Ordering sparse matrices for cache-based systems

International Nuclear Information System (INIS)

Biswas, Rupak; Oliker, Leonid

2001-01-01

The Conjugate Gradient (CG) algorithm is the oldest and best-known Krylov subspace method used to solve sparse linear systems. Most of the coating-point operations within each CG iteration is spent performing sparse matrix-vector multiplication (SPMV). We examine how various ordering and partitioning strategies affect the performance of CG and SPMV when different programming paradigms are used on current commercial cache-based computers. However, a multithreaded implementation on the cacheless Cray MTA demonstrates high efficiency and scalability without any special ordering or partitioning

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

Science.gov (United States)

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

Biclustering via Sparse Singular Value Decomposition

KAUST Repository

Lee, Mihee

2010-02-16

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. © 2010, The International Biometric Society.

Rotational image deblurring with sparse matrices

DEFF Research Database (Denmark)

Hansen, Per Christian; Nagy, James G.; Tigkos, Konstantinos

2014-01-01

We describe iterative deblurring algorithms that can handle blur caused by a rotation along an arbitrary axis (including the common case of pure rotation). Our algorithms use a sparse-matrix representation of the blurring operation, which allows us to easily handle several different boundary...

Seismic detection method for small-scale discontinuities based on dictionary learning and sparse representation

Science.gov (United States)

Yu, Caixia; Zhao, Jingtao; Wang, Yanfei

2017-02-01

Studying small-scale geologic discontinuities, such as faults, cavities and fractures, plays a vital role in analyzing the inner conditions of reservoirs, as these geologic structures and elements can provide storage spaces and migration pathways for petroleum. However, these geologic discontinuities have weak energy and are easily contaminated with noises, and therefore effectively extracting them from seismic data becomes a challenging problem. In this paper, a method for detecting small-scale discontinuities using dictionary learning and sparse representation is proposed that can dig up high-resolution information by sparse coding. A K-SVD (K-means clustering via Singular Value Decomposition) sparse representation model that contains two stage of iteration procedure: sparse coding and dictionary updating, is suggested for mathematically expressing these seismic small-scale discontinuities. Generally, the orthogonal matching pursuit (OMP) algorithm is employed for sparse coding. However, the method can only update one dictionary atom at one time. In order to improve calculation efficiency, a regularized version of OMP algorithm is presented for simultaneously updating a number of atoms at one time. Two numerical experiments demonstrate the validity of the developed method for clarifying and enhancing small-scale discontinuities. The field example of carbonate reservoirs further demonstrates its effectiveness in revealing masked tiny faults and small-scale cavities.

Fast wavelet based sparse approximate inverse preconditioner

Energy Technology Data Exchange (ETDEWEB)

Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

1996-12-31

Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

Tensor Dictionary Learning for Positive Definite Matrices.

Science.gov (United States)

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

2015-11-01

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

Sparse Channel Estimation Including the Impact of the Transceiver Filters with Application to OFDM

DEFF Research Database (Denmark)

Barbu, Oana-Elena; Pedersen, Niels Lovmand; Manchón, Carles Navarro

2014-01-01

Traditionally, the dictionary matrices used in sparse wireless channel estimation have been based on the discrete Fourier transform, following the assumption that the channel frequency response (CFR) can be approximated as a linear combination of a small number of multipath components, each one......) and receive (demodulation) filters. Hence, the assumption of the CFR being sparse in the canonical Fourier dictionary may no longer hold. In this work, we derive a signal model and subsequently a novel dictionary matrix for sparse estimation that account for the impact of transceiver filters. Numerical...... results obtained in an OFDM transmission scenario demonstrate the superior accuracy of a sparse estimator that uses our proposed dictionary rather than the classical Fourier dictionary, and its robustness against a mismatch in the assumed transmit filter characteristics....

A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems

Czech Academy of Sciences Publication Activity Database

Benzi, M.; Tůma, Miroslav

1998-01-01

Roč. 19, č. 3 (1998), s. 968-994 ISSN 1064-8275 R&D Projects: GA ČR GA201/93/0067; GA AV ČR IAA230401 Keywords : large sparse systems * interative methods * preconditioning * approximate inverse * sparse linear systems * sparse matrices * incomplete factorizations * conjugate gradient -type methods Subject RIV: BA - General Mathematics Impact factor: 1.378, year: 1998

P-SPARSLIB: A parallel sparse iterative solution package

Energy Technology Data Exchange (ETDEWEB)

Saad, Y. [Univ. of Minnesota, Minneapolis, MN (United States)

1994-12-31

Iterative methods are gaining popularity in engineering and sciences at a time where the computational environment is changing rapidly. P-SPARSLIB is a project to build a software library for sparse matrix computations on parallel computers. The emphasis is on iterative methods and the use of distributed sparse matrices, an extension of the domain decomposition approach to general sparse matrices. One of the goals of this project is to develop a software package geared towards specific applications. For example, the author will test the performance and usefulness of P-SPARSLIB modules on linear systems arising from CFD applications. Equally important is the goal of portability. In the long run, the author wishes to ensure that this package is portable on a variety of platforms, including SIMD environments and shared memory environments.

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

Science.gov (United States)

Zubair, M.; Ghose, M.

1992-01-01

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

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

Science.gov (United States)

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.

Design Patterns for Sparse-Matrix Computations on Hybrid CPU/GPU Platforms

Directory of Open Access Journals (Sweden)

Valeria Cardellini

2014-01-01

Full Text Available We apply object-oriented software design patterns to develop code for scientific software involving sparse matrices. Design patterns arise when multiple independent developments produce similar designs which converge onto a generic solution. We demonstrate how to use design patterns to implement an interface for sparse matrix computations on NVIDIA GPUs starting from PSBLAS, an existing sparse matrix library, and from existing sets of GPU kernels for sparse matrices. We also compare the throughput of the PSBLAS sparse matrix–vector multiplication on two platforms exploiting the GPU with that obtained by a CPU-only PSBLAS implementation. Our experiments exhibit encouraging results regarding the comparison between CPU and GPU executions in double precision, obtaining a speedup of up to 35.35 on NVIDIA GTX 285 with respect to AMD Athlon 7750, and up to 10.15 on NVIDIA Tesla C2050 with respect to Intel Xeon X5650.

Cavity approach to the first eigenvalue problem in a family of symmetric random sparse matrices

International Nuclear Information System (INIS)

Kabashima, Yoshiyuki; Takahashi, Hisanao; Watanabe, Osamu

2010-01-01

A methodology to analyze the properties of the first (largest) eigenvalue and its eigenvector is developed for large symmetric random sparse matrices utilizing the cavity method of statistical mechanics. Under a tree approximation, which is plausible for infinitely large systems, in conjunction with the introduction of a Lagrange multiplier for constraining the length of the eigenvector, the eigenvalue problem is reduced to a bunch of optimization problems of a quadratic function of a single variable, and the coefficients of the first and the second order terms of the functions act as cavity fields that are handled in cavity analysis. We show that the first eigenvalue is determined in such a way that the distribution of the cavity fields has a finite value for the second order moment with respect to the cavity fields of the first order coefficient. The validity and utility of the developed methodology are examined by applying it to two analytically solvable and one simple but non-trivial examples in conjunction with numerical justification.

First results in the application of silicon photomultiplier matrices to small animal PET

Energy Technology Data Exchange (ETDEWEB)

Llosa, G. [University of Pisa, Department of Physics, Pisa (Italy)], E-mail: gabriela.llosa@pi.infn.it; Belcari, N.; Bisogni, M.G. [University of Pisa, Department of Physics, Pisa (Italy); INFN Pisa (Italy); Collazuol, G. [University of Pisa, Department of Physics, Pisa (Italy); Scuola Normale Superiore, Pisa (Italy); Marcatili, S. [University of Pisa, Department of Physics, Pisa (Italy); INFN Pisa (Italy); Boscardin, M.; Melchiorri, M.; Tarolli, A.; Piemonte, C.; Zorzi, N. [FBK irst, Trento (Italy); Barrillon, P.; Bondil-Blin, S.; Chaumat, V.; La Taille, C. de; Dinu, N.; Puill, V.; Vagnucci, J-F. [Laboratoire de l' Accelerateur Lineaire, IN2P3-CNRS, Orsay (France); Del Guerra, A. [University of Pisa, Department of Physics, Pisa (Italy); INFN Pisa (Italy)

2009-10-21

A very high resolution small animal PET scanner that employs matrices of silicon photomultipliers as photodetectors is under development at the University of Pisa and INFN Pisa. The first SiPM matrices composed of 16 (4x4)1mmx1mm pixel elements on a common substrate have been produced at FBK-irst, and are being evaluated for this application. The MAROC2 ASIC developed at LAL-Orsay has been employed for the readout of the SiPM matrices. The devices have been tested with pixelated and continuous LYSO crystals. The results show the good performance of the matrices and lead to the fabrication of matrices with 64 SiPM elements.

First results in the application of silicon photomultiplier matrices to small animal PET

International Nuclear Information System (INIS)

Llosa, G.; Belcari, N.; Bisogni, M.G.; Collazuol, G.; Marcatili, S.; Boscardin, M.; Melchiorri, M.; Tarolli, A.; Piemonte, C.; Zorzi, N.; Barrillon, P.; Bondil-Blin, S.; Chaumat, V.; La Taille, C. de; Dinu, N.; Puill, V.; Vagnucci, J-F.; Del Guerra, A.

2009-01-01

A very high resolution small animal PET scanner that employs matrices of silicon photomultipliers as photodetectors is under development at the University of Pisa and INFN Pisa. The first SiPM matrices composed of 16 (4x4)1mmx1mm pixel elements on a common substrate have been produced at FBK-irst, and are being evaluated for this application. The MAROC2 ASIC developed at LAL-Orsay has been employed for the readout of the SiPM matrices. The devices have been tested with pixelated and continuous LYSO crystals. The results show the good performance of the matrices and lead to the fabrication of matrices with 64 SiPM elements.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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

2018-04-01

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

Tunable Sparse Network Coding for Multicast Networks

DEFF Research Database (Denmark)

Feizi, Soheil; Roetter, Daniel Enrique Lucani; Sørensen, Chres Wiant

2014-01-01

This paper shows the potential and key enabling mechanisms for tunable sparse network coding, a scheme in which the density of network coded packets varies during a transmission session. At the beginning of a transmission session, sparsely coded packets are transmitted, which benefits decoding...... complexity. At the end of a transmission, when receivers have accumulated degrees of freedom, coding density is increased. We propose a family of tunable sparse network codes (TSNCs) for multicast erasure networks with a controllable trade-off between completion time performance to decoding complexity...... a mechanism to perform efficient Gaussian elimination over sparse matrices going beyond belief propagation but maintaining low decoding complexity. Supporting simulation results are provided showing the trade-off between decoding complexity and completion time....

The application of sparse estimation of covariance matrix to quadratic discriminant analysis.

Science.gov (United States)

Sun, Jiehuan; Zhao, Hongyu

2015-02-18

Although Linear Discriminant Analysis (LDA) is commonly used for classification, it may not be directly applied in genomics studies due to the large p, small n problem in these studies. Different versions of sparse LDA have been proposed to address this significant challenge. One implicit assumption of various LDA-based methods is that the covariance matrices are the same across different classes. However, rewiring of genetic networks (therefore different covariance matrices) across different diseases has been observed in many genomics studies, which suggests that LDA and its variations may be suboptimal for disease classifications. However, it is not clear whether considering differing genetic networks across diseases can improve classification in genomics studies. We propose a sparse version of Quadratic Discriminant Analysis (SQDA) to explicitly consider the differences of the genetic networks across diseases. Both simulation and real data analysis are performed to compare the performance of SQDA with six commonly used classification methods. SQDA provides more accurate classification results than other methods for both simulated and real data. Our method should prove useful for classification in genomics studies and other research settings, where covariances differ among classes.

Solving sparse linear least squares problems on some supercomputers by using large dense blocks

DEFF Research Database (Denmark)

Hansen, Per Christian; Ostromsky, T; Sameh, A

1997-01-01

technique is preferable to sparse matrix technique when the matrices are not large, because the high computational speed compensates fully the disadvantages of using more arithmetic operations and more storage. For very large matrices the computations must be organized as a sequence of tasks in each......Efficient subroutines for dense matrix computations have recently been developed and are available on many high-speed computers. On some computers the speed of many dense matrix operations is near to the peak-performance. For sparse matrices storage and operations can be saved by operating only...... and storing only nonzero elements. However, the price is a great degradation of the speed of computations on supercomputers (due to the use of indirect addresses, to the need to insert new nonzeros in the sparse storage scheme, to the lack of data locality, etc.). On many high-speed computers a dense matrix...

Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-09-03

We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, since H-matrices can approximate inhomogeneous covariance functions, with a fairly general mesh that is not necessarily axes-parallel, and neither the covariance matrix itself nor its inverse have to be sparse. We demonstrate our method with Monte Carlo simulations and an application to soil moisture data. The C, C++ codes and data are freely available.

The Development of Novel Nanodiamond Based MALDI Matrices for the Analysis of Small Organic Pharmaceuticals

Science.gov (United States)

Chitanda, Jackson M.; Zhang, Haixia; Pahl, Erica; Purves, Randy W.; El-Aneed, Anas

2016-10-01

The utility of novel functionalized nanodiamonds (NDs) as matrices for matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS) is described herein. MALDI-MS analysis of small organic compounds (<1000 Da) is typically complex because of interferences from numerous cluster ions formed when using conventional matrices. To expand the use of MALDI for the analysis of small molecules, novel matrices were designed by covalently linking conventional matrices (or a lysine moiety) to detonated NDs. Four new functionalized NDs were evaluated for their ionization capabilities using five pharmaceuticals with varying molecular structures. Two ND matrices were able to ionize all tested pharmaceuticals in the negative ion mode, producing the deprotonated ions [M - H]-. Ion intensity for target analytes was generally strong with enhanced signal-to-noise ratios compared with conventional matrices. The negative ion mode is of great importance for biological samples as interference from endogenous compounds is inherently minimized in the negative ion mode. Since the molecular structures of the tested pharmaceuticals did not suggest that negative ion mode would be preferable, this result magnifies the importance of these findings. On the other hand, conventional matrices primarily facilitated the ionization as expected in the positive ion mode, producing either the protonated molecules [M + H]+ or cationic adducts (typically producing complex spectra with numerous adduct peaks). The data presented in this study suggests that these matrices may offer advantages for the analysis of low molecular weight pharmaceuticals/metabolites.

Large-deviation theory for diluted Wishart random matrices

Science.gov (United States)

Castillo, Isaac Pérez; Metz, Fernando L.

2018-03-01

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x ) smaller than x ∈R+ , from which all cumulants of IN(x ) and the rate function Ψx(k ) controlling its large-deviation probability Prob[IN(x ) =k N ] ≍e-N Ψx(k ) follow. Explicit results for the mean value and the variance of IN(x ) , its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016), 10.1103/PhysRevLett.117.104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.

Aliasing-free wideband beamforming using sparse signal representation

NARCIS (Netherlands)

Tang, Z.; Blacquière, G.; Leus, G.

2011-01-01

Sparse signal representation (SSR) is considered to be an appealing alternative to classical beamforming for direction-of-arrival (DOA) estimation. For wideband signals, the SSR-based approach constructs steering matrices, referred to as dictionaries in this paper, corresponding to different

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

Science.gov (United States)

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.

Sample size reduction in groundwater surveys via sparse data assimilation

KAUST Repository

Hussain, Z.; Muhammad, A.

2013-01-01

In this paper, we focus on sparse signal recovery methods for data assimilation in groundwater models. The objective of this work is to exploit the commonly understood spatial sparsity in hydrodynamic models and thereby reduce the number of measurements to image a dynamic groundwater profile. To achieve this we employ a Bayesian compressive sensing framework that lets us adaptively select the next measurement to reduce the estimation error. An extension to the Bayesian compressive sensing framework is also proposed which incorporates the additional model information to estimate system states from even lesser measurements. Instead of using cumulative imaging-like measurements, such as those used in standard compressive sensing, we use sparse binary matrices. This choice of measurements can be interpreted as randomly sampling only a small subset of dug wells at each time step, instead of sampling the entire grid. Therefore, this framework offers groundwater surveyors a significant reduction in surveying effort without compromising the quality of the survey. © 2013 IEEE.

Sample size reduction in groundwater surveys via sparse data assimilation

KAUST Repository

Hussain, Z.

2013-04-01

In this paper, we focus on sparse signal recovery methods for data assimilation in groundwater models. The objective of this work is to exploit the commonly understood spatial sparsity in hydrodynamic models and thereby reduce the number of measurements to image a dynamic groundwater profile. To achieve this we employ a Bayesian compressive sensing framework that lets us adaptively select the next measurement to reduce the estimation error. An extension to the Bayesian compressive sensing framework is also proposed which incorporates the additional model information to estimate system states from even lesser measurements. Instead of using cumulative imaging-like measurements, such as those used in standard compressive sensing, we use sparse binary matrices. This choice of measurements can be interpreted as randomly sampling only a small subset of dug wells at each time step, instead of sampling the entire grid. Therefore, this framework offers groundwater surveyors a significant reduction in surveying effort without compromising the quality of the survey. © 2013 IEEE.

Sparse matrix test collections

Energy Technology Data Exchange (ETDEWEB)

Duff, I.

1996-12-31

This workshop will discuss plans for coordinating and developing sets of test matrices for the comparison and testing of sparse linear algebra software. We will talk of plans for the next release (Release 2) of the Harwell-Boeing Collection and recent work on improving the accessibility of this Collection and others through the World Wide Web. There will only be three talks of about 15 to 20 minutes followed by a discussion from the floor.

Performance optimization of Sparse Matrix-Vector Multiplication for multi-component PDE-based applications using GPUs

KAUST Repository

Abdelfattah, Ahmad

2016-05-23

Simulations of many multi-component PDE-based applications, such as petroleum reservoirs or reacting flows, are dominated by the solution, on each time step and within each Newton step, of large sparse linear systems. The standard solver is a preconditioned Krylov method. Along with application of the preconditioner, memory-bound Sparse Matrix-Vector Multiplication (SpMV) is the most time-consuming operation in such solvers. Multi-species models produce Jacobians with a dense block structure, where the block size can be as large as a few dozen. Failing to exploit this dense block structure vastly underutilizes hardware capable of delivering high performance on dense BLAS operations. This paper presents a GPU-accelerated SpMV kernel for block-sparse matrices. Dense matrix-vector multiplications within the sparse-block structure leverage optimization techniques from the KBLAS library, a high performance library for dense BLAS kernels. The design ideas of KBLAS can be applied to block-sparse matrices. Furthermore, a technique is proposed to balance the workload among thread blocks when there are large variations in the lengths of nonzero rows. Multi-GPU performance is highlighted. The proposed SpMV kernel outperforms existing state-of-the-art implementations using matrices with real structures from different applications. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Performance optimization of Sparse Matrix-Vector Multiplication for multi-component PDE-based applications using GPUs

KAUST Repository

Abdelfattah, Ahmad; Ltaief, Hatem; Keyes, David E.; Dongarra, Jack

2016-01-01

Simulations of many multi-component PDE-based applications, such as petroleum reservoirs or reacting flows, are dominated by the solution, on each time step and within each Newton step, of large sparse linear systems. The standard solver is a preconditioned Krylov method. Along with application of the preconditioner, memory-bound Sparse Matrix-Vector Multiplication (SpMV) is the most time-consuming operation in such solvers. Multi-species models produce Jacobians with a dense block structure, where the block size can be as large as a few dozen. Failing to exploit this dense block structure vastly underutilizes hardware capable of delivering high performance on dense BLAS operations. This paper presents a GPU-accelerated SpMV kernel for block-sparse matrices. Dense matrix-vector multiplications within the sparse-block structure leverage optimization techniques from the KBLAS library, a high performance library for dense BLAS kernels. The design ideas of KBLAS can be applied to block-sparse matrices. Furthermore, a technique is proposed to balance the workload among thread blocks when there are large variations in the lengths of nonzero rows. Multi-GPU performance is highlighted. The proposed SpMV kernel outperforms existing state-of-the-art implementations using matrices with real structures from different applications. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Porting of the DBCSR library for Sparse Matrix-Matrix Multiplications to Intel Xeon Phi systems

OpenAIRE

Bethune, Iain; Gloess, Andeas; Hutter, Juerg; Lazzaro, Alfio; Pabst, Hans; Reid, Fiona

2017-01-01

Multiplication of two sparse matrices is a key operation in the simulation of the electronic structure of systems containing thousands of atoms and electrons. The highly optimized sparse linear algebra library DBCSR (Distributed Block Compressed Sparse Row) has been specifically designed to efficiently perform such sparse matrix-matrix multiplications. This library is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. It is para...

Advanced incomplete factorization algorithms for Stiltijes matrices

Energy Technology Data Exchange (ETDEWEB)

Il`in, V.P. [Siberian Division RAS, Novosibirsk (Russian Federation)

1996-12-31

The modern numerical methods for solving the linear algebraic systems Au = f with high order sparse matrices A, which arise in grid approximations of multidimensional boundary value problems, are based mainly on accelerated iterative processes with easily invertible preconditioning matrices presented in the form of approximate (incomplete) factorization of the original matrix A. We consider some recent algorithmic approaches, theoretical foundations, experimental data and open questions for incomplete factorization of Stiltijes matrices which are {open_quotes}the best{close_quotes} ones in the sense that they have the most advanced results. Special attention is given to solving the elliptic differential equations with strongly variable coefficients, singular perturbated diffusion-convection and parabolic equations.

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

OpenAIRE

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

2012-01-01

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 ...

A Nonnegative Latent Factor Model for Large-Scale Sparse Matrices in Recommender Systems via Alternating Direction Method.

Science.gov (United States)

Luo, Xin; Zhou, MengChu; Li, Shuai; You, Zhuhong; Xia, Yunni; Zhu, Qingsheng

2016-03-01

Nonnegative matrix factorization (NMF)-based models possess fine representativeness of a target matrix, which is critically important in collaborative filtering (CF)-based recommender systems. However, current NMF-based CF recommenders suffer from the problem of high computational and storage complexity, as well as slow convergence rate, which prevents them from industrial usage in context of big data. To address these issues, this paper proposes an alternating direction method (ADM)-based nonnegative latent factor (ANLF) model. The main idea is to implement the ADM-based optimization with regard to each single feature, to obtain high convergence rate as well as low complexity. Both computational and storage costs of ANLF are linear with the size of given data in the target matrix, which ensures high efficiency when dealing with extremely sparse matrices usually seen in CF problems. As demonstrated by the experiments on large, real data sets, ANLF also ensures fast convergence and high prediction accuracy, as well as the maintenance of nonnegativity constraints. Moreover, it is simple and easy to implement for real applications of learning systems.

Parallel and Scalable Sparse Basic Linear Algebra Subprograms

DEFF Research Database (Denmark)

Liu, Weifeng

and heterogeneous processors. The thesis compares the proposed methods with state-of-the-art approaches on six homogeneous and five heterogeneous processors from Intel, AMD and nVidia. Using in total 38 sparse matrices as a benchmark suite, the experimental results show that the proposed methods obtain significant...

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

Science.gov (United States)

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.

Using sparse LU factorisation to precondition GMRES for a family of similarly structured matrices arising from process modelling

Energy Technology Data Exchange (ETDEWEB)

Brooking, C. [Univ. of Bath (United Kingdom)

1996-12-31

Process engineering software is used to simulate the operation of large chemical plants. Such simulations are used for a variety of tasks, including operator training. For the software to be of practical use for this, dynamic simulations need to run in real-time. The models that the simulation is based upon are written in terms of Differential Algebraic Equations (DAE`s). In the numerical time-integration of systems of DAE`s using an implicit method such as backward Euler, the solution of nonlinear systems is required at each integration point. When solved using Newton`s method, this leads to the repeated solution of nonsymmetric sparse linear systems. These systems range in size from 500 to 20,000 variables. A typical integration may require around 3000 timesteps, and if 4 Newton iterates were needed on each time step, then this means approximately 12,000 linear systems must be solved. The matrices produced by the simulations have a similar sparsity pattern throughout the integration. They are also severely ill-conditioned, and have widely-scattered spectra.

Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

Science.gov (United States)

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.

Matrices over runtime systems at exascale

KAUST Repository

Agullo, Emmanuel

2012-11-01

The goal of Matrices Over Runtime Systems at Exascale (MORSE) project is to design dense and sparse linear algebra methods that achieve the fastest possible time to an accurate solution on large-scale multicore systems with GPU accelerators, using all the processing power that future high end systems can make available. In this poster, we propose a framework for describing linear algebra algorithms at a high level of abstraction and delegating the actual execution to a runtime system in order to design software whose performance is portable accross architectures. We illustrate our methodology on three classes of problems: dense linear algebra, sparse direct methods and fast multipole methods. The resulting codes have been incorporated into Magma, Pastix and ScalFMM solvers, respectively. © 2012 IEEE.

Massively parallel sparse matrix function calculations with NTPoly

Science.gov (United States)

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.

Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations

Energy Technology Data Exchange (ETDEWEB)

Aktulga, Hasan Metin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Buluc, Aydin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2014-08-14

Obtaining highly accurate predictions on the properties of light atomic nuclei using the configuration interaction (CI) approach requires computing a few extremal Eigen pairs of the many-body nuclear Hamiltonian matrix. In the Many-body Fermion Dynamics for nuclei (MFDn) code, a block Eigen solver is used for this purpose. Due to the large size of the sparse matrices involved, a significant fraction of the time spent on the Eigen value computations is associated with the multiplication of a sparse matrix (and the transpose of that matrix) with multiple vectors (SpMM and SpMM-T). Existing implementations of SpMM and SpMM-T significantly underperform expectations. Thus, in this paper, we present and analyze optimized implementations of SpMM and SpMM-T. We base our implementation on the compressed sparse blocks (CSB) matrix format and target systems with multi-core architectures. We develop a performance model that allows us to understand and estimate the performance characteristics of our SpMM kernel implementations, and demonstrate the efficiency of our implementation on a series of real-world matrices extracted from MFDn. In particular, we obtain 3-4 speedup on the requisite operations over good implementations based on the commonly used compressed sparse row (CSR) matrix format. The improvements in the SpMM kernel suggest we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn.

Mapping informal small-scale mining features in a data-sparse tropical environment with a small UAS

Science.gov (United States)

Chirico, Peter G.; Dewitt, Jessica D.

2017-01-01

This study evaluates the use of a small unmanned aerial system (UAS) to collect imagery over artisanal mining sites in West Africa. The purpose of this study is to consider how very high-resolution imagery and digital surface models (DSMs) derived from structure-from-motion (SfM) photogrammetric techniques from a small UAS can fill the gap in geospatial data collection between satellite imagery and data gathered during field work to map and monitor informal mining sites in tropical environments. The study compares both wide-angle and narrow field of view camera systems in the collection and analysis of high-resolution orthoimages and DSMs of artisanal mining pits. The results of the study indicate that UAS imagery and SfM photogrammetric techniques permit DSMs to be produced with a high degree of precision and relative accuracy, but highlight the challenges of mapping small artisanal mining pits in remote and data sparse terrain.

Speculative segmented sum for sparse matrix-vector multiplication on heterogeneous processors

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2015-01-01

of the same chip is triggered to re-arrange the predicted partial sums for a correct resulting vector. On three heterogeneous processors from Intel, AMD and nVidia, using 20 sparse matrices as a benchmark suite, the experimental results show that our method obtains significant performance improvement over...

Accelerating Matrix-Vector Multiplication on Hierarchical Matrices Using Graphical Processing Units

KAUST Repository

Boukaram, W.

2015-03-25

Large dense matrices arise from the discretization of many physical phenomena in computational sciences. In statistics very large dense covariance matrices are used for describing random fields and processes. One can, for instance, describe distribution of dust particles in the atmosphere, concentration of mineral resources in the earth\\'s crust or uncertain permeability coefficient in reservoir modeling. When the problem size grows, storing and computing with the full dense matrix becomes prohibitively expensive both in terms of computational complexity and physical memory requirements. Fortunately, these matrices can often be approximated by a class of data sparse matrices called hierarchical matrices (H-matrices) where various sub-blocks of the matrix are approximated by low rank matrices. These matrices can be stored in memory that grows linearly with the problem size. In addition, arithmetic operations on these H-matrices, such as matrix-vector multiplication, can be completed in almost linear time. Originally the H-matrix technique was developed for the approximation of stiffness matrices coming from partial differential and integral equations. Parallelizing these arithmetic operations on the GPU has been the focus of this work and we will present work done on the matrix vector operation on the GPU using the KSPARSE library.

A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices

Czech Academy of Sciences Publication Activity Database

Benzi, M.; Tůma, Miroslav

2003-01-01

Roč. 10, - (2003), s. 385-400 ISSN 1070-5325 R&D Projects: GA AV ČR IAA2030801; GA AV ČR IAA1030103 Institutional research plan: AV0Z1030915 Keywords : sparse linear systems * positive definite matrices * preconditioned conjugate gradient s * incomplete factorization * A-orthogonalization * SAINV Subject RIV: BA - General Mathematics Impact factor: 1.042, year: 2003

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

Science.gov (United States)

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.

Supervised Transfer Sparse Coding

KAUST Repository

Al-Shedivat, Maruan

2014-07-27

A combination of the sparse coding and transfer learn- ing techniques was shown to be accurate and robust in classification tasks where training and testing objects have a shared feature space but are sampled from differ- ent underlying distributions, i.e., belong to different do- mains. The key assumption in such case is that in spite of the domain disparity, samples from different domains share some common hidden factors. Previous methods often assumed that all the objects in the target domain are unlabeled, and thus the training set solely comprised objects from the source domain. However, in real world applications, the target domain often has some labeled objects, or one can always manually label a small num- ber of them. In this paper, we explore such possibil- ity and show how a small number of labeled data in the target domain can significantly leverage classifica- tion accuracy of the state-of-the-art transfer sparse cod- ing methods. We further propose a unified framework named supervised transfer sparse coding (STSC) which simultaneously optimizes sparse representation, domain transfer and classification. Experimental results on three applications demonstrate that a little manual labeling and then learning the model in a supervised fashion can significantly improve classification accuracy.

Sparse matrix-vector multiplication on GPGPU clusters: A new storage format and a scalable implementation

OpenAIRE

Kreutzer, Moritz; Hager, Georg; Wellein, Gerhard; Fehske, Holger; Basermann, Achim; Bishop, Alan R.

2011-01-01

Sparse matrix-vector multiplication (spMVM) is the dominant operation in many sparse solvers. We investigate performance properties of spMVM with matrices of various sparsity patterns on the nVidia “Fermi” class of GPGPUs. A new “padded jagged diagonals storage” (pJDS) format is proposed which may substantially reduce the memory overhead intrinsic to the widespread ELLPACK-R scheme while making no assumptions about the matrix structure. In our test scenarios the pJDS format cuts the ...

Sparse canonical correlation analysis: new formulation and algorithm.

Science.gov (United States)

Chu, Delin; Liao, Li-Zhi; Ng, Michael K; Zhang, Xiaowei

2013-12-01

In this paper, we study canonical correlation analysis (CCA), which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables. The main contributions of the paper are: 1) to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple CCA problem, 2) to obtain the explicit characterization for all solutions of the multiple CCA problem even when the corresponding covariance matrices are singular, 3) to develop a new sparse CCA algorithm, and 4) to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the CCA problem. We test several simulated and real-world datasets in gene classification and cross-language document retrieval to demonstrate the effectiveness of the proposed algorithm. The performance of the proposed method is competitive with the state-of-the-art sparse CCA algorithms.

Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

Directory of Open Access Journals (Sweden)

Han Guo

2012-01-01

Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

Balanced and sparse Tamo-Barg codes

KAUST Repository

Halbawi, Wael; Duursma, Iwan; Dau, Hoang; Hassibi, Babak

2017-01-01

We construct balanced and sparse generator matrices for Tamo and Barg's Locally Recoverable Codes (LRCs). More specifically, for a cyclic Tamo-Barg code of length n, dimension k and locality r, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is d + r - 1, where d is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented in this work provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures that the computational effort exerted by any storage node is essentially the same, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result previously established for Reed-Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has d nonzeros.

Balanced and sparse Tamo-Barg codes

KAUST Repository

Halbawi, Wael

2017-08-29

We construct balanced and sparse generator matrices for Tamo and Barg\\'s Locally Recoverable Codes (LRCs). More specifically, for a cyclic Tamo-Barg code of length n, dimension k and locality r, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is d + r - 1, where d is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented in this work provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures that the computational effort exerted by any storage node is essentially the same, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result previously established for Reed-Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has d nonzeros.

Ordering schemes for sparse matrices using modern programming paradigms

International Nuclear Information System (INIS)

Oliker, Leonid; Li, Xiaoye; Husbands, Parry; Biswas, Rupak

2000-01-01

The Conjugate Gradient (CG) algorithm is perhaps the best-known iterative technique to solve sparse linear systems that are symmetric and positive definite. In previous work, we investigated the effects of various ordering and partitioning strategies on the performance of CG using different programming paradigms and architectures. This paper makes several extensions to our prior research. First, we present a hybrid(MPI+OpenMP) implementation of the CG algorithm on the IBM SP and show that the hybrid paradigm increases programming complexity with little performance gains compared to a pure MPI implementation. For ill-conditioned linear systems, it is often necessary to use a preconditioning technique. We present MPI results for ILU(0) preconditioned CG (PCG) using the BlockSolve95 library, and show that the initial ordering of the input matrix dramatically affect PCG's performance. Finally, a multithreaded version of the PCG is developed on the Cray (Tera) MTA. Unlike the message-passing version, this implementation did not require the complexities of special orderings or graph dependency analysis. However, only limited scalability was achieved due to the lack of available thread level parallelism

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

Science.gov (United States)

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.

Iterative solution of large sparse systems of equations

CERN Document Server

Hackbusch, Wolfgang

2016-01-01

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

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

Science.gov (United States)

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.

Computing the real-time Green's Functions of large Hamiltonian matrices

OpenAIRE

Iitaka, Toshiaki

1998-01-01

A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a clear-cut structure reflecting the most naive definition of the Green's functions, and is very suitable to parallel and vector supercomputers. The effectiveness of the method is illustrated by applying it to simple lattice models. An application of this method...

Parallel preconditioning techniques for sparse CG solvers

Energy Technology Data Exchange (ETDEWEB)

Basermann, A.; Reichel, B.; Schelthoff, C. [Central Institute for Applied Mathematics, Juelich (Germany)

1996-12-31

Conjugate gradient (CG) methods to solve sparse systems of linear equations play an important role in numerical methods for solving discretized partial differential equations. The large size and the condition of many technical or physical applications in this area result in the need for efficient parallelization and preconditioning techniques of the CG method. In particular for very ill-conditioned matrices, sophisticated preconditioner are necessary to obtain both acceptable convergence and accuracy of CG. Here, we investigate variants of polynomial and incomplete Cholesky preconditioners that markedly reduce the iterations of the simply diagonally scaled CG and are shown to be well suited for massively parallel machines.

A Novel CSR-Based Sparse Matrix-Vector Multiplication on GPUs

Directory of Open Access Journals (Sweden)

Guixia He

2016-01-01

Full Text Available Sparse matrix-vector multiplication (SpMV is an important operation in scientific computations. Compressed sparse row (CSR is the most frequently used format to store sparse matrices. However, CSR-based SpMVs on graphic processing units (GPUs, for example, CSR-scalar and CSR-vector, usually have poor performance due to irregular memory access patterns. This motivates us to propose a perfect CSR-based SpMV on the GPU that is called PCSR. PCSR involves two kernels and accesses CSR arrays in a fully coalesced manner by introducing a middle array, which greatly alleviates the deficiencies of CSR-scalar (rare coalescing and CSR-vector (partial coalescing. Test results on a single C2050 GPU show that PCSR fully outperforms CSR-scalar, CSR-vector, and CSRMV and HYBMV in the vendor-tuned CUSPARSE library and is comparable with a most recently proposed CSR-based algorithm, CSR-Adaptive. Furthermore, we extend PCSR on a single GPU to multiple GPUs. Experimental results on four C2050 GPUs show that no matter whether the communication between GPUs is considered or not PCSR on multiple GPUs achieves good performance and has high parallel efficiency.

Solving large-scale sparse eigenvalue problems and linear systems of equations for accelerator modeling

International Nuclear Information System (INIS)

Gene Golub; Kwok Ko

2009-01-01

The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.

