Shen, Dan; Chen, Genshe

2017-05-01

Typical surveillance systems employ decision- or feature-level fusion approaches to integrate heterogeneous sensor data, which are sub-optimal and incur information loss. In this paper, we investigate data-level heterogeneous sensor fusion. Since the sensors monitor the common targets of interest, whose states can be determined by only a few parameters, it is reasonable to assume that the measurement domain has a low intrinsic dimensionality. For heterogeneous sensor data, we develop a joint-sparse data-level fusion (JSDLF) approach based on the emerging joint sparse signal recovery techniques by discretizing the target state space. This approach is applied to fuse signals from multiple distributed radio frequency (RF) signal sensors and a video camera for joint target detection and state estimation. The JSDLF approach is data-driven and requires minimum prior information, since there is no need to know the time-varying RF signal amplitudes, or the image intensity of the targets. It can handle non-linearity in the sensor data due to state space discretization and the use of frequency/pixel selection matrices. Furthermore, for a multi-target case with J targets, the JSDLF approach only requires discretization in a single-target state space, instead of discretization in a J-target state space, as in the case of the generalized likelihood ratio test (GLRT) or the maximum likelihood estimator (MLE). Numerical examples are provided to demonstrate that the proposed JSDLF approach achieves excellent performance with near real-time accurate target position and velocity estimates.

Density of large snags and logs in northern Arizona mixed-conifer and ponderosa pine forests

Treesearch

Joseph L. Ganey; Benjamin J. Bird; L. Scott Baggett; Jeffrey S. Jenness

2015-01-01

Large snags and logs provide important biological legacies and resources for native wildlife, yet data on populations of large snags and logs and factors influencing those populations are sparse. We monitored populations of large snags and logs in mixed-conifer and ponderosa pine (Pinus ponderosa) forests in northern Arizona from 1997 through 2012. We modeled density...

Evidence for Extended Aqueous Alteration in CR Carbonaceous Chondrites

NASA Technical Reports Server (NTRS)

Trigo-Rodriquez, J. M.; Moyano-Cambero, C. E.; Mestres, N.; Fraxedas, J.; Zolensky, M.; Nakamura, T.; Martins, Z.

2013-01-01

We are currently studying the chemical interrelationships between the main rockforming components of carbonaceous chondrites (hereafter CC), e.g. silicate chondrules, refractory inclusions and metal grains, and the surrounding meteorite matrices. It is thought that the fine-grained materials that form CC matrices are representing samples of relatively unprocessed protoplanetary disk materials [1-3]. In fact, modern non-destructive analytical techniques have shown that CC matrices host a large diversity of stellar grains from many distinguishable stellar sources [4]. Aqueous alteration has played a role in homogeneizing the isotopic content that allows the identification of presolar grains [5]. On the other hand, detailed analytical techniques have found that the aqueously-altered CR, CM and CI chondrite groups contain matrices in which the organic matter has experienced significant processing concomitant to the formation of clays and other minerals. In this sense, clays have been found to be directly associated with complex organics [6, 7]. CR chondrites are particularly relevant in this context as this chondrite group contains abundant metal grains in the interstitial matrix, and inside glassy silicate chondrules. It is important because CR are known for exhibiting a large complexity of organic compounds [8-10], and only metallic Fe is considered essential in Fischer-Tropsch catalysis of organics [11-13]. Therefore, CR chondrites can be considered primitive materials capable to provide clues on the role played by aqueous alteration in the chemical evolution of their parent asteroids.

Evolutionary Games with Randomly Changing Payoff Matrices

NASA Astrophysics Data System (ADS)

Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun

2015-06-01

Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.

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.

Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.

PubMed

Anzt, H; Quintana-Ortí, E S

2014-06-28

While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Amino acid Alphabet Size in Protein Evolution Experiments: Better to Search a Small library Thoroughly or a Large Library Sparsely?

PubMed Central

Muñoz, Enrique

2015-01-01

We compare the results obtained from searching a smaller library thoroughly versus searching a more diverse, larger library sparsely. We study protein evolution with reduced amino acid alphabets, by simulating directed evolution experiments at three different alphabet sizes: 20, 5 and 2. We employ a physical model for evolution, the generalized NK model, that has proved successful in modeling protein evolution, antibody evolution, and T cell selection. We find that antibodies with higher affinity are found by searching a library with a larger alphabet sparsely than by searching a smaller library thoroughly, even with well-designed reduced libraries. We find ranked amino acid usage frequencies in agreement with observations of the CDR-H3 variable region of human antibodies. PMID:18375453

On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections

NASA Astrophysics Data System (ADS)

Ebrahimi, R.; Zohren, S.

2018-03-01

In this paper we extend the orthogonal polynomials approach for extreme value calculations of Hermitian random matrices, developed by Nadal and Majumdar (J. Stat. Mech. P04001 arXiv:1102.0738), to normal random matrices and 2D Coulomb gases in general. Firstly, we show that this approach provides an alternative derivation of results in the literature. More precisely, we show convergence of the rescaled eigenvalue with largest modulus of a normal Gaussian ensemble to a Gumbel distribution, as well as universality for an arbitrary radially symmetric potential. Secondly, it is shown that this approach can be generalised to obtain convergence of the eigenvalue with smallest modulus and its universality for ring distributions. Most interestingly, the here presented techniques are used to compute all slowly varying finite N correction of the above distributions, which is important for practical applications, given the slow convergence. Another interesting aspect of this work is the fact that we can use standard techniques from Hermitian random matrices to obtain the extreme value statistics of non-Hermitian random matrices resembling the large N expansion used in context of the double scaling limit of Hermitian matrix models in string theory.

Incremental Multi-view 3D Reconstruction Starting from Two Images Taken by a Stereo Pair of Cameras

NASA Astrophysics Data System (ADS)

El hazzat, Soulaiman; Saaidi, Abderrahim; Karam, Antoine; Satori, Khalid

2015-03-01

In this paper, we present a new method for multi-view 3D reconstruction based on the use of a binocular stereo vision system constituted of two unattached cameras to initialize the reconstruction process. Afterwards , the second camera of stereo vision system (characterized by varying parameters) moves to capture more images at different times which are used to obtain an almost complete 3D reconstruction. The first two projection matrices are estimated by using a 3D pattern with known properties. After that, 3D scene points are recovered by triangulation of the matched interest points between these two images. The proposed approach is incremental. At each insertion of a new image, the camera projection matrix is estimated using the 3D information already calculated and new 3D points are recovered by triangulation from the result of the matching of interest points between the inserted image and the previous image. For the refinement of the new projection matrix and the new 3D points, a local bundle adjustment is performed. At first, all projection matrices are estimated, the matches between consecutive images are detected and Euclidean sparse 3D reconstruction is obtained. So, to increase the number of matches and have a more dense reconstruction, the Match propagation algorithm, more suitable for interesting movement of the camera, was applied on the pairs of consecutive images. The experimental results show the power and robustness of the proposed approach.

An in vitro force measurement assay to study the early mechanical interaction between corneal fibroblasts and collagen matrix.

PubMed

Roy, P; Petroll, W M; Cavanagh, H D; Chuong, C J; Jester, J V

1997-04-10

An in vitro force measurement assay has been developed to quantify the forces exerted by single corneal fibroblasts during the early interaction with a collagen matrix. Corneal fibroblasts were sparsely seeded on top of collagen matrices whose stiffness was predetermined by micromanipulation with calibrated fine glass microneedles. The forces exerted by individual cells were calculated from time-lapse videomicroscopic recordings of the 2-D elastic distortion of the matrix. In additional experiments, the degree of permanent reorganization of the collagen matrices was assessed by lysing the cells with 1% Triton X-100 solution at the end of a 2-hour incubation and recording the subsequent relaxation. The data suggest that a cell can exert comparable centripetal force during either extension of a cell process or partial retraction of an extended pseudopodia. The rates of force associated with pseudopodial extension and partial retraction were 0.180 +/- 0.091 (x 10(-8)) N/min (n = 8 experiments) and 0.213 +/- 0.063 (x 10(-8)) N/min (n = 8 experiments), respectively. Rupture of pseudopodial adhesion associated with cell locomotion causes a release of force on the matrix and a complete recoil of the pseudopodia concerned; a simultaneous release of force on the matrix was also observed at the opposite end of the cell. Lysis of cells resulted in 84 +/- 18% relaxation of the matrix, suggesting that little permanent remodeling of matrix is produced by the actions of isolated migrating cells.

Big and small: menisci in soil pores affect water pressures, dynamics of groundwater levels, and catchment-scale average matric potentials

NASA Astrophysics Data System (ADS)

de Rooij, G. H.

2010-09-01

Soil water is confined behind the menisci of its water-air interface. Catchment-scale fluxes (groundwater recharge, evaporation, transpiration, precipitation, etc.) affect the matric potential, and thereby the interface curvature and the configuration of the phases. In turn, these affect the fluxes (except precipitation), creating feedbacks between pore-scale and catchment-scale processes. Tracking pore-scale processes beyond the Darcy scale is not feasible. Instead, for a simplified system based on the classical Darcy's Law and Laplace-Young Law we i) clarify how menisci transfer pressure from the atmosphere to the soil water, ii) examine large-scale phenomena arising from pore-scale processes, and iii) analyze the relationship between average meniscus curvature and average matric potential. In stagnant water, changing the gravitational potential or the curvature of the air-water interface changes the pressure throughout the water. Adding small amounts of water can thus profoundly affect water pressures in a much larger volume. The pressure-regulating effect of the interface curvature showcases the meniscus as a pressure port that transfers the atmospheric pressure to the water with an offset directly proportional to its curvature. This property causes an extremely rapid rise of phreatic levels in soils once the capillary fringe extends to the soil surface and the menisci flatten. For large bodies of subsurface water, the curvature and vertical position of any meniscus quantify the uniform hydraulic potential under hydrostatic equilibrium. During unit-gradient flow, the matric potential corresponding to the mean curvature of the menisci should provide a good approximation of the intrinsic phase average of the matric potential.

Comparison of Compressed Sensing Algorithms for Inversion of 3-D Electrical Resistivity Tomography.