BICLUSTERING METHODS FOR RE-ORDERING DATA MATRICES IN SYSTEMS BIOLOGY, DRUG DISCOVERY AND TOXICOLOGY

Directory of Open Access Journals (Sweden)

Christodoulos A. Floudas

2010-12-01

Full Text Available Biclustering has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the ``best'' grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters. In the first part of the presentation, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric [1,2]. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. The performance of OREO is tested on several important data matrices arising in systems biology to validate the ability of the proposed method and compare it to existing biclustering and clustering methods. In the second part of the talk, we will focus on novel methods for clustering of data matrices that are very sparse [3]. These types of data matrices arise in drug discovery where the x- and y-axis of a data matrix can correspond to different functional groups for two distinct substituent sites on a molecular scaffold. Each possible x and y pair corresponds to a single molecule which can be synthesized and tested for a certain property, such as percent inhibition of a protein function. For even moderate size matrices, synthesizing and testing a small fraction of the molecules is labor intensive and not economically feasible. Thus, it is of paramount importance to have a reliable method for guiding the synthesis process to select molecules that have a high probability of success. In the second part of the presentation, we introduce a new strategy to enable efficient substituent reordering and descriptor-free property estimation. Our approach casts

Designing sparse sensing matrix for compressive sensing to reconstruct high resolution medical images

Directory of Open Access Journals (Sweden)

Vibha Tiwari

2015-12-01

Full Text Available Compressive sensing theory enables faithful reconstruction of signals, sparse in domain $ \\Psi $, at sampling rate lesser than Nyquist criterion, while using sampling or sensing matrix $ \\Phi $ which satisfies restricted isometric property. The role played by sensing matrix $ \\Phi $ and sparsity matrix $ \\Psi $ is vital in faithful reconstruction. If the sensing matrix is dense then it takes large storage space and leads to high computational cost. In this paper, effort is made to design sparse sensing matrix with least incurred computational cost while maintaining quality of reconstructed image. The design approach followed is based on sparse block circulant matrix (SBCM with few modifications. The other used sparse sensing matrix consists of 15 ones in each column. The medical images used are acquired from US, MRI and CT modalities. The image quality measurement parameters are used to compare the performance of reconstructed medical images using various sensing matrices. It is observed that, since Gram matrix of dictionary matrix ($ \\Phi \\Psi \\mathrm{} $ is closed to identity matrix in case of proposed modified SBCM, therefore, it helps to reconstruct the medical images of very good quality.

Sparse Principal Component Analysis in Medical Shape Modeling

DEFF Research Database (Denmark)

Sjöstrand, Karl; Stegmann, Mikkel Bille; Larsen, Rasmus

2006-01-01

Principal component analysis (PCA) is a widely used tool in medical image analysis for data reduction, model building, and data understanding and exploration. While PCA is a holistic approach where each new variable is a linear combination of all original variables, sparse PCA (SPCA) aims...... analysis in medicine. Results for three different data sets are given in relation to standard PCA and sparse PCA by simple thresholding of sufficiently small loadings. Focus is on a recent algorithm for computing sparse principal components, but a review of other approaches is supplied as well. The SPCA...

Sparse inpainting and isotropy

Energy Technology Data Exchange (ETDEWEB)

Feeney, Stephen M.; McEwen, Jason D.; Peiris, Hiranya V. [Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Marinucci, Domenico; Cammarota, Valentina [Department of Mathematics, University of Rome Tor Vergata, via della Ricerca Scientifica 1, Roma, 00133 (Italy); Wandelt, Benjamin D., E-mail: s.feeney@imperial.ac.uk, E-mail: marinucc@axp.mat.uniroma2.it, E-mail: jason.mcewen@ucl.ac.uk, E-mail: h.peiris@ucl.ac.uk, E-mail: wandelt@iap.fr, E-mail: cammarot@axp.mat.uniroma2.it [Kavli Institute for Theoretical Physics, Kohn Hall, University of California, 552 University Road, Santa Barbara, CA, 93106 (United States)

2014-01-01

Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide analytic computations and simulations of inpainted maps for a Gaussian isotropic model of CMB data, suggesting that the resulting angular trispectrum may exhibit small but non-negligible deviations from isotropy.

Performance of Firth-and logF-type penalized methods in risk prediction for small or sparse binary data.

Science.gov (United States)

Rahman, M Shafiqur; Sultana, Mahbuba

2017-02-23

When developing risk models for binary data with small or sparse data sets, the standard maximum likelihood estimation (MLE) based logistic regression faces several problems including biased or infinite estimate of the regression coefficient and frequent convergence failure of the likelihood due to separation. The problem of separation occurs commonly even if sample size is large but there is sufficient number of strong predictors. In the presence of separation, even if one develops the model, it produces overfitted model with poor predictive performance. Firth-and logF-type penalized regression methods are popular alternative to MLE, particularly for solving separation-problem. Despite the attractive advantages, their use in risk prediction is very limited. This paper evaluated these methods in risk prediction in comparison with MLE and other commonly used penalized methods such as ridge. The predictive performance of the methods was evaluated through assessing calibration, discrimination and overall predictive performance using an extensive simulation study. Further an illustration of the methods were provided using a real data example with low prevalence of outcome. The MLE showed poor performance in risk prediction in small or sparse data sets. All penalized methods offered some improvements in calibration, discrimination and overall predictive performance. Although the Firth-and logF-type methods showed almost equal amount of improvement, Firth-type penalization produces some bias in the average predicted probability, and the amount of bias is even larger than that produced by MLE. Of the logF(1,1) and logF(2,2) penalization, logF(2,2) provides slight bias in the estimate of regression coefficient of binary predictor and logF(1,1) performed better in all aspects. Similarly, ridge performed well in discrimination and overall predictive performance but it often produces underfitted model and has high rate of convergence failure (even the rate is higher than that

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

Science.gov (United States)

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.

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

Inverse m-matrices and ultrametric matrices

CERN Document Server

Dellacherie, Claude; San Martin, Jaime

2014-01-01

The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains. The main focus of this monograph is the so-called inverse M-matrix problem, which asks for a characterization of nonnegative matrices whose inverses are M-matrices. We present an answer in terms of discrete potential theory based on the Choquet-Deny Theorem. A distinguished subclass of inverse M-matrices is ultrametric matrices, which are important in applications such as taxonomy. Ultrametricity is revealed to be a relevant concept in linear algebra and discrete potential theory because of its relation with trees in graph theory and mean expected value matrices in probability theory. Remarkable properties of Hadamard functions and products for the class of inverse M-matrices are developed and probabilistic insights are provided throughout the monograph.

Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

Directory of Open Access Journals (Sweden)

Fan Yang

2015-07-01

Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.

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

Science.gov (United States)

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.

Analog system for computing sparse codes

Science.gov (United States)

Rozell, Christopher John; Johnson, Don Herrick; Baraniuk, Richard Gordon; Olshausen, Bruno A.; Ortman, Robert Lowell

2010-08-24

A parallel dynamical system for computing sparse representations of data, i.e., where the data can be fully represented in terms of a small number of non-zero code elements, and for reconstructing compressively sensed images. The system is based on the principles of thresholding and local competition that solves a family of sparse approximation problems corresponding to various sparsity metrics. The system utilizes Locally Competitive Algorithms (LCAs), nodes in a population continually compete with neighboring units using (usually one-way) lateral inhibition to calculate coefficients representing an input in an over complete dictionary.

MALDI matrices for low molecular weight compounds: an endless story?

Science.gov (United States)

Calvano, Cosima Damiana; Monopoli, Antonio; Cataldi, Tommaso R I; Palmisano, Francesco

2018-04-23

Since its introduction in the 1980s, matrix-assisted laser desorption/ionization mass spectrometry (MALDI MS) has gained a prominent role in the analysis of high molecular weight biomolecules such as proteins, peptides, oligonucleotides, and polysaccharides. Its application to low molecular weight compounds has remained for long time challenging due to the spectral interferences produced by conventional organic matrices in the low m/z window. To overcome this problem, specific sample preparation such as analyte/matrix derivatization, addition of dopants, or sophisticated deposition technique especially useful for imaging experiments, have been proposed. Alternative approaches based on second generation (rationally designed) organic matrices, ionic liquids, and inorganic matrices, including metallic nanoparticles, have been the object of intense and continuous research efforts. Definite evidences are now provided that MALDI MS represents a powerful and invaluable analytical tool also for small molecules, including their quantification, thus opening new, exciting applications in metabolomics and imaging mass spectrometry. This review is intended to offer a concise critical overview of the most recent achievements about MALDI matrices capable of specifically address the challenging issue of small molecules analysis. Graphical abstract An ideal Book of matrices for MALDI MS of small molecules.

MERSENNE AND HADAMARD MATRICES CALCULATION BY SCARPIS METHOD

Directory of Open Access Journals (Sweden)

N. A. Balonin

2014-05-01

Full Text Available Purpose. The paper deals with the problem of basic generalizations of Hadamard matrices associated with maximum determinant matrices or not optimal by determinant matrices with orthogonal columns (weighing matrices, Mersenne and Euler matrices, ets.; calculation methods for the quasi-orthogonal local maximum determinant Mersenne matrices are not studied enough sufficiently. The goal of this paper is to develop the theory of Mersenne and Hadamard matrices on the base of generalized Scarpis method research. Methods. Extreme solutions are found in general by minimization of maximum for absolute values of the elements of studied matrices followed by their subsequent classification according to the quantity of levels and their values depending on orders. Less universal but more effective methods are based on structural invariants of quasi-orthogonal matrices (Silvester, Paley, Scarpis methods, ets.. Results. Generalizations of Hadamard and Belevitch matrices as a family of quasi-orthogonal matrices of odd orders are observed; they include, in particular, two-level Mersenne matrices. Definitions of section and layer on the set of generalized matrices are proposed. Calculation algorithms for matrices of adjacent layers and sections by matrices of lower orders are described. Approximation examples of the Belevitch matrix structures up to 22-nd critical order by Mersenne matrix of the third order are given. New formulation of the modified Scarpis method to approximate Hadamard matrices of high orders by lower order Mersenne matrices is proposed. Williamson method is described by example of one modular level matrices approximation by matrices with a small number of levels. Practical relevance. The efficiency of developing direction for the band-pass filters creation is justified. Algorithms for Mersenne matrices design by Scarpis method are used in developing software of the research program complex. Mersenne filters are based on the suboptimal by

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

Energy Technology Data Exchange (ETDEWEB)

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.

Evaluating functions of positive-definite matrices using colored-noise thermostats

Science.gov (United States)

Nava, Marco; Ceriotti, Michele; Dryzun, Chaim; Parrinello, Michele

2014-02-01

Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scales with the cube of the size of the matrix. We present here a method that can be used to evaluate the elements of a function of a positive-definite matrix with a scaling that is linear for sparse matrices and quadratic in the general case. This methodology is based on the properties of the dynamics of a multidimensional harmonic potential coupled with colored-noise, generalized Langevin equation thermostats. This "f-thermostat" approach allows us to calculate directly elements of functions of a positive-definite matrix by carefully tailoring the properties of the stochastic dynamics. We demonstrate the scaling and the accuracy of this approach for both dense and sparse problems and compare the results with other established methodologies.

Efficient coordinated recovery of sparse channels in massive MIMO

KAUST Repository

Masood, Mudassir

2015-01-01

This paper addresses the problem of estimating sparse channels in massive MIMO-OFDM systems. Most wireless channels are sparse in nature with large delay spread. In addition, these channels as observed by multiple antennas in a neighborhood have approximately common support. The sparsity and common support properties are attractive when it comes to the efficient estimation of large number of channels in massive MIMO systems. Moreover, to avoid pilot contamination and to achieve better spectral efficiency, it is important to use a small number of pilots. We present a novel channel estimation approach which utilizes the sparsity and common support properties to estimate sparse channels and requires a small number of pilots. Two algorithms based on this approach have been developed that perform Bayesian estimates of sparse channels even when the prior is non-Gaussian or unknown. Neighboring antennas share among each other their beliefs about the locations of active channel taps to perform estimation. The coordinated approach improves channel estimates and also reduces the required number of pilots. Further improvement is achieved by the data-aided version of the algorithm. Extensive simulation results are provided to demonstrate the performance of the proposed algorithms.

Fast Solution in Sparse LDA for Binary Classification

Science.gov (United States)

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

Mutation rules and the evolution of sparseness and modularity in biological systems.

Directory of Open Access Journals (Sweden)

Tamar Friedlander

Full Text Available Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity--the near decomposability of the system into modules with distinct functionality. Recent work suggests that modularity can evolve in a variety of circumstances, including goals that vary in time such that they share the same subgoals (modularly varying goals, or when connections are costly. Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than on connection cost or variations in the goal. We use simulations of evolution with different mutation rules. We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations. In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers--a better model for the effects of biological mutations--led to sparseness naturally. When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they tend to reduce interactions, and to keep small interaction terms small.

An NoC Traffic Compiler for Efficient FPGA Implementation of Sparse Graph-Oriented Workloads

Directory of Open Access Journals (Sweden)

Nachiket Kapre

2011-01-01

synchronization to optimize our workloads for large networks up to 2025 parallel elements for BSP model and 25 parallel elements for Token Dataflow. This allows us to demonstrate speedups between 1.2× and 22× (3.5× mean, area reductions (number of Processing Elements between 3× and 15× (9× mean and dynamic energy savings between 2× and 3.5× (2.7× mean over a range of real-world graph applications in the BSP compute model. We deliver speedups of 0.5–13× (geomean 3.6× for Sparse Direct Matrix Solve (Token Dataflow compute model applied to a range of sparse matrices when using a high-quality placement algorithm. We expect such traffic optimization tools and techniques to become an essential part of the NoC application-mapping flow.

Pathological rate matrices: from primates to pathogens

Directory of Open Access Journals (Sweden)

Knight Rob

2008-12-01

Full Text Available Abstract Background Continuous-time Markov models allow flexible, parametrically succinct descriptions of sequence divergence. Non-reversible forms of these models are more biologically realistic but are challenging to develop. The instantaneous rate matrices defined for these models are typically transformed into substitution probability matrices using a matrix exponentiation algorithm that employs eigendecomposition, but this algorithm has characteristic vulnerabilities that lead to significant errors when a rate matrix possesses certain 'pathological' properties. Here we tested whether pathological rate matrices exist in nature, and consider the suitability of different algorithms to their computation. Results We used concatenated protein coding gene alignments from microbial genomes, primate genomes and independent intron alignments from primate genomes. The Taylor series expansion and eigendecomposition matrix exponentiation algorithms were compared to the less widely employed, but more robust, Padé with scaling and squaring algorithm for nucleotide, dinucleotide, codon and trinucleotide rate matrices. Pathological dinucleotide and trinucleotide matrices were evident in the microbial data set, affecting the eigendecomposition and Taylor algorithms respectively. Even using a conservative estimate of matrix error (occurrence of an invalid probability, both Taylor and eigendecomposition algorithms exhibited substantial error rates: ~100% of all exonic trinucleotide matrices were pathological to the Taylor algorithm while ~10% of codon positions 1 and 2 dinucleotide matrices and intronic trinucleotide matrices, and ~30% of codon matrices were pathological to eigendecomposition. The majority of Taylor algorithm errors derived from occurrence of multiple unobserved states. A small number of negative probabilities were detected from the Pad�� algorithm on trinucleotide matrices that were attributable to machine precision. Although the Pad

Efficient linear algebra routines for symmetric matrices stored in packed form.

Science.gov (United States)

Ahlrichs, Reinhart; Tsereteli, Kakha

2002-01-30

Quantum chemistry methods require various linear algebra routines for symmetric matrices, for example, diagonalization or Cholesky decomposition for positive matrices. We present a small set of these basic routines that are efficient and minimize memory requirements.

Semi-supervised sparse coding

KAUST Repository

Wang, Jim Jing-Yan; Gao, Xin

2014-01-01

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.

Semi-supervised sparse coding

KAUST Repository

Wang, Jim Jing-Yan

2014-07-06

Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a semi-supervised manner, where only a few training samples are labeled. By using the manifold structure spanned by the data set of both labeled and unlabeled samples and the constraints provided by the labels of the labeled samples, we learn the variable class labels for all the samples. Furthermore, to improve the discriminative ability of the learned sparse codes, we assume that the class labels could be predicted from the sparse codes directly using a linear classifier. By solving the codebook, sparse codes, class labels and classifier parameters simultaneously in a unified objective function, we develop a semi-supervised sparse coding algorithm. Experiments on two real-world pattern recognition problems demonstrate the advantage of the proposed methods over supervised sparse coding methods on partially labeled data sets.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Science.gov (United States)

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

In Defense of Sparse Tracking: Circulant Sparse Tracker

KAUST Repository

Zhang, Tianzhu; Bibi, Adel Aamer; Ghanem, Bernard

2016-01-01

Sparse representation has been introduced to visual tracking by finding the best target candidate with minimal reconstruction error within the particle filter framework. However, most sparse representation based trackers have high computational cost, less than promising tracking performance, and limited feature representation. To deal with the above issues, we propose a novel circulant sparse tracker (CST), which exploits circulant target templates. Because of the circulant structure property, CST has the following advantages: (1) It can refine and reduce particles using circular shifts of target templates. (2) The optimization can be efficiently solved entirely in the Fourier domain. (3) High dimensional features can be embedded into CST to significantly improve tracking performance without sacrificing much computation time. Both qualitative and quantitative evaluations on challenging benchmark sequences demonstrate that CST performs better than all other sparse trackers and favorably against state-of-the-art methods.

In Defense of Sparse Tracking: Circulant Sparse Tracker

KAUST Repository

Zhang, Tianzhu

2016-12-13

Sparse representation has been introduced to visual tracking by finding the best target candidate with minimal reconstruction error within the particle filter framework. However, most sparse representation based trackers have high computational cost, less than promising tracking performance, and limited feature representation. To deal with the above issues, we propose a novel circulant sparse tracker (CST), which exploits circulant target templates. Because of the circulant structure property, CST has the following advantages: (1) It can refine and reduce particles using circular shifts of target templates. (2) The optimization can be efficiently solved entirely in the Fourier domain. (3) High dimensional features can be embedded into CST to significantly improve tracking performance without sacrificing much computation time. Both qualitative and quantitative evaluations on challenging benchmark sequences demonstrate that CST performs better than all other sparse trackers and favorably against state-of-the-art methods.

Real-Time Fabric Defect Detection Using Accelerated Small-Scale Over-Completed Dictionary of Sparse Coding

Directory of Open Access Journals (Sweden)

Tianpeng Feng

2016-01-01

Full Text Available An auto fabric defect detection system via computer vision is used to replace manual inspection. In this paper, we propose a hardware accelerated algorithm based on a small-scale over-completed dictionary (SSOCD via sparse coding (SC method, which is realized on a parallel hardware platform (TMS320C6678. In order to reduce computation, the image patches projections in the training SSOCD are taken as features and the proposed features are more robust, and exhibit obvious advantages in detection results and computational cost. Furthermore, we introduce detection ratio and false ratio in order to measure the performance and reliability of the hardware accelerated algorithm. The experiments show that the proposed algorithm can run with high parallel efficiency and that the detection speed meets the real-time requirements of industrial inspection.

Combinatorial Algorithms for Computing Column Space Bases ThatHave Sparse Inverses

Energy Technology Data Exchange (ETDEWEB)

Pinar, Ali; Chow, Edmond; Pothen, Alex

2005-03-18

This paper presents a combinatorial study on the problem ofconstructing a sparse basis forthe null-space of a sparse, underdetermined, full rank matrix, A. Such a null-space is suitable forsolving solving many saddle point problems. Our approach is to form acolumn space basis of A that has a sparse inverse, by selecting suitablecolumns of A. This basis is then used to form a sparse null-space basisin fundamental form. We investigate three different algorithms forcomputing the column space basis: Two greedy approaches that rely onmatching, and a third employing a divide and conquer strategy implementedwith hypergraph partitioning followed by the greedy approach. We alsodiscuss the complexity of selecting a column basis when it is known thata block diagonal basis exists with a small given block size.

Monitoring the progression of calcium and protein solubilisation as affected by calcium chelators during small-scale manufacture of casein-based food matrices.

Science.gov (United States)

McIntyre, Irene; O'Sullivan, Michael; O'Riordan, Dolores

2017-12-15

Calcium and protein solubilisation during small-scale manufacture of semi-solid casein-based food matrices was investigated and found to be very different in the presence or absence of calcium chelating salts. Calcium concentrations in the dispersed phase increased and calcium-ion activity (A Ca ++ ) decreased during manufacture of the matrices containing calcium chelating salts; with ∼23% of total calcium solubilised by the end of manufacture. In the absence of calcium chelating salts, these concentrations were significantly lower at equivalent processing times and remained unchanged as did A Ca ++ , throughout manufacture. The protein content of the dispersed phase was low (≤3% of total protein), but was significantly higher for matrices containing calcium chelating salts. This study elucidates the critical role of calcium chelating salts in modulating casein hydration and dispersion and gives an indication of the levels of soluble calcium and protein required to allow matrix formation during manufacture of casein-based food structures e.g. processed and analogue cheese. Copyright © 2017 Elsevier Ltd. All rights reserved.

Stabilization of chromium-bearing electroplating sludge with MSWI fly ash-based Friedel matrices.

Science.gov (United States)

Qian, Guangren; Yang, Xiaoyan; Dong, Shixiang; Zhou, Jizhi; Sun, Ying; Xu, Yunfeng; Liu, Qiang

2009-06-15

This work investigated the feasibility and effectiveness of MSWI fly ash-based Friedel matrices on stabilizing/solidifying industrial chromium-bearing electroplating sludge using MSWI fly ash as the main raw material with a small addition of active aluminum. The compressive strength, leaching behavior and chemical speciation of heavy metals and hydration phases of matrices were characterized by TCLP, XRD, FTIR and other experimental methods. The results revealed that MSWI fly ash-based Friedel matrices could effectively stabilize chromium-bearing electroplating sludge, the formed ettringite and Friedel phases played a significant role in the fixation of heavy metals in electroplating sludge. The co-disposal of chromium-bearing electroplating sludge and MSWI fly ash-based Friedel matrices with a small addition of active aluminum is promising to be an effective way of stabilizing chromium-bearing electroplating sludge.

Structural Sparse Tracking

KAUST Repository

Zhang, Tianzhu

2015-06-01

Sparse representation has been applied to visual tracking by finding the best target candidate with minimal reconstruction error by use of target templates. However, most sparse representation based trackers only consider holistic or local representations and do not make full use of the intrinsic structure among and inside target candidates, thereby making the representation less effective when similar objects appear or under occlusion. In this paper, we propose a novel Structural Sparse Tracking (SST) algorithm, which not only exploits the intrinsic relationship among target candidates and their local patches to learn their sparse representations jointly, but also preserves the spatial layout structure among the local patches inside each target candidate. We show that our SST algorithm accommodates most existing sparse trackers with the respective merits. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed SST algorithm performs favorably against several state-of-the-art methods.

Hierarchical quark mass matrices

International Nuclear Information System (INIS)

Rasin, A.

1998-02-01

I define a set of conditions that the most general hierarchical Yukawa mass matrices have to satisfy so that the leading rotations in the diagonalization matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch structures, examples of such hierarchical structures include also matrices with (1,3) elements of the same order or even much larger than the (1,2) elements. Such matrices can be obtained in the framework of a flavor theory. To leading order, the values of the angle in the (2,3) plane (s 23 ) and the angle in the (1,2) plane (s 12 ) do not depend on the order in which they are taken when diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix parametrizations that consist of at least one (1,2) and one (2,3) rotation may be suitable. In the particular case when the s 13 diagonalization angles are sufficiently small compared to the product s 12 s 23 , two special CKM parametrizations emerge: the R 12 R 23 R 12 parametrization follows with s 23 taken before the s 12 rotation, and vice versa for the R 23 R 12 R 23 parametrization. (author)

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

Science.gov (United States)

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 Dsparse synchronization do contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike in the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of

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

Science.gov (United States)

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 sparse synchronization do contributions of individual neuronal dynamics to population synchronization change depending on their degrees, unlike in the case of full synchronization. Consequently, dynamics of individual neurons reveal the inhomogeneous network structure for the case of partial and sparse synchronization, which is in contrast to the case of statistically homogeneous

Averaging operations on matrices

Indian Academy of Sciences (India)

2014-07-03

Jul 3, 2014 ... Role of Positive Definite Matrices. • Diffusion Tensor Imaging: 3 × 3 pd matrices model water flow at each voxel of brain scan. • Elasticity: 6 × 6 pd matrices model stress tensors. • Machine Learning: n × n pd matrices occur as kernel matrices. Tanvi Jain. Averaging operations on matrices ...

VanderLaan Circulant Type Matrices

Directory of Open Access Journals (Sweden)

Hongyan Pan

2015-01-01

Full Text Available Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaan g-circulant matrix.

Open vessel microwave digestion of food matrices (T6)

International Nuclear Information System (INIS)

Rhodes, L.; LeBlanc, G.

2002-01-01

Full text: Advancements in the field of open vessel microwave digestion continue to provide solutions for industries requiring acid digestion of large sample sizes. Those interesting in digesting food matrices are particularly interested in working with large amounts of sample and then diluting small final volumes. This paper will show the advantages of instantaneous regent addition and post-digestion evaporation when performing an open vessel digestion and evaporation methods for various food matrices will be presented along with analyte recovery data. (author)

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

Science.gov (United States)

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.

Theoretical and experimental researches of methanol clusters in low - temperature matrices

International Nuclear Information System (INIS)

Chernolevs'ka, Je.A.; Doroshenko, Yi.Yu.; Pogorelov, V.Je.; Vas'kyivs'kij, Je.V.; Shablyinskas, V.; Balyavyichus, V.; Yasajev, O.

2015-01-01

Molecular vibrational spectra of methanol in argon and nitrogen matrices have been studied. Since methanol belongs to a class of substances with hydrogen bonds, there is a possibility of forming molecular associations and clusters with various numbers of molecules. IR spectra of methanol in Ar and N 2 matrices experimentally obtained in the temperature range from 10 to 50 K are compared with the results of computer simulation using the ab initio Car-Parrinello molecular dynamics (CPMD) method. The results obtained for small clusters in model calculations demonstrate a good correlation with experimental data for various matrices at the corresponding temperatures

Sparse-matrix factorizations for fast symmetric Fourier transforms

International Nuclear Information System (INIS)

Sequel, J.

1987-01-01

This work proposes new fast algorithms computing the discrete Fourier transform of certain families of symmetric sequences. Sequences commonly found in problems of structure determination by x-ray crystallography and in numerical solutions of boundary-value problems in partial differential equations are dealt with. In the algorithms presented, the redundancies in the input and output data, due to the presence of symmetries in the input data sequence, were eliminated. Using ring-theoretical methods a matrix representation is obtained for the remaining calculations; which factors as the product of a complex block-diagonal matrix times as integral matrix. A basic two-step algorithm scheme arises from this factorization with a first step consisting of pre-additions and a second step containing the calculations involved in computing with the blocks in the block-diagonal factor. These blocks are structured as block-Hankel matrices, and two sparse-matrix factoring formulas are developed in order to diminish their arithmetic complexity

Two-dimensional sparse wavenumber recovery for guided wavefields

Science.gov (United States)

Sabeti, Soroosh; Harley, Joel B.

2018-04-01

The multi-modal and dispersive behavior of guided waves is often characterized by their dispersion curves, which describe their frequency-wavenumber behavior. In prior work, compressive sensing based techniques, such as sparse wavenumber analysis (SWA), have been capable of recovering dispersion curves from limited data samples. A major limitation of SWA, however, is the assumption that the structure is isotropic. As a result, SWA fails when applied to composites and other anisotropic structures. There have been efforts to address this issue in the literature, but they either are not easily generalizable or do not sufficiently express the data. In this paper, we enhance the existing approaches by employing a two-dimensional wavenumber model to account for direction-dependent velocities in anisotropic media. We integrate this model with tools from compressive sensing to reconstruct a wavefield from incomplete data. Specifically, we create a modified two-dimensional orthogonal matching pursuit algorithm that takes an undersampled wavefield image, with specified unknown elements, and determines its sparse wavenumber characteristics. We then recover the entire wavefield from the sparse representations obtained with our small number of data samples.

Sparse principal component analysis in medical shape modeling

Science.gov (United States)

Sjöstrand, Karl; Stegmann, Mikkel B.; Larsen, Rasmus

2006-03-01

Principal component analysis (PCA) is a widely used tool in medical image analysis for data reduction, model building, and data understanding and exploration. While PCA is a holistic approach where each new variable is a linear combination of all original variables, sparse PCA (SPCA) aims at producing easily interpreted models through sparse loadings, i.e. each new variable is a linear combination of a subset of the original variables. One of the aims of using SPCA is the possible separation of the results into isolated and easily identifiable effects. This article introduces SPCA for shape analysis in medicine. Results for three different data sets are given in relation to standard PCA and sparse PCA by simple thresholding of small loadings. Focus is on a recent algorithm for computing sparse principal components, but a review of other approaches is supplied as well. The SPCA algorithm has been implemented using Matlab and is available for download. The general behavior of the algorithm is investigated, and strengths and weaknesses are discussed. The original report on the SPCA algorithm argues that the ordering of modes is not an issue. We disagree on this point and propose several approaches to establish sensible orderings. A method that orders modes by decreasing variance and maximizes the sum of variances for all modes is presented and investigated in detail.

SLAP, Large Sparse Linear System Solution Package

International Nuclear Information System (INIS)

Greenbaum, A.

1987-01-01

1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration

Accelerating Scientific Applications using High Performance Dense and Sparse Linear Algebra Kernels on GPUs

KAUST Repository

Abdelfattah, Ahmad

2015-01-15

High performance computing (HPC) platforms are evolving to more heterogeneous configurations to support the workloads of various applications. The current hardware landscape is composed of traditional multicore CPUs equipped with hardware accelerators that can handle high levels of parallelism. Graphical Processing Units (GPUs) are popular high performance hardware accelerators in modern supercomputers. GPU programming has a different model than that for CPUs, which means that many numerical kernels have to be redesigned and optimized specifically for this architecture. GPUs usually outperform multicore CPUs in some compute intensive and massively parallel applications that have regular processing patterns. However, most scientific applications rely on crucial memory-bound kernels and may witness bottlenecks due to the overhead of the memory bus latency. They can still take advantage of the GPU compute power capabilities, provided that an efficient architecture-aware design is achieved. This dissertation presents a uniform design strategy for optimizing critical memory-bound kernels on GPUs. Based on hierarchical register blocking, double buffering and latency hiding techniques, this strategy leverages the performance of a wide range of standard numerical kernels found in dense and sparse linear algebra libraries. The work presented here focuses on matrix-vector multiplication kernels (MVM) as repre- sentative and most important memory-bound operations in this context. Each kernel inherits the benefits of the proposed strategies. By exposing a proper set of tuning parameters, the strategy is flexible enough to suit different types of matrices, ranging from large dense matrices, to sparse matrices with dense block structures, while high performance is maintained. Furthermore, the tuning parameters are used to maintain the relative performance across different GPU architectures. Multi-GPU acceleration is proposed to scale the performance on several devices. The

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

Science.gov (United States)

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.

Group-sparse representation with dictionary learning for medical image denoising and fusion.

Science.gov (United States)

Li, Shutao; Yin, Haitao; Fang, Leyuan

2012-12-01

Recently, sparse representation has attracted a lot of interest in various areas. However, the standard sparse representation does not consider the intrinsic structure, i.e., the nonzero elements occur in clusters, called group sparsity. Furthermore, there is no dictionary learning method for group sparse representation considering the geometrical structure of space spanned by atoms. In this paper, we propose a novel dictionary learning method, called Dictionary Learning with Group Sparsity and Graph Regularization (DL-GSGR). First, the geometrical structure of atoms is modeled as the graph regularization. Then, combining group sparsity and graph regularization, the DL-GSGR is presented, which is solved by alternating the group sparse coding and dictionary updating. In this way, the group coherence of learned dictionary can be enforced small enough such that any signal can be group sparse coded effectively. Finally, group sparse representation with DL-GSGR is applied to 3-D medical image denoising and image fusion. Specifically, in 3-D medical image denoising, a 3-D processing mechanism (using the similarity among nearby slices) and temporal regularization (to perverse the correlations across nearby slices) are exploited. The experimental results on 3-D image denoising and image fusion demonstrate the superiority of our proposed denoising and fusion approaches.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint

Directory of Open Access Journals (Sweden)

Zhi Gao

2018-05-01

Full Text Available Light detection and ranging (LiDAR sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs and unmanned aerial vehicles (UAVs to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint.

Science.gov (United States)

Gao, Zhi; Lao, Mingjie; Sang, Yongsheng; Wen, Fei; Ramesh, Bharath; Zhai, Ruifang

2018-05-06

Light detection and ranging (LiDAR) sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency.

Library designs for generic C++ sparse matrix computations of iterative methods

Energy Technology Data Exchange (ETDEWEB)

Pozo, R.

1996-12-31

A new library design is presented for generic sparse matrix C++ objects for use in iterative algorithms and preconditioners. This design extends previous work on C++ numerical libraries by providing a framework in which efficient algorithms can be written *independent* of the matrix layout or format. That is, rather than supporting different codes for each (element type) / (matrix format) combination, only one version of the algorithm need be maintained. This not only reduces the effort for library developers, but also simplifies the calling interface seen by library users. Furthermore, the underlying matrix library can be naturally extended to support user-defined objects, such as hierarchical block-structured matrices, or application-specific preconditioners. Utilizing optimized kernels whenever possible, the resulting performance of such framework can be shown to be competitive with optimized Fortran programs.

When sparse coding meets ranking: a joint framework for learning sparse codes and ranking scores

KAUST Repository

Wang, Jim Jing-Yan

2017-06-28

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays an important role. Up to now, these two problems have always been considered separately, assuming that data coding and ranking are two independent and irrelevant problems. However, is there any internal relationship between sparse coding and ranking score learning? If yes, how to explore and make use of this internal relationship? In this paper, we try to answer these questions by developing the first joint sparse coding and ranking score learning algorithm. To explore the local distribution in the sparse code space, and also to bridge coding and ranking problems, we assume that in the neighborhood of each data point, the ranking scores can be approximated from the corresponding sparse codes by a local linear function. By considering the local approximation error of ranking scores, the reconstruction error and sparsity of sparse coding, and the query information provided by the user, we construct a unified objective function for learning of sparse codes, the dictionary and ranking scores. We further develop an iterative algorithm to solve this optimization problem.

Emergence of ultrafast sparsely synchronized rhythms and their responses to external stimuli in an inhomogeneous small-world complex neuronal network.

Science.gov (United States)

Kim, Sang-Yoon; Lim, Woochang

2017-09-01

We consider an inhomogeneous small-world network (SWN) composed of inhibitory short-range (SR) and long-range (LR) interneurons, and investigate the effect of network architecture on emergence of synchronized brain rhythms by varying the fraction of LR interneurons p long . The betweenness centralities of the LR and SR interneurons (characterizing the potentiality in controlling communication between other interneurons) are distinctly different. Hence, in view of the betweenness, SWNs we consider are inhomogeneous, unlike the "canonical" Watts-Strogatz SWN with nearly the same betweenness centralities. For small p long , the load of communication traffic is much concentrated on a few LR interneurons. However, as p long is increased, the number of LR connections (coming from LR interneurons) increases, and then the load of communication traffic is less concentrated on LR interneurons, which leads to better efficiency of global communication between interneurons. Sparsely synchronized rhythms are thus found to emerge when passing a small critical value p long (c) (≃0.16). The population frequency of the sparsely synchronized rhythm is ultrafast (higher than 100 Hz), while the mean firing rate of individual interneurons is much lower (∼30 Hz) due to stochastic and intermittent neural discharges. These dynamical behaviors in the inhomogeneous SWN are also compared with those in the homogeneous Watts-Strogatz SWN, in connection with their network topologies. Particularly, we note that the main difference between the two types of SWNs lies in the distribution of betweenness centralities. Unlike the case of the Watts-Strogatz SWN, dynamical responses to external stimuli vary depending on the type of stimulated interneurons in the inhomogeneous SWN. We consider two cases of external time-periodic stimuli applied to sub-populations of the LR and SR interneurons, respectively. Dynamical responses (such as synchronization suppression and enhancement) to these two cases of

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander; Genton, Marc G.; Sun, Ying

2015-01-01

We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.

Hierarchical matrix approximation of large covariance matrices

KAUST Repository

Litvinenko, Alexander

2015-11-30

We approximate large non-structured Matérn covariance matrices of size n×n in the H-matrix format with a log-linear computational cost and storage O(kn log n), where rank k ≪ n is a small integer. Applications are: spatial statistics, machine learning and image analysis, kriging and optimal design.

Information filtering in sparse online systems: recommendation via semi-local diffusion.

Science.gov (United States)

Zeng, Wei; Zeng, An; Shang, Ming-Sheng; Zhang, Yi-Cheng

2013-01-01

With the rapid growth of the Internet and overwhelming amount of information and choices that people are confronted with, recommender systems have been developed to effectively support users' decision-making process in the online systems. However, many recommendation algorithms suffer from the data sparsity problem, i.e. the user-object bipartite networks are so sparse that algorithms cannot accurately recommend objects for users. This data sparsity problem makes many well-known recommendation algorithms perform poorly. To solve the problem, we propose a recommendation algorithm based on the semi-local diffusion process on the user-object bipartite network. The simulation results on two sparse datasets, Amazon and Bookcross, show that our method significantly outperforms the state-of-the-art methods especially for those small-degree users. Two personalized semi-local diffusion methods are proposed which further improve the recommendation accuracy. Finally, our work indicates that sparse online systems are essentially different from the dense online systems, so it is necessary to reexamine former algorithms and conclusions based on dense data in sparse systems.

Infinite matrices and sequence spaces

CERN Document Server

Cooke, Richard G

2014-01-01

This clear and correct summation of basic results from a specialized field focuses on the behavior of infinite matrices in general, rather than on properties of special matrices. Three introductory chapters guide students to the manipulation of infinite matrices, covering definitions and preliminary ideas, reciprocals of infinite matrices, and linear equations involving infinite matrices.From the fourth chapter onward, the author treats the application of infinite matrices to the summability of divergent sequences and series from various points of view. Topics include consistency, mutual consi

Complex Wedge-Shaped Matrices: A Generalization of Jacobi Matrices

Czech Academy of Sciences Publication Activity Database

Hnětynková, Iveta; Plešinger, M.

2015-01-01

Roč. 487, 15 December (2015), s. 203-219 ISSN 0024-3795 R&D Projects: GA ČR GA13-06684S Keywords : eigenvalues * eigenvector * wedge-shaped matrices * generalized Jacobi matrices * band (or block) Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 0.965, year: 2015

Deep ensemble learning of sparse regression models for brain disease diagnosis.