NASA Astrophysics Data System (ADS)

Peddinti, S. R.; Ranjan, S.; Kbvn, D. P.

2016-12-01

Image reconstruction algorithms derived from electrical resistivity tomography (ERT) are highly non-linear, sparse, and ill-posed. The inverse problem is much severe, when dealing with 3-D datasets that result in large sized matrices. Conventional gradient based techniques using L2 norm minimization with some sort of regularization can impose smoothness constraint on the solution. Compressed sensing (CS) is relatively new technique that takes the advantage of inherent sparsity in parameter space in one or the other form. If favorable conditions are met, CS was proven to be an efficient image reconstruction technique that uses limited observations without losing edge sharpness. This paper deals with the development of an open source 3-D resistivity inversion tool using CS framework. The forward model was adopted from RESINVM3D (Pidlisecky et al., 2007) with CS as the inverse code. Discrete cosine transformation (DCT) function was used to induce model sparsity in orthogonal form. Two CS based algorithms viz., interior point method and two-step IST were evaluated on a synthetic layered model with surface electrode observations. The algorithms were tested (in terms of quality and convergence) under varying degrees of parameter heterogeneity, model refinement, and reduced observation data space. In comparison to conventional gradient algorithms, CS was proven to effectively reconstruct the sub-surface image with less computational cost. This was observed by a general increase in NRMSE from 0.5 in 10 iterations using gradient algorithm to 0.8 in 5 iterations using CS algorithms.

Simulation of sparse matrix array designs

NASA Astrophysics Data System (ADS)

Boehm, Rainer; Heckel, Thomas

2018-04-01

Matrix phased array probes are becoming more prominently used in industrial applications. The main drawbacks, using probes incorporating a very large number of transducer elements, are needed for an appropriate cabling and an ultrasonic device offering many parallel channels. Matrix arrays designed for extended functionality feature at least 64 or more elements. Typical arrangements are square matrices, e.g., 8 by 8 or 11 by 11 or rectangular matrixes, e.g., 8 by 16 or 10 by 12 to fit a 128-channel phased array system. In some phased array systems, the number of simultaneous active elements is limited to a certain number, e.g., 32 or 64. Those setups do not allow running the probe with all elements active, which may cause a significant change in the directivity pattern of the resulting sound beam. When only a subset of elements can be used during a single acquisition, different strategies may be applied to collect enough data for rebuilding the missing information from the echo signal. Omission of certain elements may be one approach, overlay of subsequent shots with different active areas may be another one. This paper presents the influence of a decreased number of active elements on the sound field and their distribution on the array. Solutions using subsets with different element activity patterns on matrix arrays and their advantages and disadvantages concerning the sound field are evaluated using semi-analytical simulation tools. Sound field criteria are discussed, which are significant for non-destructive testing results and for the system setup.

Evaluation of polycaprolactone matrices for the intravaginal delivery of metronidazole in the treatment of bacterial vaginosis.

PubMed

Pathak, Meenakshi; Turner, Mark; Palmer, Cheryn; Coombes, Allan G A

2014-09-01

Microporous, poly (ɛ-caprolactone) (PCL) matrices loaded with the antibacterial, metronidazole were produced by rapidly cooling suspensions of drug powder in PCL solutions in acetone. Drug incorporation in the matrices increased from 2.0% to 10.6% w/w on raising the drug loading of the PCL solution from 5% to 20% w/w measured with respect to the PCL content. Drug loading efficiencies of 40-53% were obtained. Rapid 'burst release' of 35-55% of the metronidazole content was recorded over 24 h when matrices were immersed in simulated vaginal fluid (SVF), due to the presence of large amounts of drug on matrix surface as revealed by Raman microscopy. Gradual release of around 80% of the drug content occurred over the following 12 days. Metronidazole released from PCL matrices in SVF retained antimicrobial activity against Gardnerella vaginalis in vitro at levels up to 97% compared to the free drug. Basic modelling predicted that the concentrations of metronidazole released into vaginal fluid in vivo from a PCL matrix in the form of an intravaginal ring would exceed the minimum inhibitory concentration of metronidazole against G. vaginalis. These findings recommend further investigation of PCL matrices as intravaginal devices for controlled delivery of metronidazole in the treatment and prevention of bacterial vaginosis. © The Author(s) 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

TiO2-Based Photocatalytic Geopolymers for Nitric Oxide Degradation

PubMed Central

Strini, Alberto; Roviello, Giuseppina; Ricciotti, Laura; Ferone, Claudio; Messina, Francesco; Schiavi, Luca; Corsaro, Davide; Cioffi, Raffaele

2016-01-01

This study presents an experimental overview for the development of photocatalytic materials based on geopolymer binders as catalyst support matrices. Particularly, geopolymer matrices obtained from different solid precursors (fly ash and metakaolin), composite systems (siloxane-hybrid, foamed hybrid), and curing temperatures (room temperature and 60 °C) were investigated for the same photocatalyst content (i.e., 3% TiO2 by weight of paste). The geopolymer matrices were previously designed for different applications, ranging from insulating (foam) to structural materials. The photocatalytic activity was evaluated as NO degradation in air, and the results were compared with an ordinary Portland cement reference. The studied matrices demonstrated highly variable photocatalytic performance depending on both matrix constituents and the curing temperature, with promising activity revealed by the geopolymers based on fly ash and metakaolin. Furthermore, microstructural features and titania dispersion in the matrices were assessed by scanning electron microscopy (SEM) and energy dispersive X-ray (EDS) analyses. Particularly, EDS analyses of sample sections indicated segregation effects of titania in the surface layer, with consequent enhancement or depletion of the catalyst concentration in the active sample region, suggesting non-negligible transport phenomena during the curing process. The described results demonstrated that geopolymer binders can be interesting catalyst support matrices for the development of photocatalytic materials and indicated a large potential for the exploitation of their peculiar features. PMID:28773634

Large computer simulations on elastic networks: Small eigenvalues and eigenvalue spectra of the Kirchhoff matrix

NASA Astrophysics Data System (ADS)

Shy, L. Y.; Eichinger, B. E.

1989-05-01

Computer simulations of the formation of trifunctional and tetrafunctional polydimethyl-siloxane networks that are crosslinked by condensation of telechelic chains with multifunctional crosslinking agents have been carried out on systems containing up to 1.05×106 chains. Eigenvalue spectra of Kirchhoff matrices for these networks have been evaluated at two levels of approximation: (1) inclusion of all midchain modes, and (2) suppression of midchain modes. By use of the recursion method of Haydock and Nex, we have been able to effectively diagonalize matrices with 730 498 rows and columns without actually constructing matrices of this size. The small eigenvalues have been computed by use of the Lanczos algorithm. We demonstrate the following results: (1) The smallest eigenvalues (with chain modes suppressed) vary as μ-2/3 for sufficiently large μ, where μ is the number of junctions in the network; (2) the eigenvalue spectra of the Kirchhoff matrices are well described by McKay's theory for random regular graphs in the range of the larger eigenvalues, but there are significant departures in the region of small eigenvalues where computed spectra have many more small eigenvalues than random regular graphs; (3) the smallest eigenvalues vary as n-1.78 where n is the number of Rouse beads in the chains that comprise the network. Computations are done for both monodisperse and polydisperse chain length distributions. Large eigenvalues associated with localized motion of the junctions are found as predicted by theory. The relationship between the small eigenvalues and the equilibrium modulus of elasticity is discussed, as is the relationship between viscoelasticity and the band edge of the spectrum.

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

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches.

PubMed

Mills, Jeffrey D; Ben-Nun, Michal; Rollin, Kyle; Bromley, Michael W J; Li, Jiabo; Hinde, Robert J; Winstead, Carl L; Sheehy, Jeffrey A; Boatz, Jerry A; Langhoff, Peter W

2016-08-25

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Sparse representation-based volumetric super-resolution algorithm for 3D CT images of reservoir rocks

NASA Astrophysics Data System (ADS)

Li, Zhengji; Teng, Qizhi; He, Xiaohai; Yue, Guihua; Wang, Zhengyong

2017-09-01

The parameter evaluation of reservoir rocks can help us to identify components and calculate the permeability and other parameters, and it plays an important role in the petroleum industry. Until now, computed tomography (CT) has remained an irreplaceable way to acquire the microstructure of reservoir rocks. During the evaluation and analysis, large samples and high-resolution images are required in order to obtain accurate results. Owing to the inherent limitations of CT, however, a large field of view results in low-resolution images, and high-resolution images entail a smaller field of view. Our method is a promising solution to these data collection limitations. In this study, a framework for sparse representation-based 3D volumetric super-resolution is proposed to enhance the resolution of 3D voxel images of reservoirs scanned with CT. A single reservoir structure and its downgraded model are divided into a large number of 3D cubes of voxel pairs and these cube pairs are used to calculate two overcomplete dictionaries and the sparse-representation coefficients in order to estimate the high frequency component. Future more, to better result, a new feature extract method with combine BM4D together with Laplacian filter are introduced. In addition, we conducted a visual evaluation of the method, and used the PSNR and FSIM to evaluate it qualitatively.

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.

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression *

PubMed Central

Sun, Qiang; Zhu, Hongtu; Liu, Yufeng; Ibrahim, Joseph G.

2014-01-01

The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling’s T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods. PMID:26527844

Robust visual tracking via multiscale deep sparse networks

NASA Astrophysics Data System (ADS)

Wang, Xin; Hou, Zhiqiang; Yu, Wangsheng; Xue, Yang; Jin, Zefenfen; Dai, Bo

2017-04-01

In visual tracking, deep learning with offline pretraining can extract more intrinsic and robust features. It has significant success solving the tracking drift in a complicated environment. However, offline pretraining requires numerous auxiliary training datasets and is considerably time-consuming for tracking tasks. To solve these problems, a multiscale sparse networks-based tracker (MSNT) under the particle filter framework is proposed. Based on the stacked sparse autoencoders and rectifier linear unit, the tracker has a flexible and adjustable architecture without the offline pretraining process and exploits the robust and powerful features effectively only through online training of limited labeled data. Meanwhile, the tracker builds four deep sparse networks of different scales, according to the target's profile type. During tracking, the tracker selects the matched tracking network adaptively in accordance with the initial target's profile type. It preserves the inherent structural information more efficiently than the single-scale networks. Additionally, a corresponding update strategy is proposed to improve the robustness of the tracker. Extensive experimental results on a large scale benchmark dataset show that the proposed method performs favorably against state-of-the-art methods in challenging environments.