Science.gov (United States)

Suk, Heung-Il; Lee, Seong-Whan; Shen, Dinggang

2017-04-01

Recent studies on brain imaging analysis witnessed the core roles of machine learning techniques in computer-assisted intervention for brain disease diagnosis. Of various machine-learning techniques, sparse regression models have proved their effectiveness in handling high-dimensional data but with a small number of training samples, especially in medical problems. In the meantime, deep learning methods have been making great successes by outperforming the state-of-the-art performances in various applications. In this paper, we propose a novel framework that combines the two conceptually different methods of sparse regression and deep learning for Alzheimer's disease/mild cognitive impairment diagnosis and prognosis. Specifically, we first train multiple sparse regression models, each of which is trained with different values of a regularization control parameter. Thus, our multiple sparse regression models potentially select different feature subsets from the original feature set; thereby they have different powers to predict the response values, i.e., clinical label and clinical scores in our work. By regarding the response values from our sparse regression models as target-level representations, we then build a deep convolutional neural network for clinical decision making, which thus we call 'Deep Ensemble Sparse Regression Network.' To our best knowledge, this is the first work that combines sparse regression models with deep neural network. In our experiments with the ADNI cohort, we validated the effectiveness of the proposed method by achieving the highest diagnostic accuracies in three classification tasks. We also rigorously analyzed our results and compared with the previous studies on the ADNI cohort in the literature. Copyright © 2017 Elsevier B.V. All rights reserved.

Deformable segmentation via sparse representation and dictionary learning.

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Quantitative mass spectrometry of unconventional human biological matrices

Science.gov (United States)

Dutkiewicz, Ewelina P.; Urban, Pawel L.

2016-10-01

The development of sensitive and versatile mass spectrometric methodology has fuelled interest in the analysis of metabolites and drugs in unconventional biological specimens. Here, we discuss the analysis of eight human matrices-hair, nail, breath, saliva, tears, meibum, nasal mucus and skin excretions (including sweat)-by mass spectrometry (MS). The use of such specimens brings a number of advantages, the most important being non-invasive sampling, the limited risk of adulteration and the ability to obtain information that complements blood and urine tests. The most often studied matrices are hair, breath and saliva. This review primarily focuses on endogenous (e.g. potential biomarkers, hormones) and exogenous (e.g. drugs, environmental contaminants) small molecules. The majority of analytical methods used chromatographic separation prior to MS; however, such a hyphenated methodology greatly limits analytical throughput. On the other hand, the mass spectrometric methods that exclude chromatographic separation are fast but suffer from matrix interferences. To enable development of quantitative assays for unconventional matrices, it is desirable to standardize the protocols for the analysis of each specimen and create appropriate certified reference materials. Overcoming these challenges will make analysis of unconventional human biological matrices more common in a clinical setting. This article is part of the themed issue 'Quantitative mass spectrometry'.

Transfer matrices for multilayer structures

International Nuclear Information System (INIS)

Baquero, R.

1988-08-01

We consider four of the transfer matrices defined to deal with multilayer structures. We deduce algorithms to calculate them numerically, in a simple and neat way. We illustrate their application to semi-infinite systems using SGFM formulae. These algorithms are of fast convergence and allow a calculation of bulk-, surface- and inner-layers band structure in good agreement with much more sophisticated calculations. Supermatrices, interfaces and multilayer structures can be calculated in this way with a small computational effort. (author). 10 refs

Sparse structure regularized ranking

KAUST Repository

Wang, Jim Jing-Yan; Sun, Yijun; Gao, Xin

2014-01-01

Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse

Sparse structure regularized ranking

KAUST Repository

Wang, Jim Jing-Yan

2014-04-17

Learning ranking scores is critical for the multimedia database retrieval problem. In this paper, we propose a novel ranking score learning algorithm by exploring the sparse structure and using it to regularize ranking scores. To explore the sparse structure, we assume that each multimedia object could be represented as a sparse linear combination of all other objects, and combination coefficients are regarded as a similarity measure between objects and used to regularize their ranking scores. Moreover, we propose to learn the sparse combination coefficients and the ranking scores simultaneously. A unified objective function is constructed with regard to both the combination coefficients and the ranking scores, and is optimized by an iterative algorithm. Experiments on two multimedia database retrieval data sets demonstrate the significant improvements of the propose algorithm over state-of-the-art ranking score learning algorithms.

HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

KAUST Repository

Litvinenko, Alexander

2017-01-01

matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p

Turbulent flows over sparse canopies

Science.gov (United States)

Sharma, Akshath; García-Mayoral, Ricardo

2018-04-01

Turbulent flows over sparse and dense canopies exerting a similar drag force on the flow are investigated using Direct Numerical Simulations. The dense canopies are modelled using a homogeneous drag force, while for the sparse canopy, the geometry of the canopy elements is represented. It is found that on using the friction velocity based on the local shear at each height, the streamwise velocity fluctuations and the Reynolds stress within the sparse canopy are similar to those from a comparable smooth-wall case. In addition, when scaled with the local friction velocity, the intensity of the off-wall peak in the streamwise vorticity for sparse canopies also recovers a value similar to a smooth-wall. This indicates that the sparse canopy does not significantly disturb the near-wall turbulence cycle, but causes its rescaling to an intensity consistent with a lower friction velocity within the canopy. In comparison, the dense canopy is found to have a higher damping effect on the turbulent fluctuations. For the case of the sparse canopy, a peak in the spectral energy density of the wall-normal velocity, and Reynolds stress is observed, which may indicate the formation of Kelvin-Helmholtz-like instabilities. It is also found that a sparse canopy is better modelled by a homogeneous drag applied on the mean flow alone, and not the turbulent fluctuations.

NetRaVE: constructing dependency networks using sparse linear regression

DEFF Research Database (Denmark)

Phatak, A.; Kiiveri, H.; Clemmensen, Line Katrine Harder

2010-01-01

NetRaVE is a small suite of R functions for generating dependency networks using sparse regression methods. Such networks provide an alternative to interpreting 'top n lists' of genes arising out of an analysis of microarray data, and they provide a means of organizing and visualizing the resulting...

OFDM receiver for fast time-varying channels using block-sparse Bayesian learning

DEFF Research Database (Denmark)

Barbu, Oana-Elena; Manchón, Carles Navarro; Rom, Christian

2016-01-01

characterized with a basis expansion model using a small number of terms. As a result, the channel estimation problem is posed as that of estimating a vector of complex coefficients that exhibits a block-sparse structure, which we solve with tools from block-sparse Bayesian learning. Using variational Bayesian...... inference, we embed the channel estimator in a receiver structure that performs iterative channel and noise precision estimation, intercarrier interference cancellation, detection and decoding. Simulation results illustrate the superior performance of the proposed receiver over state-of-art receivers....

On reflectionless equi-transmitting matrices

Directory of Open Access Journals (Sweden)

Pavel Kurasov

2014-01-01

Full Text Available Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.

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

Science.gov (United States)

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

2018-04-01

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

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.; Bensmail, H.; Yao, N.; Gao, Xin

2013-01-01

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Discriminative sparse coding on multi-manifolds

KAUST Repository

Wang, J.J.-Y.

2013-09-26

Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics. However, the conventional sparse coding algorithms and their manifold-regularized variants (graph sparse coding and Laplacian sparse coding), learn codebooks and codes in an unsupervised manner and neglect class information that is available in the training set. To address this problem, we propose a novel discriminative sparse coding method based on multi-manifolds, that learns discriminative class-conditioned codebooks and sparse codes from both data feature spaces and class labels. First, the entire training set is partitioned into multiple manifolds according to the class labels. Then, we formulate the sparse coding as a manifold-manifold matching problem and learn class-conditioned codebooks and codes to maximize the manifold margins of different classes. Lastly, we present a data sample-manifold matching-based strategy to classify the unlabeled data samples. Experimental results on somatic mutations identification and breast tumor classification based on ultrasonic images demonstrate the efficacy of the proposed data representation and classification approach. 2013 The Authors. All rights reserved.

Sparse Regression by Projection and Sparse Discriminant Analysis

KAUST Repository

Qi, Xin

2015-04-03

© 2015, © American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high-dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross-validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares, and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared with the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplementary materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.

Sparse distributed memory overview

Science.gov (United States)

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.

In-place sparse suffix sorting

DEFF Research Database (Denmark)

Prezza, Nicola

2018-01-01

information regarding the lexicographical order of a size-b subset of all n text suffixes is often needed. Such information can be stored space-efficiently (in b words) in the sparse suffix array (SSA). The SSA and its relative sparse LCP array (SLCP) can be used as a space-efficient substitute of the sparse...... suffix tree. Very recently, Gawrychowski and Kociumaka [11] showed that the sparse suffix tree (and therefore SSA and SLCP) can be built in asymptotically optimal O(b) space with a Monte Carlo algorithm running in O(n) time. The main reason for using the SSA and SLCP arrays in place of the sparse suffix...... tree is, however, their reduced space of b words each. This leads naturally to the quest for in-place algorithms building these arrays. Franceschini and Muthukrishnan [8] showed that the full suffix array can be built in-place and in optimal running time. On the other hand, finding sub-quadratic in...

Semi-blind sparse image reconstruction with application to MRFM.

Science.gov (United States)

Park, Se Un; Dobigeon, Nicolas; Hero, Alfred O

2012-09-01

We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high-dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.

Classification of multispectral or hyperspectral satellite imagery using clustering of sparse approximations on sparse representations in learned dictionaries obtained using efficient convolutional sparse coding

Science.gov (United States)

Moody, Daniela; Wohlberg, Brendt

2018-01-02

An approach for land cover classification, seasonal and yearly change detection and monitoring, and identification of changes in man-made features may use a clustering of sparse approximations (CoSA) on sparse representations in learned dictionaries. The learned dictionaries may be derived using efficient convolutional sparse coding to build multispectral or hyperspectral, multiresolution dictionaries that are adapted to regional satellite image data. Sparse image representations of images over the learned dictionaries may be used to perform unsupervised k-means clustering into land cover categories. The clustering process behaves as a classifier in detecting real variability. This approach may combine spectral and spatial textural characteristics to detect geologic, vegetative, hydrologic, and man-made features, as well as changes in these features over time.

Nonuniform Sparse Data Clustering Cascade Algorithm Based on Dynamic Cumulative Entropy

Directory of Open Access Journals (Sweden)

Ning Li

2016-01-01

Full Text Available A small amount of prior knowledge and randomly chosen initial cluster centers have a direct impact on the accuracy of the performance of iterative clustering algorithm. In this paper we propose a new algorithm to compute initial cluster centers for k-means clustering and the best number of the clusters with little prior knowledge and optimize clustering result. It constructs the Euclidean distance control factor based on aggregation density sparse degree to select the initial cluster center of nonuniform sparse data and obtains initial data clusters by multidimensional diffusion density distribution. Multiobjective clustering approach based on dynamic cumulative entropy is adopted to optimize the initial data clusters and the best number of the clusters. The experimental results show that the newly proposed algorithm has good performance to obtain the initial cluster centers for the k-means algorithm and it effectively improves the clustering accuracy of nonuniform sparse data by about 5%.

Discrete Sparse Coding.

Science.gov (United States)

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.

Mini-lecture course: Introduction into hierarchical matrix technique

KAUST Repository

Litvinenko, Alexander

2017-12-14

The H-matrix format has a log-linear computational cost and storage O(kn log n), where the rank k is a small integer and n is the number of locations (mesh points). The H-matrix technique allows us to work with general class of matrices (not only structured or Toeplits or sparse). H-matrices can keep the H-matrix data format during linear algebra operations (inverse, update, Schur complement).

Construction of MDS self-dual codes from orthogonal matrices

OpenAIRE

Shi, Minjia; Sok, Lin; Solé, Patrick

2016-01-01

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.

Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy

NARCIS (Netherlands)

Marandi, Ahmadreza; de Klerk, Etienne; Dahl, Joachim

The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal

Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research.

Science.gov (United States)

Waller, Niels G

2016-01-01

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.

Integrative analysis of multiple diverse omics datasets by sparse group multitask regression

Directory of Open Access Journals (Sweden)

Dongdong eLin

2014-10-01

Full Text Available A variety of high throughput genome-wide assays enable the exploration of genetic risk factors underlying complex traits. Although these studies have remarkable impact on identifying susceptible biomarkers, they suffer from issues such as limited sample size and low reproducibility. Combining individual studies of different genetic levels/platforms has the promise to improve the power and consistency of biomarker identification. In this paper, we propose a novel integrative method, namely sparse group multitask regression, for integrating diverse omics datasets, platforms and populations to identify risk genes/factors of complex diseases. This method combines multitask learning with sparse group regularization, which will: 1 treat the biomarker identification in each single study as a task and then combine them by multitask learning; 2 group variables from all studies for identifying significant genes; 3 enforce sparse constraint on groups of variables to overcome the ‘small sample, but large variables’ problem. We introduce two sparse group penalties: sparse group lasso and sparse group ridge in our multitask model, and provide an effective algorithm for each model. In addition, we propose a significance test for the identification of potential risk genes. Two simulation studies are performed to evaluate the performance of our integrative method by comparing it with conventional meta-analysis method. The results show that our sparse group multitask method outperforms meta-analysis method significantly. In an application to our osteoporosis studies, 7 genes are identified as significant genes by our method and are found to have significant effects in other three independent studies for validation. The most significant gene SOD2 has been identified in our previous osteoporosis study involving the same expression dataset. Several other genes such as TREML2, HTR1E and GLO1 are shown to be novel susceptible genes for osteoporosis, as confirmed

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

International Nuclear Information System (INIS)

Javaherian, Ashkan; Moeller, Knut; Soleimani, Manuchehr

2015-01-01

This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT. (paper)

Preparation and characterization of chitosan-heparin composite matrices for blood contacting tissue engineering

International Nuclear Information System (INIS)

He Qing; Gong Kai; Gong Yandao; Zhang Xiufang; Ao Qiang; Zhang Lihai; Hu Min

2010-01-01

Chitosan has been widely used for biomaterial scaffolds in tissue engineering because of its good mechanical properties and cytocompatibility. However, the poor blood compatibility of chitosan has greatly limited its biomedical utilization, especially for blood contacting tissue engineering. In this study, we exploited a polymer blending procedure to heparinize the chitosan material under simple and mild conditions to improve its antithrombogenic property. By an optimized procedure, a macroscopically homogeneous chitosan-heparin (Chi-Hep) blended suspension was obtained, with which Chi-Hep composite films and porous scaffolds were fabricated. X-ray photoelectron spectroscopy and sulfur elemental analysis confirmed the successful immobilization of heparin in the composite matrices (i.e. films and porous scaffolds). Toluidine blue staining indicated that heparin was distributed homogeneously in the composite matrices. Only a small amount of heparin was released from the matrices during incubation in normal saline for 10 days. The composite matrices showed improved blood compatibility, as well as good mechanical properties and endothelial cell compatibility. These results suggest that the Chi-Hep composite matrices are promising candidates for blood contacting tissue engineering.

An algebraic model for quark mass matrices with heavy top

International Nuclear Information System (INIS)

Krolikowski, W.; Warsaw Univ.

1991-01-01

In terms of an intergeneration U(3) algebra, a numerical model is constructed for quark mass matrices, predicting the top-quark mass around 170 GeV and the CP-violating phase around 75 deg. The CKM matrix is nonsymmetric in moduli with |V ub | being very small. All moduli are consistent with their experimental limits. The model is motivated by the author's previous work on three replicas of the Dirac particle, presumably resulting into three generations of leptons and quarks. The paper may be also viewed as an introduction to a new method of intrinsic dynamical description of lepton and quark mass matrices. (author)

Double stochastic matrices in quantum mechanics

International Nuclear Information System (INIS)

Louck, J.D.

1997-01-01

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices

Bayesian Inference Methods for Sparse Channel Estimation

DEFF Research Database (Denmark)

Pedersen, Niels Lovmand

2013-01-01

This thesis deals with sparse Bayesian learning (SBL) with application to radio channel estimation. As opposed to the classical approach for sparse signal representation, we focus on the problem of inferring complex signals. Our investigations within SBL constitute the basis for the development...... of Bayesian inference algorithms for sparse channel estimation. Sparse inference methods aim at finding the sparse representation of a signal given in some overcomplete dictionary of basis vectors. Within this context, one of our main contributions to the field of SBL is a hierarchical representation...... analysis of the complex prior representation, where we show that the ability to induce sparse estimates of a given prior heavily depends on the inference method used and, interestingly, whether real or complex variables are inferred. We also show that the Bayesian estimators derived from the proposed...

Matrices and linear transformations

CERN Document Server

Cullen, Charles G

1990-01-01

""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first

When sparse coding meets ranking: a joint framework for learning sparse codes and ranking scores

KAUST Repository

Wang, Jim Jing-Yan; Cui, Xuefeng; Yu, Ge; Guo, Lili; Gao, Xin

2017-01-01

Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points plays

Efficient Statistical Extraction of the Per-Unit-Length Capacitance and Inductance Matrices of Cables with Random Parameters

Directory of Open Access Journals (Sweden)

P. Manfredi

2015-05-01

Full Text Available Cable bundles often exhibit random parameter variations due to uncertain or uncontrollable physical properties and wire positioning. Efficient tools, based on the so-called polynomial chaos, exist to rapidly assess the impact of such variations on the per-unit-length capacitance and inductance matrices, and on the pertinent cable response. Nevertheless, the state-of-the-art method for the statistical extraction of the per-unit-length capacitance and inductance matrices of cables suffers from several inefficiencies that hinder its applicability to large problems, in terms of number of random parameters and/or conductors. This paper presents an improved methodology that overcomes the aforementioned limitations by exploiting a recently-published, alternative approach to generate the pertinent polynomial chaos system of equations. A sparse and decoupled system is obtained that provides remarkable benefits in terms of speed, memory consumption and problem size that can be dealt with. The technique is thoroughly validated through the statistical analysis of two canonical structures, i.e. a ribbon cable and a shielded cable with random geometry and position.

Improved Sparse Channel Estimation for Cooperative Communication Systems

Directory of Open Access Journals (Sweden)

Guan Gui

2012-01-01

Full Text Available Accurate channel state information (CSI is necessary at receiver for coherent detection in amplify-and-forward (AF cooperative communication systems. To estimate the channel, traditional methods, that is, least squares (LS and least absolute shrinkage and selection operator (LASSO, are based on assumptions of either dense channel or global sparse channel. However, LS-based linear method neglects the inherent sparse structure information while LASSO-based sparse channel method cannot take full advantage of the prior information. Based on the partial sparse assumption of the cooperative channel model, we propose an improved channel estimation method with partial sparse constraint. At first, by using sparse decomposition theory, channel estimation is formulated as a compressive sensing problem. Secondly, the cooperative channel is reconstructed by LASSO with partial sparse constraint. Finally, numerical simulations are carried out to confirm the superiority of proposed methods over global sparse channel estimation methods.

Sparse Image Reconstruction in Computed Tomography

DEFF Research Database (Denmark)

Jørgensen, Jakob Sauer

In recent years, increased focus on the potentially harmful effects of x-ray computed tomography (CT) scans, such as radiation-induced cancer, has motivated research on new low-dose imaging techniques. Sparse image reconstruction methods, as studied for instance in the field of compressed sensing...... applications. This thesis takes a systematic approach toward establishing quantitative understanding of conditions for sparse reconstruction to work well in CT. A general framework for analyzing sparse reconstruction methods in CT is introduced and two sets of computational tools are proposed: 1...... contributions to a general set of computational characterization tools. Thus, the thesis contributions help advance sparse reconstruction methods toward routine use in...

Sparse Regression by Projection and Sparse Discriminant Analysis

KAUST Repository

Qi, Xin; Luo, Ruiyan; Carroll, Raymond J.; Zhao, Hongyu

2015-01-01

predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high-dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths

Lambda-matrices and vibrating systems

CERN Document Server

Lancaster, Peter; Stark, M; Kahane, J P

1966-01-01

Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with late

Manin matrices and Talalaev's formula

International Nuclear Information System (INIS)

Chervov, A; Falqui, G

2008-01-01

In this paper we study properties of Lax and transfer matrices associated with quantum integrable systems. Our point of view stems from the fact that their elements satisfy special commutation properties, considered by Yu I Manin some 20 years ago at the beginning of quantum group theory. These are the commutation properties of matrix elements of linear homomorphisms between polynomial rings; more explicitly these read: (1) elements of the same column commute; (2) commutators of the cross terms are equal: [M ij , M kl ] [M kj , M il ] (e.g. [M 11 , M 22 ] = [M 21 , M 12 ]). The main aim of this paper is twofold: on the one hand we observe and prove that such matrices (which we call Manin matrices in short) behave almost as well as matrices with commutative elements. Namely, the theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) have a straightforward counterpart in the case of Manin matrices. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation 'RTT=TTR' and the so-called Cartier-Foata matrices. Also, they enter Talalaev's remarkable formulae: det(∂ z -L gaudin (z)), det(1-e -∂z T Yangian (z)) for the 'quantum spectral curve', and appear in the separation of variables problem and Capelli identities. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g. in the construction of new generators in Z(U crit (gl-hat n )) (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We propose, in the appendix, a construction of quantum separated variables for the XXX-Heisenberg system

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-01-01

Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.

Introduction into Hierarchical Matrices

KAUST Repository

Litvinenko, Alexander

2013-12-05

Hierarchical matrices allow us to reduce computational storage and cost from cubic to almost linear. This technique can be applied for solving PDEs, integral equations, matrix equations and approximation of large covariance and precision matrices.

Sparse decompositions in 'incoherent' dictionaries

DEFF Research Database (Denmark)

Gribonval, R.; Nielsen, Morten

2003-01-01

a unique sparse representation in such a dictionary. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of a combinatorial optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may...

Data analysis in high-dimensional sparse spaces

DEFF Research Database (Denmark)

Clemmensen, Line Katrine Harder

classification techniques for high-dimensional problems are presented: Sparse discriminant analysis, sparse mixture discriminant analysis and orthogonality constrained support vector machines. The first two introduces sparseness to the well known linear and mixture discriminant analysis and thereby provide low...... are applied to classifications of fish species, ear canal impressions used in the hearing aid industry, microbiological fungi species, and various cancerous tissues and healthy tissues. In addition, novel applications of sparse regressions (also called the elastic net) to the medical, concrete, and food...

A sparse-grid isogeometric solver

KAUST Repository

Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo

2018-01-01

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

A sparse-grid isogeometric solver

KAUST Repository

Beck, Joakim

2018-02-28

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90’s in the context of the approximation of high-dimensional PDEs.The tests that we report show that, in accordance to the literature, a sparse-grid construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

A hybrid method for the parallel computation of Green's functions

International Nuclear Information System (INIS)

Petersen, Dan Erik; Li Song; Stokbro, Kurt; Sorensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Darve, Eric

2009-01-01

Quantum transport models for nanodevices using the non-equilibrium Green's function method require the repeated calculation of the block tridiagonal part of the Green's and lesser Green's function matrices. This problem is related to the calculation of the inverse of a sparse matrix. Because of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green's and lesser Green's function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only require computing a small number of entries of the inverse matrix. Then, we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size.

Joint Group Sparse PCA for Compressed Hyperspectral Imaging.

Science.gov (United States)

Khan, Zohaib; Shafait, Faisal; Mian, Ajmal

2015-12-01

A sparse principal component analysis (PCA) seeks a sparse linear combination of input features (variables), so that the derived features still explain most of the variations in the data. A group sparse PCA introduces structural constraints on the features in seeking such a linear combination. Collectively, the derived principal components may still require measuring all the input features. We present a joint group sparse PCA (JGSPCA) algorithm, which forces the basic coefficients corresponding to a group of features to be jointly sparse. Joint sparsity ensures that the complete basis involves only a sparse set of input features, whereas the group sparsity ensures that the structural integrity of the features is maximally preserved. We evaluate the JGSPCA algorithm on the problems of compressed hyperspectral imaging and face recognition. Compressed sensing results show that the proposed method consistently outperforms sparse PCA and group sparse PCA in reconstructing the hyperspectral scenes of natural and man-made objects. The efficacy of the proposed compressed sensing method is further demonstrated in band selection for face recognition.

Sparse representations and compressive sensing for imaging and vision

CERN Document Server

Patel, Vishal M

2013-01-01

Compressed sensing or compressive sensing is a new concept in signal processing where one measures a small number of non-adaptive linear combinations of the signal.  These measurements are usually much smaller than the number of samples that define the signal.  From these small numbers of measurements, the signal is then reconstructed by non-linear procedure.  Compressed sensing has recently emerged as a powerful tool for efficiently processing data in non-traditional ways.  In this book, we highlight some of the key mathematical insights underlying sparse representation and compressed sensing and illustrate the role of these theories in classical vision, imaging and biometrics problems.

Parallel Sparse Matrix - Vector Product

DEFF Research Database (Denmark)

Alexandersen, Joe; Lazarov, Boyan Stefanov; Dammann, Bernd

This technical report contains a case study of a sparse matrix-vector product routine, implemented for parallel execution on a compute cluster with both pure MPI and hybrid MPI-OpenMP solutions. C++ classes for sparse data types were developed and the report shows how these class can be used...

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

Science.gov (United States)

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

2015-01-01

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

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

Science.gov (United States)

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Xin Tang

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

Intrinsic character of Stokes matrices

Science.gov (United States)

Gagnon, Jean-François; Rousseau, Christiane

2017-02-01

Two germs of linear analytic differential systems x k + 1Y‧ = A (x) Y with a non-resonant irregular singularity are analytically equivalent if and only if they have the same eigenvalues and equivalent collections of Stokes matrices. The Stokes matrices are the transition matrices between sectors on which the system is analytically equivalent to its formal normal form. Each sector contains exactly one separating ray for each pair of eigenvalues. A rotation in S allows supposing that R+ lies in the intersection of two sectors. Reordering of the coordinates of Y allows ordering the real parts of the eigenvalues, thus yielding triangular Stokes matrices. However, the choice of the rotation in x is not canonical. In this paper we establish how the collection of Stokes matrices depends on this rotation, and hence on a chosen order of the projection of the eigenvalues on a line through the origin.

Hierarchical matrices algorithms and analysis

CERN Document Server

Hackbusch, Wolfgang

2015-01-01

This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists ...

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

Energy Technology Data Exchange (ETDEWEB)

Deveci, Mehmet [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Trott, Christian Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rajamanickam, Sivasankaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2018-01-01

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

Quark mass matrices in left-right symmetric gauge theories

International Nuclear Information System (INIS)

Ecker, G.; Grimus, W.; Konetschny, W.

1981-01-01

The most general left-right symmetry for SU(2)sub(L) x SU(2)sub(R) x U(1) gauge theories with any number of flavours and with at most two scalar multiplets transforming as anti qq bilinears is analyzed. In order to get additional constraints on the structure of quark mass matrices all possible horizontal groups (continuous or discrete) are investigated. A complete classification of physically inequivalent quark mass matrices is given for four and six flavours. It is argued that the methods and results are also applicable in the case of dynamical symmetry breaking. Parity invariance and horizontal symmetry are shown to imply CP conservation on the Lagrangian level. For all non-trivial three-generation models there is spontaneous CP violation which in most cases turns out to be naturally small. (Auth.)

Statistical mechanics of semi-supervised clustering in sparse graphs

International Nuclear Information System (INIS)

Ver Steeg, Greg; Galstyan, Aram; Allahverdyan, Armen E

2011-01-01

We theoretically study semi-supervised clustering in sparse graphs in the presence of pair-wise constraints on the cluster assignments of nodes. We focus on bi-cluster graphs and study the impact of semi-supervision for varying constraint density and overlap between the clusters. Recent results for unsupervised clustering in sparse graphs indicate that there is a critical ratio of within-cluster and between-cluster connectivities below which clusters cannot be recovered with better than random accuracy. The goal of this paper is to examine the impact of pair-wise constraints on the clustering accuracy. Our results suggest that the addition of constraints does not provide automatic improvement over the unsupervised case. When the density of the constraints is sufficiently small, their only impact is to shift the detection threshold while preserving the criticality. Conversely, if the density of (hard) constraints is above the percolation threshold, the criticality is suppressed and the detection threshold disappears

Sparse approximation with bases

CERN Document Server

2015-01-01

This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

Efficient convolutional sparse coding

Science.gov (United States)

Wohlberg, Brendt

2017-06-20

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

Hyperspectral Unmixing with Robust Collaborative Sparse Regression

Directory of Open Access Journals (Sweden)

Chang Li

2016-07-01

Full Text Available Recently, sparse unmixing (SU of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM, which ignores the possible nonlinear effects (i.e., nonlinearity. In this paper, we propose a new method named robust collaborative sparse regression (RCSR based on the robust LMM (rLMM for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.

Special matrices of mathematical physics stochastic, circulant and Bell matrices

CERN Document Server

Aldrovandi, R

2001-01-01

This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas co

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

Science.gov (United States)

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)].

Image fusion using sparse overcomplete feature dictionaries

Science.gov (United States)

Brumby, Steven P.; Bettencourt, Luis; Kenyon, Garrett T.; Chartrand, Rick; Wohlberg, Brendt

2015-10-06

Approaches for deciding what individuals in a population of visual system "neurons" are looking for using sparse overcomplete feature dictionaries are provided. A sparse overcomplete feature dictionary may be learned for an image dataset and a local sparse representation of the image dataset may be built using the learned feature dictionary. A local maximum pooling operation may be applied on the local sparse representation to produce a translation-tolerant representation of the image dataset. An object may then be classified and/or clustered within the translation-tolerant representation of the image dataset using a supervised classification algorithm and/or an unsupervised clustering algorithm.

Semiparametric estimation of covariance matrices for longitudinal data.

Science.gov (United States)

Fan, Jianqing; Wu, Yichao

2008-12-01

Estimation of longitudinal data covariance structure poses significant challenges because the data are usually collected at irregular time points. A viable semiparametric model for covariance matrices was proposed in Fan, Huang and Li (2007) that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically via aggregating information from irregular and sparse data points within each subject. However, the asymptotic properties of their quasi-maximum likelihood estimator (QMLE) of parameters in the covariance model are largely unknown. In the current work, we address this problem in the context of more general models for the conditional mean function including parametric, nonparametric, or semi-parametric. We also consider the possibility of rough mean regression function and introduce the difference-based method to reduce biases in the context of varying-coefficient partially linear mean regression models. This provides a more robust estimator of the covariance function under a wider range of situations. Under some technical conditions, consistency and asymptotic normality are obtained for the QMLE of the parameters in the correlation function. Simulation studies and a real data example are used to illustrate the proposed approach.

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

Science.gov (United States)

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

Manifold regularization for sparse unmixing of hyperspectral images.

Science.gov (United States)

Liu, Junmin; Zhang, Chunxia; Zhang, Jiangshe; Li, Huirong; Gao, Yuelin

2016-01-01

Recently, sparse unmixing has been successfully applied to spectral mixture analysis of remotely sensed hyperspectral images. Based on the assumption that the observed image signatures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance, unmixing of each mixed pixel in the scene is to find an optimal subset of signatures in a very large spectral library, which is cast into the framework of sparse regression. However, traditional sparse regression models, such as collaborative sparse regression , ignore the intrinsic geometric structure in the hyperspectral data. In this paper, we propose a novel model, called manifold regularized collaborative sparse regression , by introducing a manifold regularization to the collaborative sparse regression model. The manifold regularization utilizes a graph Laplacian to incorporate the locally geometrical structure of the hyperspectral data. An algorithm based on alternating direction method of multipliers has been developed for the manifold regularized collaborative sparse regression model. Experimental results on both the simulated and real hyperspectral data sets have demonstrated the effectiveness of our proposed model.

Enhancing Scalability of Sparse Direct Methods

International Nuclear Information System (INIS)

Li, Xiaoye S.; Demmel, James; Grigori, Laura; Gu, Ming; Xia, Jianlin; Jardin, Steve; Sovinec, Carl; Lee, Lie-Quan

2007-01-01

TOPS is providing high-performance, scalable sparse direct solvers, which have had significant impacts on the SciDAC applications, including fusion simulation (CEMM), accelerator modeling (COMPASS), as well as many other mission-critical applications in DOE and elsewhere. Our recent developments have been focusing on new techniques to overcome scalability bottleneck of direct methods, in both time and memory. These include parallelizing symbolic analysis phase and developing linear-complexity sparse factorization methods. The new techniques will make sparse direct methods more widely usable in large 3D simulations on highly-parallel petascale computers

Regression with Sparse Approximations of Data

DEFF Research Database (Denmark)

Noorzad, Pardis; Sturm, Bob L.

2012-01-01

We propose sparse approximation weighted regression (SPARROW), a method for local estimation of the regression function that uses sparse approximation with a dictionary of measurements. SPARROW estimates the regression function at a point with a linear combination of a few regressands selected...... by a sparse approximation of the point in terms of the regressors. We show SPARROW can be considered a variant of \\(k\\)-nearest neighbors regression (\\(k\\)-NNR), and more generally, local polynomial kernel regression. Unlike \\(k\\)-NNR, however, SPARROW can adapt the number of regressors to use based...

Sparse adaptive filters for echo cancellation

CERN Document Server

Paleologu, Constantin

2011-01-01

Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellati

Parallel sparse direct solver for integrated circuit simulation

CERN Document Server

Chen, Xiaoming; Yang, Huazhong

2017-01-01

This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...

Frequency filtering decompositions for unsymmetric matrices and matrices with strongly varying coefficients

Energy Technology Data Exchange (ETDEWEB)

Wagner, C.

1996-12-31

In 1992, Wittum introduced the frequency filtering decompositions (FFD), which yield a fast method for the iterative solution of large systems of linear equations. Based on this method, the tangential frequency filtering decompositions (TFFD) have been developed. The TFFD allow the robust and efficient treatment of matrices with strongly varying coefficients. The existence and the convergence of the TFFD can be shown for symmetric and positive definite matrices. For a large class of matrices, it is possible to prove that the convergence rate of the TFFD and of the FFD is independent of the number of unknowns. For both methods, schemes for the construction of frequency filtering decompositions for unsymmetric matrices have been developed. Since, in contrast to Wittums`s FFD, the TFFD needs only one test vector, an adaptive test vector can be used. The TFFD with respect to the adaptive test vector can be combined with other iterative methods, e.g. multi-grid methods, in order to improve the robustness of these methods. The frequency filtering decompositions have been successfully applied to the problem of the decontamination of a heterogeneous porous medium by flushing.

Introduction to matrices and vectors

CERN Document Server

Schwartz, Jacob T

2001-01-01

In this concise undergraduate text, the first three chapters present the basics of matrices - in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition.

Robust Face Recognition Via Gabor Feature and Sparse Representation

Directory of Open Access Journals (Sweden)

Hao Yu-Juan

2016-01-01

Full Text Available Sparse representation based on compressed sensing theory has been widely used in the field of face recognition, and has achieved good recognition results. but the face feature extraction based on sparse representation is too simple, and the sparse coefficient is not sparse. In this paper, we improve the classification algorithm based on the fusion of sparse representation and Gabor feature, and then improved algorithm for Gabor feature which overcomes the problem of large dimension of the vector dimension, reduces the computation and storage cost, and enhances the robustness of the algorithm to the changes of the environment.The classification efficiency of sparse representation is determined by the collaborative representation,we simplify the sparse constraint based on L1 norm to the least square constraint, which makes the sparse coefficients both positive and reduce the complexity of the algorithm. Experimental results show that the proposed method is robust to illumination, facial expression and pose variations of face recognition, and the recognition rate of the algorithm is improved.

Sparse Learning with Stochastic Composite Optimization.

Science.gov (United States)

Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei

2017-06-01

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).

Shearlets and Optimally Sparse Approximations

DEFF Research Database (Denmark)

Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q

2012-01-01

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...... to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field....

Multilevel sparse functional principal component analysis.

Science.gov (United States)

Di, Chongzhi; Crainiceanu, Ciprian M; Jank, Wolfgang S

2014-01-29

We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we consider the case when functions are sparsely sampled and may contain only a few observations per function. We exploit the multilevel structure of covariance operators and achieve data reduction by principal component decompositions at both between and within subject levels. We address inherent methodological differences in the sparse sampling context to: 1) estimate the covariance operators; 2) estimate the functional principal component scores; 3) predict the underlying curves. Through simulations the proposed method is able to discover dominating modes of variations and reconstruct underlying curves well even in sparse settings. Our approach is illustrated by two applications, the Sleep Heart Health Study and eBay auctions.

A sparse version of IGA solvers

KAUST Repository

Beck, Joakim; Sangalli, Giancarlo; Tamellini, Lorenzo

2017-01-01

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

A sparse version of IGA solvers

KAUST Repository

Beck, Joakim

2017-07-30

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids construction in its combination technique form, which was first introduced in the early 90s in the context of the approximation of high-dimensional PDEs. The tests that we report show that, in accordance to the literature, a sparse grids construction can indeed be useful if the solution of the PDE at hand is sufficiently smooth. Sparse grids can also be useful in the case of non-smooth solutions when some a-priori knowledge on the location of the singularities of the solution can be exploited to devise suitable non-equispaced meshes. Finally, we remark that sparse grids can be seen as a simple way to parallelize pre-existing serial IGA solvers in a straightforward fashion, which can be beneficial in many practical situations.