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.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Hi-Corrector: a fast, scalable and memory-efficient package for normalizing large-scale Hi-C data.

PubMed

Li, Wenyuan; Gong, Ke; Li, Qingjiao; Alber, Frank; Zhou, Xianghong Jasmine

2015-03-15

Genome-wide proximity ligation assays, e.g. Hi-C and its variant TCC, have recently become important tools to study spatial genome organization. Removing biases from chromatin contact matrices generated by such techniques is a critical preprocessing step of subsequent analyses. The continuing decline of sequencing costs has led to an ever-improving resolution of the Hi-C data, resulting in very large matrices of chromatin contacts. Such large-size matrices, however, pose a great challenge on the memory usage and speed of its normalization. Therefore, there is an urgent need for fast and memory-efficient methods for normalization of Hi-C data. We developed Hi-Corrector, an easy-to-use, open source implementation of the Hi-C data normalization algorithm. Its salient features are (i) scalability-the software is capable of normalizing Hi-C data of any size in reasonable times; (ii) memory efficiency-the sequential version can run on any single computer with very limited memory, no matter how little; (iii) fast speed-the parallel version can run very fast on multiple computing nodes with limited local memory. The sequential version is implemented in ANSI C and can be easily compiled on any system; the parallel version is implemented in ANSI C with the MPI library (a standardized and portable parallel environment designed for solving large-scale scientific problems). The package is freely available at http://zhoulab.usc.edu/Hi-Corrector/. © The Author 2014. Published by Oxford University Press.

Sparse PLS discriminant analysis: biologically relevant feature selection and graphical displays for multiclass problems.

PubMed

Lê Cao, Kim-Anh; Boitard, Simon; Besse, Philippe

2011-06-22

Variable selection on high throughput biological data, such as gene expression or single nucleotide polymorphisms (SNPs), becomes inevitable to select relevant information and, therefore, to better characterize diseases or assess genetic structure. There are different ways to perform variable selection in large data sets. Statistical tests are commonly used to identify differentially expressed features for explanatory purposes, whereas Machine Learning wrapper approaches can be used for predictive purposes. In the case of multiple highly correlated variables, another option is to use multivariate exploratory approaches to give more insight into cell biology, biological pathways or complex traits. A simple extension of a sparse PLS exploratory approach is proposed to perform variable selection in a multiclass classification framework. sPLS-DA has a classification performance similar to other wrapper or sparse discriminant analysis approaches on public microarray and SNP data sets. More importantly, sPLS-DA is clearly competitive in terms of computational efficiency and superior in terms of interpretability of the results via valuable graphical outputs. sPLS-DA is available in the R package mixOmics, which is dedicated to the analysis of large biological data sets.

Structural performance analysis and redesign

NASA Technical Reports Server (NTRS)

Whetstone, W. D.

1978-01-01

Program performs stress buckling and vibrational analysis of large, linear, finite-element systems in excess of 50,000 degrees of freedom. Cost, execution time, and storage requirements are kept reasonable through use of sparse matrix solution techniques, and other computational and data management procedures designed for problems of very large size.

LANZ: Software solving the large sparse symmetric generalized eigenproblem

NASA Technical Reports Server (NTRS)

Jones, Mark T.; Patrick, Merrell L.

1990-01-01

A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.

Large-Capacity Three-Party Quantum Digital Secret Sharing Using Three Particular Matrices Coding

NASA Astrophysics Data System (ADS)

Lai, Hong; Luo, Ming-Xing; Pieprzyk, Josef; Tao, Li; Liu, Zhi-Ming; Orgun, Mehmet A.

2016-11-01

In this paper, we develop a large-capacity quantum digital secret sharing (QDSS) scheme, combined the Fibonacci- and Lucas-valued orbital angular momentum (OAM) entanglement with the recursive Fibonacci and Lucas matrices. To be exact, Alice prepares pairs of photons in the Fibonacci- and Lucas-valued OAM entangled states, and then allocates them to two participants, say, Bob and Charlie, to establish the secret key. Moreover, the available Fibonacci and Lucas values from the matching entangled states are used as the seed for generating the Fibonacci and Lucas matrices. This is achieved because the entries of the Fibonacci and Lucas matrices are recursive. The secret key can only be obtained jointly by Bob and Charlie, who can further recover the secret. Its security is based on the facts that nonorthogonal states are indistinguishable, and Bob or Charlie detects a Fibonacci number, there is still a twofold uncertainty for Charlie' (Bob') detected value. Supported by the Fundamental Research Funds for the Central Universities under Grant No. XDJK2016C043 and the Doctoral Program of Higher Education under Grant No. SWU115091, the National Natural Science Foundation of China under Grant No. 61303039, the Fundamental Research Funds for the Central Universities under Grant No. XDJK2015C153 and the Doctoral Program of Higher Education under Grant No. SWU114112, and the Financial Support the 1000-Plan of Chongqing by Southwest University under Grant No. SWU116007

Beyond the functional matrix hypothesis: a network null model of human skull growth for the formation of bone articulations

PubMed Central

Esteve-Altava, Borja; Rasskin-Gutman, Diego

2014-01-01

Craniofacial sutures and synchondroses form the boundaries among bones in the human skull, providing functional, developmental and evolutionary information. Bone articulations in the skull arise due to interactions between genetic regulatory mechanisms and epigenetic factors such as functional matrices (soft tissues and cranial cavities), which mediate bone growth. These matrices are largely acknowledged for their influence on shaping the bones of the skull; however, it is not fully understood to what extent functional matrices mediate the formation of bone articulations. Aiming to identify whether or not functional matrices are key developmental factors guiding the formation of bone articulations, we have built a network null model of the skull that simulates unconstrained bone growth. This null model predicts bone articulations that arise due to a process of bone growth that is uniform in rate, direction and timing. By comparing predicted articulations with the actual bone articulations of the human skull, we have identified which boundaries specifically need the presence of functional matrices for their formation. We show that functional matrices are necessary to connect facial bones, whereas an unconstrained bone growth is sufficient to connect non-facial bones. This finding challenges the role of the brain in the formation of boundaries between bones in the braincase without neglecting its effect on skull shape. Ultimately, our null model suggests where to look for modified developmental mechanisms promoting changes in bone growth patterns that could affect the development and evolution of the head skeleton. PMID:24975579

Location Prediction Based on Transition Probability Matrices Constructing from Sequential Rules for Spatial-Temporal K-Anonymity Dataset

PubMed Central

Liu, Zhao; Zhu, Yunhong; Wu, Chenxue

2016-01-01

Spatial-temporal k-anonymity has become a mainstream approach among techniques for protection of users’ privacy in location-based services (LBS) applications, and has been applied to several variants such as LBS snapshot queries and continuous queries. Analyzing large-scale spatial-temporal anonymity sets may benefit several LBS applications. In this paper, we propose two location prediction methods based on transition probability matrices constructing from sequential rules for spatial-temporal k-anonymity dataset. First, we define single-step sequential rules mined from sequential spatial-temporal k-anonymity datasets generated from continuous LBS queries for multiple users. We then construct transition probability matrices from mined single-step sequential rules, and normalize the transition probabilities in the transition matrices. Next, we regard a mobility model for an LBS requester as a stationary stochastic process and compute the n-step transition probability matrices by raising the normalized transition probability matrices to the power n. Furthermore, we propose two location prediction methods: rough prediction and accurate prediction. The former achieves the probabilities of arriving at target locations along simple paths those include only current locations, target locations and transition steps. By iteratively combining the probabilities for simple paths with n steps and the probabilities for detailed paths with n-1 steps, the latter method calculates transition probabilities for detailed paths with n steps from current locations to target locations. Finally, we conduct extensive experiments, and correctness and flexibility of our proposed algorithm have been verified. PMID:27508502

Solar photocatalytic treatment of trimethoprim in four environmental matrices at a pilot scale: transformation products and ecotoxicity evaluation.

PubMed

Michael, I; Hapeshi, E; Osorio, V; Perez, S; Petrovic, M; Zapata, A; Malato, S; Barceló, D; Fatta-Kassinos, D

2012-07-15

The pilot-scale solar degradation of trimethoprim (TMP) in different water matrices (demineralized water: DW, simulated natural freshwater: SW; simulated wastewater: SWW; and real effluent: RE) was investigated in this study. DOC removal was lower in the case of SW compared to DW, which can be attributed to the presence of inorganic anions which may act as scavengers of the HO·. Furthermore, the presence of organic carbon and higher salt content in SWW and RE led to lower mineralization per dose of hydrogen peroxide compared to DW and SW. Toxicity assays in SWW and RE were also performed indicating that toxicity is attributed to the compounds present in RE and their by-products formed during solar Fenton treatment and not to the intermediates formed by the oxidation of TMP. A large number of compounds generated by the photocatalytic transformation of TMP were identified by UPLC-QToF/MS. The degradation pathway revealed differences among the four matrices; however hydroxylation, demethylation and cleavage reactions were observed in all matrices. To the best of our knowledge this is the first time that TMP degradation products have been identified by adopting a solar Fenton process at a pilot-scale set-up, using four different aqueous matrices. Copyright © 2012 Elsevier B.V. All rights reserved.

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

NASA Astrophysics Data System (ADS)

He, Song; Lin, Feng-Li; Zhang, Jia-ju

2017-12-01

We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length ℓ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the Rényi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of ℓ9 for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.

Analysis of large power systems

NASA Technical Reports Server (NTRS)

Dommel, H. W.

1975-01-01

Computer-oriented power systems analysis procedures in the electric utilities are surveyed. The growth of electric power systems is discussed along with the solution of sparse network equations, power flow, and stability studies.

Visual properties and memorising scenes: Effects of image-space sparseness and uniformity.

PubMed

Lukavský, Jiří; Děchtěrenko, Filip

2017-10-01

Previous studies have demonstrated that humans have a remarkable capacity to memorise a large number of scenes. The research on memorability has shown that memory performance can be predicted by the content of an image. We explored how remembering an image is affected by the image properties within the context of the reference set, including the extent to which it is different from its neighbours (image-space sparseness) and if it belongs to the same category as its neighbours (uniformity). We used a reference set of 2,048 scenes (64 categories), evaluated pairwise scene similarity using deep features from a pretrained convolutional neural network (CNN), and calculated the image-space sparseness and uniformity for each image. We ran three memory experiments, varying the memory workload with experiment length and colour/greyscale presentation. We measured the sensitivity and criterion value changes as a function of image-space sparseness and uniformity. Across all three experiments, we found separate effects of 1) sparseness on memory sensitivity, and 2) uniformity on the recognition criterion. People better remembered (and correctly rejected) images that were more separated from others. People tended to make more false alarms and fewer miss errors in images from categorically uniform portions of the image-space. We propose that both image-space properties affect human decisions when recognising images. Additionally, we found that colour presentation did not yield better memory performance over grayscale images.

Sparse Measurement Systems: Applications, Analysis, Algorithms and Design

ERIC Educational Resources Information Center

Narayanaswamy, Balakrishnan

2011-01-01

This thesis deals with "large-scale" detection problems that arise in many real world applications such as sensor networks, mapping with mobile robots and group testing for biological screening and drug discovery. These are problems where the values of a large number of inputs need to be inferred from noisy observations and where the…

The shared and unique values of optical, fluorescence, thermal and microwave satellite data for estimating large-scale crop yields

USDA-ARS?s Scientific Manuscript database

Large-scale crop monitoring and yield estimation are important for both scientific research and practical applications. Satellite remote sensing provides an effective means for regional and global cropland monitoring, particularly in data-sparse regions that lack reliable ground observations and rep...

High-sensitivity direct analysis of aflatoxins in peanuts and cereal matrices by ultra-performance liquid chromatography with fluorescence detection involving a large volume flow cell.

PubMed

Oulkar, Dasharath; Goon, Arnab; Dhanshetty, Manisha; Khan, Zareen; Satav, Sagar; Banerjee, Kaushik

2018-04-03

This paper reports a sensitive and cost effective method of analysis for aflatoxins B1, B2, G1 and G2. The sample preparation method was primarily optimised in peanuts, followed by its validation in a range of peanut-processed products and cereal (rice, corn, millets) matrices. Peanut slurry [12.5 g peanut + 12.5 mL water] was extracted with methanol: water (8:2, 100 mL), cleaned through an immunoaffinity column and thereafter measured directly by ultra-performance liquid chromatography-fluorescence (UPLC-FLD) detection, within a chromatographic runtime of 5 minutes. The use of a large volume flow cell in the FLD nullified the requirement of any post-column derivatisation and provided the lowest ever reported limits of quantification of 0.025 for B1 and G1 and 0.01 μg/kg for B2 and G2. The single laboratory validation of the method provided acceptable selectivity, linearity, recovery and precision for reliable quantifications in all the test matrices as well as demonstrated compliance with the EC 401/2006 guidelines for analytical quality control of aflatoxins in foodstuffs.

Magnostics: Image-Based Search of Interesting Matrix Views for Guided Network Exploration.

PubMed

Behrisch, Michael; Bach, Benjamin; Hund, Michael; Delz, Michael; Von Ruden, Laura; Fekete, Jean-Daniel; Schreck, Tobias

2017-01-01

In this work we address the problem of retrieving potentially interesting matrix views to support the exploration of networks. We introduce Matrix Diagnostics (or Magnostics), following in spirit related approaches for rating and ranking other visualization techniques, such as Scagnostics for scatter plots. Our approach ranks matrix views according to the appearance of specific visual patterns, such as blocks and lines, indicating the existence of topological motifs in the data, such as clusters, bi-graphs, or central nodes. Magnostics can be used to analyze, query, or search for visually similar matrices in large collections, or to assess the quality of matrix reordering algorithms. While many feature descriptors for image analyzes exist, there is no evidence how they perform for detecting patterns in matrices. In order to make an informed choice of feature descriptors for matrix diagnostics, we evaluate 30 feature descriptors-27 existing ones and three new descriptors that we designed specifically for MAGNOSTICS-with respect to four criteria: pattern response, pattern variability, pattern sensibility, and pattern discrimination. We conclude with an informed set of six descriptors as most appropriate for Magnostics and demonstrate their application in two scenarios; exploring a large collection of matrices and analyzing temporal networks.

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

NASA Technical Reports Server (NTRS)

Ghosh, Amitabha

1997-01-01

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunnel. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally some results of the current investigation are presented.

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

NASA Technical Reports Server (NTRS)

Ghosh, Amitabha

1997-01-01

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunell. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally, some results of the current investigation are presented.

Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas

2018-04-01

We prove that Gibbs measures based on 1D defocusing nonlinear Schrödinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity, and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices.

Analysis, tuning and comparison of two general sparse solvers for distributed memory computers

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

Amestoy, P.R.; Duff, I.S.; L'Excellent, J.-Y.

2000-06-30

We describe the work performed in the context of a Franco-Berkeley funded project between NERSC-LBNL located in Berkeley (USA) and CERFACS-ENSEEIHT located in Toulouse (France). We discuss both the tuning and performance analysis of two distributed memory sparse solvers (superlu from Berkeley and mumps from Toulouse) on the 512 processor Cray T3E from NERSC (Lawrence Berkeley National Laboratory). This project gave us the opportunity to improve the algorithms and add new features to the codes. We then quite extensively analyze and compare the two approaches on a set of large problems from real applications. We further explain the main differencesmore » in the behavior of the approaches on artificial regular grid problems. As a conclusion to this activity report, we mention a set of parallel sparse solvers on which this type of study should be extended.« less

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.

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.

Modified conjugate gradient method for diagonalizing large matrices.

PubMed

Jie, Quanlin; Liu, Dunhuan

2003-11-01

We present an iterative method to diagonalize large matrices. The basic idea is the same as the conjugate gradient (CG) method, i.e, minimizing the Rayleigh quotient via its gradient and avoiding reintroducing errors to the directions of previous gradients. Each iteration step is to find lowest eigenvector of the matrix in a subspace spanned by the current trial vector and the corresponding gradient of the Rayleigh quotient, as well as some previous trial vectors. The gradient, together with the previous trial vectors, play a similar role as the conjugate gradient of the original CG algorithm. Our numeric tests indicate that this method converges significantly faster than the original CG method. And the computational cost of one iteration step is about the same as the original CG method. It is suitable for first principle calculations.

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

The w-effect in interferometric imaging: from a fast sparse measurement operator to superresolution

NASA Astrophysics Data System (ADS)

Dabbech, A.; Wolz, L.; Pratley, L.; McEwen, J. D.; Wiaux, Y.

2017-11-01

Modern radio telescopes, such as the Square Kilometre Array, will probe the radio sky over large fields of view, which results in large w-modulations of the sky image. This effect complicates the relationship between the measured visibilities and the image under scrutiny. In algorithmic terms, it gives rise to massive memory and computational time requirements. Yet, it can be a blessing in terms of reconstruction quality of the sky image. In recent years, several works have shown that large w-modulations promote the spread spectrum effect. Within the compressive sensing framework, this effect increases the incoherence between the sensing basis and the sparsity basis of the signal to be recovered, leading to better estimation of the sky image. In this article, we revisit the w-projection approach using convex optimization in realistic settings, where the measurement operator couples the w-terms in Fourier and the de-gridding kernels. We provide sparse, thus fast, models of the Fourier part of the measurement operator through adaptive sparsification procedures. Consequently, memory requirements and computational cost are significantly alleviated at the expense of introducing errors on the radio interferometric data model. We present a first investigation of the impact of the sparse variants of the measurement operator on the image reconstruction quality. We finally analyse the interesting superresolution potential associated with the spread spectrum effect of the w-modulation, and showcase it through simulations. Our c++ code is available online on GitHub.

Human exposure assessment in the near field of GSM base-station antennas using a hybrid finite element/method of moments technique.

PubMed

Meyer, Frans J C; Davidson, David B; Jakobus, Ulrich; Stuchly, Maria A

2003-02-01

A hybrid finite-element method (FEM)/method of moments (MoM) technique is employed for specific absorption rate (SAR) calculations in a human phantom in the near field of a typical group special mobile (GSM) base-station antenna. The MoM is used to model the metallic surfaces and wires of the base-station antenna, and the FEM is used to model the heterogeneous human phantom. The advantages of each of these frequency domain techniques are, thus, exploited, leading to a highly efficient and robust numerical method for addressing this type of bioelectromagnetic problem. The basic mathematical formulation of the hybrid technique is presented. This is followed by a discussion of important implementation details-in particular, the linear algebra routines for sparse, complex FEM matrices combined with dense MoM matrices. The implementation is validated by comparing results to MoM (surface equivalence principle implementation) and finite-difference time-domain (FDTD) solutions of human exposure problems. A comparison of the computational efficiency of the different techniques is presented. The FEM/MoM implementation is then used for whole-body and critical-organ SAR calculations in a phantom at different positions in the near field of a base-station antenna. This problem cannot, in general, be solved using the MoM or FDTD due to computational limitations. This paper shows that the specific hybrid FEM/MoM implementation is an efficient numerical tool for accurate assessment of human exposure in the near field of base-station antennas.