Language Recognition via Sparse Coding

Science.gov (United States)

2016-09-08

explanation is that sparse coding can achieve a near-optimal approximation of much complicated nonlinear relationship through local and piecewise linear...training examples, where x(i) ∈ RN is the ith example in the batch. Optionally, X can be normalized and whitened before sparse coding for better result...normalized input vectors are then ZCA- whitened [20]. Em- pirically, we choose ZCA- whitening over PCA- whitening , and there is no dimensionality reduction

A New Precision Measurement of the Small-scale Line-of-sight Power Spectrum of the Lyα Forest

Science.gov (United States)

Walther, Michael; Hennawi, Joseph F.; Hiss, Hector; Oñorbe, Jose; Lee, Khee-Gan; Rorai, Alberto; O’Meara, John

2018-01-01

We present a new measurement of the Lyα forest power spectrum at 1.8 masking missing data, damped Lyα absorption systems, and metal absorption lines. Our measurement results in unprecedented precision on the small-scale modes k> 0.02 {{s}} {{km}}-1, inaccessible to previous SDSS/BOSS analyses. It is well known that these high-k modes are highly sensitive to the thermal state of the intergalactic medium, but contamination by narrow metal lines is a significant concern. We quantify the effect of metals on the small-scale power and find a modest effect on modes with kmasking metals and restricting to kmasking as our data are generated from Lyα forest simulations. These mock spectra are used to build a custom emulator, enabling us to interpolate between a sparse grid of models and perform Markov chain Monte Carlo fits. Our results agree well with BOSS on scales kdata set for precisely constraining the thermal history of the intergalactic medium, cosmological parameters, and the nature of dark matter. The power spectra and their covariance matrices are provided as electronic tables.

Sparse seismic imaging using variable projection

NARCIS (Netherlands)

Aravkin, Aleksandr Y.; Tu, Ning; van Leeuwen, Tristan

2013-01-01

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using

Sparse PCA with Oracle Property.

Science.gov (United States)

Gu, Quanquan; Wang, Zhaoran; Liu, Han

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

Structural Sparse Tracking

KAUST Repository

Zhang, Tianzhu; Yang, Ming-Hsuan; Ahuja, Narendra; Ghanem, Bernard; Yan, Shuicheng; Xu, Changsheng; Liu, Si

2015-01-01

candidate. We show that our SST algorithm accommodates most existing sparse trackers with the respective merits. Both qualitative and quantitative evaluations on challenging benchmark image sequences demonstrate that the proposed SST algorithm performs

Sparse Representations of Hyperspectral Images

KAUST Repository

Swanson, Robin J.

2015-11-23

Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.

Sparse Representations of Hyperspectral Images

KAUST Repository

Swanson, Robin J.

2015-01-01

Hyperspectral image data has long been an important tool for many areas of sci- ence. The addition of spectral data yields significant improvements in areas such as object and image classification, chemical and mineral composition detection, and astronomy. Traditional capture methods for hyperspectral data often require each wavelength to be captured individually, or by sacrificing spatial resolution. Recently there have been significant improvements in snapshot hyperspectral captures using, in particular, compressed sensing methods. As we move to a compressed sensing image formation model the need for strong image priors to shape our reconstruction, as well as sparse basis become more important. Here we compare several several methods for representing hyperspectral images including learned three dimensional dictionaries, sparse convolutional coding, and decomposable nonlocal tensor dictionaries. Addi- tionally, we further explore their parameter space to identify which parameters provide the most faithful and sparse representations.

Supervised Convolutional Sparse Coding

KAUST Repository

Affara, Lama Ahmed

2018-04-08

Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional sparse coding, which aims at learning discriminative dictionaries instead of purely reconstructive ones. We incorporate a supervised regularization term into the traditional unsupervised CSC objective to encourage the final dictionary elements to be discriminative. Experimental results show that using supervised convolutional learning results in two key advantages. First, we learn more semantically relevant filters in the dictionary and second, we achieve improved image reconstruction on unseen data.

Structure-aware Local Sparse Coding for Visual Tracking

KAUST Repository

Qi, Yuankai

2018-01-24

Sparse coding has been applied to visual tracking and related vision problems with demonstrated success in recent years. Existing tracking methods based on local sparse coding sample patches from a target candidate and sparsely encode these using a dictionary consisting of patches sampled from target template images. The discriminative strength of existing methods based on local sparse coding is limited as spatial structure constraints among the template patches are not exploited. To address this problem, we propose a structure-aware local sparse coding algorithm which encodes a target candidate using templates with both global and local sparsity constraints. For robust tracking, we show local regions of a candidate region should be encoded only with the corresponding local regions of the target templates that are the most similar from the global view. Thus, a more precise and discriminative sparse representation is obtained to account for appearance changes. To alleviate the issues with tracking drifts, we design an effective template update scheme. Extensive experiments on challenging image sequences demonstrate the effectiveness of the proposed algorithm against numerous stateof- the-art methods.

Improved image registration by sparse patch-based deformation estimation.

Science.gov (United States)

Kim, Minjeong; Wu, Guorong; Wang, Qian; Lee, Seong-Whan; Shen, Dinggang

2015-01-15

Despite intensive efforts for decades, deformable image registration is still a challenging problem due to the potential large anatomical differences across individual images, which limits the registration performance. Fortunately, this issue could be alleviated if a good initial deformation can be provided for the two images under registration, which are often termed as the moving subject and the fixed template, respectively. In this work, we present a novel patch-based initial deformation prediction framework for improving the performance of existing registration algorithms. Our main idea is to estimate the initial deformation between subject and template in a patch-wise fashion by using the sparse representation technique. We argue that two image patches should follow the same deformation toward the template image if their patch-wise appearance patterns are similar. To this end, our framework consists of two stages, i.e., the training stage and the application stage. In the training stage, we register all training images to the pre-selected template, such that the deformation of each training image with respect to the template is known. In the application stage, we apply the following four steps to efficiently calculate the initial deformation field for the new test subject: (1) We pick a small number of key points in the distinctive regions of the test subject; (2) for each key point, we extract a local patch and form a coupled appearance-deformation dictionary from training images where each dictionary atom consists of the image intensity patch as well as their respective local deformations; (3) a small set of training image patches in the coupled dictionary are selected to represent the image patch of each subject key point by sparse representation. Then, we can predict the initial deformation for each subject key point by propagating the pre-estimated deformations on the selected training patches with the same sparse representation coefficients; and (4) we

Chemiluminescence in cryogenic matrices

Science.gov (United States)

Lotnik, S. V.; Kazakov, Valeri P.

1989-04-01

The literature data on chemiluminescence (CL) in cryogenic matrices have been classified and correlated for the first time. The role of studies on phosphorescence and CL at low temperatures in the development of cryochemistry is shown. The features of low-temperature CL in matrices of nitrogen and inert gases (fine structure of spectra, matrix effects) and the data on the mobility and reactivity of atoms and radicals at very low temperatures are examined. The trends in the development of studies on CL in cryogenic matrices, such as the search for systems involving polyatomic molecules and extending the forms of CL reactions, are followed. The reactions of active nitrogen with hydrocarbons that are accompanied by light emission and CL in the oxidation of carbenes at T >= 77 K are examined. The bibliography includes 112 references.

Sparse Frequency Waveform Design for Radar-Embedded Communication

Directory of Open Access Journals (Sweden)

Chaoyun Mai

2016-01-01

Full Text Available According to the Tag application with function of covert communication, a method for sparse frequency waveform design based on radar-embedded communication is proposed. Firstly, sparse frequency waveforms are designed based on power spectral density fitting and quasi-Newton method. Secondly, the eigenvalue decomposition of the sparse frequency waveform sequence is used to get the dominant space. Finally the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the vertical subspace. Compared with the linear frequency modulation waveform, the sparse frequency waveform can further improve the bandwidth occupation of communication signals, thus achieving higher communication rate. A certain correlation exists between the reciprocally orthogonal communication signals samples and the sparse frequency waveform, which guarantees the low SER (signal error rate and LPI (low probability of intercept. The simulation results verify the effectiveness of this method.

Scaling Sparse Matrices for Optimization Algorithms

OpenAIRE

Gajulapalli Ravindra S; Lasdon Leon S

2006-01-01

To iteratively solve large scale optimization problems in various contexts like planning, operations, design etc., we need to generate descent directions that are based on linear system solutions. Irrespective of the optimization algorithm or the solution method employed for the linear systems, ill conditioning introduced by problem characteristics or the algorithm or both need to be addressed. In [GL01] we used an intuitive heuristic approach in scaling linear systems that improved performan...

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

Science.gov (United States)

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.

Massive Asynchronous Parallelization of Sparse Matrix Factorizations

Energy Technology Data Exchange (ETDEWEB)

Chow, Edmond [Georgia Inst. of Technology, Atlanta, GA (United States)

2018-01-08

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.

Skew-adjacency matrices of graphs

NARCIS (Netherlands)

Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.

2012-01-01

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic

The invariant theory of matrices

CERN Document Server

Concini, Corrado De

2017-01-01

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of m\\times m matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving the first fundamental theorem that describes a set of generators in the ring of invariants, and the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case...

Exact Inverse Matrices of Fermat and Mersenne Circulant Matrix

Directory of Open Access Journals (Sweden)

Yanpeng Zheng

2015-01-01

Full Text Available The well known circulant matrices are applied to solve networked systems. In this paper, circulant and left circulant matrices with the Fermat and Mersenne numbers are considered. The nonsingularity of these special matrices is discussed. Meanwhile, the exact determinants and inverse matrices of these special matrices are presented.

Analytical stiffness matrices with Green-Lagrange strain measure

DEFF Research Database (Denmark)

Pedersen, Pauli

2005-01-01

Separating the dependence on material and stress/strain state from the dependence on initial geometry, we obtain analytical secant and tangent stiffness matrices. For the case of a linear displacement triangle with uniform thickness and uniform constitutive behaviour closed-form results are listed...... a solution based on Green-Lagrange strain measure. The approach is especially useful in design optimization, because analytical sensitivity analysis then can be performed. The case of a three node triangular ring element for axisymmetric analysis involves small modifications and extension to four node...

Empirically Determined Response Matrices for On-Line Orbit and Energy Correction at Jefferson Lab

International Nuclear Information System (INIS)

Leigh Harwood; Alicia Hofler; Michele Joyce; Valeri Lebedev; David Bryan

2001-01-01

Jefferson Lab uses feedback loops (less than 1 hertz update rate) to correct drifts in CEBAF's electron beam orbit and energy. Previous incarnations of these loops used response matrices that were computed by a numerical model of the machine. Jefferson Lab is transitioning this feedback system to use empirically determined response matrices whereby the software introduces small orbit or energy deviations using the loop's actuators and measures the system response with the loop's sensors. This method is in routine use for orbit correction. This paper will describe the orbit correction system and future plans to extend this method to energy correction

Enhancing Understanding of Transformation Matrices

Science.gov (United States)

Dick, Jonathan; Childrey, Maria

2012-01-01

With the Common Core State Standards' emphasis on transformations, teachers need a variety of approaches to increase student understanding. Teaching matrix transformations by focusing on row vectors gives students tools to create matrices to perform transformations. This empowerment opens many doors: Students are able to create the matrices for…

Diclofenac sodium sustained release hot melt extruded lipid matrices.

Science.gov (United States)

Vithani, K; Cuppok, Y; Mostafa, S; Slipper, I J; Snowden, M J; Douroumis, D

2014-08-01

Sustained release diclofenac sodium (Df-Na) solid lipid matrices with Compritol® 888 ATO were developed in this study. The drug/lipid powders were processed via cold and hot melt extrusion at various drug loadings. The influence of the processing temperatures, drug loading and the addition of excipients on the obtained dissolution rates was investigated. The physicochemical characterization of the extruded batches showed the existence of crystalline drug in the extrudates with a small amount being solubilized in the lipid matrix. The drug content and uniformity on the tablet surface were also investigated by using energy dispersive X-ray microanalysis. The dissolution rates were found to depend on the actual Df-Na loading and the nature of the added excipients, while the effect of the processing temperatures was negligible. The dissolution mechanism of all extruded formulations followed Peppas-Korsemeyer law, based on the estimated determination coefficients and the dissolution constant rates, indicating drug diffusion from the lipid matrices.

Sparse representation for infrared Dim target detection via a discriminative over-complete dictionary learned online.

Science.gov (United States)

Li, Zheng-Zhou; Chen, Jing; Hou, Qian; Fu, Hong-Xia; Dai, Zhen; Jin, Gang; Li, Ru-Zhang; Liu, Chang-Ju

2014-05-27

It is difficult for structural over-complete dictionaries such as the Gabor function and discriminative over-complete dictionary, which are learned offline and classified manually, to represent natural images with the goal of ideal sparseness and to enhance the difference between background clutter and target signals. This paper proposes an infrared dim target detection approach based on sparse representation on a discriminative over-complete dictionary. An adaptive morphological over-complete dictionary is trained and constructed online according to the content of infrared image by K-singular value decomposition (K-SVD) algorithm. Then the adaptive morphological over-complete dictionary is divided automatically into a target over-complete dictionary describing target signals, and a background over-complete dictionary embedding background by the criteria that the atoms in the target over-complete dictionary could be decomposed more sparsely based on a Gaussian over-complete dictionary than the one in the background over-complete dictionary. This discriminative over-complete dictionary can not only capture significant features of background clutter and dim targets better than a structural over-complete dictionary, but also strengthens the sparse feature difference between background and target more efficiently than a discriminative over-complete dictionary learned offline and classified manually. The target and background clutter can be sparsely decomposed over their corresponding over-complete dictionaries, yet couldn't be sparsely decomposed based on their opposite over-complete dictionary, so their residuals after reconstruction by the prescribed number of target and background atoms differ very visibly. Some experiments are included and the results show that this proposed approach could not only improve the sparsity more efficiently, but also enhance the performance of small target detection more effectively.

Sparse Representation for Infrared Dim Target Detection via a Discriminative Over-Complete Dictionary Learned Online

Directory of Open Access Journals (Sweden)

Zheng-Zhou Li

2014-05-01

Full Text Available It is difficult for structural over-complete dictionaries such as the Gabor function and discriminative over-complete dictionary, which are learned offline and classified manually, to represent natural images with the goal of ideal sparseness and to enhance the difference between background clutter and target signals. This paper proposes an infrared dim target detection approach based on sparse representation on a discriminative over-complete dictionary. An adaptive morphological over-complete dictionary is trained and constructed online according to the content of infrared image by K-singular value decomposition (K-SVD algorithm. Then the adaptive morphological over-complete dictionary is divided automatically into a target over-complete dictionary describing target signals, and a background over-complete dictionary embedding background by the criteria that the atoms in the target over-complete dictionary could be decomposed more sparsely based on a Gaussian over-complete dictionary than the one in the background over-complete dictionary. This discriminative over-complete dictionary can not only capture significant features of background clutter and dim targets better than a structural over-complete dictionary, but also strengthens the sparse feature difference between background and target more efficiently than a discriminative over-complete dictionary learned offline and classified manually. The target and background clutter can be sparsely decomposed over their corresponding over-complete dictionaries, yet couldn’t be sparsely decomposed based on their opposite over-complete dictionary, so their residuals after reconstruction by the prescribed number of target and background atoms differ very visibly. Some experiments are included and the results show that this proposed approach could not only improve the sparsity more efficiently, but also enhance the performance of small target detection more effectively.

Group inverses of M-matrices and their applications

CERN Document Server

Kirkland, Stephen J

2013-01-01

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix f

Storage of sparse files using parallel log-structured file system

Science.gov (United States)

Bent, John M.; Faibish, Sorin; Grider, Gary; Torres, Aaron

2017-11-07

A sparse file is stored without holes by storing a data portion of the sparse file using a parallel log-structured file system; and generating an index entry for the data portion, the index entry comprising a logical offset, physical offset and length of the data portion. The holes can be restored to the sparse file upon a reading of the sparse file. The data portion can be stored at a logical end of the sparse file. Additional storage efficiency can optionally be achieved by (i) detecting a write pattern for a plurality of the data portions and generating a single patterned index entry for the plurality of the patterned data portions; and/or (ii) storing the patterned index entries for a plurality of the sparse files in a single directory, wherein each entry in the single directory comprises an identifier of a corresponding sparse file.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander; Sun, Ying; Genton, Marc G.; Keyes, David E.

2017-01-01

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\H$-) matrix format with computational cost $\\mathcal{O}(k^2n \\log^2 n/p)$ and storage $\\mathcal{O}(kn \\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

Likelihood Approximation With Parallel Hierarchical Matrices For Large Spatial Datasets

KAUST Repository

Litvinenko, Alexander

2017-11-01

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Matérn covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

Sparse reconstruction using distribution agnostic bayesian matching pursuit

KAUST Repository

Masood, Mudassir

2013-11-01

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data if not available. The method utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean-square error (MMSE) estimate of the sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.

Image understanding using sparse representations

CERN Document Server

Thiagarajan, Jayaraman J; Turaga, Pavan; Spanias, Andreas

2014-01-01

Image understanding has been playing an increasingly crucial role in several inverse problems and computer vision. Sparse models form an important component in image understanding, since they emulate the activity of neural receptors in the primary visual cortex of the human brain. Sparse methods have been utilized in several learning problems because of their ability to provide parsimonious, interpretable, and efficient models. Exploiting the sparsity of natural signals has led to advances in several application areas including image compression, denoising, inpainting, compressed sensing, blin

Sparse regularization for force identification using dictionaries

Science.gov (United States)

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

2016-04-01

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

Validação em métodos cromatográficos para análises de pequenas moléculas em matrizes biológicas Chromatographic methods validation for analysis of small molecules in biological matrices

OpenAIRE

Neila Maria Cassiano; Juliana Cristina Barreiro; Lúcia Regina Rocha Martins; Regina Vincenzi Oliveira; Quezia Bezerra Cass

2009-01-01

Chromatographic methods are commonly used for analysis of small molecules in different biological matrices. An important step to be considered upon a bioanalytical method's development is the capacity to yield reliable and reproducible results. This review discusses validation procedures adopted by different governmental agencies, such as Food and Drug Administration (USA), European Union (EU) and Agência Nacional de Vigilância Sanitária (BR) for quantification of small molecules by bioanalyt...

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

Science.gov (United States)

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.

Phenomenological mass matrices with a democratic warp

International Nuclear Information System (INIS)

Kleppe, A.

2018-01-01

Taking into account all available data on the mass sector, we obtain unitary rotation matrices that diagonalize the quark matrices by using a specific parametrization of the Cabibbo-Kobayashi-Maskawa mixing matrix. In this way, we find mass matrices for the up- and down-quark sectors of a specific, symmetric form, with traces of a democratic texture.

A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging

KAUST Repository

Desmal, Abdulla

2015-03-01

A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.

Elastomer modified polypropylene–polyethylene blends as matrices for wood flour–plastic composites

Science.gov (United States)

Craig Clemons

2010-01-01

Blends of polyethylene (PE) and polypropylene (PP) could potentially be used as matrices for wood–plastic composites (WPCs). The mechanical performance and morphology of both the unfilled blends and wood-filled composites with various elastomers and coupling agents were investigated. Blending of the plastics resulted in either small domains of the minor phase in a...

Object tracking by occlusion detection via structured sparse learning

KAUST Repository

Zhang, Tianzhu

2013-06-01

Sparse representation based methods have recently drawn much attention in visual tracking due to good performance against illumination variation and occlusion. They assume the errors caused by image variations can be modeled as pixel-wise sparse. However, in many practical scenarios these errors are not truly pixel-wise sparse but rather sparsely distributed in a structured way. In fact, pixels in error constitute contiguous regions within the object\\'s track. This is the case when significant occlusion occurs. To accommodate for non-sparse occlusion in a given frame, we assume that occlusion detected in previous frames can be propagated to the current one. This propagated information determines which pixels will contribute to the sparse representation of the current track. In other words, pixels that were detected as part of an occlusion in the previous frame will be removed from the target representation process. As such, this paper proposes a novel tracking algorithm that models and detects occlusion through structured sparse learning. We test our tracker on challenging benchmark sequences, such as sports videos, which involve heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that our tracker consistently outperforms the state-of-the-art. © 2013 IEEE.

Interactions between Food Additive Silica Nanoparticles and Food Matrices

Directory of Open Access Journals (Sweden)

Mi-Ran Go

2017-06-01

Full Text Available Nanoparticles (NPs have been widely utilized in the food industry as additives with their beneficial characteristics, such as improving sensory property and processing suitability, enhancing functional and nutritional values, and extending shelf-life of foods. Silica is used as an anti-caking agent to improve flow property of powered ingredients and as a carrier for flavors or active compounds in food. Along with the rapid development of nanotechnology, the sizes of silica fall into nanoscale, thereby raising concerns about the potential toxicity of nano-sized silica materials. There have been a number of studies carried out to investigate possible adverse effects of NPs on the gastrointestinal tract. The interactions between NPs and surrounding food matrices should be also taken into account since the interactions can affect their bioavailability, efficacy, and toxicity. In the present study, we investigated the interactions between food additive silica NPs and food matrices, such as saccharides, proteins, lipids, and minerals. Quantitative analysis was performed to determine food component-NP corona using HPLC, fluorescence quenching, GC-MS, and ICP-AES. The results demonstrate that zeta potential and hydrodynamic radius of silica NPs changed in the presence of all food matrices, but their solubility was not affected. However, quantitative analysis on the interactions revealed that a small portion of food matrices interacted with silica NPs and the interactions were highly dependent on the type of food component. Moreover, minor nutrients could also affect the interactions, as evidenced by higher NP interaction with honey rather than with a simple sugar mixture containing an equivalent amount of fructose, glucose, sucrose, and maltose. These findings provide fundamental information to extend our understanding about the interactions between silica NPs and food components and to predict the interaction effect on the safety aspects of food

Integrative sparse principal component analysis of gene expression data.

Science.gov (United States)

Liu, Mengque; Fan, Xinyan; Fang, Kuangnan; Zhang, Qingzhao; Ma, Shuangge

2017-12-01

In the analysis of gene expression data, dimension reduction techniques have been extensively adopted. The most popular one is perhaps the PCA (principal component analysis). To generate more reliable and more interpretable results, the SPCA (sparse PCA) technique has been developed. With the "small sample size, high dimensionality" characteristic of gene expression data, the analysis results generated from a single dataset are often unsatisfactory. Under contexts other than dimension reduction, integrative analysis techniques, which jointly analyze the raw data of multiple independent datasets, have been developed and shown to outperform "classic" meta-analysis and other multidatasets techniques and single-dataset analysis. In this study, we conduct integrative analysis by developing the iSPCA (integrative SPCA) method. iSPCA achieves the selection and estimation of sparse loadings using a group penalty. To take advantage of the similarity across datasets and generate more accurate results, we further impose contrasted penalties. Different penalties are proposed to accommodate different data conditions. Extensive simulations show that iSPCA outperforms the alternatives under a wide spectrum of settings. The analysis of breast cancer and pancreatic cancer data further shows iSPCA's satisfactory performance. © 2017 WILEY PERIODICALS, INC.

Diagonalization of the mass matrices

International Nuclear Information System (INIS)

Rhee, S.S.

1984-01-01

It is possible to make 20 types of 3x3 mass matrices which are hermitian. We have obtained unitary matrices which could diagonalize each mass matrix. Since the three elements of mass matrix can be expressed in terms of the three eigenvalues, msub(i), we can also express the unitary matrix in terms of msub(i). (Author)

Sparse Vector Distributions and Recovery from Compressed Sensing

DEFF Research Database (Denmark)

Sturm, Bob L.

It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I...... empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two morals of this work are: 1) any judgement of the recovery performance of one algorithm over that of another must be prefaced by the conditions for which this is observed to be true, including sparse vector...... distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal....

Exhaustive Search for Sparse Variable Selection in Linear Regression

Science.gov (United States)

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.

The construction of factorized S-matrices

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1981-01-01

We study the relationships between factorized S-matrices given as representations of the Zamolodchikov algebra and exactly solvable models constructed using the Baxter method. Several new examples of symmetric and non-symmetric factorized S-matrices are proposed. (orig.)

Matrices in Engineering Problems

CERN Document Server

Tobias, Marvin

2011-01-01

This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo

Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo

International Nuclear Information System (INIS)

Overy, Catherine; Blunt, N. S.; Shepherd, James J.; Booth, George H.; Cleland, Deidre; Alavi, Ali

2014-01-01

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems

A Brief Historical Introduction to Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

Structure-based bayesian sparse reconstruction

KAUST Repository

Quadeer, Ahmed Abdul

2012-12-01

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical information (Gaussian or otherwise) to obtain near optimal estimates. In addition, we make use of the rich structure of the sensing matrix encountered in many signal processing applications to develop a fast sparse recovery algorithm. The computational complexity of the proposed algorithm is very low compared with the widely used convex relaxation methods as well as greedy matching pursuit techniques, especially at high sparsity. © 1991-2012 IEEE.

Hypercyclic Abelian Semigroups of Matrices on Cn

International Nuclear Information System (INIS)

Ayadi, Adlene; Marzougui, Habib

2010-07-01

We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on C n . For finitely generated semigroups, this characterization is explicit and is used to determine the minimal number of matrices in normal form over C which forms a hypercyclic abelian semigroup on C n . In particular, we show that no abelian semigroup generated by n matrices on C n can be hypercyclic. (author)

Generalized Perron--Frobenius Theorem for Nonsquare Matrices

OpenAIRE

Avin, Chen; Borokhovich, Michael; Haddad, Yoram; Kantor, Erez; Lotker, Zvi; Parter, Merav; Peleg, David

2013-01-01

The celebrated Perron--Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many real-life scenarios give rise to nonsquare matrices. A natural question is whether the...

Formal matrices

CERN Document Server

Krylov, Piotr

2017-01-01

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory. While various special types of formal matrix rings have been studied for a long time from several points of view and appear in various textbooks, for instance to examine equivalences of module categories and to illustrate rings with one-sided non-symmetric properties, this particular class of rings has, so far, not been treated systematically. Exploring formal matrix rings of order 2 and introducing the notion of the determinant of a formal matrix over a commutative ring, this monograph further covers the Grothendieck and Whitehead groups of rings. Graduate students and researchers interested in ring theory, module theory and operator algebras will find this book particularly valuable. Containing numerous examples, Formal Matrices is a largely self-contained and accessible introduction to the topic, assuming a sol...

Greedy vs. L1 convex optimization in sparse coding

DEFF Research Database (Denmark)

Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor

2015-01-01

Sparse representation has been applied successfully in many image analysis applications, including abnormal event detection, in which a baseline is to learn a dictionary from the training data and detect anomalies from its sparse codes. During this procedure, sparse codes which can be achieved...... solutions. Considering the property of abnormal event detection, i.e., only normal videos are used as training data due to practical reasons, effective codes in classification application may not perform well in abnormality detection. Therefore, we compare the sparse codes and comprehensively evaluate...... their performance from various aspects to better understand their applicability, including computation time, reconstruction error, sparsity, detection...

A sparse matrix based full-configuration interaction algorithm

International Nuclear Information System (INIS)

Rolik, Zoltan; Szabados, Agnes; Surjan, Peter R.

2008-01-01

We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers

An in-depth study of sparse codes on abnormality detection

DEFF Research Database (Denmark)

Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor

2016-01-01

Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no comparative studies of sparse codes regarding abnormality...... are carried out from various angles to better understand the applicability of sparse codes, including computation time, reconstruction error, sparsity, detection accuracy, and their performance combining various detection methods. The experiment results show that combining OMP codes with maximum coordinate...

A fast algorithm for sparse matrix computations related to inversion

International Nuclear Information System (INIS)

Li, S.; Wu, W.; Darve, E.

2013-01-01

We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G r and G for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round-off errors

A fast algorithm for sparse matrix computations related to inversion

Energy Technology Data Exchange (ETDEWEB)

Li, S., E-mail: lisong@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Stanford, CA 94305 (United States); Wu, W. [Department of Electrical Engineering, Stanford University, 350 Serra Mall, Packard Building, Room 268, Stanford, CA 94305 (United States); Darve, E. [Institute for Computational and Mathematical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Stanford, CA 94305 (United States); Department of Mechanical Engineering, Stanford University, 496 Lomita Mall, Durand Building, Room 209, Stanford, CA 94305 (United States)

2013-06-01

We have developed a fast algorithm for computing certain entries of the inverse of a sparse matrix. Such computations are critical to many applications, such as the calculation of non-equilibrium Green’s functions G{sup r} and G{sup <} for nano-devices. The FIND (Fast Inverse using Nested Dissection) algorithm is optimal in the big-O sense. However, in practice, FIND suffers from two problems due to the width-2 separators used by its partitioning scheme. One problem is the presence of a large constant factor in the computational cost of FIND. The other problem is that the partitioning scheme used by FIND is incompatible with most existing partitioning methods and libraries for nested dissection, which all use width-1 separators. Our new algorithm resolves these problems by thoroughly decomposing the computation process such that width-1 separators can be used, resulting in a significant speedup over FIND for realistic devices — up to twelve-fold in simulation. The new algorithm also has the added advantage that desired off-diagonal entries can be computed for free. Consequently, our algorithm is faster than the current state-of-the-art recursive methods for meshes of any size. Furthermore, the framework used in the analysis of our algorithm is the first attempt to explicitly apply the widely-used relationship between mesh nodes and matrix computations to the problem of multiple eliminations with reuse of intermediate results. This framework makes our algorithm easier to generalize, and also easier to compare against other methods related to elimination trees. Finally, our accuracy analysis shows that the algorithms that require back-substitution are subject to significant extra round-off errors, which become extremely large even for some well-conditioned matrices or matrices with only moderately large condition numbers. When compared to these back-substitution algorithms, our algorithm is generally a few orders of magnitude more accurate, and our produced round

Sparse reconstruction using distribution agnostic bayesian matching pursuit

KAUST Repository

Masood, Mudassir; Al-Naffouri, Tareq Y.

2013-01-01

A fast matching pursuit method using a Bayesian approach is introduced for sparse signal recovery. This method performs Bayesian estimates of sparse signals even when the signal prior is non-Gaussian or unknown. It is agnostic on signal statistics

THE ALGORITHM AND PROGRAM OF M-MATRICES SEARCH AND STUDY

Directory of Open Access Journals (Sweden)

Y. N. Balonin

2013-05-01

Full Text Available The algorithm and software for search and study of orthogonal bases matrices – minimax matrices (M-matrix are considered. The algorithm scheme is shown, comments on calculation blocks are given, and interface of the MMatrix software system developed with participation of the authors is explained. The results of the universal algorithm work are presented as Hadamard matrices, Belevitch matrices (C-matrices, conference matrices and matrices of even and odd orders complementary and closely related to those ones by their properties, in particular, the matrix of the 22-th order for which there is no C-matrix. Examples of portraits for alternative matrices of the 255-th and the 257-th orders are given corresponding to the sequences of Mersenne and Fermat numbers. A new way to get Hadamard matrices is explained, different from the previously known procedures based on iterative processes and calculations of Lagrange symbols, with theoretical and practical meaning.

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

International Nuclear Information System (INIS)

Brown, Kristen A.; Harlim, John

2013-01-01

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable

The modified Gauss diagonalization of polynomial matrices

International Nuclear Information System (INIS)

Saeed, K.

1982-10-01

The Gauss algorithm for diagonalization of constant matrices is modified for application to polynomial matrices. Due to this modification the diagonal elements become pure polynomials rather than rational functions. (author)

Quantum Hilbert matrices and orthogonal polynomials

DEFF Research Database (Denmark)

Andersen, Jørgen Ellegaard; Berg, Christian

2009-01-01

Using the notion of quantum integers associated with a complex number q≠0 , we define the quantum Hilbert matrix and various extensions. They are Hankel matrices corresponding to certain little q -Jacobi polynomials when |q|<1 , and for the special value they are closely related to Hankel matrice...

Discrete canonical transforms that are Hadamard matrices

International Nuclear Information System (INIS)

Healy, John J; Wolf, Kurt Bernardo

2011-01-01

The group Sp(2,R) of symplectic linear canonical transformations has an integral kernel which has quadratic and linear phases, and which is realized by the geometric paraxial optical model. The discrete counterpart of this model is a finite Hamiltonian system that acts on N-point signals through N x N matrices whose elements also have a constant absolute value, although they do not form a representation of that group. Those matrices that are also unitary are Hadamard matrices. We investigate the manifolds of these N x N matrices under the Sp(2,R) equivalence imposed by the model, and find them to be on two-sided cosets. By means of an algorithm we determine representatives that lead to collections of mutually unbiased bases.

Abel-grassmann's groupoids of modulo matrices

International Nuclear Information System (INIS)

Javaid, Q.; Awan, M.D.; Naqvi, S.H.A.

2016-01-01

The binary operation of usual addition is associative in all matrices over R. However, a binary operation of addition in matrices over Z/sub n/ of a nonassociative structures of AG-groupoids and AG-groups are defined and investigated here. It is shown that both these structures exist for every integer n >≥ 3. Various properties of these structures are explored like: (i) Every AG-groupoid of matrices over Z/sub n/ is transitively commutative AG-groupoid and is a cancellative AG-groupoid if n is prime. (ii) Every AG-groupoid of matrices over Z/sub n/ of Type-II is a T/sup 3/-AG-groupoid. (iii) An AG-groupoid of matrices over Z/sub n/ ; G /sub nAG/(t,u), is an AG-band, if t+u=1(mod n). (author)

Parallel transposition of sparse data structures

DEFF Research Database (Denmark)

Wang, Hao; Liu, Weifeng; Hou, Kaixi

2016-01-01

Many applications in computational sciences and social sciences exploit sparsity and connectivity of acquired data. Even though many parallel sparse primitives such as sparse matrix-vector (SpMV) multiplication have been extensively studied, some other important building blocks, e.g., parallel tr...... transposition in the latest vendor-supplied library on an Intel multicore CPU platform, and the MergeTrans approach achieves on average of 3.4-fold (up to 11.7-fold) speedup on an Intel Xeon Phi many-core processor....

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

Meurant, Gerard; Golub, Gene.

1982-02-01

This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

Free probability and random matrices

CERN Document Server

Mingo, James A

2017-01-01

This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.

Speeding up the flash calculations in two-phase compositional flow simulations - The application of sparse grids

KAUST Repository

Wu, Yuanqing

2015-03-01

Flash calculations have become a performance bottleneck in the simulation of compositional flow in subsurface reservoirs. We apply a sparse grid surrogate model to substitute the flash calculation and thus try to remove the bottleneck from the reservoir simulation. So instead of doing a flash calculation in each time step of the simulation, we just generate a sparse grid approximation of all possible results of the flash calculation before the reservoir simulation. Then we evaluate the constructed surrogate model to approximate the values of the flash calculation results from this surrogate during the simulations. The execution of the true flash calculation has been shifted from the online phase during the simulation to the offline phase before the simulation. Sparse grids are known to require only few unknowns in order to obtain good approximation qualities. In conjunction with local adaptivity, sparse grids ensure that the accuracy of the surrogate is acceptable while keeping the memory usage small by only storing a minimal amount of values for the surrogate. The accuracy of the sparse grid surrogate during the reservoir simulation is compared to the accuracy of using a surrogate based on regular Cartesian grids and the original flash calculation. The surrogate model improves the speed of the flash calculations and the simulation of the whole reservoir. In an experiment, it is shown that the speed of the online flash calculations is increased by about 2000 times and as a result the speed of the reservoir simulations has been enhanced by 21 times in the best conditions.

Quantum matrices in two dimensions

International Nuclear Information System (INIS)

Ewen, H.; Ogievetsky, O.; Wess, J.

1991-01-01

Quantum matrices in two-dimensions, admitting left and right quantum spaces, are classified: they fall into two families, the 2-parametric family GL p,q (2) and a 1-parametric family GL α J (2). Phenomena previously found for GL p,q (2) hold in this general situation: (a) powers of quantum matrices are again quantum and (b) entries of the logarithm of a two-dimensional quantum matrix form a Lie algebra. (orig.)

Sparse Source EEG Imaging with the Variational Garrote

DEFF Research Database (Denmark)

Hansen, Sofie Therese; Stahlhut, Carsten; Hansen, Lars Kai

2013-01-01

EEG imaging, the estimation of the cortical source distribution from scalp electrode measurements, poses an extremely ill-posed inverse problem. Recent work by Delorme et al. (2012) supports the hypothesis that distributed source solutions are sparse. We show that direct search for sparse solutions...

Low-count PET image restoration using sparse representation

Science.gov (United States)

Li, Tao; Jiang, Changhui; Gao, Juan; Yang, Yongfeng; Liang, Dong; Liu, Xin; Zheng, Hairong; Hu, Zhanli

2018-04-01

In the field of positron emission tomography (PET), reconstructed images are often blurry and contain noise. These problems are primarily caused by the low resolution of projection data. Solving this problem by improving hardware is an expensive solution, and therefore, we attempted to develop a solution based on optimizing several related algorithms in both the reconstruction and image post-processing domains. As sparse technology is widely used, sparse prediction is increasingly applied to solve this problem. In this paper, we propose a new sparse method to process low-resolution PET images. Two dictionaries (D1 for low-resolution PET images and D2 for high-resolution PET images) are learned from a group real PET image data sets. Among these two dictionaries, D1 is used to obtain a sparse representation for each patch of the input PET image. Then, a high-resolution PET image is generated from this sparse representation using D2. Experimental results indicate that the proposed method exhibits a stable and superior ability to enhance image resolution and recover image details. Quantitatively, this method achieves better performance than traditional methods. This proposed strategy is a new and efficient approach for improving the quality of PET images.

X-ray computed tomography using curvelet sparse regularization.