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

PubMed

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

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

A revised MRCI-algorithm. I. Efficient combination of spin adaptation with individual configuration selection coupled to an effective valence-shell Hamiltonian

NASA Astrophysics Data System (ADS)

Strodel, Paul; Tavan, Paul

2002-09-01

We present a revised multi-reference configuration interaction (MRCI) algorithm for balanced and efficient calculation of electronic excitations in molecules. The revision takes up an earlier method, which had been designed for flexible, state-specific, and individual selection (IS) of MRCI expansions, included perturbational corrections (PERT), and used the spin-coupled hole-particle formalism of Tavan and Schulten (1980) for matrix-element evaluation. It removes the deficiencies of this method by introducing tree structures, which code the CI bases and allow us to efficiently exploit the sparseness of the Hamiltonian matrices. The algorithmic complexity is shown to be optimal for IS/MRCI applications. The revised IS/MRCI/PERT module is combined with the effective valence shell Hamiltonian OM2 suggested by Weber and Thiel (2000). This coupling serves the purpose of making excited state surfaces of organic dye molecules accessible to relatively cheap and sufficiently precise descriptions.

Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems

DOE PAGES

Jia, C. J.; Wang, Y.; Mendl, C. B.; ...

2017-12-02

Here, we describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the “checkerboard” decomposition of the Hamiltonian matrixmore » for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.« less

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.

Characterisation of cold plasma treated beef and dairy lipids using spectroscopic and chromatographic methods.

PubMed

Sarangapani, Chaitanya; Ryan Keogh, David; Dunne, Julie; Bourke, Paula; Cullen, P J

2017-11-15

The efficacy of cold plasma for inactivation of food-borne pathogens in foods is established. However, insights on cold plasma-food interactions in terms of quality effects, particularly for oils and fats, are sparse. This study evaluated plasma-induced lipid oxidation of model matrices, namely dairy and meat fats. Product characterisation was performed using FTIR, 1 H NMR and chromatographic techniques. The oxidation of lipids by cold plasma followed the Criegee mechanism and typical oxidation products identified included ozonides, aldehydes (hexanal, pentenal, nonanal and nonenal) and carboxylic acids (9-oxononanoic acid, octanoic acid, nonanoic acid), along with hydroperoxides (9- and 13-hydroperoxy-octadecadienoylglycerol species). However, these oxidation products were only identified following extended treatment times of 30min and were also a function of applied voltage level. Understanding cold plasma interactions with food lipids and the critical parameters governing lipid oxidation is required prior to the industrial adoption of this technology for food products with high fat contents. Copyright © 2017 Elsevier Ltd. All rights reserved.

Ultrastructure of periprosthetic Dacron knee ligament tissue. Two cases of ruptured anterior cruciate ligament reconstruction.

PubMed

Salvi, M; Velluti, C; Misasi, M; Bartolozzi, P; Quacci, D; Dell'Orbo, C

1991-04-01

Light- and electron-microscopic investigations were performed on two failed Dacron ligaments that had been removed from 2 patients shortly after failure of the implant 2-3 years after reconstruction of the anterior cruciate ligament. Two different cell populations and matrices were correlated with closeness to the Dacron threads. Fibroblasts surrounded by connective tissue with collagen fibrils were located far from the Dacron threads. Roundish cells, appearing to be myofibroblasts surrounded by a more lax connective tissue and elastic fibers, were found close to the Dacron threads. The presence of myofibroblasts and the matrix differentiation could be attributed to the different mechanical forces acting on the Dacron and on the connective tissue because of their different coefficients of elasticity. The sparse occurrence of inflammatory cells in the synovial membrane and in the connective tissue surrounding the Dacron supports the biologic inertness of this artificial material. However, the repair tissue was not structured to resist tension stresses.

Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity.

PubMed

Chang, Jinyuan; Zheng, Chao; Zhou, Wen-Xin; Zhou, Wen

2017-12-01

In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic data sets and an human acute lymphoblastic leukemia gene expression data set, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN. © 2017, The International Biometric Society.

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

DOE PAGES

Zhang, Hong; Zapol, Peter; Dixon, David A.; ...

2015-11-17

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPsmore » is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.« less

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.

Shift-and-invert parallel spectral transformation eigensolver: Massively parallel performance for density-functional based tight-binding

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

Zhang, Hong; Zapol, Peter; Dixon, David A.

The Shift-and-invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density-functional based tight-binding (DFTB) Hamiltonian and overlap matrices for single-wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ~330,000 (~5600) eigenvalues and eigenfunctions are obtained in ~190 (~5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPsmore » is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time-to-solution at the strong scaling limit. As a result, a parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated.« less

Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems

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

Jia, C. J.; Wang, Y.; Mendl, C. B.

Here, we describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the “checkerboard” decomposition of the Hamiltonian matrixmore » for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.« less

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.

Parallel solution of sparse one-dimensional dynamic programming problems

NASA Technical Reports Server (NTRS)

Nicol, David M.

1989-01-01

Parallel computation offers the potential for quickly solving large computational problems. However, it is often a non-trivial task to effectively use parallel computers. Solution methods must sometimes be reformulated to exploit parallelism; the reformulations are often more complex than their slower serial counterparts. We illustrate these points by studying the parallelization of sparse one-dimensional dynamic programming problems, those which do not obviously admit substantial parallelization. We propose a new method for parallelizing such problems, develop analytic models which help us to identify problems which parallelize well, and compare the performance of our algorithm with existing algorithms on a multiprocessor.

Jaccard distance based weighted sparse representation for coarse-to-fine plant species recognition.

PubMed

Zhang, Shanwen; Wu, Xiaowei; You, Zhuhong

2017-01-01

Leaf based plant species recognition plays an important role in ecological protection, however its application to large and modern leaf databases has been a long-standing obstacle due to the computational cost and feasibility. Recognizing such limitations, we propose a Jaccard distance based sparse representation (JDSR) method which adopts a two-stage, coarse to fine strategy for plant species recognition. In the first stage, we use the Jaccard distance between the test sample and each training sample to coarsely determine the candidate classes of the test sample. The second stage includes a Jaccard distance based weighted sparse representation based classification(WSRC), which aims to approximately represent the test sample in the training space, and classify it by the approximation residuals. Since the training model of our JDSR method involves much fewer but more informative representatives, this method is expected to overcome the limitation of high computational and memory costs in traditional sparse representation based classification. Comparative experimental results on a public leaf image database demonstrate that the proposed method outperforms other existing feature extraction and SRC based plant recognition methods in terms of both accuracy and computational speed.

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.

CT Image Sequence Restoration Based on Sparse and Low-Rank Decomposition

PubMed Central

Gou, Shuiping; Wang, Yueyue; Wang, Zhilong; Peng, Yong; Zhang, Xiaopeng; Jiao, Licheng; Wu, Jianshe

2013-01-01

Blurry organ boundaries and soft tissue structures present a major challenge in biomedical image restoration. In this paper, we propose a low-rank decomposition-based method for computed tomography (CT) image sequence restoration, where the CT image sequence is decomposed into a sparse component and a low-rank component. A new point spread function of Weiner filter is employed to efficiently remove blur in the sparse component; a wiener filtering with the Gaussian PSF is used to recover the average image of the low-rank component. And then we get the recovered CT image sequence by combining the recovery low-rank image with all recovery sparse image sequence. Our method achieves restoration results with higher contrast, sharper organ boundaries and richer soft tissue structure information, compared with existing CT image restoration methods. The robustness of our method was assessed with numerical experiments using three different low-rank models: Robust Principle Component Analysis (RPCA), Linearized Alternating Direction Method with Adaptive Penalty (LADMAP) and Go Decomposition (GoDec). Experimental results demonstrated that the RPCA model was the most suitable for the small noise CT images whereas the GoDec model was the best for the large noisy CT images. PMID:24023764

Exploiting sparsity and low-rank structure for the recovery of multi-slice breast MRIs with reduced sampling error.

PubMed

Yin, X X; Ng, B W-H; Ramamohanarao, K; Baghai-Wadji, A; Abbott, D

2012-09-01

It has been shown that, magnetic resonance images (MRIs) with sparsity representation in a transformed domain, e.g. spatial finite-differences (FD), or discrete cosine transform (DCT), can be restored from undersampled k-space via applying current compressive sampling theory. The paper presents a model-based method for the restoration of MRIs. The reduced-order model, in which a full-system-response is projected onto a subspace of lower dimensionality, has been used to accelerate image reconstruction by reducing the size of the involved linear system. In this paper, the singular value threshold (SVT) technique is applied as a denoising scheme to reduce and select the model order of the inverse Fourier transform image, and to restore multi-slice breast MRIs that have been compressively sampled in k-space. The restored MRIs with SVT for denoising show reduced sampling errors compared to the direct MRI restoration methods via spatial FD, or DCT. Compressive sampling is a technique for finding sparse solutions to underdetermined linear systems. The sparsity that is implicit in MRIs is to explore the solution to MRI reconstruction after transformation from significantly undersampled k-space. The challenge, however, is that, since some incoherent artifacts result from the random undersampling, noise-like interference is added to the image with sparse representation. These recovery algorithms in the literature are not capable of fully removing the artifacts. It is necessary to introduce a denoising procedure to improve the quality of image recovery. This paper applies a singular value threshold algorithm to reduce the model order of image basis functions, which allows further improvement of the quality of image reconstruction with removal of noise artifacts. The principle of the denoising scheme is to reconstruct the sparse MRI matrices optimally with a lower rank via selecting smaller number of dominant singular values. The singular value threshold algorithm is performed by minimizing the nuclear norm of difference between the sampled image and the recovered image. It has been illustrated that this algorithm improves the ability of previous image reconstruction algorithms to remove noise artifacts while significantly improving the quality of MRI recovery.

Beyond the functional matrix hypothesis: a network null model of human skull growth for the formation of bone articulations.

PubMed

Esteve-Altava, Borja; Rasskin-Gutman, Diego

2014-09-01

Craniofacial sutures and synchondroses form the boundaries among bones in the human skull, providing functional, developmental and evolutionary information. Bone articulations in the skull arise due to interactions between genetic regulatory mechanisms and epigenetic factors such as functional matrices (soft tissues and cranial cavities), which mediate bone growth. These matrices are largely acknowledged for their influence on shaping the bones of the skull; however, it is not fully understood to what extent functional matrices mediate the formation of bone articulations. Aiming to identify whether or not functional matrices are key developmental factors guiding the formation of bone articulations, we have built a network null model of the skull that simulates unconstrained bone growth. This null model predicts bone articulations that arise due to a process of bone growth that is uniform in rate, direction and timing. By comparing predicted articulations with the actual bone articulations of the human skull, we have identified which boundaries specifically need the presence of functional matrices for their formation. We show that functional matrices are necessary to connect facial bones, whereas an unconstrained bone growth is sufficient to connect non-facial bones. This finding challenges the role of the brain in the formation of boundaries between bones in the braincase without neglecting its effect on skull shape. Ultimately, our null model suggests where to look for modified developmental mechanisms promoting changes in bone growth patterns that could affect the development and evolution of the head skeleton. © 2014 Anatomical Society.

Improved sparse decomposition based on a smoothed L0 norm using a Laplacian kernel to select features from fMRI data.

PubMed

Zhang, Chuncheng; Song, Sutao; Wen, Xiaotong; Yao, Li; Long, Zhiying

2015-04-30

Feature selection plays an important role in improving the classification accuracy of multivariate classification techniques in the context of fMRI-based decoding due to the "few samples and large features" nature of functional magnetic resonance imaging (fMRI) data. Recently, several sparse representation methods have been applied to the voxel selection of fMRI data. Despite the low computational efficiency of the sparse representation methods, they still displayed promise for applications that select features from fMRI data. In this study, we proposed the Laplacian smoothed L0 norm (LSL0) approach for feature selection of fMRI data. Based on the fast sparse decomposition using smoothed L0 norm (SL0) (Mohimani, 2007), the LSL0 method used the Laplacian function to approximate the L0 norm of sources. Results of the simulated and real fMRI data demonstrated the feasibility and robustness of LSL0 for the sparse source estimation and feature selection. Simulated results indicated that LSL0 produced more accurate source estimation than SL0 at high noise levels. The classification accuracy using voxels that were selected by LSL0 was higher than that by SL0 in both simulated and real fMRI experiment. Moreover, both LSL0 and SL0 showed higher classification accuracy and required less time than ICA and t-test for the fMRI decoding. LSL0 outperformed SL0 in sparse source estimation at high noise level and in feature selection. Moreover, LSL0 and SL0 showed better performance than ICA and t-test for feature selection. Copyright © 2015 Elsevier B.V. All rights reserved.

Combining DCQGMP-Based Sparse Decomposition and MPDR Beamformer for Multi-Type Interferences Mitigation for GNSS Receivers.

PubMed

Guo, Qiang; Qi, Liangang

2017-04-10

In the coexistence of multiple types of interfering signals, the performance of interference suppression methods based on time and frequency domains is degraded seriously, and the technique using an antenna array requires a large enough size and huge hardware costs. To combat multi-type interferences better for GNSS receivers, this paper proposes a cascaded multi-type interferences mitigation method combining improved double chain quantum genetic matching pursuit (DCQGMP)-based sparse decomposition and an MPDR beamformer. The key idea behind the proposed method is that the multiple types of interfering signals can be excised by taking advantage of their sparse features in different domains. In the first stage, the single-tone (multi-tone) and linear chirp interfering signals are canceled by sparse decomposition according to their sparsity in the over-complete dictionary. In order to improve the timeliness of matching pursuit (MP)-based sparse decomposition, a DCQGMP is introduced by combining an improved double chain quantum genetic algorithm (DCQGA) and the MP algorithm, and the DCQGMP algorithm is extended to handle the multi-channel signals according to the correlation among the signals in different channels. In the second stage, the minimum power distortionless response (MPDR) beamformer is utilized to nullify the residuary interferences (e.g., wideband Gaussian noise interferences). Several simulation results show that the proposed method can not only improve the interference mitigation degree of freedom (DoF) of the array antenna, but also effectively deal with the interference arriving from the same direction with the GNSS signal, which can be sparse represented in the over-complete dictionary. Moreover, it does not bring serious distortions into the navigation signal.

Combining DCQGMP-Based Sparse Decomposition and MPDR Beamformer for Multi-Type Interferences Mitigation for GNSS Receivers

PubMed Central

Guo, Qiang; Qi, Liangang

2017-01-01

In the coexistence of multiple types of interfering signals, the performance of interference suppression methods based on time and frequency domains is degraded seriously, and the technique using an antenna array requires a large enough size and huge hardware costs. To combat multi-type interferences better for GNSS receivers, this paper proposes a cascaded multi-type interferences mitigation method combining improved double chain quantum genetic matching pursuit (DCQGMP)-based sparse decomposition and an MPDR beamformer. The key idea behind the proposed method is that the multiple types of interfering signals can be excised by taking advantage of their sparse features in different domains. In the first stage, the single-tone (multi-tone) and linear chirp interfering signals are canceled by sparse decomposition according to their sparsity in the over-complete dictionary. In order to improve the timeliness of matching pursuit (MP)-based sparse decomposition, a DCQGMP is introduced by combining an improved double chain quantum genetic algorithm (DCQGA) and the MP algorithm, and the DCQGMP algorithm is extended to handle the multi-channel signals according to the correlation among the signals in different channels. In the second stage, the minimum power distortionless response (MPDR) beamformer is utilized to nullify the residuary interferences (e.g., wideband Gaussian noise interferences). Several simulation results show that the proposed method can not only improve the interference mitigation degree of freedom (DoF) of the array antenna, but also effectively deal with the interference arriving from the same direction with the GNSS signal, which can be sparse represented in the over-complete dictionary. Moreover, it does not bring serious distortions into the navigation signal. PMID:28394290

A uniform object-oriented solution to the eigenvalue problem for real symmetric and Hermitian matrices

NASA Astrophysics Data System (ADS)

Castro, María Eugenia; Díaz, Javier; Muñoz-Caro, Camelia; Niño, Alfonso

2011-09-01

We present a system of classes, SHMatrix, to deal in a unified way with the computation of eigenvalues and eigenvectors in real symmetric and Hermitian matrices. Thus, two descendant classes, one for the real symmetric and other for the Hermitian cases, override the abstract methods defined in a base class. The use of the inheritance relationship and polymorphism allows handling objects of any descendant class using a single reference of the base class. The system of classes is intended to be the core element of more sophisticated methods to deal with large eigenvalue problems, as those arising in the variational treatment of realistic quantum mechanical problems. The present system of classes allows computing a subset of all the possible eigenvalues and, optionally, the corresponding eigenvectors. Comparison with well established solutions for analogous eigenvalue problems, as those included in LAPACK, shows that the present solution is competitive against them. Program summaryProgram title: SHMatrix Catalogue identifier: AEHZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHZ_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.: 2616 No. of bytes in distributed program, including test data, etc.: 127 312 Distribution format: tar.gz Programming language: Standard ANSI C++. Computer: PCs and workstations. Operating system: Linux, Windows. Classification: 4.8. Nature of problem: The treatment of problems involving eigensystems is a central topic in the quantum mechanical field. Here, the use of the variational approach leads to the computation of eigenvalues and eigenvectors of real symmetric and Hermitian Hamiltonian matrices. Realistic models with several degrees of freedom leads to large (sometimes very large) matrices. Different techniques, such as divide and conquer, can be used to factorize the matrices in order to apply a parallel computing approach. However, it is still interesting to have a core procedure able to tackle the computation of eigenvalues and eigenvectors once the matrix has been factorized to pieces of enough small size. Several available software packages, such as LAPACK, tackled this problem under the traditional imperative programming paradigm. In order to ease the modelling of complex quantum mechanical models it could be interesting to apply an object-oriented approach to the treatment of the eigenproblem. This approach offers the advantage of a single, uniform treatment for the real symmetric and Hermitian cases. Solution method: To reach the above goals, we have developed a system of classes: SHMatrix. SHMatrix is composed by an abstract base class and two descendant classes, one for real symmetric matrices and the other for the Hermitian case. The object-oriented characteristics of inheritance and polymorphism allows handling both cases using a single reference of the base class. The basic computing strategy applied in SHMatrix allows computing subsets of eigenvalues and (optionally) eigenvectors. The tests performed show that SHMatrix is competitive, and more efficient for large matrices, than the equivalent routines of the LAPACK package. Running time: The examples included in the distribution take only a couple of seconds to run.

Optimization-based image reconstruction from sparse-view data in offset-detector CBCT

NASA Astrophysics Data System (ADS)

Bian, Junguo; Wang, Jiong; Han, Xiao; Sidky, Emil Y.; Shao, Lingxiong; Pan, Xiaochuan

2013-01-01

The field of view (FOV) of a cone-beam computed tomography (CBCT) unit in a single-photon emission computed tomography (SPECT)/CBCT system can be increased by offsetting the CBCT detector. Analytic-based algorithms have been developed for image reconstruction from data collected at a large number of densely sampled views in offset-detector CBCT. However, the radiation dose involved in a large number of projections can be of a health concern to the imaged subject. CBCT-imaging dose can be reduced by lowering the number of projections. As analytic-based algorithms are unlikely to reconstruct accurate images from sparse-view data, we investigate and characterize in the work optimization-based algorithms, including an adaptive steepest descent-weighted projection onto convex sets (ASD-WPOCS) algorithms, for image reconstruction from sparse-view data collected in offset-detector CBCT. Using simulated data and real data collected from a physical pelvis phantom and patient, we verify and characterize properties of the algorithms under study. Results of our study suggest that optimization-based algorithms such as ASD-WPOCS may be developed for yielding images of potential utility from a number of projections substantially smaller than those used currently in clinical SPECT/CBCT imaging, thus leading to a dose reduction in CBCT imaging.

Disrupted Brain Functional Organization in Epilepsy Revealed by Graph Theory Analysis.