Science.gov (United States)

Wieczorek, Matthias; Frikel, Jürgen; Vogel, Jakob; Eggl, Elena; Kopp, Felix; Noël, Peter B; Pfeiffer, Franz; Demaret, Laurent; Lasser, Tobias

2015-04-01

Reconstruction of x-ray computed tomography (CT) data remains a mathematically challenging problem in medical imaging. Complementing the standard analytical reconstruction methods, sparse regularization is growing in importance, as it allows inclusion of prior knowledge. The paper presents a method for sparse regularization based on the curvelet frame for the application to iterative reconstruction in x-ray computed tomography. In this work, the authors present an iterative reconstruction approach based on the alternating direction method of multipliers using curvelet sparse regularization. Evaluation of the method is performed on a specifically crafted numerical phantom dataset to highlight the method's strengths. Additional evaluation is performed on two real datasets from commercial scanners with different noise characteristics, a clinical bone sample acquired in a micro-CT and a human abdomen scanned in a diagnostic CT. The results clearly illustrate that curvelet sparse regularization has characteristic strengths. In particular, it improves the restoration and resolution of highly directional, high contrast features with smooth contrast variations. The authors also compare this approach to the popular technique of total variation and to traditional filtered backprojection. The authors conclude that curvelet sparse regularization is able to improve reconstruction quality by reducing noise while preserving highly directional features.

Synchronous correlation matrices and Connes’ embedding conjecture

Energy Technology Data Exchange (ETDEWEB)

Dykema, Kenneth J., E-mail: kdykema@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, Texas 77843-3368 (United States); Paulsen, Vern, E-mail: vern@math.uh.edu [Department of Mathematics, University of Houston, Houston, Texas 77204 (United States)

2016-01-15

In the work of Paulsen et al. [J. Funct. Anal. (in press); preprint arXiv:1407.6918], the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain C*-algebras. In particular, synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters. In this paper, we develop these ideas further, focusing on the relations between synchronous correlation matrices and microstates. We prove that Connes’ embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices. We prove that if Connes’ embedding conjecture has a positive answer, then the tracial rank and projective rank are equal for every graph. We then apply these results to more general non-local games.

Multimodal approach to characterization of hydrophilic matrices manufactured by wet and dry granulation or direct compression methods.

Science.gov (United States)

Kulinowski, Piotr; Woyna-Orlewicz, Krzysztof; Obrał, Jadwiga; Rappen, Gerd-Martin; Haznar-Garbacz, Dorota; Węglarz, Władysław P; Jachowicz, Renata; Wyszogrodzka, Gabriela; Klaja, Jolanta; Dorożyński, Przemysław P

2016-02-29

The purpose of the research was to investigate the effect of the manufacturing process of the controlled release hydrophilic matrix tablets on their hydration behavior, internal structure and drug release. Direct compression (DC) quetiapine hemifumarate matrices and matrices made of powders obtained by dry granulation (DG) and high shear wet granulation (HS) were prepared. They had the same quantitative composition and they were evaluated using X-ray microtomography, magnetic resonance imaging and biorelevant stress test dissolution. Principal results concerned matrices after 2 h of hydration: (i) layered structure of the DC and DG hydrated tablets with magnetic resonance image intensity decreasing towards the center of the matrix was observed, while in HS matrices layer of lower intensity appeared in the middle of hydrated part; (ii) the DC and DG tablets retained their core and consequently exhibited higher resistance to the physiological stresses during simulation of small intestinal passage than HS formulation. Comparing to DC, HS granulation changed properties of the matrix in terms of hydration pattern and resistance to stress in biorelevant dissolution apparatus. Dry granulation did not change these properties-similar hydration pattern and dissolution in biorelevant conditions were observed for DC and DG matrices. Copyright © 2015 Elsevier B.V. All rights reserved.

Realm of Matrices

Indian Academy of Sciences (India)

IAS Admin

harmonic analysis and complex analysis, in ... gebra describes not only the study of linear transforma- tions and .... special case of the Jordan canonical form of matrices. ..... Richard Bronson, Schaum's Outline Series Theory And Problems Of.

Virial expansion for almost diagonal random matrices

Science.gov (United States)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\

Computing the sparse matrix vector product using block-based kernels without zero padding on processors with AVX-512 instructions

Directory of Open Access Journals (Sweden)

Bérenger Bramas

2018-04-01

Full Text Available The sparse matrix-vector product (SpMV is a fundamental operation in many scientific applications from various fields. The High Performance Computing (HPC community has therefore continuously invested a lot of effort to provide an efficient SpMV kernel on modern CPU architectures. Although it has been shown that block-based kernels help to achieve high performance, they are difficult to use in practice because of the zero padding they require. In the current paper, we propose new kernels using the AVX-512 instruction set, which makes it possible to use a blocking scheme without any zero padding in the matrix memory storage. We describe mask-based sparse matrix formats and their corresponding SpMV kernels highly optimized in assembly language. Considering that the optimal blocking size depends on the matrix, we also provide a method to predict the best kernel to be used utilizing a simple interpolation of results from previous executions. We compare the performance of our approach to that of the Intel MKL CSR kernel and the CSR5 open-source package on a set of standard benchmark matrices. We show that we can achieve significant improvements in many cases, both for sequential and for parallel executions. Finally, we provide the corresponding code in an open source library, called SPC5.

Human elastin polypeptides improve the biomechanical properties of three-dimensional matrices through the regulation of elastogenesis.

Science.gov (United States)

Boccafoschi, Francesca; Ramella, Martina; Sibillano, Teresa; De Caro, Liberato; Giannini, Cinzia; Comparelli, Roberto; Bandiera, Antonella; Cannas, Mario

2015-03-01

The replacement of diseased tissues with biological substitutes with suitable biomechanical properties is one of the most important goal in tissue engineering. Collagen represents a satisfactory choice for scaffolds. Unfortunately, the lack of elasticity represents a restriction to a wide use of collagen for several applications. In this work, we studied the effect of human elastin-like polypeptide (HELP) as hybrid collagen-elastin matrices. In particular, we studied the biomechanical properties of collagen/HELP scaffolds considering several components involved in ECM remodeling (elastin, collagen, fibrillin, lectin-like receptor, metalloproteinases) and cell phenotype (myogenin, myosin heavy chain) with particular awareness for vascular tissue engineering applications. Elastin and collagen content resulted upregulated in collagen-HELP matrices, even showing an improved structural remodeling through the involvement of proteins to a ECM remodeling activity. Moreover, the hybrid matrices enhanced the contractile activity of C2C12 cells concurring to improve the mechanical properties of the scaffold. Finally, small-angle X-ray scattering analyses were performed to enable a very detailed analysis of the matrices at the nanoscale, comparing the scaffolds with native blood vessels. In conclusion, our work shows the use of recombinant HELP, as a very promising complement able to significantly improve the biomechanical properties of three-dimensional collagen matrices in terms of tensile stress and elastic modulus. © 2014 Wiley Periodicals, Inc.

Sparse dictionary for synthetic transmit aperture medical ultrasound imaging.

Science.gov (United States)

Wang, Ping; Jiang, Jin-Yang; Li, Na; Luo, Han-Wu; Li, Fang; Cui, Shi-Gang

2017-07-01

It is possible to recover a signal below the Nyquist sampling limit using a compressive sensing technique in ultrasound imaging. However, the reconstruction enabled by common sparse transform approaches does not achieve satisfactory results. Considering the ultrasound echo signal's features of attenuation, repetition, and superposition, a sparse dictionary with the emission pulse signal is proposed. Sparse coefficients in the proposed dictionary have high sparsity. Images reconstructed with this dictionary were compared with those obtained with the three other common transforms, namely, discrete Fourier transform, discrete cosine transform, and discrete wavelet transform. The performance of the proposed dictionary was analyzed via a simulation and experimental data. The mean absolute error (MAE) was used to quantify the quality of the reconstructions. Experimental results indicate that the MAE associated with the proposed dictionary was always the smallest, the reconstruction time required was the shortest, and the lateral resolution and contrast of the reconstructed images were also the closest to the original images. The proposed sparse dictionary performed better than the other three sparse transforms. With the same sampling rate, the proposed dictionary achieved excellent reconstruction quality.

Chequered surfaces and complex matrices

International Nuclear Information System (INIS)

Morris, T.R.; Southampton Univ.

1991-01-01

We investigate a large-N matrix model involving general complex matrices. It can be reinterpreted as a model of two hermitian matrices with specific couplings, and as a model of positive definite hermitian matrices. Large-N perturbation theory generates dynamical triangulations in which the triangles can be chequered (i.e. coloured so that neighbours are opposite colours). On a sphere there is a simple relation between such triangulations and those generated by the single hermitian matrix model. For the torus (and a quartic potential) we solve the counting problem for the number of triangulations that cannot be quechered. The critical physics of chequered triangulations is the same as that of the hermitian matrix model. We show this explicitly by solving non-perturbatively pure two-dimensional ''chequered'' gravity. The interpretative framework given here applies to a number of other generalisations of the hermitian matrix model. (orig.)

A sparse electromagnetic imaging scheme using nonlinear landweber iterations

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

Development and use of electromagnetic inverse scattering techniques for imagining sparse domains have been on the rise following the recent advancements in solving sparse optimization problems. Existing techniques rely on iteratively converting

Scalable group level probabilistic sparse factor analysis

DEFF Research Database (Denmark)

Hinrich, Jesper Løve; Nielsen, Søren Føns Vind; Riis, Nicolai Andre Brogaard

2017-01-01

Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a scalable group level probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component...... pruning using automatic relevance determination (ARD) and subject specific heteroscedastic spatial noise modeling. For task-based and resting state fMRI, we show that the sparsity constraint gives rise to components similar to those obtained by group independent component analysis. The noise modeling...... shows that noise is reduced in areas typically associated with activation by the experimental design. The psFA model identifies sparse components and the probabilistic setting provides a natural way to handle parameter uncertainties. The variational Bayesian framework easily extends to more complex...

Local posterior concentration rate for multilevel sparse sequences

NARCIS (Netherlands)

Belitser, E.N.; Nurushev, N.

2017-01-01

We consider empirical Bayesian inference in the many normal means model in the situation when the high-dimensional mean vector is multilevel sparse, that is,most of the entries of the parameter vector are some fixed values. For instance, the traditional sparse signal is a particular case (with one

Sparse modeling of EELS and EDX spectral imaging data by nonnegative matrix factorization

Energy Technology Data Exchange (ETDEWEB)

Shiga, Motoki, E-mail: shiga_m@gifu-u.ac.jp [Department of Electrical, Electronic and Computer Engineering, Gifu University, 1-1, Yanagido, Gifu 501-1193 (Japan); Tatsumi, Kazuyoshi; Muto, Shunsuke [Advanced Measurement Technology Center, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603 (Japan); Tsuda, Koji [Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561 (Japan); Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba 305-0047 (Japan); Biotechnology Research Institute for Drug Discovery, National Institute of Advanced Industrial Science and Technology, 2-4-7 Aomi Koto-ku, Tokyo 135-0064 (Japan); Yamamoto, Yuta [High-Voltage Electron Microscope Laboratory, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603 (Japan); Mori, Toshiyuki [Environment and Energy Materials Division, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044 (Japan); Tanji, Takayoshi [Division of Materials Research, Institute of Materials and Systems for Sustainability, Nagoya University, Chikusa-ku, Nagoya 464-8603 (Japan)

2016-11-15

Advances in scanning transmission electron microscopy (STEM) techniques have enabled us to automatically obtain electron energy-loss (EELS)/energy-dispersive X-ray (EDX) spectral datasets from a specified region of interest (ROI) at an arbitrary step width, called spectral imaging (SI). Instead of manually identifying the potential constituent chemical components from the ROI and determining the chemical state of each spectral component from the SI data stored in a huge three-dimensional matrix, it is more effective and efficient to use a statistical approach for the automatic resolution and extraction of the underlying chemical components. Among many different statistical approaches, we adopt a non-negative matrix factorization (NMF) technique, mainly because of the natural assumption of non-negative values in the spectra and cardinalities of chemical components, which are always positive in actual data. This paper proposes a new NMF model with two penalty terms: (i) an automatic relevance determination (ARD) prior, which optimizes the number of components, and (ii) a soft orthogonal constraint, which clearly resolves each spectrum component. For the factorization, we further propose a fast optimization algorithm based on hierarchical alternating least-squares. Numerical experiments using both phantom and real STEM-EDX/EELS SI datasets demonstrate that the ARD prior successfully identifies the correct number of physically meaningful components. The soft orthogonal constraint is also shown to be effective, particularly for STEM-EELS SI data, where neither the spatial nor spectral entries in the matrices are sparse. - Highlights: • Automatic resolution of chemical components from spectral imaging is considered. • We propose a new non-negative matrix factorization with two new penalties. • The first penalty is sparseness to choose the number of components from data. • Experimental results with real data demonstrate effectiveness of our method.

Sparse modeling of spatial environmental variables associated with asthma.

Science.gov (United States)

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.

Intrinsic Density Matrices of the Nuclear Shell Model

International Nuclear Information System (INIS)

Deveikis, A.; Kamuntavichius, G.

1996-01-01

A new method for calculation of shell model intrinsic density matrices, defined as two-particle density matrices integrated over the centre-of-mass position vector of two last particles and complemented with isospin variables, has been developed. The intrinsic density matrices obtained are completely antisymmetric, translation-invariant, and do not employ a group-theoretical classification of antisymmetric states. They are used for exact realistic density matrix expansion within the framework of the reduced Hamiltonian method. The procedures based on precise arithmetic for calculation of the intrinsic density matrices that involve no numerical diagonalization or orthogonalization have been developed and implemented in the computer code. (author). 11 refs., 2 tabs

Efficient Pseudorecursive Evaluation Schemes for Non-adaptive Sparse Grids

KAUST Repository

Buse, Gerrit; Pflü ger, Dirk; Jacob, Riko

2014-01-01

In this work we propose novel algorithms for storing and evaluating sparse grid functions, operating on regular (not spatially adaptive), yet potentially dimensionally adaptive grid types. Besides regular sparse grids our approach includes truncated

Study of remobilization polycyclic aromatic hydrocarbons (PAHs) in contaminated matrices

International Nuclear Information System (INIS)

Belkessam, L.; Vessigaud, S.; Laboudigue, A.; Vessigaud, S.; Perrin-Ganier, C.; Schiavon, M.; Denys, S.

2005-01-01

Polycyclic aromatic hydrocarbons (PAHs) originate from many pyrolysis processes. They are widespread environmental pollutants because some of them present toxic and genotoxic properties. In coal pyrolysis sites such as former manufactured gas plants and coke production plants, coal tar is a major source of PAHs. The management of such sites requires better understanding of the mechanisms that control release of PAHs to the biosphere. Determining total PAH concentrations is not sufficient since it does not inform about the pollutants availability to environmental processes. The fate and transport of PAHs in soil are governed by sorption and microbial processes which are well documented. Globally, enhancing retention of the compounds by a solid matrix reduces the risk of pollutant dispersion, but decreases their accessibility to microbial microflora. Conversely, the remobilization of organics from contaminated solid matrices represents a potential hazard since these pollutants can reach groundwater resources. However the available data are often obtained from laboratory experiments in which many field parameters can not be taken into account (long term, temperature, co-pollution, ageing phenomenon, heterogenous distribution of pollution). The present work focuses on the influence assessment and understanding of some of these parameters on PAHs remobilization from heavily polluted matrices in near-field conditions (industrial contaminated matrices, high contact time, ..). Results concerning effects of temperature and physical state of pollution (dispersed among the soil or condensed in small clusters or in coal tar) are presented. (authors)

Resampling-based methods in single and multiple testing for equality of covariance/correlation matrices.

Science.gov (United States)

Yang, Yang; DeGruttola, Victor

2012-06-22

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients.

Occlusion detection via structured sparse learning for robust object tracking

KAUST Repository

Zhang, Tianzhu

2014-01-01

Sparse representation based methods have recently drawn much attention in visual tracking due to good performance against illumination variation and occlusion. They assume the errors caused by image variations can be modeled as pixel-wise sparse. However, in many practical scenarios, these errors are not truly pixel-wise sparse but rather sparsely distributed in a structured way. In fact, pixels in error constitute contiguous regions within the object’s track. This is the case when significant occlusion occurs. To accommodate for nonsparse occlusion in a given frame, we assume that occlusion detected in previous frames can be propagated to the current one. This propagated information determines which pixels will contribute to the sparse representation of the current track. In other words, pixels that were detected as part of an occlusion in the previous frame will be removed from the target representation process. As such, this paper proposes a novel tracking algorithm that models and detects occlusion through structured sparse learning. We test our tracker on challenging benchmark sequences, such as sports videos, which involve heavy occlusion, drastic illumination changes, and large pose variations. Extensive experimental results show that our proposed tracker consistently outperforms the state-of-the-art trackers.

Sparse Representation Based SAR Vehicle Recognition along with Aspect Angle

Directory of Open Access Journals (Sweden)

Xiangwei Xing

2014-01-01

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

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

Science.gov (United States)

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

Random matrices and random difference equations

International Nuclear Information System (INIS)

Uppuluri, V.R.R.

1975-01-01

Mathematical models leading to products of random matrices and random difference equations are discussed. A one-compartment model with random behavior is introduced, and it is shown how the average concentration in the discrete time model converges to the exponential function. This is of relevance to understanding how radioactivity gets trapped in bone structure in blood--bone systems. The ideas are then generalized to two-compartment models and mammillary systems, where products of random matrices appear in a natural way. The appearance of products of random matrices in applications in demography and control theory is considered. Then random sequences motivated from the following problems are studied: constant pulsing and random decay models, random pulsing and constant decay models, and random pulsing and random decay models

Quantum Entanglement and Reduced Density Matrices

Science.gov (United States)

Purwanto, Agus; Sukamto, Heru; Yuwana, Lila

2018-05-01

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.

An investigation of 'sparse channel networks'. Characteristic behaviours and their causes

International Nuclear Information System (INIS)

Black, J.H.; Barker, J.A.; Woodman, N.D.

2007-09-01

This report represents a third study in a series concerned with groundwater flow in poorly permeable fractured crystalline rocks. The study has brought together three linked, but distinct, elements; a mathematical analysis of the intersection of ellipses, a review of field measurements associated with nuclear waste repository investigations and probabilistic simulations using a lattice network numerical model. We conclude that the model of channels that traverse fracture intersections without necessarily branching is a very likely representation of reality. More generally, assembling all the lines of evidence, it is suggested that groundwater flow systems in fractured crystalline rocks in the environs of underground laboratories have the following characteristics: Groundwater flows within a sparse network of channels just above the percolation limit. The frequency of intersections is low in that individual channels extend considerable distances between significant junctions. Individual channels often extend over many fracture surfaces and the resulting flow system is only weakly related to the density or size of mappable fractures. The sparseness of systems compared to the size of drifts and tunnels means that only a very few flow channels are intersected by drifts and tunnels. Highly convergent flow is required to connect to the rest of the network and this is misinterpreted as a skin of low hydraulic conductivity. Systems are so sparse that they are controlled by a few 'chokes' that give rise to compartments of head, and probably, of groundwater chemistry. Channels occur on all fracture planes, including those within fracture zones, and although the characteristics of the fracture zone channel networks may differ from those in surrounding rocks, they are nonetheless still channel networks. The actively flowing sparse channel network, occurring within any particular rock, is a naturally selected, small sub-set of the available channels. Hence, there are many

Learning sparse generative models of audiovisual signals

OpenAIRE

Monaci, Gianluca; Sommer, Friedrich T.; Vandergheynst, Pierre

2008-01-01

This paper presents a novel framework to learn sparse represen- tations for audiovisual signals. An audiovisual signal is modeled as a sparse sum of audiovisual kernels. The kernels are bimodal functions made of synchronous audio and video components that can be positioned independently and arbitrarily in space and time. We design an algorithm capable of learning sets of such audiovi- sual, synchronous, shift-invariant functions by alternatingly solving a coding and a learning pr...

Multivariate analysis of nutritional information of foodstuff of plant origin for the selection of representative matrices for the analysis of pesticide residues

International Nuclear Information System (INIS)

Neves Bettencourt da Silva, Ricardo Jorge; Gomes Ferreira Crujo Camoes, Maria Filomena

2010-01-01

Testing safety of foodstuffs of plant origin involves the analysis of hundreds of pesticide residues. This control is only cost-effective through the use of methods validated for the analysis of many thousands of analyte/matrix combinations. Several documents propose representative matrices of groups of matrices from which the validity of the analytical method can be extrapolated to the represented matrices after summarised experimental check of within group method performance homogeneity. Those groups are based on an evolved expert consensus based on the empirical knowledge on the current analytical procedures; they are not exhaustive, they are not objectively defined and they propose a large list of representative matrices which makes their application difficult. This work proposes grouping 240 matrices, based on the nutritional composition pattern equivalence of the analytical portion right after hydration and before solvent extraction, aiming at defining groups that observe method performance homogeneity. This grouping was based on the combined outcome of three multivariate tools, namely: Principal Component Analysis, Hierarchical Cluster Analysis and K-Mean Cluster Analysis. These tools allowed the selection of eight groups for which representative matrices with average characteristics and objective criteria to test inclusion of new matrices were established. The proposed matrices groups are homogeneous to nutritional data not considered in their definition but correlated with the studied multivariate nutritional pattern. The developed grouping that must be checked with experimental test before use was tested against small deviations in food composition and for the integration of new matrices.

Support agnostic Bayesian matching pursuit for block sparse signals

KAUST Repository

Masood, Mudassir

2013-05-01

A fast matching pursuit method using a Bayesian approach is introduced for block-sparse signal recovery. This method performs Bayesian estimates of block-sparse signals even when the distribution of active blocks is non-Gaussian or unknown. It is agnostic to the distribution of active blocks in the signal and utilizes a priori statistics of additive noise and the sparsity rate of the signal, which are shown to be easily estimated from data and no user intervention is required. The method requires a priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal. Simulation results demonstrate the power and robustness of our proposed estimator. © 2013 IEEE.

Malware analysis using visualized image matrices.

Science.gov (United States)

Han, KyoungSoo; Kang, BooJoong; Im, Eul Gyu

2014-01-01

This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API) calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.

Malware Analysis Using Visualized Image Matrices

Directory of Open Access Journals (Sweden)

KyoungSoo Han

2014-01-01

Full Text Available This paper proposes a novel malware visual analysis method that contains not only a visualization method to convert binary files into images, but also a similarity calculation method between these images. The proposed method generates RGB-colored pixels on image matrices using the opcode sequences extracted from malware samples and calculates the similarities for the image matrices. Particularly, our proposed methods are available for packed malware samples by applying them to the execution traces extracted through dynamic analysis. When the images are generated, we can reduce the overheads by extracting the opcode sequences only from the blocks that include the instructions related to staple behaviors such as functions and application programming interface (API calls. In addition, we propose a technique that generates a representative image for each malware family in order to reduce the number of comparisons for the classification of unknown samples and the colored pixel information in the image matrices is used to calculate the similarities between the images. Our experimental results show that the image matrices of malware can effectively be used to classify malware families both statically and dynamically with accuracy of 0.9896 and 0.9732, respectively.

Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla

2014-05-04

Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla

2014-01-06

Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

Electromagnetic Formation Flight (EMFF) for Sparse Aperture Arrays

Science.gov (United States)

Kwon, Daniel W.; Miller, David W.; Sedwick, Raymond J.

2004-01-01

Traditional methods of actuating spacecraft in sparse aperture arrays use propellant as a reaction mass. For formation flying systems, propellant becomes a critical consumable which can be quickly exhausted while maintaining relative orientation. Additional problems posed by propellant include optical contamination, plume impingement, thermal emission, and vibration excitation. For these missions where control of relative degrees of freedom is important, we consider using a system of electromagnets, in concert with reaction wheels, to replace the consumables. Electromagnetic Formation Flight sparse apertures, powered by solar energy, are designed differently from traditional propulsion systems, which are based on V. This paper investigates the design of sparse apertures both inside and outside the Earth's gravity field.

Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2014-01-01

Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.

A comprehensive study of sparse codes on abnormality detection

DEFF Research Database (Denmark)

Ren, Huamin; Pan, Hong; Olsen, Søren Ingvor

2017-01-01

Sparse representation has been applied successfully in abnor-mal event detection, in which the baseline is to learn a dic-tionary accompanied by sparse codes. While much empha-sis is put on discriminative dictionary construction, there areno comparative studies of sparse codes regarding abnormal-ity...... detection. We comprehensively study two types of sparsecodes solutions - greedy algorithms and convex L1-norm so-lutions - and their impact on abnormality detection perfor-mance. We also propose our framework of combining sparsecodes with different detection methods. Our comparative ex-periments are carried...

Support agnostic Bayesian matching pursuit for block sparse signals

KAUST Repository

Masood, Mudassir; Al-Naffouri, Tareq Y.

2013-01-01

priori knowledge of block partition and utilizes a greedy approach and order-recursive updates of its metrics to find the most dominant sparse supports to determine the approximate minimum mean square error (MMSE) estimate of the block-sparse signal

Production and characterization of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices

Energy Technology Data Exchange (ETDEWEB)

Zepon, Karine Modolon [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Petronilho, Fabricia [FICEXP, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil); Soldi, Valdir [POLIMAT, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Salmoria, Gean Vitor [CIMJECT, Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Kanis, Luiz Alberto, E-mail: luiz.kanis@unisul.br [TECFARMA, Universidade do Sul de Santa Catarina, 88704-900 Tubarão, SC (Brazil)

2014-11-01

The production and evaluation of cornstarch/cellulose acetate/silver sulfadiazine extrudate matrices are reported herein. The matrices were melt extruded under nine different conditions, altering the temperature and the screw speed values. The surface morphology of the matrices was examined by scanning electron microscopy. The micrographs revealed the presence of non-melted silver sulfadiazine microparticles in the matrices extruded at lower temperature and screw speed values. The thermal properties were evaluated and the results for both the biopolymer and the drug indicated no thermal degradation during the melt extrusion process. The differential scanning analysis of the extrudate matrices showed a shift to lower temperatures for the silver sulfadiazine melting point compared with the non-extruded drug. The starch/cellulose acetate matrices containing silver sulfadiazine demonstrated significant inhibition of the growth of Pseudomonas aeruginosa and Staphylococcus aureus. In vivo inflammatory response tests showed that the extrudate matrices, with or without silver sulfadiazine, did not trigger chronic inflammatory processes. - Highlights: • Melt extruded bio-based matrices containing silver sulfadiazine was produced. • The silver sulfadiazine is stable during melt-extrusion. • The extrudate matrices shown bacterial growth inhibition. • The matrices obtained have potential to development wound healing membranes.

Polynomial sequences generated by infinite Hessenberg matrices

Directory of Open Access Journals (Sweden)

Verde-Star Luis

2017-01-01

Full Text Available We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is also Toeplitz the polynomial sequences turn out to be of interpolatory type and we obtain additional results. For example, we show that every nonderogative finite square matrix is similar to a unique Toeplitz-Hessenberg matrix.

S-matrices and integrability

International Nuclear Information System (INIS)

Bombardelli, Diego

2016-01-01

In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering processes due to integrability. We then focus on the analytic properties of the two-particle scattering amplitude and illustrate the derivation of the S-matrices for all the possible bound states using the so-called bootstrap principle. General algebraic structures underlying the S-matrix theory and its relation with the form factors axioms are briefly mentioned. Finally, we discuss the S-matrices of sine-Gordon and SU (2), SU (3) chiral Gross–Neveu models. (topical review)

Matrices Aléatoires Tri-diagonales et Par Blocs.

OpenAIRE

MEKKI, Slimane

2014-01-01

Dans ce mémoire l'étude porte sur la densité de matrice aléatoire, les densités des valeurs propres d'une matrice pour les trois ensembles G.O.E, G.U.E, G.S.E. Après nous avons explicité les formules des densités de valeurs propres des matrices tri-diagonales dans les cas HERMITE et LAGUERRE Des simulations sur les constantes de normalisations pour les densités des matrices aléatoires ou des valeurs propres sont présentées.

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

Science.gov (United States)

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.

Selectivity and sparseness in randomly connected balanced networks.

Directory of Open Access Journals (Sweden)

Cengiz Pehlevan

Full Text Available Neurons in sensory cortex show stimulus selectivity and sparse population response, even in cases where no strong functionally specific structure in connectivity can be detected. This raises the question whether selectivity and sparseness can be generated and maintained in randomly connected networks. We consider a recurrent network of excitatory and inhibitory spiking neurons with random connectivity, driven by random projections from an input layer of stimulus selective neurons. In this architecture, the stimulus-to-stimulus and neuron-to-neuron modulation of total synaptic input is weak compared to the mean input. Surprisingly, we show that in the balanced state the network can still support high stimulus selectivity and sparse population response. In the balanced state, strong synapses amplify the variation in synaptic input and recurrent inhibition cancels the mean. Functional specificity in connectivity emerges due to the inhomogeneity caused by the generative statistical rule used to build the network. We further elucidate the mechanism behind and evaluate the effects of model parameters on population sparseness and stimulus selectivity. Network response to mixtures of stimuli is investigated. It is shown that a balanced state with unselective inhibition can be achieved with densely connected input to inhibitory population. Balanced networks exhibit the "paradoxical" effect: an increase in excitatory drive to inhibition leads to decreased inhibitory population firing rate. We compare and contrast selectivity and sparseness generated by the balanced network to randomly connected unbalanced networks. Finally, we discuss our results in light of experiments.

Laminin active peptide/agarose matrices as multifunctional biomaterials for tissue engineering.

Science.gov (United States)

Yamada, Yuji; Hozumi, Kentaro; Aso, Akihiro; Hotta, Atsushi; Toma, Kazunori; Katagiri, Fumihiko; Kikkawa, Yamato; Nomizu, Motoyoshi

2012-06-01

Cell adhesive peptides derived from extracellular matrix components are potential candidates to afford bio-adhesiveness to cell culture scaffolds for tissue engineering. Previously, we covalently conjugated bioactive laminin peptides to polysaccharides, such as chitosan and alginate, and demonstrated their advantages as biomaterials. Here, we prepared functional polysaccharide matrices by mixing laminin active peptides and agarose gel. Several laminin peptide/agarose matrices showed cell attachment activity. In particular, peptide AG73 (RKRLQVQLSIRT)/agarose matrices promoted strong cell attachment and the cell behavior depended on the stiffness of agarose matrices. Fibroblasts formed spheroid structures on the soft AG73/agarose matrices while the cells formed a monolayer with elongated morphologies on the stiff matrices. On the stiff AG73/agarose matrices, neuronal cells extended neuritic processes and endothelial cells formed capillary-like networks. In addition, salivary gland cells formed acini-like structures on the soft matrices. These results suggest that the peptide/agarose matrices are useful for both two- and three-dimensional cell culture systems as a multifunctional biomaterial for tissue engineering. Copyright © 2012 Elsevier Ltd. All rights reserved.

Visual recognition and inference using dynamic overcomplete sparse learning.

Science.gov (United States)

Murray, Joseph F; Kreutz-Delgado, Kenneth

2007-09-01

We present a hierarchical architecture and learning algorithm for visual recognition and other visual inference tasks such as imagination, reconstruction of occluded images, and expectation-driven segmentation. Using properties of biological vision for guidance, we posit a stochastic generative world model and from it develop a simplified world model (SWM) based on a tractable variational approximation that is designed to enforce sparse coding. Recent developments in computational methods for learning overcomplete representations (Lewicki & Sejnowski, 2000; Teh, Welling, Osindero, & Hinton, 2003) suggest that overcompleteness can be useful for visual tasks, and we use an overcomplete dictionary learning algorithm (Kreutz-Delgado, et al., 2003) as a preprocessing stage to produce accurate, sparse codings of images. Inference is performed by constructing a dynamic multilayer network with feedforward, feedback, and lateral connections, which is trained to approximate the SWM. Learning is done with a variant of the back-propagation-through-time algorithm, which encourages convergence to desired states within a fixed number of iterations. Vision tasks require large networks, and to make learning efficient, we take advantage of the sparsity of each layer to update only a small subset of elements in a large weight matrix at each iteration. Experiments on a set of rotated objects demonstrate various types of visual inference and show that increasing the degree of overcompleteness improves recognition performance in difficult scenes with occluded objects in clutter.

SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

KAUST Repository

Desmal, Abdulla

2015-07-29

A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

Decorin-transforming growth factor- interaction regulates matrix organization and mechanical characteristics of three-dimensional collagen matrices.

Science.gov (United States)

Ferdous, Zannatul; Wei, Victoria Mariko; Iozzo, Renato; Höök, Magnus; Grande-Allen, Kathryn Jane

2007-12-07

The small leucine-rich proteoglycan decorin has been demonstrated to be a key regulator of collagen fibrillogenesis; decorin deficiencies lead to irregularly shaped collagen fibrils and weakened material behavior in postnatal murine connective tissues. In an in vitro investigation of the contributions of decorin to tissue organization and material behavior, model tissues were engineered by seeding embryonic fibroblasts, harvested from 12.5-13.5 days gestational aged decorin null (Dcn(-/-)) or wild-type mice, within type I collagen gels. The resulting three-dimensional collagen matrices were cultured for 4 weeks under static tension. The collagen matrices seeded with Dcn(-/-) cells exhibited greater contraction, cell density, ultimate tensile strength, and elastic modulus than those seeded with wild-type cells. Ultrastructurally, the matrices seeded with Dcn(-/-) cells contained a greater density of collagen. The decorin-null tissues contained more biglycan than control tissues, suggesting that this related proteoglycan compensated for the absence of decorin. The effect of transforming growth factor-beta (TGF-beta), which is normally sequestered by decorin, was also investigated in this study. The addition of TGF-beta1 to the matrices seeded with wild-type cells improved their contraction and mechanical strength, whereas blocking TGF-beta1 in the Dcn(-/-) cell-seeded matrices significantly reduced the collagen gel contraction. These results indicate that the inhibitory interaction between decorin and TGF-beta1 significantly influenced the matrix organization and material behavior of these in vitro model tissues.

Vector sparse representation of color image using quaternion matrix analysis.

Science.gov (United States)

Xu, Yi; Yu, Licheng; Xu, Hongteng; Zhang, Hao; Nguyen, Truong

2015-04-01

Traditional sparse image models treat color image pixel as a scalar, which represents color channels separately or concatenate color channels as a monochrome image. In this paper, we propose a vector sparse representation model for color images using quaternion matrix analysis. As a new tool for color image representation, its potential applications in several image-processing tasks are presented, including color image reconstruction, denoising, inpainting, and super-resolution. The proposed model represents the color image as a quaternion matrix, where a quaternion-based dictionary learning algorithm is presented using the K-quaternion singular value decomposition (QSVD) (generalized K-means clustering for QSVD) method. It conducts the sparse basis selection in quaternion space, which uniformly transforms the channel images to an orthogonal color space. In this new color space, it is significant that the inherent color structures can be completely preserved during vector reconstruction. Moreover, the proposed sparse model is more efficient comparing with the current sparse models for image restoration tasks due to lower redundancy between the atoms of different color channels. The experimental results demonstrate that the proposed sparse image model avoids the hue bias issue successfully and shows its potential as a general and powerful tool in color image analysis and processing domain.

Sparse Representation Based Binary Hypothesis Model for Hyperspectral Image Classification

Directory of Open Access Journals (Sweden)

Yidong Tang

2016-01-01

Full Text Available The sparse representation based classifier (SRC and its kernel version (KSRC have been employed for hyperspectral image (HSI classification. However, the state-of-the-art SRC often aims at extended surface objects with linear mixture in smooth scene and assumes that the number of classes is given. Considering the small target with complex background, a sparse representation based binary hypothesis (SRBBH model is established in this paper. In this model, a query pixel is represented in two ways, which are, respectively, by background dictionary and by union dictionary. The background dictionary is composed of samples selected from the local dual concentric window centered at the query pixel. Thus, for each pixel the classification issue becomes an adaptive multiclass classification problem, where only the number of desired classes is required. Furthermore, the kernel method is employed to improve the interclass separability. In kernel space, the coding vector is obtained by using kernel-based orthogonal matching pursuit (KOMP algorithm. Then the query pixel can be labeled by the characteristics of the coding vectors. Instead of directly using the reconstruction residuals, the different impacts the background dictionary and union dictionary have on reconstruction are used for validation and classification. It enhances the discrimination and hence improves the performance.

In vivo biocompatibility of carbodiimide-crosslinked collagen matrices : Effects of crosslink density, heparin immobilization, and bFGF loading

NARCIS (Netherlands)

van Wachem, PB; Plantinga, JA; Wissink, MJB; Poot, AA; Engbers, GHM; Beugeling, T; van Aken, WG; Feijen, J; van Luyn, MJA

2001-01-01

Collagen matrices, crosslinked using N-(3-dimethylaminopropyl)-N'-ethylcarbodiimide (E) and N-hydroxvsuccinimide (N), were previously developed as a substrate for endothelial cell seeding of small-diameter vascular grafts. In the present study, the biocompatibility of various EN-crosslinked collagen

Fast convolutional sparse coding using matrix inversion lemma

Czech Academy of Sciences Publication Activity Database

Šorel, Michal; Šroubek, Filip

2016-01-01

Roč. 55, č. 1 (2016), s. 44-51 ISSN 1051-2004 R&D Projects: GA ČR GA13-29225S Institutional support: RVO:67985556 Keywords : Convolutional sparse coding * Feature learning * Deconvolution networks * Shift-invariant sparse coding Subject RIV: JD - Computer Applications, Robotics Impact factor: 2.337, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/sorel-0459332.pdf

Structure-based bayesian sparse reconstruction

KAUST Repository

Quadeer, Ahmed Abdul; Al-Naffouri, Tareq Y.

2012-01-01

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical

The Antitriangular Factorization of Saddle Point Matrices

KAUST Repository

Pestana, J.