PubMed

Song, Jie; Nair, Veena A; Gaggl, Wolfgang; Prabhakaran, Vivek

2015-06-01

The human brain is a complex and dynamic system that can be modeled as a large-scale brain network to better understand the reorganizational changes secondary to epilepsy. In this study, we developed a brain functional network model using graph theory methods applied to resting-state fMRI data acquired from a group of epilepsy patients and age- and gender-matched healthy controls. A brain functional network model was constructed based on resting-state functional connectivity. A minimum spanning tree combined with proportional thresholding approach was used to obtain sparse connectivity matrices for each subject, which formed the basis of brain networks. We examined the brain reorganizational changes in epilepsy thoroughly at the level of the whole brain, the functional network, and individual brain regions. At the whole-brain level, local efficiency was significantly decreased in epilepsy patients compared with the healthy controls. However, global efficiency was significantly increased in epilepsy due to increased number of functional connections between networks (although weakly connected). At the functional network level, there were significant proportions of newly formed connections between the default mode network and other networks and between the subcortical network and other networks. There was a significant proportion of decreasing connections between the cingulo-opercular task control network and other networks. Individual brain regions from different functional networks, however, showed a distinct pattern of reorganizational changes in epilepsy. These findings suggest that epilepsy alters brain efficiency in a consistent pattern at the whole-brain level, yet alters brain functional networks and individual brain regions differently.

On Facilitating the use of HARDI in population studies by creating Rotation-Invariant Markers

PubMed Central

Caruyer, Emmanuel; Verma, Ragini

2014-01-01

We design and evaluate a novel method to compute rotationally invariant features using High Angular Resolution Diffusion Imaging (HARDI) data. These measures quantify the complexity of the angular diffusion profile modeled using a higher order model, thereby giving more information than classical diffusion tensor-derived parameters. The method is based on the spherical harmonic (SH) representation of the angular diffusion information, and is generalizable to a range of HARDI reconstruction models. These scalars are obtained as homogeneous polynomials of the SH representation of a HARDI reconstruction model. We show that finding such polynomials is equivalent to solving a large linear system of equations, and present a numerical method based on sparse matrices to efficiently solve this system. Among the solutions, we only keep a subset of algebraically independent polynomials, using an algorithm based on a numerical implementation of the Jacobian criterion. We compute a set of 12 or 25 rotationally invariant measures representative of the underlying white matter for the rank-4 or rank-6 spherical harmonics (SH) representation of the apparent diffusion coefficient (ADC) profile, respectively. Synthetic data was used to investigate and quantify the difference in contrast. Real data acquired with multiple repetitions showed that within subject variation in the invariants was less than the difference across subjects - facilitating their use to study population differences. These results demonstrate that our measures are able to characterize white matter, especially complex white matter found in regions of fiber crossings and hence can be used to derive new biomarkers for HARDI and can be used for HARDI-based population analysis. PMID:25465846

“SNP Snappy”: A Strategy for Fast Genome-Wide Association Studies Fitting a Full Mixed Model

PubMed Central

Meyer, Karin; Tier, Bruce

2012-01-01

A strategy to reduce computational demands of genome-wide association studies fitting a mixed model is presented. Improvements are achieved by utilizing a large proportion of calculations that remain constant across the multiple analyses for individual markers involved, with estimates obtained without inverting large matrices. PMID:22021386

Bridging the gap between strategic and management forest inventories

Treesearch

Ronald E. McRoberts

2009-01-01

Strategic forest inventory programs collect information for a large number of variables on a relatively sparse array of field plots. Data from these inventories are used to produce estimates for large areas such as states and provinces, regions, or countries. The purpose of management forest inventories is to guide management decisions for small areas such as stands....

Non-local transport in turbulent MHD convection

NASA Technical Reports Server (NTRS)

Miesch, Mark; Brandenburg, Axel; Zweibel, Ellen; Toomre, Juri

1995-01-01

The nonlocal non-diffusive transport of passive scalars in turbulent magnetohydrodynamic (MHD) convection is investigated using transilient matrices. These matrices describe the probability that a tracer particle beginning at one position in a flow will be advected to another position after some time. A method for the calculation of these matrices from simulation data which involves following the trajectories of passive tracer particles and calculating their transport statistics, is presented. The method is applied to study the transport in several simulations of turbulent, rotating, three dimensional compressible, penetrative MDH convection. Transport coefficients and other diagnostics are used to quantify the transport, which is found to resemble advection more closely than diffusion. Some of the results are found to have direct relevance to other physical problems, such as the light element depletion in sun-type stars. The large kurtosis found for downward moving particles at the base of the convection zone implies several extreme events.

Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices

NASA Astrophysics Data System (ADS)

Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd; Thompson, Daniel C.

2017-09-01

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associ-ated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.

Medium-induced change of the optical response of metal clusters in rare-gas matrices

NASA Astrophysics Data System (ADS)

Xuan, Fengyuan; Guet, Claude

2017-10-01

Interaction with the surrounding medium modifies the optical response of embedded metal clusters. For clusters from about ten to a few hundreds of silver atoms, embedded in rare-gas matrices, we study the environment effect within the matrix random phase approximation with exact exchange (RPAE) quantum approach, which has proved successful for free silver clusters. The polarizable surrounding medium screens the residual two-body RPAE interaction, adds a polarization term to the one-body potential, and shifts the vacuum energy of the active delocalized valence electrons. Within this model, we calculate the dipole oscillator strength distribution for Ag clusters embedded in helium droplets, neon, argon, krypton, and xenon matrices. The main contribution to the dipole surface plasmon red shift originates from the rare-gas polarization screening of the two-body interaction. The large size limit of the dipole surface plasmon agrees well with the classical prediction.

NDMA formation kinetics from three pharmaceuticals in four water matrices.

PubMed

Shen, Ruqiao; Andrews, Susan A

2011-11-01

N, N-nitrosodimethylamine (NDMA) is an emerging disinfection by-product (DBP) that has been widely detected in many drinking water systems and commonly associated with the chloramine disinfection process. Some amine-based pharmaceuticals have been demonstrated to form NDMA during chloramination, but studies regarding the reaction kinetics are largely lacking. This study investigates the NDMA formation kinetics from ranitidine, chlorphenamine, and doxylamine under practical chloramine disinfection conditions. The formation profile was monitored in both lab-grade water and real water matrices, and a statistical model is proposed to describe and predict the NDMA formation from selected pharmaceuticals in various water matrices. The results indicate the significant impact of water matrix components and reaction time on the NDMA formation from selected pharmaceuticals, and provide fresh insights on the estimation of ultimate NDMA formation potential from pharmaceutical precursors. Copyright © 2011 Elsevier Ltd. All rights reserved.

Production of mycotoxins by filamentous fungi in untreated surface water.

PubMed

Oliveira, Beatriz R; Mata, Ana T; Ferreira, João P; Barreto Crespo, Maria T; Pereira, Vanessa J; Bronze, Maria R

2018-04-16

Several research studies reported that mycotoxins and other metabolites can be produced by fungi in certain matrices such as food. In recent years, attention has been drawn to the wide occurrence and identification of fungi in drinking water sources. Due to the large demand of water for drinking, watering, or food production purposes, it is imperative that further research is conducted to investigate if mycotoxins may be produced in water matrices. This paper describes the results obtained when a validated analytical method was applied to detect and quantify the presence of mycotoxins as a result of fungi inoculation and growth in untreated surface water. Aflatoxins B1 and B2, fumonisin B3, and ochratoxin A were detected at concentrations up to 35 ng/L. These results show that fungi can produce mycotoxins in water matrices in a non-negligible quantity and, as such, attention must be given to the presence of fungi in water.

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

Sparse regressions for predicting and interpreting subcellular localization of multi-label proteins.

PubMed

Wan, Shibiao; Mak, Man-Wai; Kung, Sun-Yuan

2016-02-24

Predicting protein subcellular localization is indispensable for inferring protein functions. Recent studies have been focusing on predicting not only single-location proteins, but also multi-location proteins. Almost all of the high performing predictors proposed recently use gene ontology (GO) terms to construct feature vectors for classification. Despite their high performance, their prediction decisions are difficult to interpret because of the large number of GO terms involved. This paper proposes using sparse regressions to exploit GO information for both predicting and interpreting subcellular localization of single- and multi-location proteins. Specifically, we compared two multi-label sparse regression algorithms, namely multi-label LASSO (mLASSO) and multi-label elastic net (mEN), for large-scale predictions of protein subcellular localization. Both algorithms can yield sparse and interpretable solutions. By using the one-vs-rest strategy, mLASSO and mEN identified 87 and 429 out of more than 8,000 GO terms, respectively, which play essential roles in determining subcellular localization. More interestingly, many of the GO terms selected by mEN are from the biological process and molecular function categories, suggesting that the GO terms of these categories also play vital roles in the prediction. With these essential GO terms, not only where a protein locates can be decided, but also why it resides there can be revealed. Experimental results show that the output of both mEN and mLASSO are interpretable and they perform significantly better than existing state-of-the-art predictors. Moreover, mEN selects more features and performs better than mLASSO on a stringent human benchmark dataset. For readers' convenience, an online server called SpaPredictor for both mLASSO and mEN is available at http://bioinfo.eie.polyu.edu.hk/SpaPredictorServer/.

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.

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.

Empirical Performance of Cross-Validation With Oracle Methods in a Genomics Context.

PubMed

Martinez, Josue G; Carroll, Raymond J; Müller, Samuel; Sampson, Joshua N; Chatterjee, Nilanjan

2011-11-01

When employing model selection methods with oracle properties such as the smoothly clipped absolute deviation (SCAD) and the Adaptive Lasso, it is typical to estimate the smoothing parameter by m-fold cross-validation, for example, m = 10. In problems where the true regression function is sparse and the signals large, such cross-validation typically works well. However, in regression modeling of genomic studies involving Single Nucleotide Polymorphisms (SNP), the true regression functions, while thought to be sparse, do not have large signals. We demonstrate empirically that in such problems, the number of selected variables using SCAD and the Adaptive Lasso, with 10-fold cross-validation, is a random variable that has considerable and surprising variation. Similar remarks apply to non-oracle methods such as the Lasso. Our study strongly questions the suitability of performing only a single run of m-fold cross-validation with any oracle method, and not just the SCAD and Adaptive Lasso.

Solving very large, sparse linear systems on mesh-connected parallel computers

NASA Technical Reports Server (NTRS)

Opsahl, Torstein; Reif, John

1987-01-01

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

A Variable Step-Size Proportionate Affine Projection Algorithm for Identification of Sparse Impulse Response

NASA Astrophysics Data System (ADS)

Liu, Ligang; Fukumoto, Masahiro; Saiki, Sachio; Zhang, Shiyong

2009-12-01

Proportionate adaptive algorithms have been proposed recently to accelerate convergence for the identification of sparse impulse response. When the excitation signal is colored, especially the speech, the convergence performance of proportionate NLMS algorithms demonstrate slow convergence speed. The proportionate affine projection algorithm (PAPA) is expected to solve this problem by using more information in the input signals. However, its steady-state performance is limited by the constant step-size parameter. In this article we propose a variable step-size PAPA by canceling the a posteriori estimation error. This can result in high convergence speed using a large step size when the identification error is large, and can then considerably decrease the steady-state misalignment using a small step size after the adaptive filter has converged. Simulation results show that the proposed approach can greatly improve the steady-state misalignment without sacrificing the fast convergence of PAPA.

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Seismic data restoration with a fast L1 norm trust region method

NASA Astrophysics Data System (ADS)

Cao, Jingjie; Wang, Yanfei

2014-08-01

Seismic data restoration is a major strategy to provide reliable wavefield when field data dissatisfy the Shannon sampling theorem. Recovery by sparsity-promoting inversion often get sparse solutions of seismic data in a transformed domains, however, most methods for sparsity-promoting inversion are line-searching methods which are efficient but are inclined to obtain local solutions. Using trust region method which can provide globally convergent solutions is a good choice to overcome this shortcoming. A trust region method for sparse inversion has been proposed, however, the efficiency should be improved to suitable for large-scale computation. In this paper, a new L1 norm trust region model is proposed for seismic data restoration and a robust gradient projection method for solving the sub-problem is utilized. Numerical results of synthetic and field data demonstrate that the proposed trust region method can get excellent computation speed and is a viable alternative for large-scale computation.

Study of alumina-trichite reinforcement of a nickel-based matric by means of powder metallurgy

NASA Technical Reports Server (NTRS)

Walder, A.; Hivert, A.

1982-01-01

Research was conducted on reinforcing nickel based matrices with alumina trichites by using powder metallurgy. Alumina trichites previously coated with nickel are magnetically aligned. The felt obtained is then sintered under a light pressure at a temperature just below the melting point of nickel. The halogenated atmosphere technique makes it possible to incorporate a large number of additive elements such as chromium, titanium, zirconium, tantalum, niobium, aluminum, etc. It does not appear that going from laboratory scale to a semi-industrial scale in production would create any major problems.

Boundary formulations for sensitivity analysis without matrix derivatives

NASA Technical Reports Server (NTRS)

Kane, J. H.; Guru Prasad, K.

1993-01-01

A new hybrid approach to continuum structural shape sensitivity analysis employing boundary element analysis (BEA) is presented. The approach uses iterative reanalysis to obviate the need to factor perturbed matrices in the determination of surface displacement and traction sensitivities via a univariate perturbation/finite difference (UPFD) step. The UPFD approach makes it possible to immediately reuse existing subroutines for computation of BEA matrix coefficients in the design sensitivity analysis process. The reanalysis technique computes economical response of univariately perturbed models without factoring perturbed matrices. The approach provides substantial computational economy without the burden of a large-scale reprogramming effort.

Matrices pattern using FIB; 'Out-of-the-box' way of thinking.

PubMed

Fleger, Y; Gotlib-Vainshtein, K; Talyosef, Y

2017-03-01

Focused ion beam (FIB) is an extremely valuable tool in nanopatterning and nanofabrication for potentially high-resolution patterning, especially when refers to He ion beam microscopy. The work presented here demonstrates an 'out-of-the-box' method of writing using FIB, which enables creating very large matrices, up to the beam-shift limitation, in short times and with high accuracy unachievable by any other writing technique. The new method allows combining different shapes in nanometric dimensions and high resolutions for wide ranges. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

The pearl oyster Pinctada fucata martensii genome and multi-omic analyses provide insights into biomineralization

PubMed Central

Fan, Guangyi; Jiao, Yu; Zhang, He; Huang, Ronglian; Zheng, Zhe; Bian, Chao; Deng, Yuewen; Wang, Qingheng; Wang, Zhongduo; Liang, Xinming; Liang, Haiying; Shi, Chengcheng; Zhao, Xiaoxia; Sun, Fengming; Hao, Ruijuan; Bai, Jie; Liu, Jialiang; Chen, Wenbin; Liang, Jinlian; Liu, Weiqing; Xu, Zhe; Shi, Qiong; Xu, Xun

2017-01-01

Abstract Nacre, the iridescent material found in pearls and shells of molluscs, is formed through an extraordinary process of matrix-assisted biomineralization. Despite recent advances, many aspects of the biomineralization process and its evolutionary origin remain unknown. The pearl oyster Pinctada fucata martensii is a well-known master of biomineralization, but the molecular mechanisms that underlie its production of shells and pearls are not fully understood. We sequenced the highly polymorphic genome of the pearl oyster and conducted multi-omic and biochemical studies to probe nacre formation. We identified a large set of novel proteins participating in matrix-framework formation, many in expanded families, including components similar to that found in vertebrate bones such as collagen-related VWA-containing proteins, chondroitin sulfotransferases, and regulatory elements. Considering that there are only collagen-based matrices in vertebrate bones and chitin-based matrices in most invertebrate skeletons, the presence of both chitin and elements of collagen-based matrices in nacre suggests that elements of chitin- and collagen-based matrices have deep roots and might be part of an ancient biomineralizing matrix. Our results expand the current shell matrix-framework model and provide new insights into the evolution of diverse biomineralization systems. PMID:28873964

Visualization of newt aragonitic otoconial matrices using transmission electron microscopy

NASA Technical Reports Server (NTRS)

Steyger, P. S.; Wiederhold, M. L.

1995-01-01

Otoconia are calcified protein matrices within the gravity-sensing organs of the vertebrate vestibular system. These protein matrices are thought to originate from the supporting or hair cells in the macula during development. Previous studies of mammalian calcitic, barrel-shaped otoconia revealed an organized protein matrix consisting of a thin peripheral layer, a well-defined organic core and a flocculent matrix inbetween. No studies have reported the microscopic organization of the aragonitic otoconial matrix, despite its protein characterization. Pote et al. (1993b) used densitometric methods and inferred that prismatic (aragonitic) otoconia have a peripheral protein distribution, compared to that described for the barrel-shaped, calcitic otoconia of birds, mammals, and the amphibian utricle. By using tannic acid as a negative stain, we observed three kinds of organic matrices in preparations of fixed, decalcified saccular otoconia from the adult newt: (1) fusiform shapes with a homogenous electron-dense matrix; (2) singular and multiple strands of matrix; and (3) more significantly, prismatic shapes outlined by a peripheral organic matrix. These prismatic shapes remain following removal of the gelatinous matrix, revealing an internal array of organic matter. We conclude that prismatic otoconia have a largely peripheral otoconial matrix, as inferred by densitometry.

Workshop report on large-scale matrix diagonalization methods in chemistry theory institute

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

Bischof, C.H.; Shepard, R.L.; Huss-Lederman, S.

The Large-Scale Matrix Diagonalization Methods in Chemistry theory institute brought together 41 computational chemists and numerical analysts. The goal was to understand the needs of the computational chemistry community in problems that utilize matrix diagonalization techniques. This was accomplished by reviewing the current state of the art and looking toward future directions in matrix diagonalization techniques. This institute occurred about 20 years after a related meeting of similar size. During those 20 years the Davidson method continued to dominate the problem of finding a few extremal eigenvalues for many computational chemistry problems. Work on non-diagonally dominant and non-Hermitian problems asmore » well as parallel computing has also brought new methods to bear. The changes and similarities in problems and methods over the past two decades offered an interesting viewpoint for the success in this area. One important area covered by the talks was overviews of the source and nature of the chemistry problems. The numerical analysts were uniformly grateful for the efforts to convey a better understanding of the problems and issues faced in computational chemistry. An important outcome was an understanding of the wide range of eigenproblems encountered in computational chemistry. The workshop covered problems involving self- consistent-field (SCF), configuration interaction (CI), intramolecular vibrational relaxation (IVR), and scattering problems. In atomic structure calculations using the Hartree-Fock method (SCF), the symmetric matrices can range from order hundreds to thousands. These matrices often include large clusters of eigenvalues which can be as much as 25% of the spectrum. However, if Cl methods are also used, the matrix size can be between 10{sup 4} and 10{sup 9} where only one or a few extremal eigenvalues and eigenvectors are needed. Working with very large matrices has lead to the development of« less

Determination of tributyltin in environmental water matrices using stir bar sorptive extraction with in-situ derivatisation and large volume injection-gas chromatography-mass spectrometry.

PubMed

Neng, N R; Santalla, R P; Nogueira, J M F

2014-08-01

Stir bar sorptive extraction with in-situ derivatization using sodium tetrahydridoborate (NaBH4) followed by liquid desorption and large volume injection-gas chromatography-mass spectrometry detection under the selected ion monitoring mode (SBSE(NaBH4)in-situ-LD/LVI-GC-MS(SIM)) was successfully developed for the determination of tributyltin (TBT) in environmental water matrices. NaBH4 proved to be an effective and easy in-situ speciation agent for TBT in aqueous media, allowing the formation of adducts with enough stability and suitable polarity for SBSE analysis. Assays performed on water samples spiked at the 10.0μg/L, yielded convenient recoveries (68.2±3.0%), showed good accuracy, suitable precision (RSD<9.0%), low detection limits (23ng/L) and excellent linear dynamic range (r(2)=0.9999) from 0.1 to 170.0µg/L, under optimized experimental conditions. By using the standard addition method, the application of the present methodology to real surface water samples allowed very good performance at the trace level. The proposed methodology proved to be a feasible alternative for routine quality control analysis, easy to implement, reliable and sensitive to monitor TBT in environmental water matrices. Copyright © 2014 Elsevier B.V. All rights reserved.