2014-01-01

Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173-196] recently introduced the block antitriangular ("Batman") decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners. © 2014 Society for Industrial and Applied Mathematics.

Binary Sparse Phase Retrieval via Simulated Annealing

Directory of Open Access Journals (Sweden)

Wei Peng

2016-01-01

Full Text Available This paper presents the Simulated Annealing Sparse PhAse Recovery (SASPAR algorithm for reconstructing sparse binary signals from their phaseless magnitudes of the Fourier transform. The greedy strategy version is also proposed for a comparison, which is a parameter-free algorithm. Sufficient numeric simulations indicate that our method is quite effective and suggest the binary model is robust. The SASPAR algorithm seems competitive to the existing methods for its efficiency and high recovery rate even with fewer Fourier measurements.

Graphs and matrices

CERN Document Server

Bapat, Ravindra B

2014-01-01

This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...

Bayesian Nonparametric Clustering for Positive Definite Matrices.

Science.gov (United States)

Cherian, Anoop; Morellas, Vassilios; Papanikolopoulos, Nikolaos

2016-05-01

Symmetric Positive Definite (SPD) matrices emerge as data descriptors in several applications of computer vision such as object tracking, texture recognition, and diffusion tensor imaging. Clustering these data matrices forms an integral part of these applications, for which soft-clustering algorithms (K-Means, expectation maximization, etc.) are generally used. As is well-known, these algorithms need the number of clusters to be specified, which is difficult when the dataset scales. To address this issue, we resort to the classical nonparametric Bayesian framework by modeling the data as a mixture model using the Dirichlet process (DP) prior. Since these matrices do not conform to the Euclidean geometry, rather belongs to a curved Riemannian manifold,existing DP models cannot be directly applied. Thus, in this paper, we propose a novel DP mixture model framework for SPD matrices. Using the log-determinant divergence as the underlying dissimilarity measure to compare these matrices, and further using the connection between this measure and the Wishart distribution, we derive a novel DPM model based on the Wishart-Inverse-Wishart conjugate pair. We apply this model to several applications in computer vision. Our experiments demonstrate that our model is scalable to the dataset size and at the same time achieves superior accuracy compared to several state-of-the-art parametric and nonparametric clustering algorithms.

Confidence of model based shape reconstruction from sparse data

DEFF Research Database (Denmark)

Baka, N.; de Bruijne, Marleen; Reiber, J. H. C.

2010-01-01

Statistical shape models (SSM) are commonly applied for plausible interpolation of missing data in medical imaging. However, when fitting a shape model to sparse information, many solutions may fit the available data. In this paper we derive a constrained SSM to fit noisy sparse input landmarks...

Proportionate Minimum Error Entropy Algorithm for Sparse System Identification

Directory of Open Access Journals (Sweden)

Zongze Wu

2015-08-01

Full Text Available Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.

Sparse PDF Volumes for Consistent Multi-Resolution Volume Rendering

KAUST Repository

Sicat, Ronell Barrera

2014-12-31

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.

A hybrid method for the parallel computation of Green's functions

DEFF Research Database (Denmark)

Petersen, Dan Erik; Li, Song; Stokbro, Kurt

2009-01-01

of the large number of times this calculation needs to be performed, this is computationally very expensive even on supercomputers. The classical approach is based on recurrence formulas which cannot be efficiently parallelized. This practically prevents the solution of large problems with hundreds...... of thousands of atoms. We propose new recurrences for a general class of sparse matrices to calculate Green's and lesser Green's function matrices which extend formulas derived by Takahashi and others. We show that these recurrences may lead to a dramatically reduced computational cost because they only...... require computing a small number of entries of the inverse matrix. Then. we propose a parallelization strategy for block tridiagonal matrices which involves a combination of Schur complement calculations and cyclic reduction. It achieves good scalability even on problems of modest size....

On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

Directory of Open Access Journals (Sweden)

Zhaolin Jiang

2014-01-01

inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

Immanant Conversion on Symmetric Matrices

Directory of Open Access Journals (Sweden)

Purificação Coelho M.

2014-01-01

Full Text Available Letr Σn(C denote the space of all n χ n symmetric matrices over the complex field C. The main objective of this paper is to prove that the maps Φ : Σn(C -> Σn (C satisfying for any fixed irre- ducible characters X, X' -SC the condition dx(A +aB = dχ·(Φ(Α + αΦ(Β for all matrices A,В ε Σ„(С and all scalars a ε C are automatically linear and bijective. As a corollary of the above result we characterize all such maps Φ acting on ΣИ(С.

A flexible framework for sparse simultaneous component based data integration

Directory of Open Access Journals (Sweden)

Van Deun Katrijn

2011-11-01

Full Text Available Abstract 1 Background High throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins have to be taken into account. 2 Results We propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks. 3 Conclusion Sparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such

A flexible framework for sparse simultaneous component based data integration.

Science.gov (United States)

Van Deun, Katrijn; Wilderjans, Tom F; van den Berg, Robert A; Antoniadis, Anestis; Van Mechelen, Iven

2011-11-15

High throughput data are complex and methods that reveal structure underlying the data are most useful. Principal component analysis, frequently implemented as a singular value decomposition, is a popular technique in this respect. Nowadays often the challenge is to reveal structure in several sources of information (e.g., transcriptomics, proteomics) that are available for the same biological entities under study. Simultaneous component methods are most promising in this respect. However, the interpretation of the principal and simultaneous components is often daunting because contributions of each of the biomolecules (transcripts, proteins) have to be taken into account. We propose a sparse simultaneous component method that makes many of the parameters redundant by shrinking them to zero. It includes principal component analysis, sparse principal component analysis, and ordinary simultaneous component analysis as special cases. Several penalties can be tuned that account in different ways for the block structure present in the integrated data. This yields known sparse approaches as the lasso, the ridge penalty, the elastic net, the group lasso, sparse group lasso, and elitist lasso. In addition, the algorithmic results can be easily transposed to the context of regression. Metabolomics data obtained with two measurement platforms for the same set of Escherichia coli samples are used to illustrate the proposed methodology and the properties of different penalties with respect to sparseness across and within data blocks. Sparse simultaneous component analysis is a useful method for data integration: First, simultaneous analyses of multiple blocks offer advantages over sequential and separate analyses and second, interpretation of the results is highly facilitated by their sparseness. The approach offered is flexible and allows to take the block structure in different ways into account. As such, structures can be found that are exclusively tied to one data platform

The 'golden' matrices and a new kind of cryptography

International Nuclear Information System (INIS)

Stakhov, A.P.

2007-01-01

We consider a new class of square matrices called the 'golden' matrices. They are a generalization of the classical Fibonacci Q-matrix for continuous domain. The 'golden' matrices can be used for creation of a new kind of cryptography called the 'golden' cryptography. The method is very fast and simple for technical realization and can be used for cryptographic protection of digital signals (telecommunication and measurement systems)

Feature selection and multi-kernel learning for sparse representation on a manifold

KAUST Repository

Wang, Jim Jing-Yan

2014-03-01

Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao etal. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. © 2013 Elsevier Ltd.

Feature selection and multi-kernel learning for sparse representation on a manifold.

Science.gov (United States)

Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin

2014-03-01

Sparse representation has been widely studied as a part-based data representation method and applied in many scientific and engineering fields, such as bioinformatics and medical imaging. It seeks to represent a data sample as a sparse linear combination of some basic items in a dictionary. Gao et al. (2013) recently proposed Laplacian sparse coding by regularizing the sparse codes with an affinity graph. However, due to the noisy features and nonlinear distribution of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection and multiple kernel learning into the sparse coding on the manifold. To this end, unified objectives are defined for feature selection, multiple kernel learning, sparse coding, and graph regularization. By optimizing the objective functions iteratively, we develop novel data representation algorithms with feature selection and multiple kernel learning respectively. Experimental results on two challenging tasks, N-linked glycosylation prediction and mammogram retrieval, demonstrate that the proposed algorithms outperform the traditional sparse coding methods. Copyright © 2013 Elsevier Ltd. All rights reserved.

On the Eigenvalues and Eigenvectors of Block Triangular Preconditioned Block Matrices

KAUST Repository

Pestana, Jennifer

2014-01-01

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related. © 2014 Society for Industrial and Applied Mathematics.

Sparse representation, modeling and learning in visual recognition theory, algorithms and applications

CERN Document Server

Cheng, Hong

2015-01-01

This unique text/reference presents a comprehensive review of the state of the art in sparse representations, modeling and learning. The book examines both the theoretical foundations and details of algorithm implementation, highlighting the practical application of compressed sensing research in visual recognition and computer vision. Topics and features: provides a thorough introduction to the fundamentals of sparse representation, modeling and learning, and the application of these techniques in visual recognition; describes sparse recovery approaches, robust and efficient sparse represen

An Efficient GPU General Sparse Matrix-Matrix Multiplication for Irregular Data

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2014-01-01

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method, breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM algorithm has to handle extra...... irregularity from three aspects: (1) the number of the nonzero entries in the result sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the result sparse matrix dominate the execution time, and (3) load balancing must account for sparse data in both input....... Load balancing builds on the number of the necessary arithmetic operations on the nonzero entries and is guaranteed in all stages. Compared with the state-of-the-art GPU SpGEMM methods in the CUSPARSE library and the CUSP library and the latest CPU SpGEMM method in the Intel Math Kernel Library, our...

Comparison of Methods for Sparse Representation of Musical Signals

DEFF Research Database (Denmark)

Endelt, Line Ørtoft; la Cour-Harbo, Anders

2005-01-01

by a number of sparseness measures and results are shown on the ℓ1 norm of the coefficients, using a dictionary containing a Dirac basis, a Discrete Cosine Transform, and a Wavelet Packet. Evaluated only on the sparseness Matching Pursuit is the best method, and it is also relatively fast....

NMR studies of metallic tin confined within porous matrices

International Nuclear Information System (INIS)

Charnaya, E. V.; Tien, Cheng; Lee, M. K.; Kumzerov, Yu. A.

2007-01-01

119 Sn NMR studies were carried out for metallic tin confined within synthetic opal and porous glass. Tin was embedded into nanoporous matrices in the melted state under pressure. The Knight shift for liquid confined tin was found to decrease with decreasing pore size. Correlations between NMR line shapes, Knight shift, and pore filling were observed. The melting and freezing phase transitions of tin under confinement were studied through temperature dependences of NMR signals upon warming and cooling. Melting of tin within the opal matrix agreed well with the liquid skin model suggested for small isolated particles. The influence of the pore filling on the melting process was shown

Joint-2D-SL0 Algorithm for Joint Sparse Matrix Reconstruction

Directory of Open Access Journals (Sweden)

Dong Zhang

2017-01-01

Full Text Available Sparse matrix reconstruction has a wide application such as DOA estimation and STAP. However, its performance is usually restricted by the grid mismatch problem. In this paper, we revise the sparse matrix reconstruction model and propose the joint sparse matrix reconstruction model based on one-order Taylor expansion. And it can overcome the grid mismatch problem. Then, we put forward the Joint-2D-SL0 algorithm which can solve the joint sparse matrix reconstruction problem efficiently. Compared with the Kronecker compressive sensing method, our proposed method has a higher computational efficiency and acceptable reconstruction accuracy. Finally, simulation results validate the superiority of the proposed method.

On Investigating GMRES Convergence using Unitary Matrices

Czech Academy of Sciences Publication Activity Database

Duintjer Tebbens, Jurjen; Meurant, G.; Sadok, H.; Strakoš, Z.

2014-01-01

Roč. 450, 1 June (2014), s. 83-107 ISSN 0024-3795 Grant - others:GA AV ČR(CZ) M100301201; GA MŠk(CZ) LL1202 Institutional support: RVO:67985807 Keywords : GMRES convergence * unitary matrices * unitary spectra * normal matrices * Krylov residual subspace * Schur parameters Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

Novel and simple alternative to create nanofibrillar matrices of interest for tissue engineering.

Science.gov (United States)

Sohier, Jérôme; Corre, Pierre; Perret, Christophe; Pilet, Paul; Weiss, Pierre

2014-04-01

Synthetic analogs to natural extracellular matrix (ECM) at the nanometer level are of great potential for regenerative medicine. This study introduces a novel and simple method to produce polymer nanofibers and evaluates the properties of the resulting structures, as well as their suitability to support cells and their potential interest for bone and vascular applications. The devised approach diffracts a polymer solution by means of a spraying apparatus and of an airstream as sole driving force. The resulting nanofibers were produced in an effective fashion and a factorial design allowed isolating the processing parameters that control nanofiber size and distribution. The nanofibrillar matrices revealed to be of very high porosity and were effectively colonized by human bone marrow mesenchymal cells, while allowing ECM production and osteoblastic differentiation. In vivo, the matrices provided support for new bone formation and provided a good patency as small diameter vessel grafts.

Decentralized modal identification using sparse blind source separation

International Nuclear Information System (INIS)

Sadhu, A; Hazra, B; Narasimhan, S; Pandey, M D

2011-01-01

Popular ambient vibration-based system identification methods process information collected from a dense array of sensors centrally to yield the modal properties. In such methods, the need for a centralized processing unit capable of satisfying large memory and processing demands is unavoidable. With the advent of wireless smart sensor networks, it is now possible to process information locally at the sensor level, instead. The information at the individual sensor level can then be concatenated to obtain the global structure characteristics. A novel decentralized algorithm based on wavelet transforms to infer global structure mode information using measurements obtained using a small group of sensors at a time is proposed in this paper. The focus of the paper is on algorithmic development, while the actual hardware and software implementation is not pursued here. The problem of identification is cast within the framework of under-determined blind source separation invoking transformations of measurements to the time–frequency domain resulting in a sparse representation. The partial mode shape coefficients so identified are then combined to yield complete modal information. The transformations are undertaken using stationary wavelet packet transform (SWPT), yielding a sparse representation in the wavelet domain. Principal component analysis (PCA) is then performed on the resulting wavelet coefficients, yielding the partial mixing matrix coefficients from a few measurement channels at a time. This process is repeated using measurements obtained from multiple sensor groups, and the results so obtained from each group are concatenated to obtain the global modal characteristics of the structure

Decentralized modal identification using sparse blind source separation

Science.gov (United States)

Sadhu, A.; Hazra, B.; Narasimhan, S.; Pandey, M. D.

2011-12-01

Popular ambient vibration-based system identification methods process information collected from a dense array of sensors centrally to yield the modal properties. In such methods, the need for a centralized processing unit capable of satisfying large memory and processing demands is unavoidable. With the advent of wireless smart sensor networks, it is now possible to process information locally at the sensor level, instead. The information at the individual sensor level can then be concatenated to obtain the global structure characteristics. A novel decentralized algorithm based on wavelet transforms to infer global structure mode information using measurements obtained using a small group of sensors at a time is proposed in this paper. The focus of the paper is on algorithmic development, while the actual hardware and software implementation is not pursued here. The problem of identification is cast within the framework of under-determined blind source separation invoking transformations of measurements to the time-frequency domain resulting in a sparse representation. The partial mode shape coefficients so identified are then combined to yield complete modal information. The transformations are undertaken using stationary wavelet packet transform (SWPT), yielding a sparse representation in the wavelet domain. Principal component analysis (PCA) is then performed on the resulting wavelet coefficients, yielding the partial mixing matrix coefficients from a few measurement channels at a time. This process is repeated using measurements obtained from multiple sensor groups, and the results so obtained from each group are concatenated to obtain the global modal characteristics of the structure.

"G.P.S Matrices" programme: A method to improve the mastery level of social science students in matrices operations

Science.gov (United States)

Lee, Ken Voon

2013-04-01

The purpose of this action research was to increase the mastery level of Form Five Social Science students in Tawau II National Secondary School in the operations of addition, subtraction and multiplication of matrices in Mathematics. A total of 30 students were involved. Preliminary findings through the analysis of pre-test results and questionnaire had identified the main problem faced in which the students felt confused with the application of principles of the operations of matrices when performing these operations. Therefore, an action research was conducted using an intervention programme called "G.P.S Matrices" to overcome the problem. This programme was divided into three phases. 'Gift of Matrices' phase aimed at forming matrix teaching aids. The second and third phases were 'Positioning the Elements of Matrices' and 'Strenghtening the Concept of Matrices'. These two phases were aimed at increasing the level of understanding and memory of the students towards the principles of matrix operations. Besides, this third phase was also aimed at creating an interesting learning environment. A comparison between the results of pre-test and post-test had shown a remarkable improvement in students' performances after implementing the programme. In addition, the analysis of interview findings also indicated a positive feedback on the changes in students' attitude, particularly in the aspect of students' understanding level. Moreover, the level of students' memory also increased following the use of the concrete matrix teaching aids created in phase one. Besides, teachers felt encouraging when conducive learning environment was created through students' presentation activity held in third phase. Furthermore, students were voluntarily involved in these student-centred activities. In conclusion, this research findings showed an increase in the mastery level of students in these three matrix operations and thus the objective of the research had been achieved.

Discussion of CoSA: Clustering of Sparse Approximations

Energy Technology Data Exchange (ETDEWEB)

Armstrong, Derek Elswick [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-03-07

The purpose of this talk is to discuss the possible applications of CoSA (Clustering of Sparse Approximations) to the exploitation of HSI (HyperSpectral Imagery) data. CoSA is presented by Moody et al. in the Journal of Applied Remote Sensing (“Land cover classification in multispectral imagery using clustering of sparse approximations over learned feature dictionaries”, Vol. 8, 2014) and is based on machine learning techniques.

Optimal Sparse Upstream Sensor Placement for Hydrokinetic Turbines

Science.gov (United States)

Cavagnaro, Robert; Strom, Benjamin; Ross, Hannah; Hill, Craig; Polagye, Brian

2016-11-01

Accurate measurement of the flow field incident upon a hydrokinetic turbine is critical for performance evaluation during testing and setting boundary conditions in simulation. Additionally, turbine controllers may leverage real-time flow measurements. Particle image velocimetry (PIV) is capable of rendering a flow field over a wide spatial domain in a controlled, laboratory environment. However, PIV's lack of suitability for natural marine environments, high cost, and intensive post-processing diminish its potential for control applications. Conversely, sensors such as acoustic Doppler velocimeters (ADVs), are designed for field deployment and real-time measurement, but over a small spatial domain. Sparsity-promoting regression analysis such as LASSO is utilized to improve the efficacy of point measurements for real-time applications by determining optimal spatial placement for a small number of ADVs using a training set of PIV velocity fields and turbine data. The study is conducted in a flume (0.8 m2 cross-sectional area, 1 m/s flow) with laboratory-scale axial and cross-flow turbines. Predicted turbine performance utilizing the optimal sparse sensor network and associated regression model is compared to actual performance with corresponding PIV measurements.

Robust Small Target Co-Detection from Airborne Infrared Image Sequences.

Science.gov (United States)

Gao, Jingli; Wen, Chenglin; Liu, Meiqin

2017-09-29

In this paper, a novel infrared target co-detection model combining the self-correlation features of backgrounds and the commonality features of targets in the spatio-temporal domain is proposed to detect small targets in a sequence of infrared images with complex backgrounds. Firstly, a dense target extraction model based on nonlinear weights is proposed, which can better suppress background of images and enhance small targets than weights of singular values. Secondly, a sparse target extraction model based on entry-wise weighted robust principal component analysis is proposed. The entry-wise weight adaptively incorporates structural prior in terms of local weighted entropy, thus, it can extract real targets accurately and suppress background clutters efficiently. Finally, the commonality of targets in the spatio-temporal domain are used to construct target refinement model for false alarms suppression and target confirmation. Since real targets could appear in both of the dense and sparse reconstruction maps of a single frame, and form trajectories after tracklet association of consecutive frames, the location correlation of the dense and sparse reconstruction maps for a single frame and tracklet association of the location correlation maps for successive frames have strong ability to discriminate between small targets and background clutters. Experimental results demonstrate that the proposed small target co-detection method can not only suppress background clutters effectively, but also detect targets accurately even if with target-like interference.

Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding

Directory of Open Access Journals (Sweden)

Ying Chen

2014-05-01

Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.

Batched Triangular DLA for Very Small Matrices on GPUs

KAUST Repository

Charara, Ali; Keyes, David E.; Ltaief, Hatem

2017-01-01

linear algebra operations on very small matrix sizes (usually less than 100). Batched dense linear algebra kernels are becoming ubiquitous for such scientific computations. Within a single API call, these kernels are capable of simultaneously launching a

Sparse Representation Based Multi-Instance Learning for Breast Ultrasound Image Classification

Directory of Open Access Journals (Sweden)

Lu Bing

2017-01-01

Full Text Available We propose a novel method based on sparse representation for breast ultrasound image classification under the framework of multi-instance learning (MIL. After image enhancement and segmentation, concentric circle is used to extract the global and local features for improving the accuracy in diagnosis and prediction. The classification problem of ultrasound image is converted to sparse representation based MIL problem. Each instance of a bag is represented as a sparse linear combination of all basis vectors in the dictionary, and then the bag is represented by one feature vector which is obtained via sparse representations of all instances within the bag. The sparse and MIL problem is further converted to a conventional learning problem that is solved by relevance vector machine (RVM. Results of single classifiers are combined to be used for classification. Experimental results on the breast cancer datasets demonstrate the superiority of the proposed method in terms of classification accuracy as compared with state-of-the-art MIL methods.

Sparse Representation Based Multi-Instance Learning for Breast Ultrasound Image Classification.

Science.gov (United States)

Bing, Lu; Wang, Wei

2017-01-01

We propose a novel method based on sparse representation for breast ultrasound image classification under the framework of multi-instance learning (MIL). After image enhancement and segmentation, concentric circle is used to extract the global and local features for improving the accuracy in diagnosis and prediction. The classification problem of ultrasound image is converted to sparse representation based MIL problem. Each instance of a bag is represented as a sparse linear combination of all basis vectors in the dictionary, and then the bag is represented by one feature vector which is obtained via sparse representations of all instances within the bag. The sparse and MIL problem is further converted to a conventional learning problem that is solved by relevance vector machine (RVM). Results of single classifiers are combined to be used for classification. Experimental results on the breast cancer datasets demonstrate the superiority of the proposed method in terms of classification accuracy as compared with state-of-the-art MIL methods.

CONVERGENCE OF POWERS OF CONTROLLABLE INTUITIONISTIC FUZZY MATRICES

OpenAIRE

Riyaz Ahmad Padder; P. Murugadas

2016-01-01

Convergences of powers of controllable intuitionistic fuzzy matrices have been stud¬ied. It is shown that they oscillate with period equal to 2, in general. Some equalities and sequences of inequalities about powers of controllable intuitionistic fuzzy matrices have been obtained.

Xenogenic extracellular matrices as potential biomaterials for interposition grafting in urological surgery.

LENUS (Irish Health Repository)

Davis, N F

2012-01-31

PURPOSE: The field of tissue engineering focuses on developing strategies for reconstructing injured, diseased, and congenitally absent tissues and organs. During the last decade urologists have benefited from remodeling and regenerative properties of bioscaffolds derived from xenogenic extracellular matrices. We comprehensively reviewed the current literature on structural and functional characteristics of xenogenic extracellular matrix grafting since it was first described in urological surgery. We also reviewed the clinical limitations, and assessed the potential for safe and effective urological application of extracellular matrix grafting in place of autogenous tissue. MATERIALS AND METHODS: We performed literature searches for English language publications using the PubMed(R) and MEDLINE(R) databases. Keywords included "xenogenic," "extracellular matrix" and "genitourinary tract applications." A total of 112 articles were scrutinized, of which 50 were suitable for review based on clinical relevance and importance of content. RESULTS: Since the mid 1990s xenogenic extracellular matrices have been used to successfully treat a number of pathological conditions that affect the upper and lower genitourinary tract. They are typically prepared from porcine organs such as small intestine and bladder. These organs are harvested and subjected to decellularization and sterilization techniques before surgical implantation. Bioinductive growth factors that are retained during the preparation process induce constructive tissue remodeling as the extracellular matrix is simultaneously degraded and excreted. However, recent documented concerns over durability, decreased mechanical strength and residual porcine DNA after preparation techniques have temporarily hampered the potential of extracellular matrices as a reliable replacement for genitourinary tract structures. CONCLUSIONS: Extracellular matrices are a useful alternative for successfully treating a number of urological

Joint sparse representation for robust multimodal biometrics recognition.

Science.gov (United States)

Shekhar, Sumit; Patel, Vishal M; Nasrabadi, Nasser M; Chellappa, Rama

2014-01-01

Traditional biometric recognition systems rely on a single biometric signature for authentication. While the advantage of using multiple sources of information for establishing the identity has been widely recognized, computational models for multimodal biometrics recognition have only recently received attention. We propose a multimodal sparse representation method, which represents the test data by a sparse linear combination of training data, while constraining the observations from different modalities of the test subject to share their sparse representations. Thus, we simultaneously take into account correlations as well as coupling information among biometric modalities. A multimodal quality measure is also proposed to weigh each modality as it gets fused. Furthermore, we also kernelize the algorithm to handle nonlinearity in data. The optimization problem is solved using an efficient alternative direction method. Various experiments show that the proposed method compares favorably with competing fusion-based methods.

Robust Visual Tracking Via Consistent Low-Rank Sparse Learning

KAUST Repository

Zhang, Tianzhu

2014-06-19

Object tracking is the process of determining the states of a target in consecutive video frames based on properties of motion and appearance consistency. In this paper, we propose a consistent low-rank sparse tracker (CLRST) that builds upon the particle filter framework for tracking. By exploiting temporal consistency, the proposed CLRST algorithm adaptively prunes and selects candidate particles. By using linear sparse combinations of dictionary templates, the proposed method learns the sparse representations of image regions corresponding to candidate particles jointly by exploiting the underlying low-rank constraints. In addition, the proposed CLRST algorithm is computationally attractive since temporal consistency property helps prune particles and the low-rank minimization problem for learning joint sparse representations can be efficiently solved by a sequence of closed form update operations. We evaluate the proposed CLRST algorithm against 14 state-of-the-art tracking methods on a set of 25 challenging image sequences. Experimental results show that the CLRST algorithm performs favorably against state-of-the-art tracking methods in terms of accuracy and execution time.

Loop diagrams without γ matrices

International Nuclear Information System (INIS)

McKeon, D.G.C.; Rebhan, A.

1993-01-01

By using a quantum-mechanical path integral to compute matrix elements of the form left-angle x|exp(-iHt)|y right-angle, radiative corrections in quantum-field theory can be evaluated without encountering loop-momentum integrals. In this paper we demonstrate how Dirac γ matrices that occur in the proper-time ''Hamiltonian'' H lead to the introduction of a quantum-mechanical path integral corresponding to a superparticle analogous to one proposed recently by Fradkin and Gitman. Direct evaluation of this path integral circumvents many of the usual algebraic manipulations of γ matrices in the computation of quantum-field-theoretical Green's functions involving fermions

Efficient collaborative sparse channel estimation in massive MIMO

KAUST Repository

Masood, Mudassir

2015-08-12

We propose a method for estimation of sparse frequency selective channels within MIMO-OFDM systems. These channels are independently sparse and share a common support. The method estimates the impulse response for each channel observed by the antennas at the receiver. Estimation is performed in a coordinated manner by sharing minimal information among neighboring antennas to achieve results better than many contemporary methods. Simulations demonstrate the superior performance of the proposed method.

Efficient collaborative sparse channel estimation in massive MIMO

KAUST Repository

Masood, Mudassir; Afify, Laila H.; Al-Naffouri, Tareq Y.

2015-01-01

We propose a method for estimation of sparse frequency selective channels within MIMO-OFDM systems. These channels are independently sparse and share a common support. The method estimates the impulse response for each channel observed by the antennas at the receiver. Estimation is performed in a coordinated manner by sharing minimal information among neighboring antennas to achieve results better than many contemporary methods. Simulations demonstrate the superior performance of the proposed method.

Sparse dictionary learning of resting state fMRI networks.

Science.gov (United States)

Eavani, Harini; Filipovych, Roman; Davatzikos, Christos; Satterthwaite, Theodore D; Gur, Raquel E; Gur, Ruben C

2012-07-02

Research in resting state fMRI (rsfMRI) has revealed the presence of stable, anti-correlated functional subnetworks in the brain. Task-positive networks are active during a cognitive process and are anti-correlated with task-negative networks, which are active during rest. In this paper, based on the assumption that the structure of the resting state functional brain connectivity is sparse, we utilize sparse dictionary modeling to identify distinct functional sub-networks. We propose two ways of formulating the sparse functional network learning problem that characterize the underlying functional connectivity from different perspectives. Our results show that the whole-brain functional connectivity can be concisely represented with highly modular, overlapping task-positive/negative pairs of sub-networks.

Classification en référence à une matrice stochastique

OpenAIRE

Verdun , Stéphane; Cariou , Véronique; Qannari , El Mostafa

2009-01-01

International audience; Etant donné un tableau de données X portant sur un ensemble de n objets, et une matrice stochastique S qui peut être assimilée à une matrice de transition d'une chaîne de Markov, nous proposons une méthode de partitionnement consistant à appliquer la matrice S sur X de manière itérative jusqu'à convergence. Les classes formant la partition sont déterminées à partir des états stationnaires de la matrice stochastique. Cette matrice stochastique peut être issue d'une matr...

Low-Rank Sparse Coding for Image Classification

KAUST Repository

Zhang, Tianzhu; Ghanem, Bernard; Liu, Si; Xu, Changsheng; Ahuja, Narendra

2013-01-01

In this paper, we propose a low-rank sparse coding (LRSC) method that exploits local structure information among features in an image for the purpose of image-level classification. LRSC represents densely sampled SIFT descriptors, in a spatial neighborhood, collectively as low-rank, sparse linear combinations of code words. As such, it casts the feature coding problem as a low-rank matrix learning problem, which is different from previous methods that encode features independently. This LRSC has a number of attractive properties. (1) It encourages sparsity in feature codes, locality in codebook construction, and low-rankness for spatial consistency. (2) LRSC encodes local features jointly by considering their low-rank structure information, and is computationally attractive. We evaluate the LRSC by comparing its performance on a set of challenging benchmarks with that of 7 popular coding and other state-of-the-art methods. Our experiments show that by representing local features jointly, LRSC not only outperforms the state-of-the-art in classification accuracy but also improves the time complexity of methods that use a similar sparse linear representation model for feature coding.

Low-Rank Sparse Coding for Image Classification

KAUST Repository

Zhang, Tianzhu

2013-12-01

In this paper, we propose a low-rank sparse coding (LRSC) method that exploits local structure information among features in an image for the purpose of image-level classification. LRSC represents densely sampled SIFT descriptors, in a spatial neighborhood, collectively as low-rank, sparse linear combinations of code words. As such, it casts the feature coding problem as a low-rank matrix learning problem, which is different from previous methods that encode features independently. This LRSC has a number of attractive properties. (1) It encourages sparsity in feature codes, locality in codebook construction, and low-rankness for spatial consistency. (2) LRSC encodes local features jointly by considering their low-rank structure information, and is computationally attractive. We evaluate the LRSC by comparing its performance on a set of challenging benchmarks with that of 7 popular coding and other state-of-the-art methods. Our experiments show that by representing local features jointly, LRSC not only outperforms the state-of-the-art in classification accuracy but also improves the time complexity of methods that use a similar sparse linear representation model for feature coding.

Capture Matrices Handbook

Science.gov (United States)

2014-04-01

materials, the affinity ligand would need identification , as well as chemistries that graft the affinity ligand onto the surface of magnetic...ACTIVE CAPTURE MATRICES FOR THE DETECTION/ IDENTIFICATION OF PHARMACEUTICALS...6 As shown in Figure 2.3-1a, the spectra exhibit similar baselines and the spectral peaks lineup . Under these circumstances, the spectral

Regularized generalized eigen-decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis

DEFF Research Database (Denmark)

Han, Xixuan; Clemmensen, Line Katrine Harder

2015-01-01

We propose a general technique for obtaining sparse solutions to generalized eigenvalue problems, and call it Regularized Generalized Eigen-Decomposition (RGED). For decades, Fisher's discriminant criterion has been applied in supervised feature extraction and discriminant analysis, and it is for...

Binary Positive Semidefinite Matrices and Associated Integer Polytopes

DEFF Research Database (Denmark)

Letchford, Adam N.; Sørensen, Michael Malmros

2012-01-01

We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes. We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature-the cut, boolean qua...

Chain of matrices, loop equations and topological recursion

CERN Document Server

Orantin, Nicolas

2009-01-01

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.

Theoretical Properties for Neural Networks with Weight Matrices of Low Displacement Rank

OpenAIRE

Zhao, Liang; Liao, Siyu; Wang, Yanzhi; Li, Zhe; Tang, Jian; Pan, Victor; Yuan, Bo

2017-01-01

Recently low displacement rank (LDR) matrices, or so-called structured matrices, have been proposed to compress large-scale neural networks. Empirical results have shown that neural networks with weight matrices of LDR matrices, referred as LDR neural networks, can achieve significant reduction in space and computational complexity while retaining high accuracy. We formally study LDR matrices in deep learning. First, we prove the universal approximation property of LDR neural networks with a ...

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

Science.gov (United States)

Yu, Guoxian; Lu, Chang; Wang, Jun

2017-07-21

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

Validação em métodos cromatográficos para análises de pequenas moléculas em matrizes biológicas Chromatographic methods validation for analysis of small molecules in biological matrices

Directory of Open Access Journals (Sweden)

Neila Maria Cassiano

2009-01-01

Full Text Available Chromatographic methods are commonly used for analysis of small molecules in different biological matrices. An important step to be considered upon a bioanalytical method's development is the capacity to yield reliable and reproducible results. This review discusses validation procedures adopted by different governmental agencies, such as Food and Drug Administration (USA, European Union (EU and Agência Nacional de Vigilância Sanitária (BR for quantification of small molecules by bioanalytical chromatographic methods. The main parameters addressed in this review are: selectivity, linearity, precision, accuracy, quantification and detection limits, recovery, dilution integrity, stability and robustness. Also, the acceptance criterions are clearly specified.

l1- and l2-Norm Joint Regularization Based Sparse Signal Reconstruction Scheme

Directory of Open Access Journals (Sweden)

Chanzi Liu

2016-01-01

Full Text Available Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations. This is also the application condition of compressive sensing (CS which can find the sparse solution from the measurements far less than the original signal. In this paper, we propose l1- and l2-norm joint regularization based reconstruction framework to approach the original l0-norm based sparseness-inducing constrained sparse signal reconstruction problem. Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem with l0-norm regularization item. Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error than l1-norm relaxation approaches can be realized by using the proposed scheme in most cases. Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach.

Image fusion via nonlocal sparse K-SVD dictionary learning.

Science.gov (United States)

Li, Ying; Li, Fangyi; Bai, Bendu; Shen, Qiang

2016-03-01

Image fusion aims to merge two or more images captured via various sensors of the same scene to construct a more informative image by integrating their details. Generally, such integration is achieved through the manipulation of the representations of the images concerned. Sparse representation plays an important role in the effective description of images, offering a great potential in a variety of image processing tasks, including image fusion. Supported by sparse representation, in this paper, an approach for image fusion by the use of a novel dictionary learning scheme is proposed. The nonlocal self-similarity property of the images is exploited, not only at the stage of learning the underlying description dictionary but during the process of image fusion. In particular, the property of nonlocal self-similarity is combined with the traditional sparse dictionary. This results in an improved learned dictionary, hereafter referred to as the nonlocal sparse K-SVD dictionary (where K-SVD stands for the K times singular value decomposition that is commonly used in the literature), and abbreviated to NL_SK_SVD. The performance of the NL_SK_SVD dictionary is applied for image fusion using simultaneous orthogonal matching pursuit. The proposed approach is evaluated with different types of images, and compared with a number of alternative image fusion techniques. The resultant superior fused images using the present approach demonstrates the efficacy of the NL_SK_SVD dictionary in sparse image representation.

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

International Nuclear Information System (INIS)

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

2013-01-01

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. (paper)

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

Science.gov (United States)

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.

Detection of Pitting in Gears Using a Deep Sparse Autoencoder

Directory of Open Access Journals (Sweden)

Yongzhi Qu

2017-05-01

Full Text Available In this paper; a new method for gear pitting fault detection is presented. The presented method is developed based on a deep sparse autoencoder. The method integrates dictionary learning in sparse coding into a stacked autoencoder network. Sparse coding with dictionary learning is viewed as an adaptive feature extraction method for machinery fault diagnosis. An autoencoder is an unsupervised machine learning technique. A stacked autoencoder network with multiple hidden layers is considered to be a deep learning network. The presented method uses a stacked autoencoder network to perform the dictionary learning in sparse coding and extract features from raw vibration data automatically. These features are then used to perform gear pitting fault detection. The presented method is validated with vibration data collected from gear tests with pitting faults in a gearbox test rig and compared with an existing deep learning-based approach.

The Modern Origin of Matrices and Their Applications

Science.gov (United States)

Debnath, L.

2014-01-01

This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

Noisy covariance matrices and portfolio optimization II

Science.gov (United States)

Pafka, Szilárd; Kondor, Imre

2003-03-01

Recent studies inspired by results from random matrix theory (Galluccio et al.: Physica A 259 (1998) 449; Laloux et al.: Phys. Rev. Lett. 83 (1999) 1467; Risk 12 (3) (1999) 69; Plerou et al.: Phys. Rev. Lett. 83 (1999) 1471) found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be regarded as random. This seems, however, to be in contradiction with the fundamental role played by covariance matrices in finance, which constitute the pillars of modern investment theory and have also gained industry-wide applications in risk management. Our paper is an attempt to resolve this embarrassing paradox. The key observation is that the effect of noise strongly depends on the ratio r= n/ T, where n is the size of the portfolio and T the length of the available time series. On the basis of numerical experiments and analytic results for some toy portfolio models we show that for relatively large values of r (e.g. 0.6) noise does, indeed, have the pronounced effect suggested by Galluccio et al. (1998), Laloux et al. (1999) and Plerou et al. (1999) and illustrated later by Laloux et al. (Int. J. Theor. Appl. Finance 3 (2000) 391), Plerou et al. (Phys. Rev. E, e-print cond-mat/0108023) and Rosenow et al. (Europhys. Lett., e-print cond-mat/0111537) in a portfolio optimization context, while for smaller r (around 0.2 or below), the error due to noise drops to acceptable levels. Since the length of available time series is for obvious reasons limited in any practical application, any bound imposed on the noise-induced error translates into a bound on the size of the portfolio. In a related set of experiments we find that the effect of noise depends also on whether the problem arises in asset allocation or in a risk measurement context: if covariance matrices are used simply for measuring the risk of portfolios with a fixed composition rather than as inputs to optimization, the

Flux Jacobian Matrices For Equilibrium Real Gases

Science.gov (United States)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris

2017-06-26

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

Data depth and rank-based tests for covariance and spectral density matrices

KAUST Repository

Chau, Joris; Ombao, Hernando; Sachs, Rainer von

2017-01-01

In multivariate time series analysis, objects of primary interest to study cross-dependences in the time series are the autocovariance or spectral density matrices. Non-degenerate covariance and spectral density matrices are necessarily Hermitian and positive definite, and our primary goal is to develop new methods to analyze samples of such matrices. The main contribution of this paper is the generalization of the concept of statistical data depth for collections of covariance or spectral density matrices by exploiting the geometric properties of the space of Hermitian positive definite matrices as a Riemannian manifold. This allows one to naturally characterize most central or outlying matrices, but also provides a practical framework for rank-based hypothesis testing in the context of samples of covariance or spectral density matrices. First, the desired properties of a data depth function acting on the space of Hermitian positive definite matrices are presented. Second, we propose two computationally efficient pointwise and integrated data depth functions that satisfy each of these requirements. Several applications of the developed methodology are illustrated by the analysis of collections of spectral matrices in multivariate brain signal time series datasets.

In-Storage Embedded Accelerator for Sparse Pattern Processing

OpenAIRE

Jun, Sang-Woo; Nguyen, Huy T.; Gadepally, Vijay N.; Arvind

2016-01-01

We present a novel architecture for sparse pattern processing, using flash storage with embedded accelerators. Sparse pattern processing on large data sets is the essence of applications such as document search, natural language processing, bioinformatics, subgraph matching, machine learning, and graph processing. One slice of our prototype accelerator is capable of handling up to 1TB of data, and experiments show that it can outperform C/C++ software solutions on a 16-core system at a fracti...

Process Knowledge Discovery Using Sparse Principal Component Analysis

DEFF Research Database (Denmark)

Gao, Huihui; Gajjar, Shriram; Kulahci, Murat

2016-01-01

As the goals of ensuring process safety and energy efficiency become ever more challenging, engineers increasingly rely on data collected from such processes for informed decision making. During recent decades, extracting and interpreting valuable process information from large historical data sets...... SPCA approach that helps uncover the underlying process knowledge regarding variable relations. This approach systematically determines the optimal sparse loadings for each sparse PC while improving interpretability and minimizing information loss. The salient features of the proposed approach...

Sparseness- and continuity-constrained seismic imaging

Science.gov (United States)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

Almost commuting self-adjoint matrices: The real and self-dual cases

Science.gov (United States)

Loring, Terry A.; Sørensen, Adam P. W.

2016-08-01

We show that a pair of almost commuting self-adjoint, symmetric matrices is close to a pair of commuting self-adjoint, symmetric matrices (in a uniform way). Moreover, we prove that the same holds with self-dual in place of symmetric and also for paths of self-adjoint matrices. Since a symmetric, self-adjoint matrix is real, we get a real version of Huaxin Lin’s famous theorem on almost commuting matrices. Similarly, the self-dual case gives a version for matrices over the quaternions. To prove these results, we develop a theory of semiprojectivity for real C*-algebras and also examine various definitions of low-rank for real C*-algebras.

Hg-Xe exciplex formation in mixed Xe/Ar matrices: molecular dynamics and luminescence study.

Science.gov (United States)

Lozada-García, Rolando; Rojas-Lorenzo, Germán; Crépin, Claudine; Ryan, Maryanne; McCaffrey, John G

2015-03-19

Luminescence of Hg((3)P1) atoms trapped in mixed Ar/Xe matrices containing a small amount of Xe is reported. Broad emission bands, strongly red-shifted from absorption are recorded which are assigned to strong complexes formed between the excited mercury Hg* and xenon atoms. Molecular dynamics calculations are performed on simulated Xe/Ar samples doped with Hg to follow the behavior of Hg* in the mixed rare gas matrices leading to exciplex formation. The role of Xe atoms in the first solvation shell (SS1) around Hg was investigated in detail, revealing the formation of two kinds of triatomic exciplexes; namely, Xe-Hg*-Xe and Ar-Hg*-Xe. The first species exists only when two xenon atoms are present in SS1 with specific geometries allowing the formation of a linear or quasi-linear exciplex. In the other geometries, or in the presence of only one Xe in SS1, a linear Ar-Hg*-Xe exciplex is formed. The two kinds of exciplexes have different emission bands, the most red-shifted being that involving two Xe atoms, whose emission is very close to that observed in pure Xe matrices. Simulations give a direct access to the analysis of the experimental absorption, emission, and excitation spectra, together with the dynamics of exciplexes formation.

Forecasting Covariance Matrices: A Mixed Frequency Approach

DEFF Research Database (Denmark)

Halbleib, Roxana; Voev, Valeri

This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows for flexi......This paper proposes a new method for forecasting covariance matrices of financial returns. The model mixes volatility forecasts from a dynamic model of daily realized volatilities estimated with high-frequency data with correlation forecasts based on daily data. This new approach allows...... for flexible dependence patterns for volatilities and correlations, and can be applied to covariance matrices of large dimensions. The separate modeling of volatility and correlation forecasts considerably reduces the estimation and measurement error implied by the joint estimation and modeling of covariance...

Image Super-Resolution Algorithm Based on an Improved Sparse Autoencoder

Directory of Open Access Journals (Sweden)

Detian Huang

2018-01-01

Full Text Available Due to the limitations of the resolution of the imaging system and the influence of scene changes and other factors, sometimes only low-resolution images can be acquired, which cannot satisfy the practical application’s requirements. To improve the quality of low-resolution images, a novel super-resolution algorithm based on an improved sparse autoencoder is proposed. Firstly, in the training set preprocessing stage, the high- and low-resolution image training sets are constructed, respectively, by using high-frequency information of the training samples as the characterization, and then the zero-phase component analysis whitening technique is utilized to decorrelate the formed joint training set to reduce its redundancy. Secondly, a constructed sparse regularization term is added to the cost function of the traditional sparse autoencoder to further strengthen the sparseness constraint on the hidden layer. Finally, in the dictionary learning stage, the improved sparse autoencoder is adopted to achieve unsupervised dictionary learning to improve the accuracy and stability of the dictionary. Experimental results validate that the proposed algorithm outperforms the existing algorithms both in terms of the subjective visual perception and the objective evaluation indices, including the peak signal-to-noise ratio and the structural similarity measure.

Propositional matrices as alternative representation of truth values ...

African Journals Online (AJOL)

The paper considered the subject of representation of truth values in symbolic logic. An alternative representation was given based on the rows and columns properties of matrices, with the operations involving the logical connectives subjected to the laws of algebra of propositions. Matrices of various propositions detailing ...

Diagnosis and prognosis of Ostheoarthritis by texture analysis using sparse linear models

DEFF Research Database (Denmark)

Marques, Joselene; Clemmensen, Line Katrine Harder; Dam, Erik

We present a texture analysis methodology that combines uncommitted machine-learning techniques and sparse feature transformation methods in a fully automatic framework. We compare the performances of a partial least squares (PLS) forward feature selection strategy to a hard threshold sparse PLS...... algorithm and a sparse linear discriminant model. The texture analysis framework was applied to diagnosis of knee osteoarthritis (OA) and prognosis of cartilage loss. For this investigation, a generic texture feature bank was extracted from magnetic resonance images of tibial knee bone. The features were...... used as input to the sparse algorithms, which dened the best features to retain in the model. To cope with the limited number of samples, the data was evaluated using 10 fold cross validation (CV). The diagnosis evaluation using sparse PLS reached a generalization area-under-the-ROC curve (AUC) of 0...

Efficient implementations of block sparse matrix operations on shared memory vector machines

International Nuclear Information System (INIS)

Washio, T.; Maruyama, K.; Osoda, T.; Doi, S.; Shimizu, F.

2000-01-01

In this paper, we propose vectorization and shared memory-parallelization techniques for block-type random sparse matrix operations in finite element (FEM) applications. Here, a block corresponds to unknowns on one node in the FEM mesh and we assume that the block size is constant over the mesh. First, we discuss some basic vectorization ideas (the jagged diagonal (JAD) format and the segmented scan algorithm) for the sparse matrix-vector product. Then, we extend these ideas to the shared memory parallelization. After that, we show that the techniques can be applied not only to the sparse matrix-vector product but also to the sparse matrix-matrix product, the incomplete or complete sparse LU factorization and preconditioning. Finally, we report the performance evaluation results obtained on an NEC SX-4 shared memory vector machine for linear systems in some FEM applications. (author)

A Projected Conjugate Gradient Method for Sparse Minimax Problems

DEFF Research Database (Denmark)

Madsen, Kaj; Jonasson, Kristjan

1993-01-01

A new method for nonlinear minimax problems is presented. The method is of the trust region type and based on sequential linear programming. It is a first order method that only uses first derivatives and does not approximate Hessians. The new method is well suited for large sparse problems...... as it only requires that software for sparse linear programming and a sparse symmetric positive definite equation solver are available. On each iteration a special linear/quadratic model of the function is minimized, but contrary to the usual practice in trust region methods the quadratic model is only...... with the method are presented. In fact, we find that the number of iterations required is comparable to that of state-of-the-art quasi-Newton codes....

Identification of MIMO systems with sparse transfer function coefficients

Science.gov (United States)

Qiu, Wanzhi; Saleem, Syed Khusro; Skafidas, Efstratios

2012-12-01

We study the problem of estimating transfer functions of multivariable (multiple-input multiple-output--MIMO) systems with sparse coefficients. We note that subspace identification methods are powerful and convenient tools in dealing with MIMO systems since they neither require nonlinear optimization nor impose any canonical form on the systems. However, subspace-based methods are inefficient for systems with sparse transfer function coefficients since they work on state space models. We propose a two-step algorithm where the first step identifies the system order using the subspace principle in a state space format, while the second step estimates coefficients of the transfer functions via L1-norm convex optimization. The proposed algorithm retains good features of subspace methods with improved noise-robustness for sparse systems.

MULTISCALE SPARSE APPEARANCE MODELING AND SIMULATION OF PATHOLOGICAL DEFORMATIONS

Directory of Open Access Journals (Sweden)

Rami Zewail

2017-08-01

Full Text Available Machine learning and statistical modeling techniques has drawn much interest within the medical imaging research community. However, clinically-relevant modeling of anatomical structures continues to be a challenging task. This paper presents a novel method for multiscale sparse appearance modeling in medical images with application to simulation of pathological deformations in X-ray images of human spine. The proposed appearance model benefits from the non-linear approximation power of Contourlets and its ability to capture higher order singularities to achieve a sparse representation while preserving the accuracy of the statistical model. Independent Component Analysis is used to extract statistical independent modes of variations from the sparse Contourlet-based domain. The new model is then used to simulate clinically-relevant pathological deformations in radiographic images.

Theoretical calculations of L alpha one x-ray emission intensity ratios for uranium in various matrices: a comparison with experimental values

International Nuclear Information System (INIS)

Anderson, L.D.

1976-01-01

The U L/sub α1/ x-ray emission intensity ratios (I/sub lambda/sub L//I sub lambda/sub L/, sub 100 percent/sub UO 2 /) in various matrices were calculated using the fundamental parameters formula of Criss and Birks and mass absorption coefficients calculated from a formula developed by Dewey. The use of the intensity ratio made it unnecessary to know the fluorescence yield for the U L/sub III/ level, the probability of emission of the U L/sub α1/ line, and the jump ratios for the three absorption edges of uranium. Also, since an intensity ratio was used, the results are independent of the x-ray tube current and the spectral distribution of the x-ray tube. A method is presented to calculate the intensity ratios for x-ray tube voltages other than the value (45 kV) used in the calculations. The theoretical results are calculated and compared with the experimental results obtained for 141 matrices. Difficulties due to oxidation of some of the metal powders used in the sample preparation, to small concentrations of uranium, and to an excessively large number of elements present in some of the samples resulted in the invalidation of the experimental results for 91 of the matrices. For the remaining 50 matrices, the theoretical and experimental values agreed to within +-5 percent relative error for 36 matrices; to within +-5 percent to +- 10 percent for 7 matrices; to within +-10 percent to +-20 percent for 6 matrices; and was greater than +-20 percent for 1 matrix

An Adaptive Sparse Grid Algorithm for Elliptic PDEs with Lognormal Diffusion Coefficient

KAUST Repository

Nobile, Fabio

2016-03-18

In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version capable of using non-nested collocation points, and supporting quadrature and interpolation on unbounded sets. We also consider several profit indicators that are suitable to drive the adaptation process. We then use such algorithm to solve an important test case in Uncertainty Quantification problem, namely the Darcy equation with lognormal permeability random field, and compare the results with those obtained with the quasi-optimal sparse grids based on profit estimates, which we have proposed in our previous works (cf. e.g. Convergence of quasi-optimal sparse grids approximation of Hilbert-valued functions: application to random elliptic PDEs). To treat the case of rough permeability fields, in which a sparse grid approach may not be suitable, we propose to use the adaptive sparse grid quadrature as a control variate in a Monte Carlo simulation. Numerical results show that the adaptive sparse grids have performances similar to those of the quasi-optimal sparse grids and are very effective in the case of smooth permeability fields. Moreover, their use as control variate in a Monte Carlo simulation allows to tackle efficiently also problems with rough coefficients, significantly improving the performances of a standard Monte Carlo scheme.

Genetically-directed, cell type-specific sparse labeling for the analysis of neuronal morphology.

Directory of Open Access Journals (Sweden)

Thomas Rotolo

Full Text Available In mammals, genetically-directed cell labeling technologies have not yet been applied to the morphologic analysis of neurons with very large and complex arbors, an application that requires extremely sparse labeling and that is only rendered practical by limiting the labeled population to one or a few predetermined neuronal subtypes.In the present study we have addressed this application by using CreER technology to non-invasively label very small numbers of neurons so that their morphologies can be fully visualized. Four lines of IRES-CreER knock-in mice were constructed to permit labeling selectively in cholinergic or catecholaminergic neurons [choline acetyltransferase (ChAT-IRES-CreER or tyrosine hydroxylase (TH-IRES-CreER], predominantly in projection neurons [neurofilament light chain (NFL-IRES-CreER], or broadly in neurons and some glia [vesicle-associated membrane protein2 (VAMP2-IRES-CreER]. When crossed to the Z/AP reporter and exposed to 4-hydroxytamoxifen in the early postnatal period, the number of neurons expressing the human placental alkaline phosphatase reporter can be reproducibly lowered to fewer than 50 per brain. Sparse Cre-mediated recombination in ChAT-IRES-CreER;Z/AP mice shows the full axonal and dendritic arbors of individual forebrain cholinergic neurons, the first time that the complete morphologies of these very large neurons have been revealed in any species.Sparse genetically-directed, cell type-specific neuronal labeling with IRES-creER lines should prove useful for studying a wide variety of questions in neuronal development and disease.

Wishart and anti-Wishart random matrices

International Nuclear Information System (INIS)

Janik, Romuald A; Nowak, Maciej A

2003-01-01

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices A † A, for any finite number of rows and columns of A, without any large N approximations. In particular, we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure for reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks

Information geometry of density matrices and state estimation

International Nuclear Information System (INIS)

Brody, Dorje C

2011-01-01

Given a pure state vector |x) and a density matrix ρ-hat, the function p(x|ρ-hat)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived. (fast track communication)

Inference algorithms and learning theory for Bayesian sparse factor analysis

International Nuclear Information System (INIS)

Rattray, Magnus; Sharp, Kevin; Stegle, Oliver; Winn, John

2009-01-01

Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

Inference algorithms and learning theory for Bayesian sparse factor analysis

Energy Technology Data Exchange (ETDEWEB)

Rattray, Magnus; Sharp, Kevin [School of Computer Science, University of Manchester, Manchester M13 9PL (United Kingdom); Stegle, Oliver [Max-Planck-Institute for Biological Cybernetics, Tuebingen (Germany); Winn, John, E-mail: magnus.rattray@manchester.ac.u [Microsoft Research Cambridge, Roger Needham Building, Cambridge, CB3 0FB (United Kingdom)

2009-12-01

Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB/EP algorithm then provides a very useful computationally efficient alternative.

Supercritical fluid extraction behaviour of polymer matrices

International Nuclear Information System (INIS)

Sujatha, K.; Kumar, R.; Sivaraman, N.; Srinivasan, T.G.; Vasudeva Rao, P.R.

2007-01-01

Organic compounds present in polymeric matrices such as neoprene, surgical gloves and PVC were co-extracted during the removal of uranium using supercritical fluid extraction (SFE) technique. Hence SFE studies of these matrices were carried out to establish the extracted species using HPLC, IR and mass spectrometry techniques. The initial study indicated that uranium present in the extract could be purified from the co-extracted organic species. (author)

Universal Regularizers For Robust Sparse Coding and Modeling

OpenAIRE

Ramirez, Ignacio; Sapiro, Guillermo

2010-01-01

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding...

Hierarchical Bayesian sparse image reconstruction with application to MRFM.

Science.gov (United States)

Dobigeon, Nicolas; Hero, Alfred O; Tourneret, Jean-Yves

2009-09-01

This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate Bayes priors. We propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero. The prior has hyperparameters that are tuned automatically by marginalization over the hierarchical Bayesian model. To overcome the complexity of the posterior distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be used to estimate the image to be recovered, e.g., by maximizing the estimated posterior distribution. In our fully Bayesian approach, the posteriors of all the parameters are available. Thus, our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate. The performance of the proposed hierarchical Bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype MRFM instrument.

Towards the low-dose characterization of beam sensitive nanostructures via implementation of sparse image acquisition in scanning transmission electron microscopy

International Nuclear Information System (INIS)

Hwang, Sunghwan; Han, Chang Wan; Ortalan, Volkan; Venkatakrishnan, Singanallur V; Bouman, Charles A

2017-01-01

Scanning transmission electron microscopy (STEM) has been successfully utilized to investigate atomic structure and chemistry of materials with atomic resolution. However, STEM’s focused electron probe with a high current density causes the electron beam damages including radiolysis and knock-on damage when the focused probe is exposed onto the electron-beam sensitive materials. Therefore, it is highly desirable to decrease the electron dose used in STEM for the investigation of biological/organic molecules, soft materials and nanomaterials in general. With the recent emergence of novel sparse signal processing theories, such as compressive sensing and model-based iterative reconstruction, possibilities of operating STEM under a sparse acquisition scheme to reduce the electron dose have been opened up. In this paper, we report our recent approach to implement a sparse acquisition in STEM mode executed by a random sparse-scan and a signal processing algorithm called model-based iterative reconstruction (MBIR). In this method, a small portion, such as 5% of randomly chosen unit sampling areas (i.e. electron probe positions), which corresponds to pixels of a STEM image, within the region of interest (ROI) of the specimen are scanned with an electron probe to obtain a sparse image. Sparse images are then reconstructed using the MBIR inpainting algorithm to produce an image of the specimen at the original resolution that is consistent with an image obtained using conventional scanning methods. Experimental results for down to 5% sampling show consistency with the full STEM image acquired by the conventional scanning method. Although, practical limitations of the conventional STEM instruments, such as internal delays of the STEM control electronics and the continuous electron gun emission, currently hinder to achieve the full potential of the sparse acquisition STEM in realizing the low dose imaging condition required for the investigation of beam-sensitive materials

An investigation of 'sparse channel networks'. Characteristic behaviours and their causes

Energy Technology Data Exchange (ETDEWEB)

Black, J.H. (In Situ Solutions, East Bridgford (GB)); Barker, J.A.; Woodman, N.D. (Univ. of Southampton (GB))

2007-09-15

This report represents a third study in a series concerned with groundwater flow in poorly permeable fractured crystalline rocks. The study has brought together three linked, but distinct, elements; a mathematical analysis of the intersection of ellipses, a review of field measurements associated with nuclear waste repository investigations and probabilistic simulations using a lattice network numerical model. We conclude that the model of channels that traverse fracture intersections without necessarily branching is a very likely representation of reality. More generally, assembling all the lines of evidence, it is suggested that groundwater flow systems in fractured crystalline rocks in the environs of underground laboratories have the following characteristics: Groundwater flows within a sparse network of channels just above the percolation limit. The frequency of intersections is low in that individual channels extend considerable distances between significant junctions. Individual channels often extend over many fracture surfaces and the resulting flow system is only weakly related to the density or size of mappable fractures. The sparseness of systems compared to the size of drifts and tunnels means that only a very few flow channels are intersected by drifts and tunnels. Highly convergent flow is required to connect to the rest of the network and this is misinterpreted as a skin of low hydraulic conductivity. Systems are so sparse that they are controlled by a few 'chokes' that give rise to compartments of head, and probably, of groundwater chemistry. Channels occur on all fracture planes, including those within fracture zones, and although the characteristics of the fracture zone channel networks may differ from those in surrounding rocks, they are nonetheless still channel networks. The actively flowing sparse channel network, occurring within any particular rock, is a naturally selected, small sub-set of the available channels. Hence, there are

A MRI-CT prostate registration using sparse representation technique

Science.gov (United States)

Yang, Xiaofeng; Jani, Ashesh B.; Rossi, Peter J.; Mao, Hui; Curran, Walter J.; Liu, Tian

2016-03-01

Purpose: To develop a new MRI-CT prostate registration using patch-based deformation prediction framework to improve MRI-guided prostate radiotherapy by incorporating multiparametric MRI into planning CT images. Methods: The main contribution is to estimate the deformation between prostate MRI and CT images in a patch-wise fashion by using the sparse representation technique. We assume that two image patches should follow the same deformation if their patch-wise appearance patterns are similar. Specifically, there are two stages in our proposed framework, i.e., the training stage and the application stage. In the training stage, each prostate MR images are carefully registered to the corresponding CT images and all training MR and CT images are carefully registered to a selected CT template. Thus, we obtain the dense deformation field for each training MR and CT image. In the application stage, for registering a new subject MR image with the same subject CT image, we first select a small number of key points at the distinctive regions of this subject CT image. Then, for each key point in the subject CT image, we extract the image patch, centered at the underlying key point. Then, we adaptively construct the coupled dictionary for the underlying point where each atom in the dictionary consists of image patches and the respective deformations obtained from training pair-wise MRI-CT images. Next, the subject image patch can be sparsely represented by a linear combination of training image patches in the dictionary, where we apply the same sparse coefficients to the respective deformations in the dictionary to predict the deformation for the subject MR image patch. After we repeat the same procedure for each subject CT key point, we use B-splines to interpolate a dense deformation field, which is used as the initialization to allow the registration algorithm estimating the remaining small segment of deformations from MRI to CT image. Results: Our MRI-CT registration

Fabrication of Aligned Carbon Nanotube/Polycaprolactone/Gelatin Nanofibrous Matrices for Schwann Cell Immobilization

Directory of Open Access Journals (Sweden)

Shiao-Wen Tsai

2014-01-01

Full Text Available In this study, we utilized a mandrel rotating collector consisting of two parallel, electrically conductive pieces of tape to fabricate aligned electrospun polycaprolactone/gelatin (PG and carbon nanotube/polycaprolactone/gelatin (PGC nanofibrous matrices. Furthermore, we examined the biological performance of the PGC nanofibrous and film matrices using an in vitro culture of RT4-D6P2T rat Schwann cells. Using cell adhesion tests, we found that carbon nanotube inhibited Schwann cell attachment on PGC nanofibrous and film matrices. However, the proliferation rates of Schwann cells were higher when they were immobilized on PGC nanofibrous matrices compared to PGC film matrices. Using western blot analysis, we found that NRG1 and P0 protein expression levels were higher for cells immobilized on PGC nanofibrous matrices compared to PG nanofibrous matrices. However, the carbon nanotube inhibited NRG1 and P0 protein expression in cells immobilized on PGC film matrices. Moreover, the NRG1 and P0 protein expression levels were higher for cells immobilized on PGC nanofibrous matrices compared to PGC film matrices. We found that the matrix topography and composition influenced Schwann cell behavior.

Robust Fringe Projection Profilometry via Sparse Representation.

Science.gov (United States)

Budianto; Lun, Daniel P K

2016-04-01

In this paper, a robust fringe projection profilometry (FPP) algorithm using the sparse dictionary learning and sparse coding techniques is proposed. When reconstructing the 3D model of objects, traditional FPP systems often fail to perform if the captured fringe images have a complex scene, such as having multiple and occluded objects. It introduces great difficulty to the phase unwrapping process of an FPP system that can result in serious distortion in the final reconstructed 3D model. For the proposed algorithm, it encodes the period order information, which is essential to phase unwrapping, into some texture patterns and embeds them to the projected fringe patterns. When the encoded fringe image is captured, a modified morphological component analysis and a sparse classification procedure are performed to decode and identify the embedded period order information. It is then used to assist the phase unwrapping process to deal with the different artifacts in the fringe images. Experimental results show that the proposed algorithm can significantly improve the robustness of an FPP system. It performs equally well no matter the fringe images have a simple or complex scene, or are affected due to the ambient lighting of the working environment.

Efficient Techniques of Sparse Signal Analysis for Enhanced Recovery of Information in Biomedical Engineering and Geosciences

KAUST Repository

Sana, Furrukh

2016-11-01

Sparse signals are abundant among both natural and man-made signals. Sparsity implies that the signal essentially resides in a small dimensional subspace. The sparsity of the signal can be exploited to improve its recovery from limited and noisy observations. Traditional estimation algorithms generally lack the ability to take advantage of signal sparsity. This dissertation considers several problems in the areas of biomedical engineering and geosciences with the aim of enhancing the recovery of information by exploiting the underlying sparsity in the problem. The objective is to overcome the fundamental bottlenecks, both in terms of estimation accuracies and required computational resources. In the first part of dissertation, we present a high precision technique for the monitoring of human respiratory movements by exploiting the sparsity of wireless ultra-wideband signals. The proposed technique provides a novel methodology of overcoming the Nyquist sampling constraint and enables robust performance in the presence of noise and interferences. We also present a comprehensive framework for the important problem of extracting the fetal electrocardiogram (ECG) signals from abdominal ECG recordings of pregnant women. The multiple measurement vectors approach utilized for this purpose provides an efficient mechanism of exploiting the common structure of ECG signals, when represented in sparse transform domains, and allows leveraging information from multiple ECG electrodes under a joint estimation formulation. In the second part of dissertation, we adopt sparse signal processing principles for improved information recovery in large-scale subsurface reservoir characterization problems. We propose multiple new algorithms for sparse representation of the subsurface geological structures, incorporation of useful prior information in the estimation process, and for reducing computational complexities of the problem. The techniques presented here enable significantly

Determination of radiation-induced hydrocarbons in processed food and complex lipid matrices. A new solid phase extraction (SPE) method for detection of irradiated components in food

International Nuclear Information System (INIS)

Hartmann, M.; Ammon, J.; Berg, H.

1997-01-01

Detection of irradiated components in processed food with complex lipid matrices can be affected by two problems. First, the processed food may contain only a small amount of the irradiated component, and the radiation-induced hydrocarbons may be diluted throughout the lipid matrix of the whole food. Second, in complex lipid matrices, the detection of prior irradiation is often disturbed by fat-associated compounds. In these cases, common solid phase extraction (SPE) Florisil clean-up alone is inadequate in the detection of prior irradiation. Subsequent SPE argentation chromatography of the Florisil eluate allows the measurement of small amounts of irradiated lipid-containing ingredients in processed food as well as the detection of prior irradiation in complex lipid matrices such as paprika and chilli. SPE argetation chromatography is the first method available for the selective enrichment of radiation-specific hydrocarbons from even complex lipid matrices, thus enabling the detection of irradiation does as low as 0.025 kGy. Furthermore, by using radiation-induced hydrocarbons in the detection of prior irradiation of paprika and chilli powder, a second independent method, the first being measurement of thermoluminescence, is available for the analysis of these matrices. Such analysis could be achieved by using this highly sensitive, cheap and easy to perform combined SPE Florisil/argentation chromatography method, without the need for sophisticated techniques like SFE-GC/MS or LC-GC/MS, so that highly sensitive detection of prior irradiation colud be performed in almost every laboratory

Sparse DOA estimation with polynomial rooting

DEFF Research Database (Denmark)

Xenaki, Angeliki; Gerstoft, Peter; Fernandez Grande, Efren

2015-01-01

Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve highresol......Direction-of-arrival (DOA) estimation involves the localization of a few sources from a limited number of observations on an array of sensors. Thus, DOA estimation can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing (CS) to achieve...... highresolution imaging. Utilizing the dual optimal variables of the CS optimization problem, it is shown with Monte Carlo simulations that the DOAs are accurately reconstructed through polynomial rooting (Root-CS). Polynomial rooting is known to improve the resolution in several other DOA estimation methods...

A General Sparse Tensor Framework for Electronic Structure Theory.

Science.gov (United States)

Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I; Head-Gordon, Martin

2017-03-14

Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. However, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We avoid cumbersome machine-generated code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.

Effect of inflow discharges on the development of matric suction and volumetric water content for dike during overtopping tests

Science.gov (United States)

Hassan, Marwan A.; Ismail, Mohd A. M.

2017-10-01

The point of this review is to depict the impact of various inflow discharge rate releases on the instruments of matric suction and volumetric water content during an experimental test of spatial overtopping failure at school of civil engineering in universiti Sains of Malaysia. A dry sand dike was conducted inside small flume channel with twelve sensors of tensiometer and Time-Domain Reflectometer (TDR). Instruments are installed in the soil at different locations in downstream and upstream slopes of the dike for measuring the response of matric suction and volumetric water content, respectively. Two values of inflow discharge rates of 30 and 40 L/min are utilized as a part of these experiments to simulate the effectiveness of water reservoirs in erosion mechanism. The outcomes demonstrate that the matric suction and volumetric water content are decreased and increased, respectively for both inflow discharges. The higher inflow discharges accelerate the saturation of dike soil and the erosion process faster than that for the lower inflow discharges.

Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

Science.gov (United States)

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.

Low-rank and sparse modeling for visual analysis

CERN Document Server

Fu, Yun

2014-01-01

This book provides a view of low-rank and sparse computing, especially approximation, recovery, representation, scaling, coding, embedding and learning among unconstrained visual data. The book includes chapters covering multiple emerging topics in this new field. It links multiple popular research fields in Human-Centered Computing, Social Media, Image Classification, Pattern Recognition, Computer Vision, Big Data, and Human-Computer Interaction. Contains an overview of the low-rank and sparse modeling techniques for visual analysis by examining both theoretical analysis and real-world applic

Sparse BLIP: BLind Iterative Parallel imaging reconstruction using compressed sensing.

Science.gov (United States)

She, Huajun; Chen, Rong-Rong; Liang, Dong; DiBella, Edward V R; Ying, Leslie

2014-02-01

To develop a sensitivity-based parallel imaging reconstruction method to reconstruct iteratively both the coil sensitivities and MR image simultaneously based on their prior information. Parallel magnetic resonance imaging reconstruction problem can be formulated as a multichannel sampling problem where solutions are sought analytically. However, the channel functions given by the coil sensitivities in parallel imaging are not known exactly and the estimation error usually leads to artifacts. In this study, we propose a new reconstruction algorithm, termed Sparse BLind Iterative Parallel, for blind iterative parallel imaging reconstruction using compressed sensing. The proposed algorithm reconstructs both the sensitivity functions and the image simultaneously from undersampled data. It enforces the sparseness constraint in the image as done in compressed sensing, but is different from compressed sensing in that the sensing matrix is unknown and additional constraint is enforced on the sensitivities as well. Both phantom and in vivo imaging experiments were carried out with retrospective undersampling to evaluate the performance of the proposed method. Experiments show improvement in Sparse BLind Iterative Parallel reconstruction when compared with Sparse SENSE, JSENSE, IRGN-TV, and L1-SPIRiT reconstructions with the same number of measurements. The proposed Sparse BLind Iterative Parallel algorithm reduces the reconstruction errors when compared to the state-of-the-art parallel imaging methods. Copyright © 2013 Wiley Periodicals, Inc.

Real-time SPARSE-SENSE cardiac cine MR imaging: optimization of image reconstruction and sequence validation.

Science.gov (United States)

Goebel, Juliane; Nensa, Felix; Bomas, Bettina; Schemuth, Haemi P; Maderwald, Stefan; Gratz, Marcel; Quick, Harald H; Schlosser, Thomas; Nassenstein, Kai

2016-12-01

Improved real-time cardiac magnetic resonance (CMR) sequences have currently been introduced, but so far only limited practical experience exists. This study aimed at image reconstruction optimization and clinical validation of a new highly accelerated real-time cine SPARSE-SENSE sequence. Left ventricular (LV) short-axis stacks of a real-time free-breathing SPARSE-SENSE sequence with high spatiotemporal resolution and of a standard segmented cine SSFP sequence were acquired at 1.5 T in 11 volunteers and 15 patients. To determine the optimal iterations, all volunteers' SPARSE-SENSE images were reconstructed using 10-200 iterations, and contrast ratios, image entropies, and reconstruction times were assessed. Subsequently, the patients' SPARSE-SENSE images were reconstructed with the clinically optimal iterations. LV volumetric values were evaluated and compared between both sequences. Sufficient image quality and acceptable reconstruction times were achieved when using 80 iterations. Bland-Altman plots and Passing-Bablok regression showed good agreement for all volumetric parameters. 80 iterations are recommended for iterative SPARSE-SENSE image reconstruction in clinical routine. Real-time cine SPARSE-SENSE yielded comparable volumetric results as the current standard SSFP sequence. Due to its intrinsic low image acquisition times, real-time cine SPARSE-SENSE imaging with iterative image reconstruction seems to be an attractive alternative for LV function analysis. • A highly accelerated real-time CMR sequence using SPARSE-SENSE was evaluated. • SPARSE-SENSE allows free breathing in real-time cardiac cine imaging. • For clinically optimal SPARSE-SENSE image reconstruction, 80 iterations are recommended. • Real-time SPARSE-SENSE imaging yielded comparable volumetric results as the reference SSFP sequence. • The fast SPARSE-SENSE sequence is an attractive alternative to standard SSFP sequences.

Nano-Fiber Reinforced Enhancements in Composite Polymer Matrices

Science.gov (United States)

Chamis, Christos C.

2009-01-01

Nano-fibers are used to reinforce polymer matrices to enhance the matrix dependent properties that are subsequently used in conventional structural composites. A quasi isotropic configuration is used in arranging like nano-fibers through the thickness to ascertain equiaxial enhanced matrix behavior. The nano-fiber volume ratios are used to obtain the enhanced matrix strength properties for 0.01,0.03, and 0.05 nano-fiber volume rates. These enhanced nano-fiber matrices are used with conventional fiber volume ratios of 0.3 and 0.5 to obtain the composite properties. Results show that nano-fiber enhanced matrices of higher than 0.3 nano-fiber volume ratio are degrading the composite properties.

Security-enhanced phase encryption assisted by nonlinear optical correlation via sparse phase

International Nuclear Information System (INIS)

Chen, Wen; Chen, Xudong; Wang, Xiaogang

2015-01-01

We propose a method for security-enhanced phase encryption assisted by a nonlinear optical correlation via a sparse phase. Optical configurations are established based on a phase retrieval algorithm for embedding an input image and the secret data into phase-only masks. We found that when one or a few phase-only masks generated during data hiding are sparse, it is possible to integrate these sparse masks into those phase-only masks generated during the encoding of the input image. Synthesized phase-only masks are used for the recovery, and sparse distributions (i.e., binary maps) for generating the incomplete phase-only masks are considered as additional parameters for the recovery of secret data. It is difficult for unauthorized receivers to know that a useful phase has been sparsely distributed in the finally generated phase-only masks for secret-data recovery. Only when the secret data are correctly verified can the input image obtained with valid keys be claimed as targeted information. (paper)

Single and Multiple Object Tracking Using a Multi-Feature Joint Sparse Representation.

Science.gov (United States)

Hu, Weiming; Li, Wei; Zhang, Xiaoqin; Maybank, Stephen

2015-04-01

In this paper, we propose a tracking algorithm based on a multi-feature joint sparse representation. The templates for the sparse representation can include pixel values, textures, and edges. In the multi-feature joint optimization, noise or occlusion is dealt with using a set of trivial templates. A sparse weight constraint is introduced to dynamically select the relevant templates from the full set of templates. A variance ratio measure is adopted to adaptively adjust the weights of different features. The multi-feature template set is updated adaptively. We further propose an algorithm for tracking multi-objects with occlusion handling based on the multi-feature joint sparse reconstruction. The observation model based on sparse reconstruction automatically focuses on the visible parts of an occluded object by using the information in the trivial templates. The multi-object tracking is simplified into a joint Bayesian inference. The experimental results show the superiority of our algorithm over several state-of-the-art tracking algorithms.

Sparse representation of sounds in the unanesthetized auditory cortex.

Directory of Open Access Journals (Sweden)

Tomás Hromádka

2008-01-01

Full Text Available How do neuronal populations in the auditory cortex represent acoustic stimuli? Although sound-evoked neural responses in the anesthetized auditory cortex are mainly transient, recent experiments in the unanesthetized preparation have emphasized subpopulations with other response properties. To quantify the relative contributions of these different subpopulations in the awake preparation, we have estimated the representation of sounds across the neuronal population using a representative ensemble of stimuli. We used cell-attached recording with a glass electrode, a method for which single-unit isolation does not depend on neuronal activity, to quantify the fraction of neurons engaged by acoustic stimuli (tones, frequency modulated sweeps, white-noise bursts, and natural stimuli in the primary auditory cortex of awake head-fixed rats. We find that the population response is sparse, with stimuli typically eliciting high firing rates (>20 spikes/second in less than 5% of neurons at any instant. Some neurons had very low spontaneous firing rates (<0.01 spikes/second. At the other extreme, some neurons had driven rates in excess of 50 spikes/second. Interestingly, the overall population response was well described by a lognormal distribution, rather than the exponential distribution that is often reported. Our results represent, to our knowledge, the first quantitative evidence for sparse representations of sounds in the unanesthetized auditory cortex. Our results are compatible with a model in which most neurons are silent much of the time, and in which representations are composed of small dynamic subsets of highly active neurons.

Meet and Join Matrices in the Poset of Exponential Divisors

Indian Academy of Sciences (India)

... exponential divisor ( G C E D ) and the least common exponential multiple ( L C E M ) do not always exist. In this paper we embed this poset in a lattice. As an application we study the G C E D and L C E M matrices, analogues of G C D and L C M matrices, which are both special cases of meet and join matrices on lattices.

Low-rank sparse learning for robust visual tracking

KAUST Repository

Zhang, Tianzhu

2012-01-01

In this paper, we propose a new particle-filter based tracking algorithm that exploits the relationship between particles (candidate targets). By representing particles as sparse linear combinations of dictionary templates, this algorithm capitalizes on the inherent low-rank structure of particle representations that are learned jointly. As such, it casts the tracking problem as a low-rank matrix learning problem. This low-rank sparse tracker (LRST) has a number of attractive properties. (1) Since LRST adaptively updates dictionary templates, it can handle significant changes in appearance due to variations in illumination, pose, scale, etc. (2) The linear representation in LRST explicitly incorporates background templates in the dictionary and a sparse error term, which enables LRST to address the tracking drift problem and to be robust against occlusion respectively. (3) LRST is computationally attractive, since the low-rank learning problem can be efficiently solved as a sequence of closed form update operations, which yield a time complexity that is linear in the number of particles and the template size. We evaluate the performance of LRST by applying it to a set of challenging video sequences and comparing it to 6 popular tracking methods. Our experiments show that by representing particles jointly, LRST not only outperforms the state-of-the-art in tracking accuracy but also significantly improves the time complexity of methods that use a similar sparse linear representation model for particles [1]. © 2012 Springer-Verlag.

Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

KAUST Repository

Desmal, Abdulla

2015-04-13

A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

Joint Estimation of Multiple Precision Matrices with Common Structures.

Science.gov (United States)

Lee, Wonyul; Liu, Yufeng

Estimation of inverse covariance matrices, known as precision matrices, is important in various areas of statistical analysis. In this article, we consider estimation of multiple precision matrices sharing some common structures. In this setting, estimating each precision matrix separately can be suboptimal as it ignores potential common structures. This article proposes a new approach to parameterize each precision matrix as a sum of common and unique components and estimate multiple precision matrices in a constrained l 1 minimization framework. We establish both estimation and selection consistency of the proposed estimator in the high dimensional setting. The proposed estimator achieves a faster convergence rate for the common structure in certain cases. Our numerical examples demonstrate that our new estimator can perform better than several existing methods in terms of the entropy loss and Frobenius loss. An application to a glioblastoma cancer data set reveals some interesting gene networks across multiple cancer subtypes.

On the Automatic Parallelization of Sparse and Irregular Fortran Programs

Directory of Open Access Journals (Sweden)

Yuan Lin

1999-01-01

Full Text Available Automatic parallelization is usually believed to be less effective at exploiting implicit parallelism in sparse/irregular programs than in their dense/regular counterparts. However, not much is really known because there have been few research reports on this topic. In this work, we have studied the possibility of using an automatic parallelizing compiler to detect the parallelism in sparse/irregular programs. The study with a collection of sparse/irregular programs led us to some common loop patterns. Based on these patterns new techniques were derived that produced good speedups when manually applied to our benchmark codes. More importantly, these parallelization methods can be implemented in a parallelizing compiler and can be applied automatically.

Split-Bregman-based sparse-view CT reconstruction

Energy Technology Data Exchange (ETDEWEB)

Vandeghinste, Bert; Vandenberghe, Stefaan [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Goossens, Bart; Pizurica, Aleksandra; Philips, Wilfried [Ghent Univ. (Belgium). Image Processing and Interpretation Research Group (IPI); Beenhouwer, Jan de [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Antwerp Univ., Wilrijk (Belgium). The Vision Lab; Staelens, Steven [Ghent Univ. (Belgium). Medical Image and Signal Processing (MEDISIP); Antwerp Univ., Edegem (Belgium). Molecular Imaging Centre Antwerp

2011-07-01

Total variation minimization has been extensively researched for image denoising and sparse view reconstruction. These methods show superior denoising performance for simple images with little texture, but result in texture information loss when applied to more complex images. It could thus be beneficial to use other regularizers within medical imaging. We propose a general regularization method, based on a split-Bregman approach. We show results for this framework combined with a total variation denoising operator, in comparison to ASD-POCS. We show that sparse-view reconstruction and noise regularization is possible. This general method will allow us to investigate other regularizers in the context of regularized CT reconstruction, and decrease the acquisition times in {mu}CT. (orig.)

Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices

Science.gov (United States)

Böttcher, A.; Bogoya, J. M.; Grudsky, S. M.; Maximenko, E. A.

2017-11-01

Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For instance, quite a number of versions of Szegő's theorem on the asymptotic behaviour of eigenvalues and of the so-called strong Szegő theorem on the asymptotic behaviour of the determinants of Toeplitz matrices are known. Starting in the 1950s, the asymptotics of the maximum and minimum eigenvalues were actively investigated. However, investigation of the individual asymptotics of all the eigenvalues and eigenvectors of Toeplitz matrices started only quite recently: the first papers on this subject were published in 2009-2010. A survey of this new field is presented here. Bibliography: 55 titles.

Mini-lecture course: Introduction into hierarchical matrix technique

KAUST Repository

Litvinenko, Alexander

2017-01-01

allows us to work with general class of matrices (not only structured or Toeplits or sparse). H-matrices can keep the H-matrix data format during linear algebra operations (inverse, update, Schur complement).

Data Sources for Trait Databases: Comparing the Phenomic Content of Monographs and Evolutionary Matrices.

Science.gov (United States)

Dececchi, T Alex; Mabee, Paula M; Blackburn, David C

2016-01-01

Databases of organismal traits that aggregate information from one or multiple sources can be leveraged for large-scale analyses in biology. Yet the differences among these data streams and how well they capture trait diversity have never been explored. We present the first analysis of the differences between phenotypes captured in free text of descriptive publications ('monographs') and those used in phylogenetic analyses ('matrices'). We focus our analysis on osteological phenotypes of the limbs of four extinct vertebrate taxa critical to our understanding of the fin-to-limb transition. We find that there is low overlap between the anatomical entities used in these two sources of phenotype data, indicating that phenotypes represented in matrices are not simply a subset of those found in monographic descriptions. Perhaps as expected, compared to characters found in matrices, phenotypes in monographs tend to emphasize descriptive and positional morphology, be somewhat more complex, and relate to fewer additional taxa. While based on a small set of focal taxa, these qualitative and quantitative data suggest that either source of phenotypes alone will result in incomplete knowledge of variation for a given taxon. As a broader community develops to use and expand databases characterizing organismal trait diversity, it is important to recognize the limitations of the data sources and develop strategies to more fully characterize variation both within species and across the tree of life.

Radiation-induced transformations of isolated organic molecules in solid rare gas matrices

International Nuclear Information System (INIS)

Feldman, V.I.

1998-01-01

Complete text of publication follows. The studies of radiation-chemical behaviour of isolated organic molecules in rigid inert media are of considerable interest for radiation chemistry and general structural chemistry. Previous efforts were limited to the ESR studies of radicals resulting from some small hydrocarbon molecules in frozen rare gas solutions. Recently, we developed an approach to the radiation chemistry of isolated organic molecules using classic matrix isolation procedure for sample preparation and a combination of ESR and IR spectroscopy for characterization of paramagnetic and diamagnetic species resulting form electron irradiation or organic molecules in solid rare gas matrices at 10-15 K. The results obtained reveal high efficiency of energy transfer from rare gas matrix to organic molecules. The total radiation-chemical yields of degradation of organic molecules in argon and xenon matrices were measured directly by IR spectroscopy. The studies of the effect of electron scavengers on the radiolysis of organic molecules in solid rare gases show that the main primary process is positive hole transfer from matrix to additive molecule. ESR spectra of a number of radical cations (alkanes, ethers, arenes) were first characterized in a low-disturbing environment. It was found that the electronic characteristics (IP, polarizability) of the matrix used had crucial effect on trapping and degradation of primary organic radical cations. Using matrices with various IP provides an unique possibility to examine the chemical meaning of excess energy resulting from exothermic positive hole transfer, that is, to follow the fate of excited cations in condensed phase

A method for eigenvalues of sparse lambda-matrices

International Nuclear Information System (INIS)

Yang, W.H.

1982-01-01

The matrix N(lambda) whose elements are functions of a parameter lambda is called the lambda-matrix. Those values of lambda that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a lambda-matrix is presented. A simple explicit convergence criterion is given as well as the algorithm and two numerical examples

On the norms of r-circulant matrices with generalized Fibonacci numbers

Directory of Open Access Journals (Sweden)

Amara Chandoul

2017-01-01

Full Text Available In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of Hadamard and Kronecker product of these matrices.

Alpha Matting with KL-Divergence Based Sparse Sampling.

Science.gov (United States)

Karacan, Levent; Erdem, Aykut; Erdem, Erkut

2017-06-22

In this paper, we present a new sampling-based alpha matting approach for the accurate estimation of foreground and background layers of an image. Previous sampling-based methods typically rely on certain heuristics in collecting representative samples from known regions, and thus their performance deteriorates if the underlying assumptions are not satisfied. To alleviate this, we take an entirely new approach and formulate sampling as a sparse subset selection problem where we propose to pick a small set of candidate samples that best explains the unknown pixels. Moreover, we describe a new dissimilarity measure for comparing two samples which is based on KLdivergence between the distributions of features extracted in the vicinity of the samples. The proposed framework is general and could be easily extended to video matting by additionally taking temporal information into account in the sampling process. Evaluation on standard benchmark datasets for image and video matting demonstrates that our approach provides more accurate results compared to the state-of-the-art methods.

A framework for general sparse matrix-matrix multiplication on GPUs and heterogeneous processors

DEFF Research Database (Denmark)

Liu, Weifeng; Vinter, Brian

2015-01-01

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines, an efficient parallel SpGEMM implementation has to handle...... extra irregularity from three aspects: (1) the number of nonzero entries in the resulting sparse matrix is unknown in advance, (2) very expensive parallel insert operations at random positions in the resulting sparse matrix dominate the execution time, and (3) load balancing must account for sparse data...... memory space and efficiently utilizes the very limited on-chip scratchpad memory. Parallel insert operations of the nonzero entries are implemented through the GPU merge path algorithm that is experimentally found to be the fastest GPU merge approach. Load balancing builds on the number of necessary...

Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices

Directory of Open Access Journals (Sweden)

A. F. Antippa

2004-01-01

Full Text Available We introduce the hypersymmetric functions of 2×2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions, and for a specific class of 2×2 matrices, having a high degree of symmetry, they reduce to these latter functions. This class of matrices includes rotations, Lorentz boosts, and discrete time generators for the harmonic oscillators. The hypersymmetric functions are defined over four sets of independent indeterminates using a triplet of interrelated binary partitions. We work out the algebra of this triplet of partitions and then make use of the results in order to simplify the expressions for the hypersymmetric functions for a special class of matrices. In addition to their obvious applications in matrix theory, in coupled difference equations, and in the theory of symmetric functions, the results obtained here also have useful applications in problems involving successive rotations, successive Lorentz transformations, discrete harmonic oscillators, and linear two-state systems.

An algorithmic characterization of P-matricity

OpenAIRE

Ben Gharbia , Ibtihel; Gilbert , Jean Charles

2013-01-01

International audience; It is shown that a matrix M is a P-matrix if and only if, whatever is the vector q, the Newton-min algorithm does not cycle between two points when it is used to solve the linear complementarity problem 0 ≤ x ⊥ (Mx+q) ≥ 0.; Nous montrons dans cet article qu'une matrice M est une P-matrice si, et seulement si, quel que soit le vecteur q, l'algorithme de Newton-min ne fait pas de cycle de deux points lorsqu'il est utilisé pour résoudre le problème de compl\\émentarité lin...

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

KAUST Repository

Labschutz, Matthias

2015-08-12

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.

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

KAUST Repository

Labschutz, Matthias; Bruckner, Stefan; Groller, M. Eduard; Hadwiger, Markus; Rautek, Peter

2015-01-01

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.

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

Science.gov (United States)

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.

Uncovering Transcriptional Regulatory Networks by Sparse Bayesian Factor Model

Directory of Open Access Journals (Sweden)

Qi Yuan(Alan

2010-01-01

Full Text Available Abstract The problem of uncovering transcriptional regulation by transcription factors (TFs based on microarray data is considered. A novel Bayesian sparse correlated rectified factor model (BSCRFM is proposed that models the unknown TF protein level activity, the correlated regulations between TFs, and the sparse nature of TF-regulated genes. The model admits prior knowledge from existing database regarding TF-regulated target genes based on a sparse prior and through a developed Gibbs sampling algorithm, a context-specific transcriptional regulatory network specific to the experimental condition of the microarray data can be obtained. The proposed model and the Gibbs sampling algorithm were evaluated on the simulated systems, and results demonstrated the validity and effectiveness of the proposed approach. The proposed model was then applied to the breast cancer microarray data of patients with Estrogen Receptor positive ( status and Estrogen Receptor negative ( status, respectively.

Magnetic Resonance Super-resolution Imaging Measurement with Dictionary-optimized Sparse Learning

Directory of Open Access Journals (Sweden)

Li Jun-Bao

2017-06-01

Full Text Available Magnetic Resonance Super-resolution Imaging Measurement (MRIM is an effective way of measuring materials. MRIM has wide applications in physics, chemistry, biology, geology, medical and material science, especially in medical diagnosis. It is feasible to improve the resolution of MR imaging through increasing radiation intensity, but the high radiation intensity and the longtime of magnetic field harm the human body. Thus, in the practical applications the resolution of hardware imaging reaches the limitation of resolution. Software-based super-resolution technology is effective to improve the resolution of image. This work proposes a framework of dictionary-optimized sparse learning based MR super-resolution method. The framework is to solve the problem of sample selection for dictionary learning of sparse reconstruction. The textural complexity-based image quality representation is proposed to choose the optimal samples for dictionary learning. Comprehensive experiments show that the dictionary-optimized sparse learning improves the performance of sparse representation.

Compact data structure and scalable algorithms for the sparse grid technique

KAUST Repository

Murarasu, Alin

2011-01-01

The sparse grid discretization technique enables a compressed representation of higher-dimensional functions. In its original form, it relies heavily on recursion and complex data structures, thus being far from well-suited for GPUs. In this paper, we describe optimizations that enable us to implement compression and decompression, the crucial sparse grid algorithms for our application, on Nvidia GPUs. The main idea consists of a bijective mapping between the set of points in a multi-dimensional sparse grid and a set of consecutive natural numbers. The resulting data structure consumes a minimum amount of memory. For a 10-dimensional sparse grid with approximately 127 million points, it consumes up to 30 times less memory than trees or hash tables which are typically used. Compared to a sequential CPU implementation, the speedups achieved on GPU are up to 17 for compression and up to 70 for decompression, respectively. We show that the optimizations are also applicable to multicore CPUs. Copyright © 2011 ACM.

Multisnapshot Sparse Bayesian Learning for DOA

DEFF Research Database (Denmark)

Gerstoft, Peter; Mecklenbrauker, Christoph F.; Xenaki, Angeliki

2016-01-01

The directions of arrival (DOA) of plane waves are estimated from multisnapshot sensor array data using sparse Bayesian learning (SBL). The prior for the source amplitudes is assumed independent zero-mean complex Gaussian distributed with hyperparameters, the unknown variances (i.e., the source...

Continuous speech recognition with sparse coding

CSIR Research Space (South Africa)

Smit, WJ

2009-04-01

Full Text Available generative model. The spike train is classified by making use of a spike train model and dynamic programming. It is computationally expensive to find a sparse code. We use an iterative subset selection algorithm with quadratic programming for this process...

A density functional for sparse matter

DEFF Research Database (Denmark)

Langreth, D.C.; Lundqvist, Bengt; Chakarova-Kack, S.D.

2009-01-01

forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators......Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional...... theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed...

Sparse learning of stochastic dynamical equations

Science.gov (United States)

Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia

2018-06-01

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.

A novel method to design sparse linear arrays for ultrasonic phased array.

Science.gov (United States)

Yang, Ping; Chen, Bin; Shi, Ke-Ren

2006-12-22

In ultrasonic phased array testing, a sparse array can increase the resolution by enlarging the aperture without adding system complexity. Designing a sparse array involves choosing the best or a better configuration from a large number of candidate arrays. We firstly designed sparse arrays by using a genetic algorithm, but found that the arrays have poor performance and poor consistency. So, a method based on the Minimum Redundancy Linear Array was then adopted. Some elements are determined by the minimum-redundancy array firstly in order to ensure spatial resolution and then a genetic algorithm is used to optimize the remaining elements. Sparse arrays designed by this method have much better performance and consistency compared to the arrays designed only by a genetic algorithm. Both simulation and experiment confirm the effectiveness.

Multiple instance learning tracking method with local sparse representation

KAUST Repository

Xie, Chengjun

2013-10-01

When objects undergo large pose change, illumination variation or partial occlusion, most existed visual tracking algorithms tend to drift away from targets and even fail in tracking them. To address this issue, in this study, the authors propose an online algorithm by combining multiple instance learning (MIL) and local sparse representation for tracking an object in a video system. The key idea in our method is to model the appearance of an object by local sparse codes that can be formed as training data for the MIL framework. First, local image patches of a target object are represented as sparse codes with an overcomplete dictionary, where the adaptive representation can be helpful in overcoming partial occlusion in object tracking. Then MIL learns the sparse codes by a classifier to discriminate the target from the background. Finally, results from the trained classifier are input into a particle filter framework to sequentially estimate the target state over time in visual tracking. In addition, to decrease the visual drift because of the accumulative errors when updating the dictionary and classifier, a two-step object tracking method combining a static MIL classifier with a dynamical MIL classifier is proposed. Experiments on some publicly available benchmarks of video sequences show that our proposed tracker is more robust and effective than others. © The Institution of Engineering and Technology 2013.

Sparse linear models: Variational approximate inference and Bayesian experimental design

International Nuclear Information System (INIS)

Seeger, Matthias W

2009-01-01

A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.

Sparse linear models: Variational approximate inference and Bayesian experimental design

Energy Technology Data Exchange (ETDEWEB)

Seeger, Matthias W [Saarland University and Max Planck Institute for Informatics, Campus E1.4, 66123 Saarbruecken (Germany)

2009-12-01

A wide range of problems such as signal reconstruction, denoising, source separation, feature selection, and graphical model search are addressed today by posterior maximization for linear models with sparsity-favouring prior distributions. The Bayesian posterior contains useful information far beyond its mode, which can be used to drive methods for sampling optimization (active learning), feature relevance ranking, or hyperparameter estimation, if only this representation of uncertainty can be approximated in a tractable manner. In this paper, we review recent results for variational sparse inference, and show that they share underlying computational primitives. We discuss how sampling optimization can be implemented as sequential Bayesian experimental design. While there has been tremendous recent activity to develop sparse estimation, little attendance has been given to sparse approximate inference. In this paper, we argue that many problems in practice, such as compressive sensing for real-world image reconstruction, are served much better by proper uncertainty approximations than by ever more aggressive sparse estimation algorithms. Moreover, since some variational inference methods have been given strong convex optimization characterizations recently, theoretical analysis may become possible, promising new insights into nonlinear experimental design.

Discriminative object tracking via sparse representation and online dictionary learning.

Science.gov (United States)

Xie, Yuan; Zhang, Wensheng; Li, Cuihua; Lin, Shuyang; Qu, Yanyun; Zhang, Yinghua

2014-04-01

We propose a robust tracking algorithm based on local sparse coding with discriminative dictionary learning and new keypoint matching schema. This algorithm consists of two parts: the local sparse coding with online updated discriminative dictionary for tracking (SOD part), and the keypoint matching refinement for enhancing the tracking performance (KP part). In the SOD part, the local image patches of the target object and background are represented by their sparse codes using an over-complete discriminative dictionary. Such discriminative dictionary, which encodes the information of both the foreground and the background, may provide more discriminative power. Furthermore, in order to adapt the dictionary to the variation of the foreground and background during the tracking, an online learning method is employed to update the dictionary. The KP part utilizes refined keypoint matching schema to improve the performance of the SOD. With the help of sparse representation and online updated discriminative dictionary, the KP part are more robust than the traditional method to reject the incorrect matches and eliminate the outliers. The proposed method is embedded into a Bayesian inference framework for visual tracking. Experimental results on several challenging video sequences demonstrate the effectiveness and robustness of our approach.

Building Input Adaptive Parallel Applications: A Case Study of Sparse Grid Interpolation

KAUST Repository

Murarasu, Alin; Weidendorfer, Josef

2012-01-01

bring a substantial contribution to the speedup. By identifying common patterns in the input data, we propose new algorithms for sparse grid interpolation that accelerate the state-of-the-art non-specialized version. Sparse grid interpolation

Fritzsch-type mass matrices and the Wolfenstein parametrization of quark mixing

International Nuclear Information System (INIS)

Kang, K.; Hadjitheodoridis, S.; Brown Univ., Providence, RI

1987-01-01

We give approximate and analytic expressions of polynomial type in small parameters defined in terms of quark mass ratios for the elements of the flavor-mixing matrix predicted from the Fritzsch-type mass matrices of quarks. The results are successfully tested against experiments as represented by the Wolfenstein parametrization of quark mixing. From the reality of the CP phases we get an allowed range for m s , which in turn implies that m t can be as large as 80.8 GeV. In addition we find that the two CP phases α and β are very close, i.e., vertical strokeα-βvertical stroke ≅ O(λ). (orig.)

Jointly-check iterative decoding algorithm for quantum sparse graph codes

International Nuclear Information System (INIS)

Jun-Hu, Shao; Bao-Ming, Bai; Wei, Lin; Lin, Zhou

2010-01-01

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with a standard belief-propagation (BP) algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms the standard BP algorithm with an obvious performance improvement. (general)

Normalization for sparse encoding of odors by a wide-field interneuron.

Science.gov (United States)

Papadopoulou, Maria; Cassenaer, Stijn; Nowotny, Thomas; Laurent, Gilles

2011-05-06

Sparse coding presents practical advantages for sensory representations and memory storage. In the insect olfactory system, the representation of general odors is dense in the antennal lobes but sparse in the mushroom bodies, only one synapse downstream. In locusts, this transformation relies on the oscillatory structure of antennal lobe output, feed-forward inhibitory circuits, intrinsic properties of mushroom body neurons, and connectivity between antennal lobe and mushroom bodies. Here we show the existence of a normalizing negative-feedback loop within the mushroom body to maintain sparse output over a wide range of input conditions. This loop consists of an identifiable "giant" nonspiking inhibitory interneuron with ubiquitous connectivity and graded release properties.

Topological expansion of the chain of matrices

International Nuclear Information System (INIS)

Eynard, B.; Ferrer, A. Prats

2009-01-01

We solve the loop equations to all orders in 1/N 2 , for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of [19]. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large N asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).

Compressive Detection Using Sub-Nyquist Radars for Sparse Signals

Directory of Open Access Journals (Sweden)

Ying Sun

2016-01-01

Full Text Available This paper investigates the compression detection problem using sub-Nyquist radars, which is well suited to the scenario of high bandwidths in real-time processing because it would significantly reduce the computational burden and save power consumption and computation time. A compressive generalized likelihood ratio test (GLRT detector for sparse signals is proposed for sub-Nyquist radars without ever reconstructing the signal involved. The performance of the compressive GLRT detector is analyzed and the theoretical bounds are presented. The compressive GLRT detection performance of sub-Nyquist radars is also compared to the traditional GLRT detection performance of conventional radars, which employ traditional analog-to-digital conversion (ADC at Nyquist sampling rates. Simulation results demonstrate that the former can perform almost as well as the latter with a very small fraction of the number of measurements required by traditional detection in relatively high signal-to-noise ratio (SNR cases.

Newton`s iteration for inversion of Cauchy-like and other structured matrices

Energy Technology Data Exchange (ETDEWEB)

Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)

1996-12-31

We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.

Sparse Representation Denoising for Radar High Resolution Range Profiling

Directory of Open Access Journals (Sweden)

Min Li

2014-01-01

Full Text Available Radar high resolution range profile has attracted considerable attention in radar automatic target recognition. In practice, radar return is usually contaminated by noise, which results in profile distortion and recognition performance degradation. To deal with this problem, in this paper, a novel denoising method based on sparse representation is proposed to remove the Gaussian white additive noise. The return is sparsely described in the Fourier redundant dictionary and the denoising problem is described as a sparse representation model. Noise level of the return, which is crucial to the denoising performance but often unknown, is estimated by performing subspace method on the sliding subsequence correlation matrix. Sliding window process enables noise level estimation using only one observation sequence, not only guaranteeing estimation efficiency but also avoiding the influence of profile time-shift sensitivity. Experimental results show that the proposed method can effectively improve the signal-to-noise ratio of the return, leading to a high-quality profile.

Agricultural matrices affect ground ant assemblage composition inside forest fragments.

Directory of Open Access Journals (Sweden)

Diego Santana Assis

Full Text Available The establishment of agricultural matrices generally involves deforestation, which leads to fragmentation of the remaining forest. This fragmentation can affect forest dynamics both positively and negatively. Since most animal species are affected, certain groups can be used to measure the impact of such fragmentation. This study aimed to measure the impacts of agricultural crops (matrices on ant communities of adjacent lower montane Atlantic rainforest fragments. We sampled nine forest fragments at locations surrounded by different agricultural matrices, namely: coffee (3 replicates; sugarcane (3; and pasture (3. At each site we installed pitfall traps along a 500 m transect from the interior of the matrix to the interior of the fragment (20 pitfall traps ~25 m apart. Each transect was partitioned into four categories: interior of the matrix; edge of the matrix; edge of the fragment; and interior of the fragment. For each sample site, we measured ant species richness and ant community composition within each transect category. Ant richness and composition differed between fragments and matrices. Each sample location had a specific composition of ants, probably because of the influence of the nature and management of the agricultural matrices. Species composition in the coffee matrix had the highest similarity to its corresponding fragment. The variability in species composition within forest fragments surrounded by pasture was greatest when compared with forest fragments surrounded by sugarcane or, to a lesser extent, coffee. Functional guild composition differed between locations, but the most representative guild was 'generalist' both in the agricultural matrices and forest fragments. Our results are important for understanding how agricultural matrices act on ant communities, and also, how these isolated forest fragments could act as an island of biodiversity in an 'ocean of crops'.

Agricultural matrices affect ground ant assemblage composition inside forest fragments.

Science.gov (United States)

Assis, Diego Santana; Dos Santos, Iracenir Andrade; Ramos, Flavio Nunes; Barrios-Rojas, Katty Elena; Majer, Jonathan David; Vilela, Evaldo Ferreira

2018-01-01

The establishment of agricultural matrices generally involves deforestation, which leads to fragmentation of the remaining forest. This fragmentation can affect forest dynamics both positively and negatively. Since most animal species are affected, certain groups can be used to measure the impact of such fragmentation. This study aimed to measure the impacts of agricultural crops (matrices) on ant communities of adjacent lower montane Atlantic rainforest fragments. We sampled nine forest fragments at locations surrounded by different agricultural matrices, namely: coffee (3 replicates); sugarcane (3); and pasture (3). At each site we installed pitfall traps along a 500 m transect from the interior of the matrix to the interior of the fragment (20 pitfall traps ~25 m apart). Each transect was partitioned into four categories: interior of the matrix; edge of the matrix; edge of the fragment; and interior of the fragment. For each sample site, we measured ant species richness and ant community composition within each transect category. Ant richness and composition differed between fragments and matrices. Each sample location had a specific composition of ants, probably because of the influence of the nature and management of the agricultural matrices. Species composition in the coffee matrix had the highest similarity to its corresponding fragment. The variability in species composition within forest fragments surrounded by pasture was greatest when compared with forest fragments surrounded by sugarcane or, to a lesser extent, coffee. Functional guild composition differed between locations, but the most representative guild was 'generalist' both in the agricultural matrices and forest fragments. Our results are important for understanding how agricultural matrices act on ant communities, and also, how these isolated forest fragments could act as an island of biodiversity in an 'ocean of crops'.

The Real-Valued Sparse Direction of Arrival (DOA Estimation Based on the Khatri-Rao Product

Directory of Open Access Journals (Sweden)

Tao Chen

2016-05-01

Full Text Available There is a problem that complex operation which leads to a heavy calculation burden is required when the direction of arrival (DOA of a sparse signal is estimated by using the array covariance matrix. The solution of the multiple measurement vectors (MMV model is difficult. In this paper, a real-valued sparse DOA estimation algorithm based on the Khatri-Rao (KR product called the L1-RVSKR is proposed. The proposed algorithm is based on the sparse representation of the array covariance matrix. The array covariance matrix is transformed to a real-valued matrix via a unitary transformation so that a real-valued sparse model is achieved. The real-valued sparse model is vectorized for transforming to a single measurement vector (SMV model, and a new virtual overcomplete dictionary is constructed according to the KR product’s property. Finally, the sparse DOA estimation is solved by utilizing the idea of a sparse representation of array covariance vectors (SRACV. The simulation results demonstrate the superior performance and the low computational complexity of the proposed algorithm.

HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

KAUST Repository

Litvinenko, Alexander

2017-09-26

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Mat\\\\\\'ern covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\H$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification

KAUST Repository

Litvinenko, Alexander

2017-09-24

The main goal of this article is to introduce the parallel hierarchical matrix library HLIBpro to the statistical community. We describe the HLIBCov package, which is an extension of the HLIBpro library for approximating large covariance matrices and maximizing likelihood functions. We show that an approximate Cholesky factorization of a dense matrix of size $2M\\\\times 2M$ can be computed on a modern multi-core desktop in few minutes. Further, HLIBCov is used for estimating the unknown parameters such as the covariance length, variance and smoothness parameter of a Mat\\\\\\'ern covariance function by maximizing the joint Gaussian log-likelihood function. The computational bottleneck here is expensive linear algebra arithmetics due to large and dense covariance matrices. Therefore covariance matrices are approximated in the hierarchical ($\\\\mathcal{H}$-) matrix format with computational cost $\\\\mathcal{O}(k^2n \\\\log^2 n/p)$ and storage $\\\\mathcal{O}(kn \\\\log n)$, where the rank $k$ is a small integer (typically $k<25$), $p$ the number of cores and $n$ the number of locations on a fairly general mesh. We demonstrate a synthetic example, where the true values of known parameters are known. For reproducibility we provide the C++ code, the documentation, and the synthetic data.

The recurrence sequences via Sylvester matrices

Science.gov (United States)

Karaduman, Erdal; Deveci, Ömür

2017-07-01

In this work, we define the Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by using the Slyvester matrices which are obtained from the characteristic polynomials of the Pell and Jacobsthal sequences and then, we study the sequences defined modulo m. Also, we obtain the cyclic groups and the semigroups from the generating matrices of these sequences when read modulo m and then, we derive the relationships among the orders of the cyclic groups and the periods of the sequences. Furthermore, we redefine Pell-Jacobsthal-Slyvester sequence and the Jacobsthal-Pell-Slyvester sequence by means of the elements of the groups and then, we examine them in the finite groups.

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

Science.gov (United States)

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.

Performance of penalized maximum likelihood in estimation of genetic covariances matrices

Directory of Open Access Journals (Sweden)

Meyer Karin

2011-11-01

Full Text Available Abstract Background Estimation of genetic covariance matrices for multivariate problems comprising more than a few traits is inherently problematic, since sampling variation increases dramatically with the number of traits. This paper investigates the efficacy of regularized estimation of covariance components in a maximum likelihood framework, imposing a penalty on the likelihood designed to reduce sampling variation. In particular, penalties that "borrow strength" from the phenotypic covariance matrix are considered. Methods An extensive simulation study was carried out to investigate the reduction in average 'loss', i.e. the deviation in estimated matrices from the population values, and the accompanying bias for a range of parameter values and sample sizes. A number of penalties are examined, penalizing either the canonical eigenvalues or the genetic covariance or correlation matrices. In addition, several strategies to determine the amount of penalization to be applied, i.e. to estimate the appropriate tuning factor, are explored. Results It is shown that substantial reductions in loss for estimates of genetic covariance can be achieved for small to moderate sample sizes. While no penalty performed best overall, penalizing the variance among the estimated canonical eigenvalues on the logarithmic scale or shrinking the genetic towards the phenotypic correlation matrix appeared most advantageous. Estimating the tuning factor using cross-validation resulted in a loss reduction 10 to 15% less than that obtained if population values were known. Applying a mild penalty, chosen so that the deviation in likelihood from the maximum was non-significant, performed as well if not better than cross-validation and can be recommended as a pragmatic strategy. Conclusions Penalized maximum likelihood estimation provides the means to 'make the most' of limited and precious data and facilitates more stable estimation for multi-dimensional analyses. It should

A mixture of sparse coding models explaining properties of face neurons related to holistic and parts-based processing.

Directory of Open Access Journals (Sweden)

Haruo Hosoya

2017-07-01

Full Text Available Experimental studies have revealed evidence of both parts-based and holistic representations of objects and faces in the primate visual system. However, it is still a mystery how such seemingly contradictory types of processing can coexist within a single system. Here, we propose a novel theory called mixture of sparse coding models, inspired by the formation of category-specific subregions in the inferotemporal (IT cortex. We developed a hierarchical network that constructed a mixture of two sparse coding submodels on top of a simple Gabor analysis. The submodels were each trained with face or non-face object images, which resulted in separate representations of facial parts and object parts. Importantly, evoked neural activities were modeled by Bayesian inference, which had a top-down explaining-away effect that enabled recognition of an individual part to depend strongly on the category of the whole input. We show that this explaining-away effect was indeed crucial for the units in the face submodel to exhibit significant selectivity to face images over object images in a similar way to actual face-selective neurons in the macaque IT cortex. Furthermore, the model explained, qualitatively and quantitatively, several tuning properties to facial features found in the middle patch of face processing in IT as documented by Freiwald, Tsao, and Livingstone (2009. These included, in particular, tuning to only a small number of facial features that were often related to geometrically large parts like face outline and hair, preference and anti-preference of extreme facial features (e.g., very large/small inter-eye distance, and reduction of the gain of feature tuning for partial face stimuli compared to whole face stimuli. Thus, we hypothesize that the coding principle of facial features in the middle patch of face processing in the macaque IT cortex may be closely related to mixture of sparse coding models.

Sparse Localization with a Mobile Beacon Based on LU Decomposition in Wireless Sensor Networks

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Chunhui Zhao

2015-09-01

Full Text Available Node localization is the core in wireless sensor network. It can be solved by powerful beacons, which are equipped with global positioning system devices to know their location information. In this article, we present a novel sparse localization approach with a mobile beacon based on LU decomposition. Our scheme firstly translates node localization problem into a 1-sparse vector recovery problem by establishing sparse localization model. Then, LU decomposition pre-processing is adopted to solve the problem that measurement matrix does not meet the re¬stricted isometry property. Later, the 1-sparse vector can be exactly recovered by compressive sensing. Finally, as the 1-sparse vector is approximate sparse, weighted Cen¬troid scheme is introduced to accurately locate the node. Simulation and analysis show that our scheme has better localization performance and lower requirement for the mobile beacon than MAP+GC, MAP-M, and MAP-MN schemes. In addition, the obstacles and DOI have little effect on the novel scheme, and it has great localization performance under low SNR, thus, the scheme proposed is robust.

A Conceptual Cost Benefit Analysis of Tailings Matrices Use in Construction Applications

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Mahmood Ali A.

2016-01-01

Full Text Available As part of a comprehensive research program, new tailings matrices are formulated of combinations of tailings and binder materials. The research program encompasses experimental and numerical analysis of the tailings matrices to investigate the feasibility of using them as construction materials in cold climates. This paper discusses a conceptual cost benefit analysis for the use of these new materials. It is shown here that the financial benefits of using the proposed new tailings matrices in terms of environmental sustainability are much higher when compared to normal sand matrices.

Robust visual tracking via multiscale deep sparse networks

Science.gov (United States)

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.

Efficient MATLAB computations with sparse and factored tensors.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

2006-12-01

In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

Flexible Bayesian Dynamic Modeling of Covariance and Correlation Matrices